President Bola, Tinnable Meanwhile, met with former Senate President Ayum Pius Ayum at the presidential villa Abuja. Ayum, who was also secretary to the government of the Federation under the Good Luck Administration, was in the villa in a company of former National Publicity Secretary of the Opposition People's Democratic Party, Chief Ulyssam Hidoo. The reason for the president's meeting with the two former PDP bigwigs could not be a certain Ayum. Who declared, who declared his aspiration in 2022 to contest the last presidential election was suspended by the PDP in March this year for alleged anti-party activity. He supported the governorship candidate of the all-progressive Congress in a Boeing state, Francis Muifu. May 2, in October 2022, announced his resignation from the PDP and partisan politics. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


good evening thank you for coming I'm glad that storm is coming tomorrow although I'm not glad for the people who have their performance tomorrow that's further recording and the live stream if the sound is not okay just wave your hand back there and we'll project more thanks to the wood art gallery if you make a donation of ten dollars in the donation box you may take a free book if you already have our books you're still well welcome to make a donation and it can be more than ten dollars thanks to the wood art gallery this is a great place we're glad to come here thanks to the Kellogg-Hubert library who sponsors this and organizes it every year and particularly to Michelle Singer who does a phenomenal job organizing all of these events for the 15th annual poem city on that bench back there are not only our books but programs for all the events you can also get those online at the Kellogg-Hubert library and thanks to the Poetry Society of Vermont many of our members have contributed to this event Scott Parker has been a minister is still a gardener has been a state senator a gubernatorial candidate he lost a devoted father and grandfather energy analyst and brings all of these things to his poetry so I just want to say thank you all for being here I want to especially thank my grandsons for coming and their father for bringing them and coming he's a poet of his own we're trying to get him out more into the public but he's just had a chapbook published and it's just so much fun this is what the poetry is for is nights like this and a chance to do this so I have a couple of introductions the first one is you may wonder who that guy sitting behind the piano is although you may not you may know already it's Jim Thompson who's the Renaissance man of my so I did you know I didn't I don't want to do a long introduction but he's known as piano Jim how many people of here have heard him in various forums yep that's what I thought when I was a minister and we both worked together at camp we a coey in Northfield so there what your kids went there okay well that that's part of it but he's also a singer a songwriter gifted musician he called us after he read the poems that we were going to read and he was going to accompany them and he said well I think I'll bring the guitar and the harmonica as well so that just shows you his range he's a creator of a musical called halfway house how many people have seen that there you go halfway there halfway there and and then I find out he's a gifted artist you paint kind kites and like large objects and things like that right mostly kites okay so if you want a special kite with a you did one with a tiger I believe that was phenomenal and he's an actor how many people saw him as lurch in the Adams family he totally stole the the whole show as lurch could you know we're not going to let you do that well yeah sure yeah well I got and George long and echo I won't I won't take as long for him he's another institution in central Vermont he taught for years at Vermont Technical College where he was the professor a professor in the chair of the Department of English Humanities and Social Sciences he's been a leader in poetry in this area for years he has a volume called Star Root it's been published widely and he's an in he's a supports everyone in the life and work of poetry so thank you for all that you do for that and for poem city as well so now am I supposed to read something I think you are okay so we're gonna read in you know about a 12 15 minute chunk and then George will read and Jim is gonna do what he's gonna do okay we don't we don't know for sure the first poem is called in the air to Sanibel and I'm reading about community but the reality is George's poems as I listened to them the other day in our rehearsal were about artwork or photographs but they're all about community too right pretty much so this is called in the air to Sanibel the plane is full again we've let them pack our restless bodies in a sleek silver cigar a brief anonymous intimacy we exchange for quick and far every seat holds purposes and hopes perhaps regret like any walk down any street but we are close as frogs eggs breathing each other's air treading each other's feet without a word of course brief reminders of peril shared turbulence image of a lost wing terror at the delicate trick that holds us in the air the daughter of the couple behind us screams as we ascend the mother soothes calmly singing itzy bitzy spider and the wheels on the bus the father silent at first joins in their voices blend kindness gathers allies that quick impulse to annoyance seems absurd the child quiets as the song continues most of us whispering the words you can do that at the end this is one I was a minister for about 20 years in East St. John'sbury and Lower Waterford and this is the old home day parade I remember it with some joy and a great deal of anxiety I think I was always I was always performing in a sense at the old home day parade but I remember it more and more fondly over the years this is the old home day parade late in the time of dying Elms down by Rod's Exxon station where the parade always forms next to the yard of the recently abandoned school four horses scuff the highway with iron shoes 60 years ago right here the ruts of May were worn down to July's dust Elwin's hands are full of reins the horses spooked by tractors the tailor boy on his crepe paper bike the town band practicing 18 wheelers grumbling and belching behind the sheriff's car this year the theme is East Village yesterday and today same theme as last year and the year before though it never seems they will enough participants and watchers show up to make it all worthwhile there are as always floats depicting the history of the town committees have been arguing all week about the way things were improvising outfits all morning up the road on a scrap of lawn that hasn't yet slipped down to the river next to the pole where Pat Bradley used to raise the flag each morning Ralph Chaffes senior sits in an aluminum folding chair the cold of 90 Vermont Winders hides in his Afghan covered knees his hands are heavy on his lap Helen is in the nursing home this year across the road on the church lawn Irene Stanton worries out loud to Anne Smith the parade is late again like always she's glad this time she doesn't have to be a judge last year in order to include everyone they invented more categories than there were contestants next year she'll sell her home to one of the Eley kids and pack a few belongings into a single room in town the parade begins crowded into a quarter mile of route to with the ghosts of all the earlier parades and all that will follow the horses first the rubber-tired wagon so no one will get hurt if elwin loses control tartle bounty follows grinning at everyone squawking a horn of his black model A which doesn't help at all they creep past the bridge where route to used to cross the river to the mill past the granite blocks of the mills foundation guarding the opposite bank plus the clay pipe choked with knot weeds through which a few homes still contribute directly to the river the Taylor boy as usual can't stay in line racing past Joyce to wit and the ladies kitchen band we weaving in and out among the Ellis children dressed as the four seasons in East Village crepe paper tattering in his wheels he has overcome with the present it is all he can feel there is no stopping Ralph's friend Mac Ford who died four years ago sits beside him there are corners of ground all over the town that he hate by hand side and a wooden break that now grow up to burdock and willow all those places belong to him now they don't belong to anyone the barn he stored the summers in has finally crumbled back into the hillside Roland Parento on the old John dear 50 drives equipment up and down this road all summer watches the people watching the parade he wonders if he will have a stroke the way his father did and not be able to keep farming maybe in 20 years there'll be a float about the last farm in East Village the church service posed on the hay wagon he's pulling doesn't look like any that Irene can remember but it's good to see the young people who quit church so promptly after Sunday school make an effort the parade has streamed into the Parento's hayfield those who have come back for the day walk over to Irene her greeting means their visit is official she's the one who does the work of recognizing and remembering she sees them and knows them at once like the print of an old dress Alaska Ohio the next town over they each bring their private past they all want to be missed and then there are those things you wake up at night thinking how did I ever do that this is called talent show this is down in the church basement she played trumpet at the talent show in the church basement badly with enormous enthusiasm we snickered with almost no restraint at the music and her enormous heaving eighth grade breasts fragments like this come flying at me like deadly pieces of space litter still in orbit after all these years and here I am in the small safety capsule of my delicate identity frozen in time she may be a grandmother by now we might recognize each other in the checkout line at Shaw's she'd ask in her husky voice about my sister and brothers I tell them the usual something perhaps I could wait for her to go through the line walk with her to the parking lot ask her about her life and listen I've learned to do that I suspect she'd forgive easily if I had the courage to ask or she might barely remember for her it was just another bunch of stupid boys acting like they did probably much worse happened yet here she is listening to an old man explain what she's so long understood this is called barn swallows and this is here millennia before the barns they're named for they promptly claimed the beams and rafters and perpetual refuge of sun-stippled dusk moats drifting weightless through light shafts between boards fields torn from forests had exploded into daisies summer grasses black-eyed Susan's asters sprawling purple vetch and teeming webs of creatures there for lightning capture on the wing they dove through openings one a fist-sized outline of a barn cut out for them to nests pasted on hand-hewn wood each summer haymows stacked tight with fragrant bales inched toward their open mouths urgency wider than their tiny heads they hinged echoed our urgency as summer was brought in we could not tell who welcomed whom they never bragged about their longer resonance my grandson has a friend whose grandfather lives in the valley still haze some fields fills an old barn we visit swallows chatter from the rafters I embarrass him in yet another way trying to find words for the ordinary joy of being in each other's company thanks gutter thanks to or media for taping this and thanks to my wife Cynthia my poetry muse she's away for two months being Nana to her grandson they need the help but she'll be able to watch this on orca great space to do ecstastic poems poems of art can't think of a better venue still life from a painting sheep in snow by Joseph Farkinson it's still as sunsets light snow in a pastor we look west into orange sunset scattered clouds and shades of pink still enough light for long shadows from trees on a small rise shades of orange in snow she prays for what grass they can find waiting for sunset when they'll return to shelter outside the picture frame the winter is brown and gray pastures full of color peaceful at solstice sunset do sheep worry like we do about what might come when night grows cold though shadows cross their pasture they're still color still life as daylight fades what more could we cold war 19 soldiers ponchos flapping in wind perhaps they're a chosen reservoir perhaps on heartbreak winter war Korea so cold they slog on through ice and snow each clutching his weapon Frank Gaylord sculptures neither alive nor dead frozen in time like war that never ended bagpies fly over the border quiet now in the DMZ where they nest in maples so many dead there some left behind a mere dimming between life and death as sunlight fades and night grows cold war 19 soldiers frozen time necrastic poem can also be about a photograph as well as a painting those sculptures like the Korean War monument newly fallen snow covers his face body facing gray sky which he can't see one arm outstretched to the right as it reaching out when he was car key under siege everything gray another cold war in the photograph nearby troop carrier a caterpillar blackened burned tread blown off nobody alive show a mother and father will get the news death doesn't take sides all decay and return to soil traffic light street lamp burn building all dark snow newly fallen salt and sorrow a kitchen in a residence in Aleppo Syria damaged Sunday and fighting our Cisco can trace this photo the New York Times walls are blackened there's a refrigerator with rust at its bottom stickers of yellow butterflies and blackbirds on the door a dish towel hangs on the door handle and a top sits evasive purple paper flowers on shells jars of spices still stand upright we can't see what's upright in the rest of the home if its power is on or if walls and windows are intact charge ceiling plaster covers the floor no mortar shells are shrapnel though a jar of beans lies on broken in a tiny drawer maybe for salt we don't know but nobody can live without salt or sorrow no matter where on a lower shelf rest three small pairs of shoes we can't see the children the parents or the photographer must all still be somewhere outside but outside is not in the picture we can't hear if there are explosions artillery fire on the wall hangs pan hang pans a strainer and measuring spoons why do some things fall and not others all the utensils are blackened but we can't tell whether from cooking or just war in a dish strainer cups dry they'll need to be washed again if the family returns if they live they're blackened kitchen sent naked around the world his self-portrait visiting Florida this winter Van Gogh gazes forever left he's painted his hair and beard red eyes blue looks a little like his brother Theo when Vincent painted this he had only a year left to live and Theo would be gone the following year having lived so his brother could paint we never know if Vincent stepped out of his frame into Florida what would he paint I'd offer him pink grapefruit we'd paint on the beach together the day would turn red turned hazy and hot maybe we'd paint rippled scallops and let it all of us on the sand perhaps we'd float into the swamp to paint alligators and herons there's a point at which we realize we'll die but we can't know when what if we could bring our brothers back and say paint this now you have only a year left but today it's just Vincent and me we paddle out paint an alligator basking by the lock so hatchy then a tricolored heron it flies off and a feather drifts slowly down I keep the herons feather I can't forget my brother's last year he drifted like a feather through the air and was gone the heron circles and calls Vincent and I drift if only he and Theo could have known if only Keith and I could have known mixing color from his palette Vincent fills in water and sky paints red the herons eyes so when I think about community I think often what we have in mind is some kind of niceness you know everything's good but community is really about an ongoing process of joy and loss finding grieving recovering learning new things about the world we live in and the people who are part of our lives and this one is about elm trees which just feel like they have you were a part of the Vermont community and I still want them to be elves all the way from Pittsburgh to Phoenix the men behind us talked marketing and never once gave a clue what the product was in college clay Hunt said it's not what you say it's the way that you say it it was a kind of a chant by the English department something they had learned so if I want to say for instance that I miss the elm trees I should tell you they held up the sky over our North Anvil farm domed and rustling alive with Orioles dancing among raised arms perfectly trained to lift the daily weight of blue or should I just admit I can't tell you how much I miss them and it's also noticing people and connecting with them which drives my grandchildren and sometimes my wife crazy but the people on the perimeter that you don't always acknowledge this is November sunlight she and her silent companions sit in a patch of unanticipated sun on a wooden bench bundled against November's cold her companion stares down at the freezing ground but she looks up at me as I cross the park's leaf littered lawn toward their small bit of warmth nothing much her smile warns a cordial sound the greeting of a different voice her glove rests on her partner's silent mitten hands unwaveringly loyal still she claims this small permission I want to stop and talk with her but that would be too much I only say how wonderful November sunlight and when I was a minister I guess I was professionally engaged in community and kept trying to figure out what the heck I was supposed to be doing with this job this is called good work for the preacher it's a practice in humility to come to a small church in a poor state where resources for pretense are scant where need wears thin clothes pride does for hope theology is less important than good chicken pie you learn to love the details not the answers trust your heart and ears kindnesses and the embarrassments they cause in other men gaining knowledge that could give control trying not to use it again and again you eat ordinary food till it becomes the food you crave stay till they no longer ask if you'll be lead leaving soon I remember a funeral performed for a man I never knew on a hilltop in Waterford and earn a sunny afternoon a family full of silences mid-service I realized he had died of AIDS the brother who had left for San Francisco gone for years home now to be buried in his family's fears I was invited to a 40th birthday party for a friend cross dressing was required I wore a kilt black tights bean boots and dance like David till the end his cousin read a poem about growing up gay in Plainfield his mother complimented on her dress bragged she had stolen it from her son I danced in the space we'd begun to claim and as welcome for the high school friend who loved me but had no name to give his love I danced for all the dead the stories carried to the grave I danced for those who watch in waiting still for the quietly subversive the outrageously braid and this is one I think of this is Susan's poem for a family and friends gathering it's called blessing you compose a table from all the tables in the house drape them with old linen till it snakes through living and dining rooms like a Chinese dragon white metal lawn chairs come up from the basement slumber antiques from the bedroom where a week of clothes lands on the floor you dig to the back of the drawer for cheap stainless and then the family silver and tie ribbons hugging it in chamois cloth wine glasses from pewter to crystal alternate around the table suggesting a symmetry in all their history you remember the spoons that melted in the fire that no one here remembers and the fourth and missing crystal glass guests bring the cold air in each with their offering of food laughter and greeting for old friends and strangers they embrace because you love them all voices rise in the living room over wine crackers chopped liver Baba Ganoush there's that last-minute rush the comfort of it this in this out of oven or refrigerator it says you bring your coogle to the table the absence races through you the laughter here invites the laughter that is gone how can we be joyful in the company of loss your knees are weak you lean into your closest friend pause slowly start to breathe and we begin now that the meal is blessed and this one is called bandstand it's no secret it's the it's the middle sex bandstand where they have wonderful summer concerts children gulp music with the air race bare feet bare legs no sleeves sun sinks clinging to the leaves on the blanket checkered lawn adults listen or talk quietly tree swallows spill their liquid sound after the concert fiddle returns to spruce and got bow stops quivering against its strings musicians step back into the presence thanked for their commission or communion with that other place they've been children finally still like instruments slumped and lovely twined and carried in the rich noodle hug of need the drive home echoes with wild song and play fading hesitant reluctant to forsake the day and then finally this is about a trip that we took on Elmore pond and we always try not to be just on the pond but to find the marshy areas or the secluded areas or the place where the ducks might be and we went up to the where the stream flows in to the pond I have to say we went back three years later nothing was recognizable no from both flood just washed everything out Lake Elmore October 1st curled beige feathers downy at the base litter the stream that wanders toward us and Elmore's Lake beavered alder branches submerged pond hair cushions duckweed corralled by viburnum roots all strewn as though by a gentle pillow fight we paddle past managed shorelines with tidy cottages to this neighborhood of lily pads and pickerel weed hidden from their sight more happens here like the basement daycare center chorus with children always cluttered doing a better business than the church this is the waters sweet meander slow channel where merganser mallard grew it's also where the storm flood races through my grandson cried when he gave up his first and favorite bike the one he trusted enough to let his feet release the ground I had to argue with myself against the urge to dry his eyes hurry him along stop honor that lonely keening sound two young ducks try to keep one bend upstream from us trapped by our invasion they finally stop one leaps to flight the other hides behind marsh grass in a small alder pocket we paddle by eyes averted our small courtesy it quivers as we pass six summer weeks this was their home now they leave for something new I think detachment that's illusion too in the next pool a heron rises scarecrow taking flight we look for it at every bend flying its silent heron tricks again but a beaver pond opens before us flood at eye level no heron but wide water sweeping seeping through a thousand sticks this summer we went up five streams the beaver dogged Calvinists seem to insist it's the effort not the dam that's permanent we postpone leaving poke up every bull rush alley given at last stroke hard across the open reach land on the expanse of beach women in bright saris watch their boisterous men play tag joined by the youngest daughter we greet them lift the boat leave our visit this is from a photo of my wife Cynthia's mom's wedding in Plainfield wedding photo in black and white the bride and her five bridesmaids pose on the stone portico of a white shirt in Vermont in white gowns holding bouquets of flowers May 1947 all in their 20s war over for two years long lives ahead today the bride's sister died the last of six in the photo nobody knows the day they'll die unless perhaps they're in a war but war had ended now at last they could live there wouldn't be another war at least they hoped certainly not in this Vermont village with its white clabbered church all six lived near the church some in the village others on back roads were families far after the war they had to be optimistic so many dead so many now it's been over 70 years and that may they weren't thinking about war they pose six young women on the steps of a church in Vermont sending off one of their own sugar maples shade the lawn and though it doesn't show in black and white leaves are fresh green and there's a scent of lilacs maples stone steps church now are all still there but the wedding party has gone Lazarus and six horses a sepia photograph 1891 the horse's ears are perked and alert they seem to watch the photographer even in sepia tone we can see their different shades of brown and gray hitched together and used to pulling as a team to thrash winter weed my great grandfather Lazarus pageant stands to the left of his horses barely holding the reins as his horses pose overalls had in hand probably the year my grandmother was born in the only other photo his horses are hitched to threshers weed and horses now on what had been Kiowa Ottawa and Potawatomi land for a millennium and more all forced on to reservations I don't know what Lazarus thought of this some of his family were probably part Kiowa or what do you think of Kingman now just a few large farms where there were once dozens wheat from his field shipped around the globe summer day is almost always over a hundred degrees a four lane highway to Wichita his great-grand children scattered across Kansas and all over the country none of us farms and only one has horses three generations apart our lifetimes overlapped only briefly but we grew up in different worlds I look at Lazarus and his six horses and wish I could ask him their names Athena's owl at half moon pond in our tent late at night we hear three barred owls call over and over mythical owls of Athena next day at the sculpture studio an artist carves an owl from pure white marble if only the owls could know that now they're almost immortal marble quarry it doesn't sculptors have reclaimed a corner of an abandoned quarry dragon flies and swallows fly over while other creatures emerge from marble out of stone a heron an owl a white whale two ballet dancers boss relief ducks and nesting moons at night the quarry is eerily quiet an owl perches atop a rusting crane her hoots echo off walls of abandoned stone sheds with shattered windows then each morning under tents and tarps carbide chisels and diamond blaze squeal as mallard ducks take flight on marble wings dancers leap from stone white slippers barely touching the ground swans swim at dawn four swans swim circles around the small pond of reeds and cat tails across the road from my hotel room drift back and forth dipping their beaks to feed not much water but just four not yades nine and fifty swans years ago when i was 13 an amusement park pleasure island was built here on the edge of wetlands where now there are condos offices hotel it was a short lived attempt to imitate disneyland in a massachusetts swamp how much pleasure or amusement kids got i'm not sure but i saw ricky nelson play right over there not far from the pond where swans swim in low light just after dawn i wondered why the teen idol had to sing on stage near goldpen gulch and a white whale in a small amusement park in a swamp but it wasn't his swan song he performed another 23 years before flying to his death ricky nelson just like small stages where he could play for a few hundred screaming teens his voice and guitar always pitch perfect i can still hear him sing unchained melody hello mary lou someday someday i'd like to swim like a white swan go back when there were songs like lonesome town when we could be so moved by an idol so easily amused pleasure island swans still swim in low light just after dawn rain taxi soft music down a windy street worn smooth by light years of frustration and traffic the fugs 1964 two red oak leaves stuck to the side window have an old checker cab headlights reflected in dark puddles the old handcock towers light glowed red for rain and from a higher building a beacon revolved in the night horns of boats and the harbor echoed through streets where water splashed up from gutters ran down sidewalks there in a corner i thought i saw you with your bag of poetry books pens first drafts a stoplight glowed red in a puddle and when my cab finally moved ahead you were gone of course i should have known it couldn't be you we wouldn't write any more poems together i'd seen you die on the first day of spring i forgot where i was going and all this rain i didn't know why the streets were so wet why this cab was so old i forgot what you had been writing about the last time we were together the rain taxi crossed rivers of streetlights this is my poem the poem city this year you can write an ecstatic poem about a building love poem to a library how can i say which book i love the most it's like asking which is my favorite child easier to say i love the library as i walk up granite steps out of rain and sleet through the portico into the reading room paper lanterns made of poems hang everywhere i wander to fiction stacks but stop at calder's animals lithographic red and yellow cats scampering with an elephant and and glance up at a grecian freeze i head for art books move on to the history shelves then get distracted by poetry posters everywhere old library the more i check you out the more i realize it's you i love eclipse robbins already back in april begin their evening songs perhaps perplexed that it's already dark through our eclipse viewers we watch moon slide slowly over sun until stars and planets shine in the sky then slowly this brief nightfall slides back into daylight as robbins sing again some days i don't understand the world so much i love has been eclipsed by banality and uncertainty but i'm glad robbins still sing and humans too even when perplexed by darkness thank you let's hear a special for jim did i tell you that he has a mean slice on his pickle ball thank you all thanks everyone thank you for being here and uh feel free to wander around enjoy the lovely creations all around us and we're here to talk if you want to do that either i i don't think we talked about a question and answer period but if anybody has anything they want to ask ask jim okay well how how was your first time playing with musical accompaniment how do you feel it i loved it um how did you like it i thought it was a delightful yeah i thought it was a really great and brave experiment yeah well um george and i decided to do this george was the instigator and then he said what about having music and i said well i have this friend and we invited jim and that's how it happened right we did one i don't think you could call it a rehearsal one a tryout a tryout a scoping session jam yeah no it wasn't a jam it was it was it was a very small jar if it was a jim so jim did you have all the poems that you were reading along with so yeah i just had the book before and we gave him notes yeah where we wasn't not words no no that's all and when we came here to practice it was just like oh my god we just started reading something you would just start playing nice incredible gift anything else so say hi to each other great to see you and we all get a chance to say i'll give you a hug before you go and enjoy the art and only 33 more home city events to go yes i guess the programs math thank you for coming you that one's in the book portrait is in the book yeah it's in the book and it's like i i mean i was hearing your words again in a very fresh way i think that's the only one of these from the book the rest of newer there's a connection to the cold rain taxes so I know, I know.  Oh, wow. What?


Good morning. Welcome to our morning prayer as we're in a holy week season and excited to be with you, those that are in the room, those that are watching and excited for our time this morning to seek the Lord in one heart and one mind. And we're gonna open up the scriptures this morning in Ephesians 5. It says to be filled with the Spirit, verse 19, addressing one another in Psalms and hymns and spiritual songs, singing and making melody to the Lord with your heart, giving thanks always and for everything to God the Father in the name of our Lord Jesus Christ, submitting to one another out of reverence for Christ on this day and this morning. Whether you're in a living room alone or a car alone or in this room, just to stir up the environment that you're in to fill it up and singing and melody in Thanksgiving that we're coming before Jesus who paid the greatest price where he actually prayed that this cup would pass from him yet I submit to the will of the Lord. And so with that submitted heart, we come before the Father saying that he is high and lifted up and we create an environment of Thanksgiving to honor him for what Jesus has done to spill out his blood for us to have a broken body for us to be betrayed, to be denied that the crowd would choose another.  My heart is swelling with the goodness of God, the goodness of Jesus, his kindness towards us. And on this holy Thursday, this Passover Thursday where it is the remembrance of the passing over in Egypt, we say Jesus that you have covered us with your blood that you have gone to great lengths that your blood covers a multitude of sins. We rely, we are dependent. We're in great need of the blood of Jesus this morning. We recall and we remember that we are lost. We are far from you without the Lamb who was slain. Your blood, your body broken. God, we remember you. We stir up our hearts right now.   Can we respond right now? We thank you, Jesus. We bless you, Jesus. We honor you, Jesus. We honor your broken body. We honor your spilled blood. We honor you, Lamb of God. So you made him. Come back to the Lord. It says, Romans 6, 5, for if we've been united with him in a death like his, we shall certainly be united with him in a resurrection like his. We know that our old self was crucified with him in order that the body of sin might be brought to nothing so that we would no longer be enslaved to sin. God, we ask, Lord, today, unify us to your death and unify us to your resurrection in the name of Jesus. We say today, once again, crucify the old self, the old life, and let the newness of Jesus reign. Let there be no dominion of sin inside of us.  We ask, Lord, unify us in heart, unify us in a mind that we would have one mind and one heart in Christ Jesus under the dominion of Jesus Christ, who rules, who reigns, who seated at the right hand of the Father. And we say today, unite us in your blood, unite us in your resurrection. Unify the body of Christ, even in this holy week where there is a spirit of division. We ask, Lord, for a spirit of unity that you're raising up a standard in these days that we would be unified under the dominion of Christ. What you purchased on the cross, we say today, you rule and you reign. We have one name that we sit under. His name is Jesus Christ. You sit on the throne. We extol you. We lift you high. You are blessed, highly exalted, honored, the dominion of Christ, ruling and reigning in our hearts and in our minds.  Unify us in you today in Jesus Christ, in your name. And we become obedient to Jesus. We become slaves to Jesus, not to sin, but to him, bond servants willingly following the way of Jesus. God, I pray today that you would cast off any, any inheritance that was a slave mentality, that was an orphan mentality and we are adopted sons and daughters due to the cross and we take on, we take on that inheritance today as sons and daughters, as co-heirs in Christ Jesus. I pray that we would be built up in our most holy faith today. Strengthen us, strengthen your church today. The adopted ones, those that have purchased by your blood. I pray that there would be a deposit and an impartation today of the inheritance and the identity that we are yours. We are in you. We are in Christ today and we say, God, thank you that we can be called sons and daughters. We are the adopted ones, your saints.  God, we pray right now. You would cast off all other ways, all other ways of thinking and we ask for the spirit of wisdom and revelation of Jesus Christ. You rule and you reign over minds and hearts. Our identities, our souls are made one in you. God, unify us. This was your prayer in John seventeen that we would be made one just as you and the father are one. Make us one in you today. Unify your body. Unify the bride. Unify the church in Jesus. We pray your manifold wisdom. Your ways are higher. The wisdom of the cross, the wisdom of brokenness, the wisdom of the meekness of Jesus. It violates our human ways and we say that you are higher. You're exalted. Hallelujah Jesus. That you're above our ways. You're above our intellect and we crown you with the God that we don't crown ourselves wields. God, we ask her for that spirit of revelation. God over the church. God that we would not be numb in this Easter Good Friday week to just continual liturgical norms. God, we ask her that you would break in in glory. The sleeping church. God, wake up your church. Wake up the saints. Wake up the sons and the daughters. We ask her for the glory of God. The glory of Jesus. How perfect are your ways. How perfect are you. We ask her for the glory of Jesus to be revealed in this time in your name and in your spirit. We pray by the red scene. You could change the verbiage here. They exchanged the glory of God and they forgot the cross. They forgot the resurrection. The same way that they forget. It's easy in these days for us to forget. Let it not be so that we would exchange the glory of God for anything. There's a I just pray for a spirit of repentance over the church for in any way that we have exalted our ways exalted our methods exalted our churches exalted our pastors over Jesus Christ in any way if there's any way within me God I repent and I say if I have exchanged the glory of God in any way that I consciously or subconsciously know I I submit and I repent and I return to the cross and I return to the resurrection that without you I am a stranger and I am alienated from you but you have purchased me you have purchased your bride and we ask her that there will be a returning and a remembrance and I pray that as Moses prayed show us your glory God that we would not exchange glory we ask Lord for a remembering and even a current reality of the glory of God at being revealed in our midst God let us not be numb let us not be asleep let us not exchange your glory for anything else we ask Lord that the glory of God the glory of Jesus the glory of the cross the glory of the resurrection God would be remembered we exalt you Jesus let us not exchange you any longer we repent and we ask Lord that you are the great shepherd you are over the church and we extol you we lift you up right now can we just lift you up Jesus we lift you right now can we just even lift up our hands and we say to you Jesus you sit on the throne you sit on the throne and we exalt you as high and lifted up to receive all glory and worth and wisdom and strength and honor we bless you today we say holy are you Jesus and we bless you we don't exchange you you are the glory being revealed in this hour we ask Lord show us your glory in the name of Jesus yes he is isn't he to receive power wealth wisdom might honor glory and blessing it says that John who's receiving this revelation he looked and he heard around the throne the living creatures the elders the voice of many angels numbering myriads of myriads of thousands of thousands I see that picture where Jesus is entering and coming out of his throne room and looking at the multitudes that have been bought and purchased by his blood those that have said yes to the free gift of salvation and so we see that and we see that image and we hear the voices that are responding to Jesus saying that you are the worthy one you have saved and redeemed me you have redeemed us we are your body we are your church and there's one voice saying worthy is the lamb who was slain to receive power and wealth and wisdom and might and honor and blessing and glory god we say we join in heaven song the myriad thousands one heart one mind one voice saying to Jesus you are the word that you would come Emmanuel and dwell among us and crucify and go to the depths of hell but you have the keys and you have redeemed and you have purchased and we on towards you Jesus over our church over our city over our nation god refresh us in the power the glory and the might of Jesus Christ saved redeemed due to you god we thank you just let that thanksgiving arise out of our hearts right now god we just thank you god the worthiness of Jesus the power of Jesus strangers we would be aliens without you but you have come to redeem you have come to reconcile you as the lamb of god laying your life down that we might have life and have it to the fullest god we pray for the fullness of life the fullness of life show us yourself god reveal yourself in these days and in these times we pray in the name of Jesus by his resurrection we have Psalm 31 there's a phrase that's just been sticking with me marvelous to marvel at his kindness that our hearts would be tenderized circumcised in this season to remember to not exchange but to remember and to marvel at the glory to marvel at his kindness god we thank you for the marvelous kindness that you have demonstrated your meekness your kindness undeserving grace god we thank you for your mercy expressed to us let our hearts be tender towards you just say that let let our hearts be tender towards your marvelous kindness we marvel at your kindness we bless you we bless you Jesus we bless you today on this holy thursday we bless you and would we remember today as we go to marvel at your kindness thank you team for leading us thank you those in the room be blessed in this holy week amen


Okay, today there is a shift in the types of topics. Up to now we have been describing classical tools of data analysis, distances, ordination, canonical ordination essentially with everything that goes with it. And today we will focus on ecological questions today and tomorrow. And of course the statistics will come to our help to better understand how ecosystems are working. But the main focus will be on ecological questions. And today in particular it will be a better diversity that will be the dominant team. And then later Danielle is going to talk about the Mantel correlogram. So, without further, if I can find my PowerPoint presentation, it is somewhere in there. Well, I can probably click here to find it. I have several versions of that talk so I must make sure that I start with the right one. Yeah, this is the one. I hope it is the right one because I have three versions of that. And then, yeah, this is just to show that I also can present a PowerPoint presentation for a change. Actually, that started as a talk that I gave in 2013. And then I have given different versions of that same talk and adding bits and pieces here and there. It is about better diversity and how to partition it in different ways. And at the end of the talk we will see that this focus on better diversity is central to everything we are doing when analyzing multivariate ecological data. And if, of course, the rows of our Y matrix are sites on a geographic map. So this will give a unifying ecological team to everything that we are doing. This is what I am going to do in this first talk. I will remind you what are these notions of alpha, beta and gamma diversities that you must have learned in elementary courses of ecology. But that will allow me to focus on better diversity and show how it is very different from alpha and gamma. Then we will see how to measure it and we will come to this way of measuring total beta diversity and how it can be decomposed into spatial components here and species components. Then there will be an example that is the fish data of the Dew River. And here will be a more mathematical part where we will go back to this similarity matrices. And there will be a landscape called a genetics example. And here there is another final example that I hope you will appreciate. This is Robert Whitaker. He was a professor at Cornell University and he has had major contributions to both ecology and quantitative methods to numerical ecology. It is in his lab that Mark Hill developed the alternating algorithm that is at the base of the Kanuko program. Mark Hill also in his lab developed the diversity numbers that unify all the alpha diversity measurements. And Yu Gauche also wrote one of the first textbooks of numerical ecology all in his lab. So he told us in two famous papers in 1960 and 1972 that alpha diversity is of course local diversity. Local diversity is what you compute for let's say a vegetation quadrat or a water sample for plankton and so on. Gamma diversity is regional diversity. If you add up everything in your data table, here's the Y matrix with sites and species. We can do the same thing with gene frequencies. We can add everything here, the columns and compute alpha diversity. The alpha diversity functions on this sum, we call it gamma diversity if the sites really are representative of the variation in the region of interest and beta diversity, we call it spatial differentiation. It is the variation in species composition among the sites. It varies from site to site. So this may be clearer with the same matrix that I was drawing here where for each site we can measure alpha using any one of these diversity numbers of hill and zero for instance species richness. H1 would be Shannon entropy and N2 would be Simpson's diversity. So if you apply that to the sum, the vector here, then you get gamma diversity. And as I was saying, beta diversity, we say that it is a variation in species composition among sites. To fix ideas, imagine that all the sites have exactly the same species composition like flower boxes that you may find along bullbars at least in my hometown in the summer there are flower boxes and they are all made in exactly the same way by people in the botanical garden. I said in the summer because in the winter we have two meters of snow and the flower boxes have been taken up. And so if all the flower boxes are exactly the same, we may have alpha diversity in each one of these boxes. There may be for instance five species of flowers present. But if they are all the same, there is no beta diversity. So this is to fix the idea that beta is of a different nature than alpha and gamma. You may have a large alpha diversity but zero beta diversity. And we will see that it can be measured in different ways. Okay, there has been a lot of discussion during the past ten years in the literature about these notions how can you measure beta diversity. And it turns out this was pointed out in various papers including this working group here that published the paper led by Marty Anderson that there are two major approaches to beta diversity. People who are working along some gradient, spatial gradient, a transect, temporal gradient, a time series or some environmental gradients like going up the slope of a mountain or choosing sites that represent a gradient in pH. Then if you have your data in this matrix for the different, the rows representing sites along this gradient, then if you compute a distance, one of our ecological distances like percentage difference or Jacquard if you're working with presence-absence data, computing distances between adjacent rows is a way to conceive beta diversity. And then you could plot the value of the distance for different pairs along the gradient. Okay, this is between one and two, between two and three, three and four and so on. And you could say, well, my beta diversity has done that for instance. Okay, so you could look at the variation in these differences along the gradient. This is a nice and valid approach. Now there is another approach that does not imply a specific direction. You can apply it to the whole map where you will be looking for a number that represents the kind of variation there can be across the map. And they are both valid approaches despite the fact that some authors have claimed very strongly with a lot of energy that only that was true beta diversity studies. I disagree with that and it seems now to be the consensus that both approaches are valid. Now in his famous 1972 paper what Whitaker told us, by the way it's interesting that this paper which is one of the foundations of modern community ecology was not published in an ecological journal, it was published in Taxon, a journal of taxonomy, including miracle taxonomy. So in that paper Whitaker described two different ways of computing a single number for beta diversity and he did that on two adjoining pages. Okay, on the left facing page he described this and on the right facing page he described that. And here he said that there were different ways of computing beta and one of these ways was to use the alpha diversities computed for the different sites and the gamma diversity computed from this vector using for instance species richness or Shannon diversity and combining them as follows. S here if you use species richness it would be the number of species in this vector and in the top alpha bar is the mean number of species in the different sites. So this ratio would indicate how many more species are present in the region than at an average site within the region. So that's a good measure of beta. And again some authors have claimed that this was the only true measure of beta but they have not read the next page of Whitaker. So yes indeed it is a very good measure of beta but it depends on alpha and gamma. Now Whitaker then on the next page said that if we want to, well I will show that on the next slide what he said on the next page. What the concept that I'm going to use in this talk is that since beta diversity is the variation among the rows well I would be damned if the variance was not a good measure of variation. So I'm simply going to use the variance of the community data table as a measure of beta diversity. You can use simply the sum of squares of the Y matrix as we were doing yesterday to compute the R square of the, in canonical analysis the denominator was the sum of squares of the Y data table. You center the data, square the values and sum them and that's it. But then if you divide by n minus 1 you obtain the variance and this will be my measure of total beta diversity that I'm going to implement. And I'll show a bit later that this is exactly what Whitaker proposed on the next page of his taxon paper except that he did that through a distance matrix. The advantage of this measure is that it is calculated directly from the data table and it is independent of the measures that you can make of alpha and gamma. So across many studies you can try and correlate this measure of beta to that measure of beta for instance because they are computed in totally different ways. It would be interesting to compare them. Now there are many other indices of beta diversity available in the literature but I will focus on that one because as you will see at the end of this talk it links everything that we have been doing since the beginning of the week ordination, canonical ordination, variation partitioning and everything to the concept of beta diversity because in all these methods we were decomposing the variance of this data table which I claim today is a good measure of beta. Okay that's the main line of this talk. Oh yes I will skip that in recent mathematical development. There is a slide that I had in one of the other presentation that is not here but we will see later what was the idea of Whitaker in computing this measure of variance from a dissimilarity measure. I must have removed that slide for some good reason. Okay now that we have this community data table y it is here again. If we simply center the data and square them so we will obtain a new matrix that I call s and I show it explicitly because we will do some things directly with the s matrix. So it is simply an intermediate step in the calculation of the total variance as we were doing it yesterday that is you center the columns on their mean you square them put them in there and then if you add all these values as we were doing yesterday the sum of all these values is the total sum of squares and dividing by n minus 1 gives you the variance that I call beta. That is fine. Now I will just make a few remarks on this measure of beta before coming back to that table and doing additional calculations from it. The first remark is that of course we know that the Euclidean distance does not correctly represent is inappropriate for to measure the variance in this data table because of the double zeros that may create values that are completely inappropriate when we compute distances. So it is the same thing for the variance and in practice in studies of beta diversity we should not compute these two equations sum of squares and variance directly on the raw species abundance data but we should use the transformations that we discussed on Monday that is the chord transformation where each value is divided by the length or the norm of each row or the Hellinger transformation where each value is divided by the sum of the row and then square root it. These are the two most used transformations before computing this total variance. So I will come back to the properties of these two distances that is the chord distance that we obtained by taking the chord transform data and applying the Euclidean distance and the Hellinger distance obtained by the Hellinger transformation plus Euclidean distance. I will come back to the properties of these two together with 15 other dissimilarity measures, their properties later during this talk. Another note here is that this total value of variance, total beta diversity measure, can be used directly right now without further developments. In particular, if at the same set of sites you measure the diversity of different taxonomic groups, let's say the ascular plants, the insects, the soil invertebrates, whatever group you want to study at the same sites, then you can compare the values of beta diversity among taxonomic groups directly because the measures of beta diversity that we obtained I will show later that they have a minimum and a maximum. For instance, when we measure beta diversity after the chord or Hellinger transformation for a data set, the maximum value of beta that we can obtain if all the sites have a different species composition is one, we have a measure between zero and one. So this is very useful and this is what makes it possible to compare among taxonomic groups because all the measures of beta have the same minimum and maximum. And you can say then rightfully that, I don't know, the color after ends are more beta diverse than the vegetation or more diverse than the soil fauna and so on. So it's very nice to be able to make this comparison. Also for a given taxonomic group you can compare results from different areas for the same reason because the measures are comparable and they are measures of variance where you divide by n minus one so that it doesn't matter that you have a different number of sampling units in area one and in area two. This is taken care of by the division by n minus one and you can compare these numbers of beta for two areas as long as the sampling units are of the same size or represent the same sampling intensity. Of course if you sampled small vegetation quadrat in one area and big vegetation quadrat in the other, you cannot compare these. But if they represent the same sampling effort or same quadrat size then you can compare them among study areas. This is already something very interesting. So what I've done up to now is simply take the Y matrix transform the species composition data, YTR and produce this S matrix where these values are centered and squared. So from that we can compute total sum of squares and total beta. As we go we will fill the rest of this picture. The first thing we can do, well let me come back here it will be more simple, from this matrix since summing all these values give us SS total we can proceed first by summing each row here. And the sum of these row sums is equal to that. So if we now take these row sums and divide them by this SS total we obtain indices that indicate the contribution of the different sites to the total beta. And all these indices sum to one so they are the composition of total beta among the sites. This is what I show here in this slide. I call them local contributions to beta diversity and it is the row sum divided by SS total. For each row i you sum over all the species from this S matrix and divide by SS total. So these LCBD values they turn out to be very interesting indices as I will show in some examples later. They represent the degree of uniqueness of the sampling units in terms of community composition. If this community composition at one site is very different from all the other sites then it will have a large value of LCBD. Now I go back again. If we can sum by rows we can also sum by columns. In the same way the sum by column here will produce indices indicating which species contribute the most to the beta diversity and these values divided by SS total are again indices that sum to one over all the species. And so we have here the species contributions to beta diversity. These are the sums by column. And the species with the highest values have high abundance at a few sites and that creates high variance. So here is a subset of the famous fish data that you have been working with this week. I chose here 11 sites and 7 species with their abbreviations as they were until recently until they were changed to English abbreviations. So these are the data from Verneau at the University of Besançon where Francois Gillette is now working. So Francois dug out the data from the library and rechecked these data recently. So here I chose these sites. Site number one is at the head of the river and as you see there is only one species at that site and it is the brown trout TRU for brown trout and the others are mostly minnows, sacreded fish, are they all? Well maybe not completely all of them. But anyway you see that some sites have very few species also these three sites have very few species but not the same as there and some sites have pretty much all the species. So when we center these columns of data the sites that have an average species composition will have values close to zero and the sites that have extreme distributions like that will the zeros become high negative values after centering and so that will create a row sum that will be then these high negative values when they are squared they become high positive numbers and then this row sum will have a high value because of that. It will be very different from the mean of all the columns. In the same way these here will have high positive values of the LCBD index because of that. So I did the calculations here after chord transformation of the abundance data and I obtained this for total sum of squares and I divided by N minus 1 N being 11, N minus 1 is 10 and I obtained 0.53 as the total beta diversity for this small data table. This index as I mentioned is between 0 and 1 so we have about half of the maximum possible value of total beta for this small data set and here I computed the LCBD local contribution and SCBD instead of showing numbers I show bubbles and large bubbles are larger numbers and we see that these sites have larger numbers larger values than these sites here that are near 0 so it means that after centering their values are very, very close to 0 and these sites have very high values also. As for the species, the brown trout that is present at only a few sites and has many zeros contribute a lot to the total beta and this is the ablet that contributes also highly to total beta but then we will... here we know why this site is very special it is at the top of the river in a very steep environment so only the trout can make it to there but we will wonder why is it that we have high contributions to beta for these three sites we'll discover that a bit later in the meantime I will focus on the LCBD indices here and the nice thing with these indices is that we can subject them to a test of significance that is we can test the hypotheses that the values of LCBD at every site are just the result of random variation and the alternative hypothesis is that these values are much stronger than they should be under the hypothesis of random distribution of each species across the sites so we do that by permuting each column in species abundance in each column separately this is an example of such a permutation here I put stupid numbers but that are easy to follow 0 to 9, 10 to 19 and so on and I show a permutation column by column so I take the values of the first column permute them and here they come in a random order the values of the second column are permuted third column, fourth, fifth column and as you see there is no mixing between the columns it is just the values in each column permuted separately the nice thing with R is that you can obtain the full permutation from this to there with a single line of R look at that we will apply to matrix Y by column the function sample as you know the function sample produces random permutation but here it is done for each column separately so this line of code produces Y perm that is this whole matrix it is very easy to include that in a permutation loop and then you can when you have this you can recompute the values if they have been centered here they are still centered you simply have to square the values and sum them or you can even sum them and square them then after the permutation simply have to sum the rows sum the columns and you accumulate the LCBD values for each site across all permutations and at the end you can compute the p-value for each row it is very simple to do thanks to the R language because of this command here you do not have to do a double loop to produce the permutations ok this is all and nice now what do the LCBDs mean this is an ordination of all the sites of the Dew River except the site number 8 that as usual has been removed and what you see here is that sites that have an average species composition would come out near the center here of the ordination plot which is the centroid of the multivariate distribution and the then sites that are far away they are the most interesting ones it means that they have species composition very different from this average site and in this case in the example the full example that I will present just after this it turns out that site number 1 has a significant LCBD and sites number 23, 24, 25 have significant LCBDs but then after correction for multiple testing these two are not quite significant they remain significant after correction for 29 simultaneous tests are 1 and 23 so the LCBD actually as I will show a bit later they are the square of the distance between the centroid and the position of the site in the principal component space in the multivariate principal component space that's what they are, the square of the distance numbers mean that they are far from the multivariate centroid that is not very interesting it is the average site but the interesting sites are those at the extreme but they can be extreme for totally different reasons for totally different ecological reasons as we will see in a moment okay so what I have done we already had the skeleton here we tested the LCBDs that is the row sums divided by SS total and the SCBDs that columns sums divided by SS total and here these can be tested for significance we cannot test, we have not found a way of testing the species contributions in that context now the full example is of course the fish data from the Dew River available on our site of the numerical ecology with our book and available in the data sets provided for this workshop with the full data set then again after chord transformation I obtained total data diversity of 0.54 with the small sample of 11 sites I had 0.53 so I was not far from that here are some pictures Francois could probably comment better than me on this map this is the Dew River this is the head site here, number 1 and the river flows like this like that like that and finally it flows into the Saun river here that goes south in Lyon it means with the Rhone and they flow together to the Mediterranean so here the brown line is the border between France and Switzerland so on part of its course here the river is the border and our sites are distributed along this river and the city of Besançon where Francois Gidet oh yes this is Francois Gidet by the way the third author of our book I'll tell you what are proof of that is there a picture oh we have a picture of the three of us on the web page as a proof of identity so Francois will address you this afternoon with topics related to our main topics so yes Francois could comment because he lives in Besançon and he has visited all these sites so here I picked some pictures from the web at the source here the flow of the water looks like that this steep slope very rapid waters and this is where we find the brown trout in this area the river flows in a nice agricultural valley it looks like ideal place to take a vacation and so on and in the middle of the city of Besançon you told me this is a canal no this is the river itself this is the river itself it is between concrete banks in the city of Besançon but then outside the city it is not like that ok so this is what it looks like here I made a schematic representation of the flow of the river Besançon is around here and this is the last site number 30 just before the river meets with the Sone river and here are the LCBD values represented by bubbles again so the two that are significant are site 1 and site 23 but we see that sites 2 and 3 also have pretty high values and sites 24 and 25 also have high values and we will wonder why for those of you who know your fish species this is the common bleak albornus albornus that is found there this is the only species I think found at all three sites anyway it is the most abundant species at these three sites while most of the other species have disappeared and here we find of course the brown trout only at site number 1 but then the Foxinus Foxinus and the Stone Loach at these sites number 2 and 3 now in order to determine what was the cause of these high values I took the LCBD values here so we can extract the LCBD values and as you know we have next matrix of environmental variables for the river for the sites in the river so I simply regress that X on all these variables in order to determine what were the most important variables that determine the variation of the LCBD so LCBD becomes a new variable a new synthetic variable of the sites that we can now study with respect to the environmental variables and we know that two sites are significant with this regression I found that LCBD was positively related to the slope of the river bed and of course that is why this site is significant it's because only the brown trout can reach there because the water is too rapid and then biological oxygen demand is also significant indicator of high LCBD values and this is what happens here going back to the data we see that these three sites have high BOD and this is a commonly used indicator of water pollution and indeed in these sites there is agricultural pollution from fertilizers by the agriculture the peasants and these fertilizers flow into the river create pollution they favor the growth of algae that increases the biological oxygen demand lowers the oxygen available in the water and makes the habitat difficult for most species except this one and maybe one or two other species so here we have the explanation of these high LCBD values and for interpretation of the LCBD we see that high LCBD may be indicator of a pristine site that could be included in preservation policy I don't know creating a natural reserve or something like that but LCBD can also indicate sites that have been polluted and are in need of restoration so LCBD is not significant is not synonymous with a good site in ecological terms it can be on the contrary indicator of a bad site in ecological terms so it is up to you then to go back and see why these sites have LCBD values and act accordingly but it is interesting to use these indicators because it tells us that if we have to look only at a few sites in detail it will be this one and these three instead of having to look in detail at all the sites LCBD is a good indicator of the fact that the site is interesting to look at in detail ok now I go back to more statistical concerns ah yes this is the slide that I was looking for earlier so on the right facing page of his 1972 paper which occurred told us that beta diversity could be computed from a dissimilarity matrix and he pointed out that indeed for presence absence data we use for instance the Jacquard and Sovenson coefficient 2 that he mentioned and we also use now also the OKI coefficient computed for pairs of sites and for quantitative community composition data he mentioned the percentage difference he called it the brain critis then and of course the Ellinger chord chi-square distance and many other distances that we will see in a table in a moment that we investigated in this paper so he suggested to take the whole dissimilarity matrix and take the mean of the dissimilarities as a single number index of beta diversity he said we compute this matrix take the mean and that's a good indicator of a good measure of beta diversity ok we will see how this connects to what we now know about dissimilarity measures we we know for instance I think I mentioned that on Monday but if not you will see it here that if the measure is Euclidean distance for instance on transform species abundances then the total sum of squares that we can measure and that leads to the total variance the total sum of squares can be measured directly from the data here transform into matrix S by summing all the values in matrix S can also be computed from the dissimilarity matrix so we can compute it from here and we can compute it also from the distances if the distances are Euclidean distances and this is done by taking the lower triangular of the dissimilarity matrix so we take this portion the portion that R shows us when we look at the dissimilarity matrix we take all the distances in there square them, sum them and divide by M and it's not the number of distances it is the number of sites the number of rows here and this gives exactly the same measure as that it is not an approximation it is exact the composition exact exact way of measuring the total sum of squares when we have the total sum of squares then division by N-1 gives us the total variance which is our measure of beta now, I discuss in a lot of detail the fact that most of the distance measures that we use in ecology including Jacquard, Sorenson the percentage difference and many others as we will see when we take the distances themselves and to make them a collision we take the square root before going to principle coordinate analysis if we do the same thing here and use the matrix D with a sub index of 0.5 in other words the matrix containing the square roots of each distance value we know that for all these coefficients the resulting matrix is Euclidean so if we put these values into that equation we obtain this so it is taking the sum of the distances divided by N to obtain total sum of squares because each of these distances is the square of the square root very simple and then this is what we do we use this equation instead of that one for these coefficients here and this will have some importance in this presentation and in the next presentation also that for all our ecologically meaningful measures of this similarity we will use the square root and this happens to be what we need to do to make them an ideal so oh yes now this looking equation is actually the equation of centering in principle coordinate analysis so I will temporarily quit my PowerPoint presentation and go back to this document where I showed you principle coordinate analysis when was it on Tuesday I think I showed you that principle coordinate analysis consists of taking this similarity matrix this is actually the small example that I had for PCA this small example here 5 rows and 2 columns if you compute the Euclidean distance between these you obtain this distance matrix and here I showed you that we first have to do this transformation 1 half of D square and then we center the resulting matrix A by removing by subtracting the row sum the column sum and adding the overall sum to obtain this matrix called delta in my PowerPoint presentation I call it G because this is known as the Gower centering John Gower again the inventor of principle component principle coordinate analysis so in this this matrix of centered data these diagonal values are very interesting and this was already shown by Gower in 1966 before you were born here are the values that we obtain in the ordination compare these 2 things I would have to show that these values last night I put them in vector these are these diagonal values here and I took the square root of these values and that gives us this so I would need 2 screens to do that properly so these values here the first one is the the distance of site number 1 from the origin and it happens to be this value because in the ordinate it is 0 it is exactly the same value for sites number 2 and 3 the distance is 2.6 like that and you can obtain this value by taking these coordinates and putting it in the Pythagorean formula square each one, add them up and take the square root and for these 2 this is the distance so in other words what we obtain after Gower centering are diagonal values that indicate the distance of each, the square distance of each site from the centroid these are our LCBD indices so it is very simple to obtain LCBD indices from this similarity matrix you simply do this and the Gower centering get the diagonal values and there you are so going back to my powerpoint presentation here is powerpoint going back to the powerpoint presentation this is what I do this is the matrix formulation of Gower centering simply, same thing as removing the row sum the column sum and adding the overall sum you can write it in one line of matrix algebra in this way where this is an identity matrix these are one is a vector of one so and so on so this does exactly the same thing does the Gower centering you extract the diagonal values with the function of G divide by total sum of squares and you obtain the LCBD indices now if you want to test the LCBD indices in a function you have to go back to the data permute the data as we did with the raw data recompute the distance recompute this equation the Gower centering under permutation so the permutation loop takes a bit more work on the part of your computer than working from a linear transform data for instance but it can be done and the function beta div that you will be able to work with this afternoon does that for you permutation test of these LCBD values for any of 21 this similarity measures that are available in the program ok so this is all very nice and it makes us able to compute these indices the total beta diversity and the LCBD indices either from raw transform data or from any one of our commonly used this similarity coefficients and that's a nice thing unfortunately when we compute the dissimilarities we lose the identity of the species so we cannot compute the species contributions there but I think the most interesting coefficients are the local contributions and we can compute them here is that clear enough now the range of values it's easy to show that if there is no variation if there is no variation all the distances among rows when you go from this to a dissimilarity matrix they are all zero there is no variation so the total beta will be zero if each site has different species composition whatever it is this site has these species next site has these species and so on if they are all different then we have the maximum value of beta and by putting these values for each type of coefficient of this distance coefficient into the distance matrix we see that Hellinger and Coord distances have a maximum value of square root of 2 when we studied these coefficients if not they are not between 0 and 1 these two distances Hellinger and Coord are between 0 and square root of 2 1.41, 42, blah blah blah so if you put square root of 2 in this equation here for computing the total variance then you put square root of 2 here and it is squared and you put it in there and you obtain 1 so this is why this coefficient varies between 0 and 1 for Coord and Hellinger on the next page I do the same thing but more quickly for all the distances that have a maximum value of 1 instead of square root of 2 and the same exercise shows that the maximum value is 0.5 now Whitaker was using the mean of all these similarities while in my way of computing the total variance the proper way of reconstructing the total variance is to take the similarities in half of the matrix so of course Whitaker did not know all this algebra back in 1972 and this is why he suggested to take the mean of all these similarities but his instinct was very good, excellent and as a result he was obtaining twice the total variance instead of the total variance as I do with my way of computing it so if you want to reconstruct the total variance we have to work with half of the distance matrix but since his values were twice that of the value then the comparisons were just as valid and this is why I claim that my way of doing the computation of total data being the total variance of the data is quite consistent with what Whitaker was suggesting okay so our calculation summary now includes this portion where we go from y to a similarity matrix and computed from presence-absence data computed from abundance data with one of the coefficients and from that we can compute total sum of squares and we can compute the LCBD indices and we can test them by permuting this, recomputing that and recomputing the LCBD indices let's say a thousand times or ten thousand times now here is a rather difficult subject and we studied properties of the similarities everything that I have shown I will show you the person in a few slides the person with whom I did that young researchers from Catalonia but when we did the first part of that we did it in about two weeks two weeks time when we were working together in China we had been invited to go there and do a project we had an apartment and in the evening we had not much to do and we could have listened to the news in Chinese but instead we decided to work on this and in two weeks time we solved all the mathematics that we have seen before but this part here took us three more months it was a very difficult and long thing to do so I will summarize that part here we studied 14 different properties of the dissimilarity functions I have already mentioned a few properties when we looked at the metric and Euclidean properties of the similarities what is necessary to make a function to be a metric is that it must have a minimum of zero and then positiveness that is the distances must be larger than or equal to zero they cannot be negative they must be symmetric and I think later down in the list I mentioned the triangles inequality thing ok now other properties here among the other properties there is only this one that I discussed in the lecture on distances that is the double zero asymmetric and you know about that Euclidean distance doesn't have that property and this is why it causes problem with ecological or genetic data so it means that the distance should not change when adding double zero but it should change when adding double anything else ok here sites without species in common should have the largest distance yes we should have that all distances have that property so you see that distance that doesn't have that property or that one or any one of those actually should not be used for better diversity studies the distance here does not increase in series of nested species assemblages nested species assemblages means that if you start with a site having three species then the next site has these three plus another one and the next has these four plus two other species and so on if the structure is nested then the distance should not decrease when you compute the similarities pairwise species replication invariance this was included as a mathematical property that is if you have the whole data table and compute the distance then if you double it you should obtain the same similarity this is just a mathematical property of stability in the calculation this may be very important if you are working with biomass data we should have invariance to measurement units that is if you measure your biomass in grams or in kilograms or in pounds if you are in the US or in ancient measures of mass from ancient Egypt we should always obtain the same distance well many of the distance some of the distance functions do not have that for instance the Euclidean distance will produce a different number if your measurement units are different so that is a very important property and the existence of a fixed upper bound is important to have a Dmax to ensure that the measures of beta are comparable among taxonomic groups and among sites well the Euclidean distance again is an example of a distance measure that doesn't have an upper bound to ensure comparability between data sets now there are extra power properties that are not essential according to us for beta diversity studies and it is for instance invariance to the number of species in each sampling unit invariance to the total abundance in each sampling unit and then there are some corrections proposed by the Taiwanese statistician Anchao that correct for under sampling that is they try to estimate the value of the dissimilarity while including the species that have not been observed because of sampling errors it is a very tricky calculation something that a mathematician a good mathematician designed Anchao and these coefficients can be very useful there are three types of these coefficients included in the beta div function that is available this afternoon so only these three coefficients Anchao have this property and this can be useful this solves a sampling issue that small samples miss rare species now there are ordination related properties that can be useful for instance we want to use a coefficient that is Euclidean or where the square root of this distances make the matrix Euclidean in that case ordination by principal coordinate analysis will not produce negative eigenvalues in complex axes and as we saw yesterday when we use principal coordinate analysis as a method of transformation of the data before redundancy analysis we want to use all the axes so this is an important property in these circumstances there are dissimilarity functions that are emulated that are produced by transformation of the data followed by a calculation of Euclidean distance and we saw these four transformations they are those available in the function they are the profile Ellinger, Kord and Chi-square these four can be obtained in this way instead of computing from the distance function okay so we have 14 properties so which of the coefficients have what properties there we go this is the list of coefficients that we investigated there are more than those that I discussed on Tuesday morning on Tuesday I discussed the Euclidean distance of course I did not talk about these two when we talked about transformations Daniel mentioned species profile we have the Ellinger transformation and Kord transformation that leads to these distances Chi-square transformation that leads to Chi-square distance so these four are obtained by transformation plus Euclidean distance then we have all of these and I think we I insisted only on the percentage difference Elias, Brian, Curtis and then there are all these others that are commonly used in ecology some of them are available in Wagen in the Wagen what's it called this Wagen the function of Wagen at least is in there, this one also maybe not the Wittaker's index and Wichard I think he has Consensi and these are the abundance-based functions of An-chao for the unseen species and here are all the properties I did not list here properties 1, 2 and 3 because all the coefficients had them they were not discriminant and then properties 4 to 9 are those that are essential for better diversity studies according to us these are the additional properties and this is the maximum value that can be taken by these coefficients either square root of 2 or 1 or in the case of this chi-square distance it has a maximum value but it is square root of 2 times the total sum of the values in the data table now if we focus on this portion we will eliminate any coefficient that has 0 so we eliminate these 4 and unfortunately to eliminate the chi-square distance that misses this property p5 that was thought important the others in the blue-gray boxes are the coefficients that are admissible for better diversity studies now at some point after writing this table I stood back and looked at it and said this looks like a data table so why don't we do this and indeed this graph tells us something interesting actually it turns out that all the coefficients the points are the coefficients and the arrows are the 14 14 properties that we saw listed and all the coefficients on the left here of the ordinate are those that are eliminated and all those to the right are those that can be used for better diversity studies and they are grouped into one to three types on this side and then two types on that side here we have the Hellinger and Court that can be obtained through transformation, plasticidian distance these are regular coefficients with a percentage difference Kandura, Wushar, Kulsinski all there and the type four are the coefficients of An-chao that correct for the species that we have missed and this tells us what are the coefficients that are admissible and then since then I discovered another coefficient called the Rujiska Discibility which is the quantitative equivalent of the Jacquard Index and I had not heard about that until recently and I checked its properties and it is fully admissible also in the same group as all these others and we will talk about in the next presentation I will talk about that one and that one in more detail but this one is another coefficient that is admissible for the better diversity studies and we have programmed it and included it in the better function that you will be able to use this afternoon ok now what we have seen are that there are we have seen some of the ways of partitioning total beta diversity and I mentioned here some other ways we can partition total beta among species and among sites the SCBD and LCBD and this is new to this talk now we know that we can partition also the total sum of squares using simple ordination or canonical ordination PCA here simple ordination or redundant analysis canonical ordination they are all ways of partitioning the total sum of squares we know that total sum of squares in PCA is partitioned into the eigenvalues in RDA it is partitioned first among the canonical eigenvalues and then the eigenvalues of the residuals but all together they sum to the total better diversity to the total sum of squares in a multivariate analysis of variance that Danielle discussed yesterday using a single factor or two or several cross factor we can partition our total sum of squares again into a portion explained by the factor and then residual or between the two factors and the interaction between them plus the residuals so that's another way of partitioning total beta diversity you have done variation partitioning yesterday and the day before so you know that we can again take total beta diversity and partition it among two or three or four matrices of explanatory variables again this is playing with total beta diversity and tomorrow we will describe the new method of Moran eigenvector maps and associated methods that allow us to partition total beta diversity among different spatial scales we will see that a part of the total beta can be explained by fine scale, middle scale, broad scale plus residual variation and so this will be another way of partitioning beta diversity in other words everything that we have been doing up to now in numerical ecology when our data represent sites in a region of interest everything is our methods of partitioning total beta diversity so it links numerical ecology with this fundamental and central concept of beta diversity in ecology and I think that's also a nice result of this of this research this work has been done with Miquel de Caceres who has spent two years as postdoc in my lab and I worked with him in China on this paper that was published in ecology letters and the PDF is available of course on my web page now I think I will go through this next example immediately landscape ecology landscape genetics example data are from Tomalemi here who did his PhD in Montpellier then he came to my lab as a postdoc and as I was working on this presentation I asked him would you have some data that I could use to show that this same sort of calculation can be done on genetic data and he said oh yes I have my thesis data on this small snail that lives in Pons in Guadeloupe you know Guadeloupe is actually in the Caribbean is actually two islands side by side this one on your left side is a volcano and the other one is coral bed that has been raised actually when the water from the ocean went into the glaciers that are now melting this coral reef emerged and this is where most of the activity in Guadeloupe is and these two islands are very close to one another and there is only a small portion of sea between the two and people there call that the salted river it looks like a river but it is actually the sea between the two islands and are two bridges between these two islands so these ponds are found in the ancient coral bed where ponds have been dug by agriculture by peasants to water the cattle and so on so they try to keep the rain water but some of these ponds during the dry season they dry out also so what happens to the genetic of these snails was the question that Tomolami studied during his PhD and he wrote very interesting articles this one in molecular ecology and another one in the American naturalist about his data that are micro-satellite data here he studied 25 populations in ponds, rivulets and swampy grass for 749 individuals of snails were genotype he looked at 10 micro-satellite loci and then the mean number of alleles per locus was 34 the mean so some loci have 3 or 4 alleles and others have 70 different alleles so it is very high genetic diversity actually and I did transform the data using the genetic core distance and computed total beta diversity which was about 0.20 for a maximum of possible value of 1 and computed the LCBD indices I'll make the story short and here's the map of this eastern island of Guadeloupe yes the salted river is here just adjacent to the capital city of Pointe-à-Pitre and so in these ponds here we have 4 bubbles whose size is proportional to the LCBD value and the 4 bubbles that are in brownish red are significant LCBD indices so they are the most genetically unique population but then why again I had access to environmental data that had been collected by Tomolami and they were pond size vegetation cover connectivity that is that pond connected to other ponds temporal stability it means essentially does the pond retain water during the whole year or does it dry out completely during the dry season and that turned out to be a very important variable here I used a regression tree as we saw during the talk on Wednesday by our colleague so regression tree analysis but it was regression tree for a single variable that was the LCBD values that I was trying to analyze not with the matrix of environmental variable but not using linear regression equation instead I used a regression tree it turned out that the high LCBD values of these four sites were ponds where temporal stability was the lowest that is these sites regularly dry out and connectivity was low with neighboring ponds no connection or nearly no connection preventing migration of snails from adjacent areas so how could snail remain in these ponds from year to year snails some of them can survive in the desiccated pond by a process known as estimating that is they just sit there in the mud during the dry season waiting for a drop of water to come at the end of the dry season and some of them survive but not all of them so every year there is strong high mortality so strong elimination of genes from the gene pool so in the end we have a much reduced gene pool in these ponds and they are replenished they cannot be replenished by snails coming from adjacent ponds because connectivity is low no connection so some snails can move from pond to pond carried by birds for instance that replenishes the gene pool but only a little and this is why these four sites have very reduced gene ponds gene pools and hence they have these high LCBD values so again the LCBDs pointed to the sites where the genetic composition was very special and here I compare the LCBD values to the allylic richness and we see that indeed that these four sites the allylic richness was very reduced that is 13 allylic locus 19 here 9, here 7 much reduced compared to all the other sites ok so we can conclude that beta diversity is the special variation in community or genetic composition among sites it can be estimated in various ways but here I focus on the variants as a general flexible method to compute beta diversity and it can be computed either from the raw transform data or from any dissimilarity matrix that is admissible to this calculation at least now 12 dissimilarity coefficients are appropriate I should correct that in my slide presentation it can be decomposed in various ways and it links this concept links beta diversity to all the methods of beta diversity analysis yeah the first time I gave that talk was when I received a prize the president prize from the Canadian Society of Ecology in evolution and sometimes students wonder what do you receive as a prize, Nobel Prize winners receive a million crores well this is what I received a nice sculpture of a Salman made by Indians from the west coast of Canada ok


When I first learned about this reason, it all clicked for me. I love to kick this off, because many in our audience are frustrated by it. How has it helped us? How has it protected us as humans? The inner critic, when I asked participants in coaching groups and Unstoppable, what their inner critic is telling them, you're not good enough, don't do this, you're going to fail, give up. Now, where would you find this evolutionarily? You can go back quite a lot of millions of years and you would still see the inner critic particularly in cooperative mammalian species. It's a little bit of a code program that says, if you're facing an equal who is stronger, give up. And that's what we as humans, we're doing now when the inner critic speaks up. It's that piece of software that is still there that makes us roll over and avoid danger.