All right, so hi everyone. My name is Elizabeth Nelson, and I'm a reference and instruction librarian at Penn State's Lehigh Valley campus, and I'm joined today by my colleagues Christina and Brian and I'll give them a moment to introduce themselves Christina do you want to start. Sure hi everyone, my name is Christina Raymond Murphy, and I'm the open and affordable educational resources librarian at Penn State. And Brian. Hi, I'm Brian McGeary. I'm the learning design and open education engagement librarian at Penn State and I'm located at the greater Allegheny campus just outside of Pittsburgh. Perfect. So today we're here to talk about how we created a multi campus train the trainer model for librarians supporting our adoption called oh a our leads. In today's session we'll start out with a brief overview of our leads as a train the trainer program will touch on our programs goals structure and the impact we're seeing so far. We'll also share some obstacles and opportunities that have emerged, as well as how we intend intend to assess our resulting adoptions, and we'll close our presentation today by sharing access to some of our materials for your adaptation and reuse. And now I'll hand it over to Christina to tell us a little bit more about the program. Thanks Elizabeth. I just started with some information about the way our leads program. One quick note, or a ER is an acronym used at Penn State to mean open and affordable educational resources. For us it's an umbrella term that includes, oh yeah, of course, as well as affordable materials and library licensed materials. And at Penn State affordable materials are defined as costing less than $50 for all the materials assigned for student. We have access to a large and broad collection of library ebooks and other licensed materials that instructors can assign as course materials at no additional cost to students. So those are included in this umbrella term as well. The way our leads program is funded from two sources, one internal and one external. We have internal funding via the Sally W Kalin librarianship for innovation which I received, and which allows me to create and support projects like this one. I have received external funding through a 2021 Penn State University libraries giving Tuesday campaign, which had of all the campaigns that happened at Penn State. One of the library ones was to support ongoing OER initiatives and to expand our adoption program. So the OER leads program is structured as a train the trainer model. Here's the program and Elizabeth and Brian joined me as co facilitators, helping to protect prepare materials to support the librarians that are going to join us in this. The librarians who became our first leads cohort learned about supporting OER and faculty adopting OER as a community of practice, sharing questions and ideas as they progress through the training portion of the program. Then the leads were able to immediately put their skills to practice via local OER adoption programs at each of our eight participating Penn State campuses across the 20, across the Commonwealth. These adoption programs were incentivized via funding from the OER, OER leads program as well. So they serve a double purpose. They help our leads get OER support started up immediately on their own campuses, and they also help us in continuing our goal of supporting faculty at all campuses to adopt OER and to learn more about open educational practices. To give you an idea of the timeline involved with this work, you can see here on the left that we started this program in spring of 2022. During that time, Elizabeth, Brian and I created our training manual, which will be sharing a link in a few minutes to in the chat. During spring 22. We also selected and began onboarding our leads librarians, and the first piece of professional development included them taking the creative comment certificate for librarians. So effectively in a community of practice started working our way through the manual, alongside a series of check-ins and discussion meetings we held to support the COP. Each of our leads librarians received a stipend to support their training, as well as their OER outreach and support work completed during the program. And at the end of this spring, we have the leads begin recruiting courses to participate in their campus adoption programs.  So you can see it was a pretty quick turnaround from creating our training materials to our leads completing the training to them actually starting the work of meeting with faculty who are going to adopt OER. In the summer of 2022, the librarians started to work with his faculty, set up meetings with them to discuss their courses, and started exploring their options for adopting OER affordable materials and or a license materials. The adopting faculty also each received stipends for each course they have accepted to the program. About half of our courses are using their adoptions right now this fall, with the remaining in the spring. So some of our librarians are still in the standing planning stages with these later courses. And as the courses progress, the librarians will be visiting each one to share two surveys one for faculty and one for students will mainly be assessing faculty and student perceptions and experiences with OER. But we're still in the process of creating those surveys so that focus may narrow as we work through it. And finally next summer in 2023 will be collating all that data back from the surveys that we get and starting to assess it, along with additional data we're collecting on cost savings and other impact measurements for each course. So we're looking to share our findings, more widely at that point as well, likely via a publication. And here you can see just to give an idea of the scope of this. They are here are the eight participating campuses circled in white Penn State has quite a few campuses. But because we have we're able to bring in eight new librarians, we have the leads working with populations across a really good portion of the state. Pennsylvania is a large state so you can kind of say that each campus is working with a little bit of a different population and in a different context than the others. Some of our campuses are quite small and some are massive. That's one reason why a big focus of this train the trainer program is making sure that each librarian can come to the program from their own context, bring their own concerns and areas of focus and leave the program with information resources and strategies that will work well for each campus. It is meant to be a trickle down approach in one location. Instead, each of our librarians is bringing their own perspective to the table, and ultimately improving our leads as a result. And now I'm going to turn it over to Elizabeth to talk about why we took this approach. Perfect thanks Christina. So I'll briefly share some of the goals we had for how the leads program might impact our libraries and our campuses. One of the primary reasons that we involved so many campuses across the Commonwealth in this project was that we specifically wanted to grow the existing network of OER expertise at Penn State by adding more OER experts at more campus locations throughout the university. Similarly, we hoped that our new OER leads librarians would join in as point people for requests for OER support at their own campuses, as well as new collaborators and OER advocacy and support projects happening across Penn State. As mentioned earlier, we also hope that by starting up these new incentivized adoption programs at various Penn State campuses, we'd help to raise awareness of and experiences with the benefits of OER among our faculty. We're happy to say that these adoption programs are already directly impacting 34 courses across our eight participating campuses. And we're also hoping that as our faculty take part in this program, we'll see a ripple effect of them sharing their experiences, the benefits they learned, and the lessons they learned with their peers. And that as a result, we'll start seeing more spontaneous requests for help finding OER from those peers as well. And finally, it's our intention to share this adaptable train the trainer model and materials more widely so that librarians, instructors, or instructional designers can adapt these materials for use at their own institutions as well. And at the end of today's presentation, we're going to start fulfilling that goal by sharing with you some of our materials under open licenses for your own reuse and adaptation. As part of making this model adaptable for anyone, we also want to share some of the challenges and opportunities that we've discovered along the way for you to consider and plan for as well. Our first challenges were around recruiting, getting enough librarians who had the capacity for the additional workload of participating in this program was difficult, but we had an even harder time getting faculty to sign on. And interestingly, it doesn't appear that that was related directly to campus size, both our smallest participating campuses and our largest campus University Park had difficulty recruiting more than one or two faculty members. However, other campuses in the program recruited between five and nine faculty members. So it seems like this may have been more of a situational challenge than an issue with the overall program. We also had some challenges with faculty who signed on to the program but really wanted to do more of an authorship project than an adoption project, which was unfortunately outside of our ability to support within this program. Some bigger picture challenges right now include the future and long term sustainability of the program within the OER environment at Penn State, as well as one of our larger goals of using this program as a stepping stone toward making connections around OER between faculty and departments at campuses. Exactly how we're going to be tackling that we're still determining. However, one of the opportunities that OER leads brought us was the beginning of making those connections, as we were able to share what's happening within this program at each participating campus. And we're also being to connect some faculty within the program with shared or related courses. We're also able to share with our faculty and our campuses just a general greater awareness of both library resources available to them and the benefits of OER as course materials. OER leads has also provided us with a proof of concept model for how we can distribute the workload of OER support around Penn State, while still sharing centralized funding and organization. Penn State's librarians have repeatedly told us that the community of practice we created together has been a significant help to them, and one that we all hope to continue to use and grow. And finally, this model of support and our new COP are both steps toward an ultimate goal of building Penn State's capacity to support OER at a scale to match the size and breadth of our institution. And now I'll hand it over to Brian to talk more about the impact of the program so far. So we're doing a number of things in terms of evaluating the impact of this program and sharing about that. First of all, we're developing surveys that will be distributed to faculty who are participating in the program, as well as to the students in the courses where they're actually deploying their newly adopted open and affordable course materials. And these surveys will help us to learn more about the qualitative impact of the new materials on student learning and on the teaching process for the faculty. But also to learn more about the success of the program in supporting the faculty to actually do this work of transforming their courses. Additionally, we'll be calculating cost savings that have been realized by shifting to these new course materials and in the leads manual we have a detailed explanation of how we'll arrive at those calculations. So because of assessing the effectiveness of the program from the librarians perspectives, we're going to collectively determine our assessment strategy within our community of practice that we have of all the librarians who are participating in the leads program. So because this program was funded through a combination of endowment funds and fundraising dollars will also be sharing this information back with our relevant internal stakeholders at Penn State to show what we've achieved with that funding, and to try to make a case to hopefully continue funding for this effort. And we'll also work with our public relations and marketing office to share more about the impact of this program more widely. We created a folder to share openly licensed versions of our program materials and the folder contains a copy of the leads manual itself, as well as an example letter that librarians can provide to the faculty for their dossiers and also a copy of the worksheet that librarians can use in their consultations with with faculty. So there's a shortened link and a QR code to access that folder on the slide, and we'll also share that link in the chat as well. And so thank you all for attending our presentation today and if you have any questions or ideas to share either for us or for our leads librarians or if you have any thoughts or requests about the materials we're sharing. Please contact us at the email addresses on the screen. And again, thank you all for attending.


All right, team, I just wanted to take a minute to review every piece that we've talked about in making the most efficient row for a big, strong upper back. As I'm doing this, I need to think about my setup, right? At most of the points that we talked about here were setup points because if I don't set up right, there's no way I'm going to be able to execute effectively. And so the first piece is we got to make sure that spine is nice and straight. And then from there, we look at the rib cage. We make sure we're not too asymmetrical on one side or the other. We try to make each side look similar. So as I do sets, I might do my right arm row and then I might do my left arm row. Again, we're talking about the three-point supported dumbbell row where we're holding one dumbbell. We got a knee on the bench, a hand on the bench and the other foot on the ground. If I, maybe I do a set and I get a sense for how side bent I am on each side. And if one is completely different than the other one, then on the next set, just try to even it out a little bit more. Sometimes you might need to exhale, remove the air in the way because that air in your thorax, pressurized air can lift a car. So I'm not just going to crunch it away. I've got to eliminate the air so that then I can get that nice symmetrical rib cage position. So straight spinal position, symmetrical rib cage position. And after that, we got to look at the head. What is the head doing? If the head is falling towards the ground while I'm bent over doing my row, then that's just another piece of the spine that isn't stabilized. That's my neck coming forward. That's my neck kind of flattening out while it does that. And it's interfering with all the nerves that come out of the head and neck that are controlling what these upper back and what these arm muscles are doing. So if you're going to activate the nerves that are controlling the muscles in your row, you have to prioritize the position of the neck. Okay, now after some of these spinal position stuff, we have to discuss what is the shoulder blade doing? And remember we talked about this little bit of turn, we talked about pushing your entire body away from the bench. So it's not just your head coming back, it's the whole body kind of coming back. And that will help secure the abs. It helps keep that spinal stability that you've worked so hard to set up effectively. And it just keeps you there while you're doing your row. After that, we've identified how far is far enough in our row. Remember we said, I like to lead with the shoulder blade first so that the arm can move. And then we row until the elbow clears the torso. And once we get there, we can just return back to the starting position. Now we talked about two different points of physics, of biomechanics that's going on here. The first one is if I want to stress those upper back muscles more, I can let my elbow flare out more. Now I might have to use lower weights because it's more challenging on these muscles that I'm targeting. But the purpose of training isn't to use the most weight possible. It's to train the muscles. It's to develop strength, to build size, right? So flaring my elbow out slightly as long as my shoulder doesn't start shrugging can be an effective way to do that.  We can pause at the bottom, we can pause at the top and make sure that we're not just relying on that stretch shortening cycle. We're not relying on the connective tissue around and attached to the muscle. We are generating active tension in the muscle itself. And that deformation is what's going to teach that muscle how to turn on. It drives those nerves to send some signals and it gives you this stimulus to keep muscle on your body. So hopefully those eight tips are super, super useful for you.  Lastly everyone, if you found this helpful it really helps out if you can send it to somebody who you think would find this also helpful. It helps if you smash that like button if you ring the little bell, if you wanna hear from me, if you don't wanna hear from me, absolutely do not ask for more notifications. But if you watched all of this, you might be interested. And lastly in the description below I have an email sign up so that you can get notified whenever I have a new video uploaded to YouTube. Thank you so much for watching. I'm Lance Goyke and enjoy your rowing.


Good morning everyone. So with this weather outside I mean when I opened the grape trees in my room and I looked outside I saw the fog you know on the sea and the little harbor and all that I thought that it was highly romantic and that I was very glad to be inside and not having to walk between buildings we just have to go to the cafeteria and then down here and we are dry and safe good so we have a lot of work to cover this morning and we will talk about measures of similarity and distance and this may look like a trivial subject but it is not it is central to the ordination of course and to what we will do in the next few days and I will come back to similarity to especially this similarity coefficients on Thursday when I talk about better diversity analysis we will revisit the properties of this similarity coefficients in order to choose those that are appropriate for better diversity study but that will be on Thursday today I will do a general presentation of the main families of similarity and this similarity coefficients and I will introduce you to a concept that maybe you're not totally familiar with and it is the concept of Euclidean distance what what is it to be Euclidean compared to being metric it is not the same thing at all and it has some importance on our choice of this similarity coefficient and then I will talk about the some the the basic statistics used in multiple regression because tomorrow we will use the same statistics and canonical analysis so I'm still preparing for the introduction of canonical analysis tomorrow then Daniel will take over after a coffee break with polynomial regression and partial regression and the important concept of variation partitioning okay I will use different documents today as I use the yesterday I yesterday most of my talk was based on one document today I will switch from one document to another instead of having a nice PowerPoint presentation that's my style of teaching and I think that when I changed the document and that type of presentation that makes people wake up and it's good it forces you to try and figure out what I'm trying to do we have a document called some measures of similarity and distance where is it just open it from here not the one to some measures ascending I'll talk first about the coefficients for binary measures I think Daniel already introduced this idea yesterday when we have binary data we can more or less summarize them I'll put that a bit smaller we can more or less summarize them using a sort of contingency table like here with ABCD a being the double presence for the site one site two let's say a is the double presence d is the double absence and this here comes the problem of double zeros and b and c are the number of variables or species present only at only at site one or only at site two so when they are for two vectors like this it's easy to count how many have double presence to go through the vectors we have one here another one there so here we have a equals to squares a b c and d here in this example a equals to how many are present only in the site one and nothing inside two here's one and there's another one we have a two here tell me if I'm making a mistake sometime when you're too close to the screen you don't really see things well here how many are present inside two and absent in site one we have one here and that's all so we have one and how many double zero do we have one and two okay so from that we can build all the coefficients here they are expressed in form of similarity for present absence data and I introduce here the two families of coefficients those that keep the double zeros as an indication of similarity and those that simply discard the value d as Danielle explained yesterday so these are the symmetric coefficients because a and d are considered in a symmetric way in the construction of the similarity coefficient and here is an example of an asymmetric coefficient where d is removed from the equation so here the similarity is simply the double presents plus the number of double absence a plus d divided by the sum total here it is the same thing but without the d we remove the d portion to obtain this this is called a simple matching coefficient and it is a nice and good in taxonomy where you can look at presence or absence of some structures or something and here is the Jacquard coefficient the most famous of all similarity coefficients designed by Paul Jacques French botanist was working in the Alps and he used that coefficient in 1896 for the first time and he wrote it in a paper with these letters a b c and d in 1901 so it is very old coefficient but old doesn't mean that it is out of fashion quite to the contrary it is found in all packages that do this sort of calculations and of course the this idea of removing the d portion is based on the theory of gradients in ecology and I think Danielle mentioned this this is a figure from a paper by Robert Whitaker we will talk again about Robert Whitaker on Thursday is the man who defined the alphabet and gamma diversity concepts and he was working at Cornell University and built a big lab where they developed numerical method this is where Mark Hill worked in particular and and you gouged also and the idea is that if you have a gradient an ecological gradient like going up a mountain for instance you have species that succeed one another each one having its optimum at some point along the gradient like if you are going up the mountain in the low altitude you may have this species that feels very good there and then it is replaced eventually by other species that are more adapted to the conditions at higher altitude the dryness the wind and all that and it is because of this idea of species having an optimum at some point this is called a unimodal distribution that we exclude eventually the d portion from the comparison it's because when we have a double one it means that the two sides for instance for this species are close to one another they are under that curve and but a double zero may mean that the two sides are here and there to the left of the curve or on to that side to the right of the curve or one is here and one is there so we cannot interpret double zeros we don't know if it means that the sites are similar or that they are very far apart and ecologists in general remove the double zeros because of that so this is a very interesting concept that in the choice between it's it's theoretical that asymmetrical coefficients is not based on mathematics it is based on ecology so there is a whole family of these coefficients and for frequency data species presence absence or gene allele for the presence absence the data is the same thing they are often used in the binary form presence absence and then these coefficients here are very much in use and the two that will be there are three actually that will be used a lot based on ABC this is the Jacquard community coefficient of community we will use also the serensin coefficient that gives double way to eight you have to a here and two ways two times a in the denominator this is a serensin coefficient and very much in use and the third one is the okay I coefficient that has a more complicated equation where the in the denominator we have the the geometric mean of the the sums of a plus b here a plus b is the sum for that site let's say did I put one or two this is site two and this is site one so the sum for site one would be a plus c and a plus b for site two and in the denominator you take the job in geometric mean of these two and these coefficients they are the limit for presence absence data of other coefficients that handle quantitative data for instance the serensin coefficient is the limit of the percentage difference called brain kurtis in some software and the okay I coefficient is the limit of the Hellinger distance and the court distance while the Jacquard coefficient is the limit of another coefficient quantitative for quantitative data called the what's it called again it was he was a ski something like that coefficient okay so so much for the present the present substance data now I'll give you two examples of coefficients for quantitative data the best known of the coefficients for quantitative data is the equilibrium distance where you simply take the difference in values in the between the two values here the difference is five square it and you do that for every variable and you take the sum of these squares and take the square root so this coefficient has a lower bound of zero but an upper bound that it can be any large number it can it can really be larger than than one for instance the distance between here and the sun in microns is larger than one that's an example so yeah this coefficient does not have an upper bound for better diversity studies we will see that there is a strong advantage in using coefficients that have an upper bound so this is another reason why the equilibrium distance will not be appropriate for these studies but you have already seen in the examples were presented by Daniel Barca yesterday that the equilibrium distance produces the wrong answer when we apply it to some simple data like the small example that he showed of the old sea paradox data the three sites with the three species abundances including distance showed that the two sites that had no species in common had the smallest distance doesn't make sense for an ecology mathematically it is perfectly all right so again the decision between this type and this type of coefficients has to be made on the basis of ecology okay so much for the equilibrium distance there are other coefficients for quantitative data and I will describe in a moment the power index that is very useful but not for species presence have abundance data here is the the percentage difference in this slide I was still using the old terminology brain practice so this is a percentage difference why the I suggested to use the original name of a percentage difference is that first this coefficient was properly described by Odom in 1951 under the name percentage difference second is that Brinkertis in 1957 did not describe the similarity coefficient their paper was about a new ordination method and they simply said we use this coefficient that was available in the literature and the coefficient that the use is not the one known as the Brinkertis coefficient they never used the Brinkertis coefficient in their paper so there's no reason to call it that way people who wrote software and called it that way have never read the Brinkertis paper so let's go back to the original name which is the percentage difference but of course in software we have to know that this name Brinkertis is just synonymous to what we wanted the idea of this coefficient here it is presented first in the form of similarity and then we turn it into a distance coefficient the idea is that for each PC we will consider that the similarity between two sites let's say that I have a site here and a site there okay the similarity is if you have that much of a species at this site and that much at that site then the similarity is the minimum of the two numbers and we add these minima to compute the similarity the difference between the two numbers is the difference so you can also rework this formula to write it in terms of the difference between the two values but here I wrote it in terms of the of the minimum that is the similarity species by species so for these numbers here are the minima two three four five one and the sum of the minima is the the essence of the similarity between the two sites for these five but it the sum is 15 we would like a coefficient that is between zero and one so we wonder what is the largest possible value that the sum could take it will be the mean of the sum of the abundances at site one which is 20 and at site two which is 22 so if w is the sum of the minima so the similarity will be w divided by the mean of a and b which are the the two sums of sites one and site two okay and so the the two migrates there giving you two w divided by a plus b it's that's the basic form this is the similarity form that was described by Polish mathematician called steinhouse during World War two and we know that I have never found the papers of steinhouse they were probably destroyed during the war maybe but this work was reported by other mathematicians Polish mathematicians after the war it was published republished in 47 49 and so on and then later authors picked up on these reports to say that this thing here is the steinhouse similarity coefficient and we turn it into a distance by taking one minus that because this formula is bounded between zero and one so you can take one minus the similarity to obtain the distance but we will see that this distance is not without problem first I will have to describe some additional properties of these similarities but before I do that I will go through two of the similar of the other similarity coefficients that we often use and then I will go back to the transformation of similarity into distance and this is the tricky part of the operation okay this is a description of the chi-square distance this is the distance preserved in correspondence analysis so it is an important one and we will see the domain of application of that distance by examining what this formula does first of all if you don't consider this portion here this is the value of the variable at site one and at site two for species j this coefficient is strictly for frequency data like species abundance data or gene frequency data okay you cannot apply this coefficient to quantitative measurements of salinity pH and things like that no this coefficient is not for that it is only for frequency data and so with frequency data you can add when you have the data table you can add the rows to say what is the total number of individuals found at the site it would not mean anything if you did that on physical or chemical variables adding temperature to pH to salinity and so on would be meaningless so you see that in the construction of this coefficient the this operation of dividing by the row sum makes sense only for frequency data you do that for site one you do that for site two and if you did only that transformation this would be the transformation into species relative frequencies what we call the profile transformation and again forgetting about that the rest of the equation is the Euclidean distance applied to these frequencies transformed by dividing each one by the row sum okay so that's the shape of the Euclidean distance that is take the difference for each species square it sum them take the square root now what is this part this part is the weighting of that difference by the total abundance of the of each species in the dataset so here I've made up a small dataset I think I should replace that example for the one that Daniel Barca showed that has six species it looks more meaningful but for the calculation this is enough for you to understand what we are doing so I have these three sites three sites with five species again and here are the row sum and now we will take into account the column sum so if we first transform each value here by the row sum we obtain these values and the distance between species profiles would be the Euclidean distance between values of that table now we will have these values that will intervene where we have the column sum here divided by the sum total 87 this actually has little effect on the coefficient it is this that has a very important effect when we divide by a small row sum like 10 or even values that can be smaller than that it means that we give high weight to this square difference whereas when we divide by a large value of the column sum this gives a low weight to this square difference so at the end of the story when a species is abundant in the whole dataset then it receives low weight in the calculation of the distance but when the species is rare in the whole dataset it receives high weight because it is a division by this column sum what does that mean ecologically it makes a lot of sense for ecologists to use a coefficient like that because it means that a rare species when it is found at two sites is a better indication of a different of a similarity of a similarity yes then finding a common species at two sites you will always find ubiquitous species species found everywhere you will always find it in the comparison of two sites so it contains little information but a rare species found at two sites it may mean that these two sites have some property physical or soil chemistry or whatever that makes these two sites suitable for that species and it is for that reason that the chi-square distance and hence correspondence analysis is interesting for the analysis of community data however in 1986 we had a workshop in we held a workshop on numerical ecology in Roscoff in Brittany professors Cardi was present at that workshop and and other people of course were about 50 participants and in the morning we had presentations of methods by methodologists and statisticians we even invited the psychometricians to talk about their methods and so on and in the afternoon they were working group of ecologists discussing the application of the present the methods presented in the morning to their date to the ecological data in the afternoon and when we discuss the application of these coefficients of this coefficient in particular it produced no position between two groups of ecologists some ecologists were saying oh yes we want to use this coefficient because of that salient property that you know it gives higher weight to rare species and it is very informative and other ecologists were saying well in my case my rare species they are badly sampled so I cannot trust the values that I have and we realized that people who sample things that they see like vegetation and you know when you look at trees they don't walk away and they are very very nice and all that so you can you can trust the fact that when you counted rare species it was really there and while other ecologists that sample things that are moving or sample in very small units like insect traps for instance there may be a rare species present in the surrounding but that you don't find in the trap because it just pass by because the units are very small so we concluded that when you can trust your rare species data then chi-square distance is fine and this is what you want but when you cannot trust your rare species data don't use the chi-square distance because it gives high weight to data that are very variable because of the sampling and at that point we were stuck because as Daniel mentioned at that time we thought that for ordination it was either principal component analysis or correspondence analysis or then principal coordinate analysis of course but the two main contenders were principal component analysis and correspondence analysis and we cannot trust principal component analysis because of the double zero problem and because it implements the Euclidean distance and now we cannot trust correspondence analysis in half of the cases because it gives high weight to rare species so for about 10 or 15 years the literature developed in trying to find ways of removing rare species from the data table before computation of correspondence analysis. Daniel even developed one of the best methods to do that to decide which of the rare species should be eliminated and by eliminating them first the most rare and then looking at the result of correspondence analysis and then you eliminate the next rare species and so on you go by steps and you look at the eigenvalues of the axis that you obtain and the total chi-square and you make a graph of that and then you can decide where to stop eliminating rare species so that lasted until about the year 2000 and at that time in discussions with Daniel in our lab and with Eugene Gallagher at the University of Boston then we talked about the transformation and I think that gave us a new avenue because with the transformed species data then we could use principle component analysis on species abundance data instead of correspondence analysis in cases where we could not trust the rare species abundance okay so that's the story of the development of ideas in this field but it is important to understand this property of the chi-square distance is that clear for everybody or you have questions about that yes simply a transformation I don't I don't see which transformation would work I mentioned that we can eliminate the rarest of the rare species yeah and that during 15 years people develop different methods to choose the species to eliminate yes that's one that's one possibility but then if you simply transform the species data using the chord or Hellinger transformation then you can use principle component analysis and principle component analysis in that case is does not react to the presence of the rare species so you can just leave them there don't have to remove them removing them or leaving them there produces the same result at the end so it is easier but then you have these two choices eliminate the rare species and go to CA or keep the rare species but transform the data and go to PCA other question yeah the log transformation is is another it is another possibility yeah for instance if you want to try that if you take the spider data that you were working with yesterday for ordination try to do an ordination with of the spider data after log transformation log of x plus one or the Hellinger transformation and do a PCA of these two and the PCA's are very similar but the log transformation is not sufficient for what we will do on Thursday because the distance at the end misses some important properties but just for the nation this is fine it's a good idea okay for this topic this is a very important topic for ecologists you know what to do people some but people are telling us to do this others are telling us to do that why I'm trying to give you the lines of reasoning leading to these different solutions and then you decide what to do I don't know that's your decision okay good now I'm going to talk about another important distance the Gower distance that was developed not for species abundance data although there is a form of the Gower distance that can be used for species abundance data but this is not our main concern the Gower distance as suddenly gain in importance for the study of species traits for instance in the FD package for instance the basic calculations for the the trait the functional that that's what it's functional diversity in the seas you can base it on the calculation of the Gower distance and this is what is done in the FD package so people now want to understand that distance and I'm going to explain it quickly it is available in several our packages but the different our packages don't necessarily implement the Gower distance to its full extent so I will try to describe how it works and what are the main variants of the Gower distance for instance in the vegan the Gower distance is calculated correctly for quantitative data only but then if you have factors no I don't think vegan takes factors but other packages take also factors and then there there's the problem of missing data in vegan doesn't handle missing data in FD it handles missing data and then you can add weights also FD does that vegan does not do it so here I'll describe the application of the Gower distance for quantitative data and then I'll briefly run you over what to do for factors and the presence absence data this is an example of seven variables let's say that they are physical or chemical variables of the environment the water the soil whatever and here I limited the example to small value and we are going to compare two objects from a data table that contains suppose it's supposed it contains 50 objects and here I made up two objects that don't really exist one that has the minimum value in the whole data table and the other one that has the maximum value in the whole data table just for illustration in a real data table there would be a search through every variable to find the minimum and maximum of each variable so the basic equation is the one at the top for the Gower coefficient which will be a sum over the different variables of a small similarity small similarity because I use small s okay computed for each variable so you compute the similarity between 0 and 1 for each variable you sum them and you divide by the number of variables that's the simple and but very efficient method that John Gower developed during the 1950s to solve this problem that was a problem commonly found with ecological data and with taxonomic data as well there is a video somewhere on YouTube where John Gower recalls the story of the development of that coefficient and what it was to use a computer at that time that was before the invention of the computer the programming languages the first one was FORTRAN formula translator for FORTRAN and before FORTRAN what did you do you had to program in computer language basic computer language in hexadecimal and using hexadecimal code in many cases so he tells the story or what it of what it was to compute a similarity coefficient at that time that's nice so he developed yeah John Gower was the successor of Ronald Fisher as chair of statistics at the Rotamsted experimental station and he spent his career developing methods for numerical taxonomy and for ecology he was with us at the conference in the Roscoff that I talked about earlier okay so what do we do here for each of the variables we will use for quantitative data this small index so this is standardized similar this similarity and we turn it into a similarity for each variable j so first we compute the difference between the two values so the difference for variable 1 is 1 the difference for this variable between the two values is 2 and so on here there's no difference we put a 0 now we look at the range in the data matrix that is the difference between the minimum and maximum and we find it here here the difference the maximum difference that you can find is 1 the maximum difference that you can find the data table is 4 and so on so you divide the actual difference but by the maximum difference to obtain these values okay and you turn them into a similarity by taking 1 minus that and you obtain this and we sum all of the what we do in the equation okay this is the sum then we divide by the number of variables which is 7 and this case and we obtain this similarity now if we want to use it as in the in the R language everything has to be a dissimilarity or a distance so we can take 1 minus that to obtain now this similarity this dissimilarity it will not have the property of being Euclidean that I will describe in a moment and so we'll wonder what to do but then if we have other types of variables presence absence data are handled with this same equation that is if the two values are identical for presence absence data if you have 0 0 or 1 1 then you obtain a similarity here of 1 or it is 0 for multi-state factors who qualitative variables you use the same logic that is if the two sites have the same state you will produce a similarity of 1 for that variable and if it is not if the two sides do not have the same state in the multi-state qualitative variable you put a 0 so it is easy to handle this sort of variable now there has been and some this for a start again for ordered variables John Gower was simply treating them as being quantitative there has been there have been some later proposals especially by Janus Podany in Hungary to rework the states of an ordered variable in different ways and this is described in the documentation of the function Gower this in FD for instance or in my book but then this is a small a small point the other main point that I would like to mention is that using this formula here the formula at the top we can add weights to these and to this these small similarities and then when we give different weights to these variables here instead of dividing by P we divide by the sum of the weights so this is rarely used but it can be useful in some circumstances where some variables are linked together to code for one thing so you may want to give them less weight than other variables that are used fully but the main use of that idea of giving weights to variable is that it can handle missing values if you have a missing value here you don't want it well you could of course exclude this variable from the data set this is what most software would do but and a more intelligent software would simply exclude this missing value from a comparison where it is found but for a comparison with another site where the value is not missing that it would keep the variable so the idea is now to say if there is a missing value here you exclude this variable from the calculation so you have one small similarity less than for the other site so you count how many of these variables do not have missing values and you divide here by that number so by the sum of the weights because the trick is to see that if you have a missing value you give a weight of zero to that comparison but if the values are fully present you give a weight of one so by summing the weights you can then have a correct coefficient that will exclude data and comparison only when there is missing value so this is a great advantage for our kind of data especially for physical chemical variables that we collect in the field if the pH meter runs off the battery is off and so on you don't you have a real missing value it is not a zero and here you can exclude these values from the comparison or people who work in paleontology and if you code the characters found on fossils fossils are rarely complete so sometimes you have pieces missing you don't know what's the value of the variable that you want to measure you put the NA in the data file miss meaning missing value and this coefficient will handle the data correctly so there are all sorts of applications for this sort of thing and all that is available in the gauze dysfunction of the fd coefficient of the fd package okay so very useful coefficient the developed by John Gower there are of course many other coefficients and I will mention many of their other of the quantitative coefficients that are in this group of the of the asymmetric coefficients when I come back to this subject on Thursday now when I showed that many of these coefficients were first computed or described as similarities and when we want to turn them into this similarities then you can do it in different ways I changed the version of this handout some measures s and d on the web page last night and I added this page from my book that it is useful to have it in this handout and so you can later go go back and download the new version that has this extra page so we are mainly concerned with transforming similarities into this similarities because in our all packages that use this sort of matrices they required that they be this similarity so there are three ways that we can use to do that we can in the most common is to take one minus the similarity when you have a coefficient that is already between zero and one or then you can take the square root of one minus the similarity and this has also been suggested but there is no not much use for that form so the big decision will have to be made between this and that and it is not a trivial trivial thing you will not obtain the same result at the end I will just mention that for coefficients that do not have a fixed maximum for instance if you had the if you had a coefficient like do you clearly understand that does not have a fixed maximum then you could take each value and divide by the maximum in the dataset to obtain a norm value of the similarity that is between zero and one or you could do it in that way also and this is if you want to turn the distances into similarities but we don't want to do that in our so I will now discuss the difference between that and that okay and this is a more mathematical subject so if you are allergic to mathematics you can go and have coffee immediately because I'm going to talk a little bit about the mathematical part so let's see I'm going to go to my chapter on distances and I will go to page 311 which is the deficient definition of a proper distance here it is so the this is the mathematical definition of proper distance a proper distance has a minimum of zero and then other values that are not zero they are positive you cannot have a negative distance okay makes sense and then all the distances that Daniel oh yes yes thank you good idea a bit more yeah why not okay so the first two properties are pretty obvious and then all the distances that we will also describe are symmetric that is if you compute it between site one and site two or between site two and site one you obtain the same value so all these the first three are found in all our coefficient number four is an important one the triangle in equality this is what makes a distance metric a triangle in equality is something that seems to be trivially simple so if you have three points x1 x2 and x3 and you look at the distances like this so the sum of any two distances is larger than or equal to the third one it cannot be smaller equal to it would mean that we have between x1 and x3 we have this and then x2 may migrate there x2 then this plus that would be equal to that one but it cannot be smaller now what happens with many of our distance coefficients that we use all the time I will go now to page 311 to give you an example it will be easier for me if I scan at lower resolution here's an example yeah so this is the kind of data that makes that makes full sense for ecologists we may have three sites with five species with these value no problem here I apply the the distance corresponding to the Sørensen binary coefficient where we have Sørensen is 2a times over 2a plus b plus c and the distance here is 1 minus the similarity of Sørensen okay so I in other words it is b plus c divided by b plus c divided by 2a plus b plus c this is what I use here so we calculate the three distances between site one and two we obtained one between site one and three we obtained point five point one if I between site two and three we obtained point forty three this plus that is smaller than maybe I did the mistake in my calculations try it you will see I would be surprised if you found another result okay so here is a coefficient that we use all the time that violates this this this rule of for a coefficient to be metric I will now show you the same thing for another example a bit further down I think it is next page yes here I am with the percentage difference alias brain Curtis in my book there is a note at the bottom of the page explaining this story that I was telling you about and their coefficient and not being what it is supposed to be and here is another example from last law lotsi work who was a vegetation scientist and then another example quantitative data so between one and two we have that between site one and three we have that between sites two and three we have that well this plus that is smaller than that another violation of the triangles inequality well these two coefficients that I showed this one and that one are related because this one is the binary form of that one but many of our coefficients violate the triangle inequality when we come to ordination this is where I want to take you when we want to do an ordination with principle coordinate analysis principle coordinate analysis can be imagined like one of these games that children had in the old days before kids received electronic games you know real games that you can handle with your hands where you have for instance blocks with holes and sticks and you can assemble the sticks and try to make a construction so kids learn to manipulate things and they may learn some principle of geometry and they may learn the the idea that some distances are not euclidean with they cannot really close their constructions what happens with this sort of distances especially if you have a lot of these distances that are not euclidean is that some of these triangles will not close because if you want to if you have joining unit here and there and you have a stick here then another joining unit then you will have this going to to that and here the stick will not reach there okay so you have a problem you cannot fully represent your distances by a fixed construction are there people from Brussels in the room nobody from Brussels you have been to Brussels many of you may have been to Brussels you may have been I've seen the the symbol of the international exhibition of 1957 I think the atomium where you have balls like that with corridors in between well imagine that some of these corridors are too short people will walk and then just fall at the end so this is what is the consequence of this violation of the triangle inequality some of the sticks are too short to reach the other end and in principle coordinate analysis we are trying to produce a euclidean representation of a multivariate data set that contains all these distances and if you have distances that are too short the method will still be able to produce a fully euclidean representation but for that it has to borrow some pieces of distances to make the sticks long enough for the construction but at the end of the list of the eigenvectors you will have to pay for that by having ugly things called negative eigenvalues negative eigenvalues measured the amount of variance that has to be invented by the method of principle coordinate analysis to make the construction fully euclidean in the first group of variables but then at the end of the list you have these extra axes that have negative eigenvalues to compensate for the variance that had to be borrowed that had to be invented to make a fully euclidean representation in the let's say if you have a hundred points you will have 99 axes all together in the first 90 axes it will be fully euclidean but in the last nine axes you may have negative eigenvalues so what do we do with negative eigenvalues the first solution is to forget about them and if you want an ordination in two dimensions you will use the first two axes that have big positive eigenvalues so even if you have a small negative eigenvalues at the end of the list you can just forget about it at the first two axes will still be will still provide you with the good representation of the distances between the points but we will see different applications in this course including on the number five where we will need all the eigenvectors and we will see that also yeah tomorrow when we will use principle coordinate analysis as a method of transformation of the data and what we will do is to start with a data matrix here why produce distance or this similarity matrix D go to principle coordinate analysis to turn that again into a rectangular data matrix and hopefully we'll want this new data matrix to recuperate the information on all axes because we want to use this the dissimilarity matrix the dissimilarity function as a transformation of y into this that will then be used in RDA to compare with a matrix of environmental variables where we will have that y transform compared to x environmental variables okay so in that case principle coordinate analysis will be a transformation of the data true well-chosen dissimilarity measure we'll do that tomorrow and in that case we want to recuperate all axes but if we have some axes that have negative like eigenvalues what happens to the eigenvectors so I have to go back quickly to the the document PCA PCA and PCOA that for which I showed you yesterday only the PCA portion if there were there is an example of PCOA in there and Danielle did not quite go through all of that in PCOA quickly you start with the your distance matrix you transform it like this each distance is squared and multiplied by minus one half then this matrix is centered by using this equation and that makes the rows and the column sum to zero in the ordination diagram it simply brings the centroid of the cloud of points in the center of the ordination diagram but we will see on Thursday that this transformation will be used again to find very interesting coefficients for beta beta diversity study the diagonal values here will be very useful but then after this transformation and that one we compute the eigenvalues and eigenvectors and this is where the negative eigenvalues pop up when there are some but then the eigenvectors in principle coordinate analysis they are I told you that the function eigen of R produces eigenvectors that have a length or a norm of one we change that norm in principle coordinate analysis we meaning John Gower told us to change that norm because this is the way to reconstruct the original distances we change that norm by taking the eigenvectors that are just fine coming out of eigen and we multiply them by the square root of the eigenvalue what is the square root of a negative eigenvalue and imaginary number quite right and when we multiply our real number eigenvectors by an imaginary number we obtain a complex number and how do you represent a complex number in an ordination or how do you use it in an RDA I don't know how to program that maybe some physicist would but I don't know so we have been looking for ways of changing that this the distance matrix if it is this is what it is to be not Euclidean it is to have the sticks that don't fit and it translate into having negative eigenvalues in the principle coordinate analysis actually the the not the criterion but the the diagnostic for non-Euclidean rt that's a word invented by John Gower the diagnostic is to do a principle coordinate analysis of the distance matrix and look at the eigenvalue and as soon as there is a negative eigenvalue in the list we say that it is not Euclidean there is a function in R it to be found in my practicals this afternoon and it is is that Euclidean is Euclidean of some matrix and the answer is true or false okay this function is in the package ADE for we ask this question about the matrix and the function tells us if it is true it is Euclidean false it means that it has negative eigenvalue okay so it is easy for us to check that and there was a lot of discussion on how to make a distance matrix that is not Euclidean to turn it into Euclidean and at first John Gower suggested two corrections that were already available but for other purposes in the literature one is called the Lingo's correction and the other one is the Kaya's correction Micaely I found the discussion between you and Daniel Chasselle about that back in 1997 I think I received copies of that from Daniel okay so it is not a trivial question but then a bit later we found that there is an even simpler way of turning a non Euclidean distance into Euclidean and that works in almost all cases and it is to take the square root of the distance taking the square root of the distances is what we had not here not here no that yeah some measures SLD is it is what we had here so in all those cases with all these distance coefficients that do not produce Euclidean distances we can solve the problem by taking the square root of the distance when we change the similarities into distances or since R produces this similarity or distance matrices we think before use we simply take the square root just write sqrt of math and that take the square root of each value and this is what we feed into principle coordinate analysis and boom the eigen negative eigen values disappear isn't that great now is that a trivial problem that concerns only one application in the ten thousand not if you are an ecologist because most of the this similarity functions that we use in ecology are like that they can produce negative eigen values before because they are not really dead and there is even a case where because they are not metric I mean even metric coefficients can produce negative eigen values in some cases and there are tables in my book in chapter 7 saying which of the similar this similarity coefficients are metric or not and then which one are Euclidean or not some may be metric but not Euclidean and the concern is those that are not Euclidean this is where we have to take the square root of the to terminate this subject I can show you just a picture all again produced by John Gower in my chapter 9 page 500 oh the famous page five hundred yeah here it is see page 500 very very famous page for a very famous picture this is an example of distances that are metric but not Euclidean look at that we have four points one two three and four for each triplet we have a well-shaped triangle where the sum of two distances is larger than the third this this one and this one but then in this triangle X four is there and this one X four is here and this one X four is there the distances are too short when you make a construction with several points they are too short for X four to meet in one point and that exists in our data we have that all the time and this makes a coefficient not in Euclidean so it produces negative eigen values in principle coordinate analysis this problem is created a lot of turmoil in the literature so much that some in some packages they said the coefficients that have this property we should never use them well that would be hindrance for ecological analysis because most of our coefficients are like that in other packages like the primer package developed at Plymouth there's somebody from Plymouth here on the yeah so the package developed by Warwick is for many years it did not have principle coordinate analysis because principle coordinate analysis could produce negative eigenvalues and they pushed on the metric multidimensional scaling for that single reason now principle coordinate analysis has been reintroduced since about the year 2000 in the primer package in the extension extension called e-primer and peace has resumed among users because now we know that with this transformation we solve the problem of the negative eigenvalues but you see when faced with problems like that ecologists and developers of software have tried different solutions in good faith to try to offer their clients things that would work but now with a bit more research we find that there are solutions that can satisfy everybody


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The streets are really good inroads. It kind of gets you a little taster. It's a community taster. What actually is going on out there?  This is the vibe of the community. This is pretty much, we have a light structure, but it's very devotional like this. In our community, we don't watch quite as many movies as we've watched in the last couple of days, but we watched them pretty consistently. And people come in all kinds of ways. Nikita flew in, was that how many years ago? Two years ago. Two years and four months. Yeah. I'm here to say. Yeah, I came here and I knew I wasn't going anywhere. And so I just stayed. And the thing is when I came here, I had no idea what I was going into. That was not in the way like, in the way that I really didn't know what it is. I didn't even know who David was to be like. I really did not know. I learned everything here. All I knew that it wasn't very clear for me that I was like, I felt like my whole world was changing. Right? I was, I like of the whole world and the next, I can't even call it a step. And it's like the next world appeared and it was here. I was to come to Utah and I was even guided not to even ask any questions. It was clear. I was guided to fill out an application. David called me the next day and two weeks later I came and from there on it was like, you'll find out everything here is just like everything. And it was like the feeling was I came into a different world and I had to learn of it every day. Every task that was given, every single meeting, every single like encounter, it was all for me to learn of a new world, to learn of a new way, to learn of a new me because I knew like there's something that's like there's a deep desire to know who I am and I couldn't live without knowing myself anymore. And I knew that I have to know capital M, myself, capital S. And so that was the experience. And so it's just like sometimes people ask me like, what is it like to live in the community? And I say, I don't know because the experience is just, it's just the experience living. It's just everything is new like to the point where I would wake up, like especially then it just became more and more so, I would wake up every day and I'd be like, I don't know anything like I don't know who anyone is. It's like, you know, if you guys have seen Fifty First Dates and then it's like, where am I? Who am I? Who, what's going on? And then I would just like, here like stay with me and then I'll hear spirit interpreting like everything. This is where you live. This is what you do. This is like, you know, this is, this is so and so, this, you know, just like really thoroughly like really interpreting the world, interpreting everything for me. And that's just become an experience. And it's like just I'm living in this new deep, deep experience. And it's like, that's all I know. And then so yeah, that's just been the journey and just deepening into the unknown, deepening like, you know, there's no like the beauty of it. There's no ever like technically, I've known some, you know, some of the seeming people, they're not people for two years, but there's no sense of like, Oh, I know you. This is like, that's David. That's cursed.  It's like the desire is to know spirit and to hear spirit. And so everything that comes, it's like that spirit and, and the beautiful thing that the ones that I give and I'm like, I'm so grateful because I am like, these are the ones where I can somehow through them, the spirit is recognized very easily. It's just, it's just easily, I don't have to sit there like, is it spirit? Who is it? It's like, who else can it be? It's like, you know, the love of your life all the time. Right. And so there's no like that casual familiarity. It's like an everyday just like, yeah, everything is new and deep and exciting and with sense of sometimes a little bit like, because you don't know, right. And, and on the other hand, it's just like the sameness of like the depth, you know, because there's still a lot of movement, seemingly, but the depth is the same to say, like that deep vibe, deep forgiveness, deep presence, that's just deepness and deepness and deepness and deepness. And it's just like, lately, I've been having experiences of just falling. And sometimes I wake up and I'll hear today, just in the fall, and I'll have these like experiences, I'm just falling. And that's, it's great. It's great. And it's just kind of like the abyss, you know, just falling. And then while I'm even falling, it feels like I'm still being very tightly held, held very tightly. It's not like I fall in crash. It's like, no, I'm very tightly held in the love. And that's why I said, that's all I ever wanted. That's that's the depth for me, just feeling that like I'm so tightly held in the love. And so, so that's my community experience.