Now, Pierre Lejeune has presented you the grandmother of ordination methods, PCA. Before that golden times of pre-transformation, there was that concern about species. All ecologists wanted to compute ordinations because they already had realized the importance and the potential of those methods. At the beginning, of course, they were not aware of the double zero problem. And so they used PCA on raw species data and they ended up with sometimes quite absurd results and some of them decided that, well, PCA and ordination altogether is not for species so we'll resort to other techniques and they abandoned it altogether. On the other hand, in the 60s, some researchers became aware that other ordination method may be interesting. And among those, what is called correspondence analysis. Correspondence analysis has first been designed to analyze tables, contingency tables. So actually, they are quite well devised to find the exceptional values in a table. They found that because it is actually one of the features of correspondence analysis. So the reason that actually a table of species or site by species data which has absolute frequencies in it like in any contingency table could be considered of some kind of very special contingency table where one variable would be, be careful, it's not the way we interpret it now. But basically they consider, wow, you could have a variable site with as many levels as you have sites and another which would be species with as many levels as you have species. So you have your table and you could analyze this by correspondence analysis. In such a computation, you have, as you may probably know, when you compute chi-square statistics on the contingency table you have those chi-square values in the cells of your contingency table. So actually, CA correspondence analysis is a PCA, but instead of computing the PCA on the raw values you first transform your table on a table of the contribution of all the cells to the chi-square and then you submit that table to a PCA. So this also means by the way that all the new values in the cells are weighted by the sites and by the species. So you have actually a method that already embeds a transformation of species in such a way that the new distance that is respected among sites or among species, we'll see the details in a moment, is actually the chi-square distance and that chi-square distance does not consider the double zeroes as a resemblance. Zeroes don't count in the computation of a chi-square value. As a consequence, CA is a method that at the outset without any pre-transformation is adapted to the analysis of species abundance later. In the document about the mathematics of the algebra of PCA, if you go further down a moment ago, you will find the algebra for correspondence. Now I'll take a little step back from the mathematical concept and take a minute to explain how I consider intuitively what an ordination does, what you have seen in mathematical terms when Pierre showed that to you and what it does of course with the mathematical differences among those methods. But all those PCA, CA and principal coordinate analysis that I will address later have in common to find in a cluster of points which are the sites expressed in the space of their variables and find the orientation of an axis that maximizes its variance. You may not have noticed it on the small example that Pierre showed you. Meaning the variances of the original variables where this memory serves me well, 8.2 and 5.8. You had the covariances here which are not relevant here. And when you put the data through that magical equation for the extraction of eigenvalues, you ended up with eigenvalues which were 9 and 5 with the same total of 14. Now 8.2, 5.8, 9, 5. It's as if a part of the information here had been transferred to the first axis because this corresponds to the first and this to the second axis. We had only two in that small example. This is actually how all those methods of ordination work. Imagine that in our minds we live in a three-dimensional, at least for the physical, for the x, y, z part, we live in a three-dimensional world. In this world we can figure out any cluster of points. Imagine your data is a cluster of your sites expressed for three species or any variables you deem appropriate here in this room. So we have a cluster with probably not completely spherical. Otherwise you can't do anything because actually this would be the case where you have no information at all in your data. It would be completely random. But of course in the overwhelming cases you have some information, meaning that some sites are expressed in different, the values of the variables are different from others and you may end up with sub-clusters or simply with a cluster that is elongated in some direction which is probably a combination of those dimensions. PCA and the other two ordination methods actually look for the axis of that elongation, the greatest elongation because this is the one that will maximize the variance. Maximizing the variance meaning you seek the direction where you have most information because if the cluster is elongated then here you see that there is information along the axis. And it probably will present for us ecologists an ecological gradient, physical chemical variables if you do a PCA and those variables or express in terms of community composition if you are with species data. So this is what the PCA does. It looks for that first elongation and when it has found it it will look for the second one provided that it is orthogonal to the first one. So let's imagine you have your first axis in that direction look for the second one, rotate actually in a three-dimensional way it amounts to rotating the second possible axis up to the first one until you find the second elongated most important elongation in that axis. You have the first axis here you have looked at from that point of view you go here and you look how it is deformed in that dimension and you look for the second one and this one is of course orthogonal it has to be orthogonal to the first one and it goes on. In three-dimension you have only three the rest of it will be orthogonal to the two previous ones and you have your third dimension and each time you see that actually the projection provides a shorter view of your data and this corresponds to smaller and smaller amounts of variance the amount of variance that you capture on the different axis is given by the eigenvalues so you have the sum of those eigenvalues which give you the total amount of variance and if you want to know the proportion of variance that is explained or not explained oh no forget that at this point we don't explain anything we present your data but the first axis the amount of variance that is expressed or represented on the first axis is given by the eigenvalue of that axis divided by the sum of all eigenvalues so for instance in one of his last examples Pierre told you I don't remember the figures but that the two first axes were presented I don't remember maybe 30 or 40% of the variance of the data this is actually what he did he took the eigenvalues of the two first axes and summed them up and divided by the total number of of the total sum of all eigenvalues of the total variance in the case of PCA and that gave him that amount this is how he could tell you that this represented so and so much variance okay so for people who are more comfortable with such kind of representations I for one I'm one of those I need an intuitive understanding of that what I'm doing something that is maybe an analogy but as close as possible to the real thing you don't deform that so as to have no relationship with the mathematics but it's another way that I suggest for you to represent and now PCA does that in a strictly Euclidean world except in the cases of pre-transformation in the case of species data correspondence analysis does this in the world of the chi-square distance which is not a distance we are familiar with in our all-day everyday life but in any case consider this as any another type of space that is adequate in that case for species abundances the consequence is that you do not pre-transform the species when you want to run a correspondence analysis you use the original raw values because the transformation is actually embedded in the method itself it does it automatically if you pre-transform maybe a chord or a helinger data to submit them to CA you end up with something that is not interpretable so don't superimpose those two don't make a mix between the two either you use PCA and you pre-transform your species data or you use them raw and you submit them to correspondence analysis now this gives exactly the same result the answer is no because for several reasons the closest pre-transformation that you could use would be the one that leads to the chi-square distance which is actually the one preserved in correspondence analysis if you pre-transform using chi-square distance and run a PCA you'll end up with something which is very close to correspondence analysis not exactly because CA has internal way of working mathematically that waits the procedure has a little mathematical characteristic that are quite a little bit different so the two results will not be exactly the same but they will be very close if you use other types of pre-transformation maybe a chord or helinger distances prior to PCA then you may end up with a result that may be a little bit different from those but equally valid now what do you need to run correspondence analysis I told you I'm a practical I'm the guy who uses the method and thinks about how to use in an optimal way so you need dimensionally homogeneous variables meaning you cannot take maybe your physical chemical variables of all kinds with pH and degrees and milligram per you cannot use them in CA in correspondence analysis you have dimensionally homogeneous which is of course the case with abundance data and the smallest value must be zero you cannot have negative values in CA if you try you simply get a narrow message and it simply doesn't work because I remind you this is based on the analysis of a table of frequencies so frequencies by definition cannot be negative for technical reasons so what you may find in CA actually produces one axis less than the minimum of the two dimensions of your data table meaning if you have 20 sites and 10 species you will end up with 9 ordination axes so if the table had more species than sites then it would be the minimum the number of sites minus 1 so this is a technical point also the fact that it depends equally on the number of sites or objects and the number of descriptors is also a heritage from the contingency table thinking which is completely symmetrical as you may remember you can define the same contingency table this way or transpose it and you will end up with the same results here you have that characteristic inherited here okay up to now understand and now I have to introduce another of those points that is important Pierre did not address that specific point in those terms but he explained you that there were two different ways of representing the results of a PCA one that emphasized but that preserved actually the Euclidean distance among sites to the detriment of the representation of the of the variables those had representation that did not correspond to their the angles did not correspond to their correlation so we have the best representation of sites but the species or well if you have point transform variables we are not optimally represented this is called scaling one so in the analysis you are going to run for PCA and for correspondence correspondence analysis you will have that choice you ask for the analysis is done the same way but when it comes to draw a biplot then you have to choose between scaling one which is the one preserving the distances among sites and scaling two which is the one preserving the distances in PCA the correlation among variables which are represented as arrows and in CA as we will see the variables are specifically here the species are also represented as points so you have the two so same as in PCA you ask for scaling one if you are primarily interested in representing the ordination of objects on the basis of sites on the basis of species sorry technically this means the objects are at the centroids of the species I show you graphical examples and you will see how this actually looks like so the chi-square distance which is at the core of the correspondence analysis method is preserved among objects for that scaling one how do you interpret it the distance among objects in the reduced space approximate the chi-square distance why do they approximate simply because you don't see all the dimensions in your in your biplot you have two dimensions if you had 15 axes you just see part of the the full ordination of course so this is an approximation but thanks to the fact that CA as well as PCA extract the most important part of the variance on the first few axes if you check that you have a good amount of variance represented on those axes you are confident that those main features that you see on the maybe the first plane the one by two plane these represent the main relationship among your sites quite well so points that are close to one another in this graph are likely to be similar in their species relative frequencies contingency table thinking if you are familiar with that so conversely any object that is found near the point representing a species is likely to have a high contribution of that species meaning that that species is probably quite abundant in that object or if you are in present substance it's likely that if you have a site point close to a species point then the species is probably present in that site I have also a small example for that by the way I started my power point presentation at slide 36 why? because all the first part the first part of my presentation concerns what Pierre has shown you before but of course presented in my way so we have complementary ways and if you are interested to see the PCA presented in that type of style that I'm presenting you the other method you are free to go to that other part of my documentation which I left in this slide for you so now we have the smallest possible example you need at least three dimensions for the three items either three variables or three objects because this will end up in CA with two dimensions as I told you you lose one for mathematical reasons so here you have those objects and the three species this is the result for scaling one that you have that I have obtained and you may see although it's not obvious I'll take I go from one to other so nobody's jealous of the other part of oh maybe to avoid that tomorrow morning everybody piles up there and there's nobody here so you may see there's a one here 0.23 rounded and lambda 2 0.08 5 9 these are already values that are reported in proportion to one or are they oh no no they are not in this case they are raw values so I'll to assess the proportion of variance or in this specific case in CA I can't speak about variance it's not true variance it's a quantity called inertia I have a slide for that so but anyway if you have if you sum up these lambda values you'll get the total in Russia and in the same way as in CA you divide this value by the total to get the proportion represented by the first and by the second axis and what you can see here in terms of interpretation for instance in though this situation you have objects 4 and 5 here which are quite close to one another relatively close because they have all species in common in relative frequency that are comparable not completely the same but they are still comparable and for instance species 3 is at approximately the same distance between objects of objects 4 and 5 this is the species because again in terms of relative representation is quite close maybe a little bit more to object 4 and 5 but in any case since it is also represented elsewhere it has been also placed accounting for all those different relative frequencies but then you could be quite sure that just looking at this that species 3 is present quite an amount in those sites and absent or smaller abundances in the other sites here a word maybe here about object number 2 object that end up close to the origin of a by plot are always tricky to interpret because and this is specific especially the case in CA you may have 2 different at least 2 different situations that could end up here in such a situation the most likely one is that this object is something like contains an equal representation of all the variables or most of the important variables which is the case here you see that the 3 species are present in abundances so this object does not distinguish itself going and therefore it is not projected in one of the corners of the by plot here it is close to the center another possibility for instance for X1 would be the unlikely case that a species would be present here and here so in the opposite corners which would also end up of the sites being present in the middle so always be careful usually objects that are close to the center have ridge objects meaning that you have a relatively balanced representation of the variables in the object of course you could continue here so this is another case here again with the oribatid mites data that I have collected with my wife in 89 during my postdoc fellowship in Pierre Lejean's lab and I told you that in scaling 1 we had the sites presented at centuries of or weighted centuries actually of species so you have the species all around here each site here is actually a weighted average of it's projected at the weighted average of abundance of all the species so you take the species scores as we call them the coordinates of the species on the axis and you weight those coordinates according to the frequency of the species and you obtain those points here so scaling 1 the chi-square distance among sites is preserved but not the chi-square distance among species but species can of course be interpreted in terms of their abundances within sites so we have the sites here and this group of sites is likely to contain many of those species here for instance and of course opposite layer you may probably expect that biplot do not contain any of those species here okay fine now you have the other scaling which is the type 2 where it is the species so the columns that are the centroids of rows so it's the opposite so it's the scaling to choose if you are mainly interested in the ordination of species for instance if you want to see if you can eliminate species association or assemblages within your ordination graph that would be the way to go in CA using scaling 2 and the chi-square distance is preserved among variables meaning here among species so in terms of interpretation the distance among species in the reduced space reduced space means simply that you see only two axes at a time approximate the chi-square distance for the same reason as with the sites so species points are close to another are likely to be represented in relatively similar frequencies in sites and any species lying close to a point representing an object is more likely to be found in that object so this is the same ordination as before I mean scaling 2 so now you see that instead of having I go back here instead of having your species at the periphery here and the objects at the center of the species you have now the reverse here so the objects are here all around and the species are here this representation optimizes the representation of species of course this is but a small example so there's not very much to be said the relationship and it's an artificial one but for instance species 2 and 3 here are at a given distance here species 2 species 3 as you may see there are on the first axes there are almost well there's almost a continuum you can also try and interpret axes by axes those ordinations so here for instance it's also true for the cA by scaling 1 you can see the gradients that had been extracted axes by axes the graded on the first axes those axes are sometimes called latent variables meaning that you have a combination of variables representing a complex ecological gradient and this ends up being represented in the one ordination axes the first and then the second one and so on so here for instance on the first axes you see that continuum between species 1, 2 and 3 according to the way they are more abundant in objects 3 and 6 for species 1 if you look them here and here well you have also here in object 2 species 1 is quite well represented as well and then you go to species 2 here which is quite in the middle here for the first axes in the first gradient but which is more separated on the second axes the second most important features present in the data as being closer to object 1 for instance then to the other ones so of course if you have if you have more complex situations like here for instance this is again my everybody might data but in scaling 2 so now you see also the reverse representation the opposite situation where you have the sites that are plotted here at the periphery and the species that are centred here so here is the represented although it's difficult to find out groups or delineate groups of species here in some cases it's clear in some other data sets you may find that sites may be here and another one here and another one here you may have some of those concentrations here but they are not extremely obvious remember that ordination is made to to show you continuums ecologies about continuity of course in special cases you may have ruptures clear cut situations where on one side you have a community and on the other you have something fully different but in those cases generally this is a trivial separation so instead of wasting axes showing what you already know you are likely to run separate analysis on the two groups because they are obviously separated if you try and analyze a real case situation where you have one group of species vegetation for instance in the forest on a dry on a dry soil without trees and just about a little bit of vegetation you already know that this is different so you don't know a need in your ordination to show you that but the structure within would be interesting to to show in an ordination so of course such an extreme case would end up with groups of sites and species completely separated on the first axis that would end up in the opposite directions and that would be true as well with PCA with pre-transformation no question? fine now attractive as they are those methods have their shortcomings nothing is perfect in this you have already discovered that you don't have an optimal display of both species and sites you have to choose between scaling 1 and 2 so this is one of those shortcomings but there are others and for CA since I'm now in CA if you look back at the slides I have some words of caution about PCA as well that limits what you should do and I'm not the uses and misuses of PCA here for CA well since it is based on contingency table thinking you know when you run a contingency or a cash square test you're looking for special cases extreme cases because those are the ones that will most contribute to this CA statistic and bring it over the critical value for your test and actually correspondence this reflects this specialty in throwing away in large distances the cases that are very special and special cases in ecology mean for instance very rare species rare in the sense that you don't find them in many sites if they are extremely rare and found just in one or two sites and on the top of it just as one or two specimens well you may have to think if you really need those in your ordination because at least graphically they won't influence the eigenvalue very much because rare species with low abundances do not contribute to the inertia of the variance if you want but they will graphically produce point that are extreme and by contrast everything else will be bunched at the center of your ordination graph and not very legible so well in some cases I tend to filter out everything that is present in less than given percent of the sites or in one or two sites it could be also something like that well be careful about that so this is all of the question of asking whether again this is meaningful information when you have sporadic species that happens in one of the other sites in any case it's extremely difficult to find meaningful ecological information about this this occurs less in plants which are less likely to run away and wander around except maybe for the ants in a lot of the rings that you may have seen where you have trees that wander around but for the rest of the practical all these situations it doesn't likely occur but for insects for instance or other mobile species it may happen quite often that you have accidentally captured one species that has nothing to do here it just happened to go there and had was unlucky enough to fall into your trap but actually it was not its destination it wanted to pass there so think about that in the case of CA especially because PCA is less prone to that kind of behavior it will end up with a very short arrow and it will not disturb you anymore but another point is important about CA it is also with PCA I'll come to the comparison in a moment but it's generally presented in the case of CA because it's there that it generated most discussions among the ecologists and this is called one of the arch effect CA and the inventor of canonical correspondence analysis which is the constrained one that you will see later on in this course brings up gradients that can be well interpreted in terms of the species packing model I mean the model that predicts that species are organized among along ecological gradients in such a way that every species has its optimum with a given tolerance around the optimum so this may be an extreme case an artificial one of course that I have presented here but the consequence of this in the so those species have the so called unimodal distributions and CA is well suited to represent this because it projects the species optimum along the ecological gradients represented by the ordination axis so this is all well and beautiful but then how on earth with a simple gradient like this do you end up with a representation like this one at last people usually scream and say this is a mathematical artifact and CA is not good because it produces such a thing it's not as long as you consider this as an artifact you cannot understand what's happening actually it's the only way the poor method has to represent what you are asking it to represent let's have a look at this packing model let's start at say at the round center here you have a species with the optimum here and another one optimum here and here and same on the other side those ones have sites in common here the first one for instance is less abundant on that side but it's still here and it shares that sites with some of the species that are around it along the ecological gradient so these are common of course a way if you sample along long gradients which is very often the case arise a point where this species is not found in common with another one which is here so this is a case where you would have a presence for that in this site an absence here and the opposite for the other species it's not the double zero here the problem of the presence of one species here and the other one so this species and the second and the third and the fourth they are progressively different in terms of their representation among the sites up to the point where they simply do not share the sites together ok so all is well up to now but if you see the same effect on the other side which is of course the case you will end up with situations where species sees to be to share common sites here and there and all the regions here at the extremes so technically the distance between this and this is maximum it could not be larger from this and this and this species there are more extreme but you have the double zeroes and then they have their distribution among a series of sites on the other side so once they do not share anything at all they are completely different in terms of representation in the sites so you are at the maximum possible but meanwhile these species continue to be progressively more different from this and this so if you consider it from the point of view of the maximum possible distance this tops off at the point where they share they are not shared by any pairs of sites but locally here and on the other side they continue to become progressively different so how would you represent those two contradictory notions or geometric situation in one single axis it's just not possible so the answer of correspondence analysis is to combine so in Pierre I hope I did not destroy your your mouth otherwise it doesn't seem to be very serious anyway so you see the two realities are represented by the two axes the first one if you project the sites although here I have many sites so it's not extremely well you cannot see it very well but if you take one out of three or four sites you will see that the distances between those will progressively decrease if you project here it's going vertical here so distance between this site and say this one is very small here while three sites away here it's larger so this is the first reality you tend to have to go to the vertical representation here because sites become progressively different from those here and they cannot be much different from one another when they reach the point where they have no spaces in common so this is the one reality and the others are represented on the second axes so they continue to become progressively different because they are close to one another the sites along the the gradient continue to be close to one another on that closer relationship so it's not an artifact in PCA creation is even worse worse even if it's more beautiful in terms of graphical representation why on earth is it possible that those sites that are most extreme come together here a clue here this is done with species data without pretransformation now I ask you how is that possible that those extremely different sites that have no species in common almost no species in common end up being closer to one another then other pairs of sites here the double zero effect exactly when you have less and less species in common you have more and more double zeroes in common and these tend to put those sites together so a PCA run on species data without having pretransformed those data ends up in such representation which is completely away from the reality in that case while in CA at least you have a limited effect as I told you for quite a time this has been considered as an artifact and people have tried to correct it and especially they tried to correct it by a method called detrended correspondence analysis meaning that by segment here you take the sites here and you put them into zero so you put it straight of course in the real world you have dispersion around there but you would take a portion here segments along the first axis and put the mean equal to zero and then represent all the thing here this is called DCA detrended correspondence analysis but to correct something that is not an artifact it's actually useless despite the fact that many people still tend to use it for whatever reason it has been rejected for many reasons that I don't have time here to prevent those reasons but there's no real reason to use that detrended correspondence analysis because even with the geometrical fiddling here the second axis is meaningless you cannot use it so remember that better have honest represent not a detrended representation that way and locally interpret the concentrations of sites of species that I showed you before here than trying to redress something here that was not an artifact in the first place and end up with something that is completely useless in terms of ecological representation oh energy, basic resource in ecology it's coming short for some people I understand that fully okay for CA sorry when you work with the transformations you still have an artifact but not the whole shoe which is really the worst situation you can try maybe extreme effects you will still have some residual whole shoe effects I don't remember having seen it in any way it's well corrected well you may have a little bit a little rest of it in some of the transformation with some data I remember having seen or tried and ended up with something like that but it's by far not as extreme I think in your paper you had something like that about the transformations you should look up the paper and see in the figures but I think we have something like that but it's by far not so extreme other yes well points near zero always mean that for given in the most general case points that are near the origin are average in terms of the variables so they have no extreme abundance on any species or if they are in the case of PCA they have no extreme values in the environment environmental variables all those environmental variables would have quite well values close to their mean to the average with that so that makes them difficult to interpret because in some particular cases it may be also the compromise between the fact that they are in the other variable that our positive one another in the graph in that case they would end up close to the middle as well so always be careful about the interpretation of points in the middle of the ordination of course that's a good point of course it's always possible that a point is close to the origin on the two first axis but if you draw the third one it happens to be very far away yes you have understood that they usually show the two first axis first because obviously they are representing the most of the variation but the third and possibly even the fourth may be interesting in such case it's customary to keep the first one and as a basis and then going to the first by three and first by fourth axis to always have the main trend as a reference but yes you're right you can do that I showed a double presentation where we he showed first by second and first by third axis yes excellent remark okay now I have couple of minutes left to present the principle coordinate analysis this well up to now we have PCA with Euclidean distance and now of course those pre transformations that opens it up to a couple of others but not many actually only though that have a Euclidean component embedded in them to call distance Hellinger distance, Chi-square distance and so on, so the five of them and then you have the choice of CA with the Chi-square distance it can be that for different reasons you are interested to produce a ordination based on another type of distance as I said community ecologist among you may be familiar with the so-called break artist distance which is often used in community ecology so the break artist cannot be is not respected in any of the flavors of the two ordination that I have shown you other situation may call for more exotic distances or dissimilarities in general terms for instance when you have a set of variables that are not only not expressed in the same units but some of them are qualitative, some semi-quantitative, ordinal and other ones quantitative so how do you put them all together there are some specialized dissimilarity measures that can cope with that kind of data Gower distance or it says Esterbrug Rogers, okay Esterbrug Rogers distance are such examples so how do you do that could you still produce an ordination the answer is yes thanks to principle coordinate analysis this is what it does it takes not the raw data but already the square symmetrical matrix of dissimilarities and produces an ordination from that as a consequence of course since your dissimilarity matrix is among sites in most cases what we call a Q-mode sites compared in terms of their variables so you have only dissimilarities among sites in this matrix the variables have disappeared all together so the ordination produces only an ordination of sites if you use other dissimilarity measures devoted to variables instead of sites it's called the R-mode and then you would have only the variables represented on the ordination but in both cases not in both cases but in case you have a dissimilarity matrix among sites which is the most frequent situation you can still afterwards a posteriori project the values of the variables in the ordination plot so PCOA the principle coordinate analysis not to be confused with principle component analysis shown before by Pierre will end up with the same result as PCA if your matrix your dissimilarity matrix is made of Euclidean distances so this shows simply that it works correctly it takes the representation you give it and it runs an ordination in an appropriate way and in the case where you have more exotic of those including the properties distance or dissimilarity those have some geometrical properties that are difficult to cope with by an ordination method because they are not fully representable in a Euclidean space as a consequence you get something very curious and this is negative eigenvalues I told before that eigenvalues were the result of a partition of the variance among the axes but there you have negative axes simply because all of the variance cannot be represented in real axes for some dissimilarity this can be corrected mathematically by a transformation again of the point but this goes a little bit beyond what I want to show you today the principle is this one so for the six objects and the three species that I have shown you before you would obtain something like this here a simple coordinate analysis based on what most people know as break artist but actually should be known as percentage difference dissimilarity so again here you can interpret this is like a representation in scaling one what you get in this case so you can interpret this in terms of distances on the ordination plot here for or about my data it would give you this so you have actually a scaling you have you have the sites represented here and you can represent the variables in two different ways on the one hand you can think of it in terms of weighted averages like in CA so you say okay there are such and so many of these species in these sites and if you average the scores of these where this species is present and multiplying each scores by the abundance of the species you end up with a point here in a very simple case if you had for instance a species that was present only in sites 38 and 67 here in equal amounts of a line connecting the two points and in terms of weighted average if the species had more had a higher abundance in 67 than in 38 it would end up closer here between the two sites closer to 67 so this is the principle this is one way but not to my idea not entirely satisfactory but it is considered the axis as some kind of summary quantitative assessment of the organization of the sites and then you try to correlate the variables to these axes and you use this information here I have presented it on another data set to be also faithful to that other data set it's the do fish data set that you will use it's used in most of the chapters of the yellow book here orange book so for these 30 sites in the do data sets here I have projected the species as arrows so this is a kind of PCA thinking I have run the PCA on the do fish data and I should have added here that it has also been run I think with the percentage difference of breakers distance and the species are simply you correlate the abundance of the species with the scores of the sites and you end up with a correlation that is positive or negative depending on the orientation yes Pierre Mille not has told you that during the computation of an ordination the orientation of the axes is arbitrary there is an arbitrary decision of the plus or minus at some point in the computation so this or a mirror image in two axes would be equally valid there is no point about that but ok in this case you end up with those arrows that can be interpreted like in a PCA ordination score where you have in this case you know that these sites have a higher abundance for these species of fish and so on and so forth almost finished was I supposed to finish at 1230? yes so ok if you allow me a couple of more seconds just to finish so principle coordinate analysis can be used as it is as I showed you here but it is also used as an intermediate technical step in more complex analysis it will be especially the case in day 5 when we presented distance based more and higher vector or maps in the context of spatial analysis where we will use principle coordinate analysis so to summary everything that has been shown you this morning in terms of ordination I present you here a graph figure by so what we have seen is first the classical approach with raw data and PCA in case of short gradients you could use here if we speak of species data if your gradients are really short and you don't have much of those zeroes and double zeroes you could use PCA but be the gradient short or long you can use CA and you end up with an ordination plot of the kinds I have shown you you can of course transform the species as I showed you and this gives the TBPCA so transformation based approach here that was the first part of my talk about the transformation and finally the distance based approach where you start with a dissimilarity matrix this is PCOA which was my last part here and as you will see here in the course the equivalent will be here available for the constrained ordinations which combine response data and explanatory data for those different methods but this is another story ok thank you so I guess we all have merited our our lunch so let's proceed to that very short Pierre is laughing we were expecting that question because well ok we did not present non-metric multidimensional scaling because actually it's not an eigenvalue based method it's not linear it represents some kind of a well how can I put this a rough ordination but the only use maybe in special cases where you really need absolutely to represent some part of the variability in a restricted number of axes that are pre-imposed I mean you need two or you need only three and not more but then at the price of a complete deformation of the structure which is not it's it tries to respect the rank order of the sites on the representation but with more or less success this being represented by so called stress factor Pierre maybe you want to yes we have a slide with a comparison because in all case where you would need that you could probably use a PCOA so principle coordinate analysis and yes we have a slide with a comparison of both okay fine so bon appétit


I'm going to show you how to make a snowman, so you can play too. This is how you use a roll of toilet paper to wrap someone into a snowman. Start at the top by the shoulders. That helps it not fall down. This is getting comfy too. If the toilet paper breaks, it's okay. Just tape on the broken piece. I can't wait till she's done. It's going to look so cool. I think we're done. And voila! So use paper to finish decorating. Like black circles for buttons. The hat of the snowman. Press this button.


Hello again, so it's time for another episode of the movie being better than the book it's adapted from and For this episode, I'm gonna talk about the fifth wave now you've you may have already seen the video I did on the fifth wave book series it's extremely long extremely in-depth and basically me just going over how terrible those books are because they really are but Throughout that video. I also brought up how the movie that was made in 2016 and only covers the first book is kind of better than the book in a lot of ways because Like the movie is bad. Yes, but the book is just so so much worse and You know, it's basically impossible to talk about how exactly that works without spoilers So from here on out it this video is gonna be full of them but basically the book is a mess in terms of plot and The movie cleans that up at least a little bit so if you're unaware this series is about aliens coming to earth and destroying most of humanity in a series of attacks called waves and It's never properly explained why the aliens came to destroy people or anything, but You know, that's what happened and so the vast majority of the human population was killed off by like some earthquakes and some EMPs that went off and a Avian flu that went out and killed most people and then we start following our main character whose name is Cassie and she winds up being separated from her brother who is the last of her family and then she goes off to find him and then From there the story just falls apart like that's done fairly well in the movie, but the book start is It's horrendous. So basically the book starts with a prologue Which specifically shows that aliens are coming in and Infecting humans so that the humans will grow up and have an alien mind in them And then they'll be on their side like we just know about that from the beginning from the prologue and So when it comes up later, it's not really a surprise or anything Okay, and then immediately after that we cut to Cassie and it's after the world's already been destroyed She goes into a store. She kills a soldier We get an intro to what her life was like before the aliens came and before everything really fell apart and then we see how the world was destroyed and That sounds fine when I describe it like that, but it goes back and forth so much like it'll be okay I'm walking into the store I hear a noise and then think back to what her life was like before the world was destroyed for a couple of pages and then I go into the back to investigate the noise and then Think about that for a few more pages and then start to think about how the world got destroyed and how we wound up in this point And then look there's a soldier there I think he has a gun have a brief conversation shoot him and then like that's the real end of the Prologue I guess you call it like that's the real intro to the story, which is Really really confusing to read like I know the way I'm describing it there It sounds bad enough, but there's really not even a transition between them Like it's not as though it'll end one chapter in the present and then it'll go into a flashback chapter But and it's not like there's a line break and then everything's in a towel It it's halux to show okay That is a flashback or anything like that it'll just go one paragraph is one subject And then a completely different subject in the next paragraph So it is just a mess and then after that we just show Again we go into permanent flashback and we just show everything from like the world being destroyed and her mom dying and stuff all the way up to her being separated from her brother and deciding to go off and find him and That's like a little better, but it's still just the beginning of this book is an absolute mess the movie is Much simpler. Okay, it just shows Cassie go into the abandoned gas station find the soldier shoot him Realize that he was innocent She didn't need to shoot him and then be upset and then after that it goes back to what her life was before Everything was destroyed and then just everything after that is in order So it's nothing really different or unique or like avant-garde or anything Which the book might have been trying to do but at least I can tell what's going on and you're never sure and you're never Wondering if it's like oh is this past present or future because like you just know and sometimes that is best Sometimes it's best to just be straightforward with these things In fact, I would go so far as to say that this movie while it is overall pretty bad The first half hour is pretty good because after that when we see the whole world get destroyed We actually see it get destroyed You know when Cassie is describing it in the book it's fine She's basically just saying yeah, there was an EMP which knocked everything out And then they caused these earthquakes which destroyed a bunch of stuff whereas In the movie we actually see her when the EMP comes and she's like oh, hey all the electronics are out That's weird and then we see her when the earthquake comes and she actually gets hit with a small tidal wave coming off of Lake Lake Erie, I think I don't remember it's not important one of the great lakes And we actually see some stuff that happens around the world which she didn't and It's an impressive scale is the thing like you really get the feeling.  This is huge This is this is horrendous And so it actually you feel some of the weight of yes the world is ending and these aliens are ungodly powerful and by doing it this way we also get to connect with Cassie a little bit and actually care about her and Well, I can't go into too much detail about that because it's it's pretty simple to do It's just like yes, here's a character. Here's them living their lives. Here's them Having some small flaws, but overall being an enjoyable person to watch like yeah, this is Cassie So much fun. Should we just take our shirts off right now and go jump in? Oh, yeah, certainly Oh, what would I even say to him? I don't know him. He doesn't even know me.  He's a boy Oh And so we actually care about her as opposed to the book where we feel kind of bad for her for accidentally killing someone But that's that's kind of it beyond that She doesn't have much personality and then after all of this both the book and the movie cut to this character named Ben Now the thing about that is that in the book He has mentioned maybe once as this guy that Cassie kind of has a crush on and then it just cuts to him Months after the world is destroyed. He's in a refugee camp and then he joins up with the military and it goes several chapters without telling us what his name is and Even once it does I had to stop and remember. Oh, right Ben. Yeah, he's he's that guy in the movie It actually shows Ben for a couple of not for very long But like for a couple of seconds at least and he he's named at the beginning intro part where it's just showing the world before everything goes to shit and Then later when it shows him joining the military. We just see okay. Yeah, it's that guy like it's it's just less confusing is the thing That was the last time I saw Ben bearish That's part of the issue with cutting between different POVs. I've talked about that before But just like cutting between first-person POVs is a very delicate process. You have to be careful with it in in the movies it's just much easier, you know and Maybe that's not really anything intelligent on the part of the scriptwriters or directors or anything But it is at least a baseline level of competence that the book is missing This is also around the time that Cassie meets Evan who is like her main love interest throughout the series and in the book it's very obvious that he's an it that he's an alien in a human body because again We have that prologue so we already know that's a thing and then we also get a chapter from his perspective Where he's like, you know, I see that girl and I want to protect her so I'm gonna do that and So there's like no tension. There's no build-up. There's no wondering Oh, what what is this guy's motivation? Is he really on her side or anything like that in the movie Cassie gets shot And then she wakes up in this guy's house And he has helped her out and she's kind of freaked out by it and tries running away And it's understandable why she might do that There is tension we don't know what's going on she doesn't quite know what's going on and so When he's hiding the fact that he's an alien and when the audience doesn't know that he's an alien there is some mystery and The book for whatever reason just doesn't have that and I really don't even know why they put those scenes in because you could Just cut them out and it wouldn't make any difference to the rest of the book It's not important for like character development or the storyline or anything like that You can just cut them out and it would make the whole thing a lot better So I really don't even know why they bothered doing that and so when the twist comes in the book It's not even a twist because we already know that But in the movie when the twist comes sure it's still pretty easy to see coming Let's be honest even if you never saw the trailers or anything. It's easy to tell like okay Yeah, this guy. He's an alien that churn good But it does at least have some weight for the story and it makes some sense why it would have weight for the character as well now we also see all of the military training stuff with like zombie aka Ben and Sammy Cassie's younger brother and That's pretty much the same in the books as it is in the movie like the books just go into more detail with it It's all kind of dumb if I'm being honest and not that interesting Easily the weakest part of an already pretty weak story, but I mean the movie's not doing it worse and At the end when they finally go on their one mission and realize oh, we're being controlled by the aliens they In the book they straight up blow up one of their teammates or rather He blows himself up because he doesn't believe that the aliens would have implanted explosive charges in them And then he's like no see look at this and they push the button and kills himself Which is honestly really funny, but it's not supposed to be funny in the movie. They just they just cut that bit out So that's handled slightly better Again, this is all just a bunch of things that are tweaked very slightly to make them a million times better It's not even that amazing.  I should do this and It makes her seem like so much less of an independent character so much less of an intelligent character so much less of a determined or skilled character it's like it's just very basic things that are wrong with this and Then we get to the real climax where Evan comes back and helps him out and then Ben runs into Cassie and they're like Oh, hey, let's get Sammy and get out of here And then they blow up the bad guy's base and there and then it ends on a note of like well now what what do we do and that That's kind of it overall Very dull movie and quite frankly. It's a bit of a mess Like it feels like not even a complete story And I don't mean that in the sense that it's part of a trilogy so there's going to be more to this I mean like it feels like they started a story and then just ended partway through and Even though there is a climax it doesn't feel like that much of a climax so the whole thing really is just a mess and Even the parts that are handled a little bit better a lot of stuff is only Explored at like a surface level like you know the characters for example their Personality and motivations are only explored at a surface level like we know that Ben's family is killed Yes, but we don't know much else about that like we like okay I want to kill the aliens because my family's dead because of them like okay That's that's about all we know about him the apocalypse as well like it's We see the world get destroyed, but we don't really feel that much of the ramifications of it You know we see people the remaining people are mostly like hiding out in the woods or they joined up with the remnants of the military and that's That's about it. You know, we don't see people trying to gather up and rebuild or anything like that It's just yep the apocalypse has happened Yeah, that's it, but All of that aside it's still better than the book It's still better than the book because the book has pretty much all of the same problems Maybe worse in some cases so and The movie also has a couple of things that are good like I said the first half hour is really solid We get to see the world get destroyed We actually get to be connected with Cassie in particular and some of the other characters We really see her relationship with her father and so it's kind of sad when he gets killed All that and just overall Chloe Grace Maritz has gives a very good performance like she She carries that entire film on her back and the script doesn't give her a whole lot to work with but she Frickin does her best and she really tries to elevate this movie beyond the schlock that it is but Even she can only do so much and same with Lee of Schreiber who plays the villain Colonel Vosch like he's clearly trying But the script gives him even less to work with than Chloe Grace Maritz. So Like what are you gonna do and to be fair? That's like that's an even worse problem in the books like Vosch is one of the shittiest villains I've read in a Very very long time Really that that's what this whole thing comes down to like the movie is not good by any stretch but It's less of a mess than the book, you know, like I I Just don't understand why the books got as popular as they did because they were fairly big But the movie I mean the movie didn't do well But if it did well, I would at least understand that like I can understand why someone would watch the movie and Enjoy it for one reason or another like I I understand that the book. I just I just don't even get it like what What what is there to be enjoyed there? There's just not much to it and While while I was getting my notes together and everything I was thinking man I would I would really like someone to just remake the books or reboot them or something like that just take most of the same basic ideas and character concepts and everything and then just Try and fix it, you know, just try and write a series that isn't total shits because of it and Yeah, that's about it really, you know I don't think that you can really go Super in-depth and analyze everything about the characters and the storyline and the world and everything about this series Or especially the movie because there's really just not that much to it. Yeah, it's a very Simple straightforward storyline which they still manage to screw up It's a very simple straightforward or most of the characters are simple and straightforward and they managed to screw most of that up But the movie the people who made it were clearly trying and they managed to fix a lot of the issues. So It is better than the book All right, you know how this works by now All the names on here are people that gave me money and the people that gave me ten dollars and more are Aposavalanian Olivia Rayan Ava tumor Brandon S. Pilcher brother Santotis Christopher Quinten Datboy 805 Mbis Pfizer Jeremy Joel Karkat Kitsune Kevin Jang Liza Rouda Cove up Madison Lewis Bennett Mel Austin microphone sad martigan tobacco crow Tom Beanie and vae victims you guys are the best if you want stuff like Early access to my videos or just voting on future video topics then consider sending me money And if you don't want to do that then become a YouTube channel member or just like this video share it around and stuff It really does help and That's about everything I'm supposed to say here, so I'll see you later. Bye


Hi, my name is Liam Rowe currency trader and trading coach at trading 180.com and welcome to this week's supply and demand Forex and gold fundamental and technical analysis if you're new a very warm welcome to you And if you're returning a weekly warm welcome to you And if you find the analysis that I do every week useful please don't forget to like subscribe and Share as it's a free way to support the channel and it gets the quality content out to Traders that really would benefit from this type of analysis. So let's get into the week ahead on trading economics and zoom in a little bit and This week the Fed and the Reserve Bank of Australia will be releasing policy meeting minutes while central banks in China and Africa Set to meet to set interest rates. So we're looking at the Federal Reserve and the RBA For For monetary guidance, I guess so what they're going to do with regards to interest rates and interest rate and monetary policy Also flash PMI surveys for the US UK Eurozone, Japan and Australia were given insight About the state of the global economy other important releases include the US building permits and housing starts Canada and the UK Inflation data that would be important and retail trade Japan And Eurozone first quarter GDP growth rates that definitely be important for Japan and especially Europe all eyes will be on that China industrial production and Australia employment figures so a very busy week depending on the currency pairs That you are looking to trade. So now let's get into the technicals and some fundamentals as well starting off as we usually do on the dollar index to DXY and The dollar is suffering a bit and I say suffering in in the sense that it's you know being being sold off Which is actually positive for the for the Federal Reserve in a currency war, which we're pretty much in This competitive devaluations the only problem that the Federal Reserve have is is inflation Right and I say the only problem they have a number of problems But they have them they have inflation problems and also a GDP in jobs problem But recently the Fed officials have six reasons to bet inflation spike will pass and why is that really important? It's because if inflation doesn't if inflation Really gets out of hand then they're going to be forced to act and raise interest rates Which is basically what they don't want to do because if they raise interest rates too soon Then it really hurt it can hurt the economy and the economy at the moment We had a massive jobs miss. I think it was last week of the week before So the Fed are very cautious We're wanting to raise rates and borrowing costs because it could really hurt the economy before it really gets going So they're in a bit of a conundrum at the moment and the Federal Reserve are really kind of talking down the the inflation Numbers, you know, they're looking for an average inflation target of two percent Which at the moment It looks like it might be going a lot higher than that But it says much is at stake the feds new policy framework approved last August pledges more patience in viewing inflation Now it aims for an average of two percent over time including some overshooting for past misses and want to achieve more inclusive employment That aids lower-income workers and minorities so Again, they're talking down the expectation the word. I think the word they're using is is is not trans Transitory is I think that's what it's what it's known as and basically what they're saying is is that It's not it's not transitioning to high inflation It's just a little bit of a spike a little bit of a blip and it will come down Soon and the average will work out. So there's no need to look to even high crates. So, yeah, they're in a bit of a They're being a bit of a conundrum at the moment So the the general consensus actually is to continue to you know, short the dollar. So With the fundamentals at play what you're looking to do is look for Selling opportunities and confluences I guess using the dollar index and the dollar index is just a measure of dollar strength against the basket of currencies like the euro the yen and the pound and So what you're looking for pretty much is is a pullback to potential supply zones And if it starts to sell off there, then you're looking for sell trades on the dollar yen dollar Swiss For example, if there is some good news and positive news around the the US dollar potentially, you know growing GDP jobs numbers, etc Then you this could actually be a decent area to look for some long trades on the dollar But I think the general consensus is for a a weaker dollar until the data supports the the the buy narrative moving on to the dollar yen and the dollar yen at the moment is Again in a bit of a predicament the yen isn't necessarily the best pair to buy in a risk on environment And the risk on environment means that the investors looking for a higher return on their investment The Japanese yen is really in the minus zero point one meaning that it's going to cost you minus zero point one percent or zero point one percent to keep your money in the bank so And we've you know the the dollar Not doing so well. You probably may see a bit of a range start to come into play so at the moment this is Quite a difficult pair to trade When it comes to looking to buy or sell obviously that would I say obviously but the tint of my my my my bias I guess would be to Maybe some dollar upside, but it's it's a bit too difficult to kind of tell fundamentally So for me, I'm personally staying up But if you do want to get you know long or short then I would say this is probably the time now to get look for Short trades or just a bit higher right here Probably delete that upper supply zone. I would say that's probably where the best zone is and Probably down here as we can see if prices do break through that demand zone the 108 is probably a decent buy If you're looking to buy the dollar against the yen moving on to the dollar at Swiss dollar Swiss We again got some more selling the Swiss Frank again just similar to the Yen is a risk is a safe haven currency meaning that the Swiss Frank tends to do well in a risk off Environment as money will flow tend to flow into the the the Swiss Frank But with a an interest rate of 0.7 minus 0.75 It's the worst out of all the the the major the major economies that we trade. So Personally, I wouldn't necessarily even look to trade this pair again not financial advice You can do what you want to do, but I'm just letting you know, you know what where my where my stance on that is But it's there are easier trades out there. So If you do want to get long on this, this is a decent opportunity to get long Not the best demand zone daily demand zone in the world. There's a few more things I would like to see before I would look to ever get long on the on the dollar Swiss And Again, if you do want to continue getting short and really kind of ride this recent downward trend from You know the beginning of April then you're looking at prices moving back up to this You know just above this 91 cent area and then looking for short trades again in conjunction with the dollar index Setoffs looking at the dollar CAD and dollar CAD. This has been You know the other CAD being actually quite quite strong with especially with the Bank of Canada looking to taper And remove support when I say remove support. They're basically Not looking to you know quantitative ease print money, etc. And devalue their currency You're pretty much seeing the the effect of of that So again the Bank of Canada potentially looking to raise rates, you know within the next, you know two years The market is pricing that in ahead of time. So For me, it's shorts all the way for now any pullbacks to this supply zone will be a decent short If you are looking to get long on this currency pair, you really want to see proof of value and prices, you know Basically move to the upside to prove that there is you know The dollar is a potential bargain down here then a pullback into that demand zone before looking at any kind of long trades Moving on to the New Zealand dollar and New Zealand dollar. I think New Zealand is is is a trade There's a currency that is a buy and prices did come down to its nice demand zone last week And this was a decent buy So the New Zealand dollar doing well and the risk on the environment the dollar US dollar not doing so well So so yeah, this was this was always a potential buy And if prices do come down again, I would say this level's probably been used several times So you probably want to wait for prices to come down to this zone before looking at any kind of long trades If you get the opportunity if you want to get short So there's a change in in sentiment on the US dollar or even the New Zealand dollar and I do think this area this 70 0.73 for Level is a really decent zone to get short technically, but I don't really like this pair for a For a sell trade if my bias is to the to the to the upside as far as a buy on the New Zealand dollar Moving on to the pound dollar and the pound has been going from strength to strength, especially since last week's US jobs miss we saw pretty much prices move to the upside as to be expected bit of a pullback And then you know we're looking at more potential upsides So At the moment again looking at the fundamentals the UK economy picked up momentum in March towards the end of the lockdown So the UK economy gained momentum in March as Britain's geared up for the lifting of Coronavirus restrictions and gross domestic products rose to a stronger than expected 2.1 percent Following a revised 0.7 increase in February. So Again, nothing but positive news around the the pound. There is a bit of a scare though With regards to the Indian variant of the coronavirus, I think four people five people have passed away due to In in the UK, so it's found that very it's found this way to the UK shores So that could have an effect really on the pound if it starts to get out of hand But let's see because Boris Johnson our Prime Minister will make, you know certain choices regarding the reopening of the economy if if you know, it starts to potentially affect The UK then you could see a potential selling opportunity But if that's so then you're looking for short trades here, but I think overall It's it's really buy trades For the foreseeable future as long as the data supports the narrative moving on to the dollar Euro dollar and the euro dollar. So there was a really nice trade setup around here intraday CPR Demand zone set up that I shared with the guys in the trading group And it really worked out well for for anyone who took those trades, but some from a daily supply and demand zone perspective We really I would say probably that's where the supply zone is There wasn't really an opportunity in this prices came down to this area here before looking at long trades the general consensus is for the Euro dollar to reach around the one to five area So we've definitely got about three three hundred fifty pips to the upside of prices do continue to you know Get to to kind of rise and the euro area to kind of support that narrative European economic outlook upgraded on fiscal fund and Vaccines to the euro economy will grow more quickly this year than previously forecasted as The region's vaccination program campaign story gathers speed Fiscal support is rolled out and a strong global rebound helps exports. So a Lot of the things that I I teach in the private members group And things that we look for, you know to help really kind of Make our trading decisions and our bias. So I've been saying for a week or two now to kind of get long on The on the euro dollar you're seeing that really kind of play out So any pullbacks to levels of you know daily demand are going to be really kind of buying opportunities But for now if you do want to get short on it on the euro dollar, you may want to wait for potential move You know for the problem now Maybe a bit higher before looking at short trades if the euro GDP does disappoint Then that could actually be an opportunity to actually buy the US dollar versus the euro or another currency's You know sell the euro against another currency or short the euro against another currency Euro yen and I just haven't been able to get into this trade. I really wanted to get involved Down here, but there's really been No, no setups per se for me to kind of get involved in this and prices have really moved like about 300 pips so I've got to be patient patience is you know Something that we need in in trading. So looking for potential pullback. I do like this zone here This demand zone between this one three one point four one and it's one three zero point nine eight Zone so there are demand zones here as well Technically you do have a demand zone right there as well I prefer price to pull back a bit more deeper pullback better bargain price and within this zone I think that's nice. We've also got bit of Confluence where we've got Some resistance here in support So there's some traders that trade support resistance that will add to the demand equation around here Hopefully, I do think that pullback is really nice for a potential buy Especially with the the euro on the up and up and the yen in fact struggling with the virus I recently moving on to the Aussie dollar and the Aussie dollar We've got let me just move this here. I think the Really the play is again more Aussie dollar upside So when prices came back down into this demand zone this week again, you saw lots of buying going on So I think more upside potential on the Aussie dollar, especially with the Australian dollar I Guess strengthening in the risk on environment. You've got commodity currencies I say commodity sorry like iron ore copper oil making, you know highs and stuff like that. So Very bullish risk on environment out of the two My bias would be to an Australian for an Australian dollar long But this the this is a decent area to get short if again There is a narrative change around the US dollar and also as well This this higher zone would be really nice for a potential short technically, but not necessarily fundamentally Moving on to the Aussie yen and Aussie yen just keeps going from strength to strengthen the risk on environment Or you what you should see is basically what's been happening now, right? We've been basically talking about this for the past six months I Said last year October November times to get long on the Aussie Yen haven't changed that bias and you're pretty much seeing what's been going on With the Australian dollar and the Japanese yen So this has been driven fundamentally prices not really driven technically unless it's really kind of short-term You know intraday, which is basically just manipulations and liquidity hunting. So again a pullback into a nice demand zone from the From a yen first rate from an Australian dollar perspective making higher highs higher lows Higher high high low. This is a bargain area and then prices came back in looking for potential long trade I do want prices to pull back a bit more before looking at getting long or if prices can pull back into this Zone here this 83 area and just below that will be even better for a long trade But let's see what happens If the narrative does change so for example if there is more risk of let's say for example an outbreak virus outbreak or the Australian dollar has a bit of a miss when it comes to the Their jobs, you know report then there could be a decent opportunity to look for potential short trades Once I change that to supply Yeah so maybe a short trade right now of as prices go up into this zone here before looking at getting short and finally looking at gold and gold has been again a bit of a Tough one if you are looking to short the dollar then the alternative rather than shorting Any kind of a currency pairs as far as you know shorting dollar Swiss dollar, you know dollar CAD etc Then you would probably look for buying gold right the only problem is is gold is that? is is the fact that Inflation is is driving Gold but we're in a risk on the environment So in a risk on environment where stock market is making you know new highs and again Maybe just pulling back a little bit, but generally the consensus is for you know more highs in the For the for the stock market you also have Commodities really making new highs Gold for me is a bit of a bit of a tough buy if you are buying it It'd be purely based off of dollar weakness and and inflation concerns, so Any kind of a pullbacks to a decent zone maybe there or if price is making new high Then this would become a nice demand zone And are you looking for a pullback into that zone before looking at getting long on potential inflation concerns and dollar weakness? but if you are looking for a potential Short trade and you see some dollar strength maybe some sort of jobs Number which is really good and and GDP figures Then you could look for potential some short trades in and around this area here But for now, I don't think it's necessarily the best buy in the world fundamentally But everyone has their you know their their bias on the US dollar And I would probably say if you are getting short on the dollar then the bias really should be you know With regards to gold and silver to you know the the upside I would say is is really the point of the path of least resistance So any pullbacks to demand zones is where you probably want to look for any kind of a long trade Again, not financial advice. Please do your own research and that brings us to the end of this week's analysis Thanks for the comments as well. By the way, keep them up again Don't forget to like subscribe and share and I will speak to you all soon Hope you have a great trading week and take care