[adegenet-forum] Interpreting results of sPCA

[Valeria Montano]

Hi Kelvin,

sorry about this reaction as prompt as the one of a stone in drunker
stupor.

I guess you have probably moved a bit further on the interpretation of your
results by now. Any how, I can try to tell you something
useful (? - who knows)


> Here are my questions:
> 1. For the sPCA based on spatial (not depth) coordinates, the barplot of
> eigenvalues shows the typical pattern of PC3 > PC4 > PC5, but if you look
> at the screeplot (the graph of PC score variance vs spatial
> autocorrelation), PC5 accounts for a larger amount of variance than PC3 and
> 4. This seems contradictory to me. Does anyone have an explanation?
>
> the eigenvalues in the spca have two components, the variance and the
spatial autocorrelation, if you type summary(yourspca)[[3]] you will see
the list of var and morane values for each of the eigenvalues. The PC5 may
be correlated with genetic variables with higher variance than the ones
contributing to pc3 and 4 but that are not spatially ordered?

2. Next, to do more exploratory analyses, I wanted to see how robust these
> results were for different distance limits (d2) in constructing the
> connection network. I noticed that when I pick an arbitrary number, like
> d2=12 for the sPCA using spatial (not depth) coordinates, the spatial
> patchiness disappears and instead there now appears to be a cline.  Because
> sPCA decomposes both genetic and spatial variance, is it possible for the
> spatial variance to swamp out the genetic variance, particularly if you
> define a connection network too arbitrarily? In other words, by defining
> d2=12, does the sPCA miss the finer scale spatial patchiness that was found
> when I defined my connection network with a more "sensible" d2?
>
> In my personal experience with spca, usually if the spatial patterns are
strong no matter what graph is used they do not change substantially, in
the worst case just a few points look a bit different. In your specific
case the fact that you decided to consider neighbours on the basis of the
positive spatial autocorrelation sounds a bit circular, in this case you
might be forcing the method to highlight the pattern of positive spatial
autocorrelation that may not be driving the genetic distribution of your
sample. I would rather go for inverse distances which are usually more
accurate. Btw, did you run the global and local tests? If they change from
significant to non significant changing the neighbouring method I would not
think that there is a spatial significant pattern.


> 3. Clearly depth and space are autocorrelated with each other. Based on
> the partial mantel tests, both are significantly, but only weakly
> correlated with genetic relatedness. Are there any general guidelines for
> interpreting low Mantel r values? As I understand it, Mantel r is not the
> same as a correlation r, because Mantel tests are based on distances and
> not raw data. I've seen other studies commenting on how small Mantel r's
> are often reported, but so far, I have not come across any studies that
> report values as small as mine.
>
> I've never seen so small mantel test values either...In this case, when I
first read about this issue of 'controlling' depth for the space I had two
different thoughts about it:

1. if you think about spatial proximities, being less or more depth does
not mean to be more or less close, clearly. Considering your results of a
spatial gradient from more to less depth, this is likely highlighting a
adaptive pattern to depth, but maybe this is exactly the reason why you run
the method on depth only.

2. If I wanted to see the effect of space and depth, I would probably use
the depth in combination with a linear simplified distance scheme (like
points on a line or a circle reproducing the spatial shape of the coral
reef) and build the spatial connection with it. In this case you would
analyse together the role of spatial distances (in 3-D) and the potential
role of adaptation, which is already disentangled in the spatial analysis
based on depth only.

End. Just to let you know I hate you a bit because you work in the Hawaii.
Ciao

Valeria


On 30 January 2013 21:10, Kelvin Gorospe <kgorospe at hawaii.edu> wrote:

> Hello all,
>
> I'd like to ask some input on interpreting some results. I have
> microsatellite genotypes, depth, and spatial coordinates for 2352 corals
> from a single coral reef. I ran partial mantel tests looking at the
> relationship between genetic relatedness and space (controlling for depth)
> as well as the relationship between genetic relatedness and depth
> (controlling for space) and found highly significant p values (p=0.001) but
> very small Mantel r values (0.008 for space and 0.01 for depth). So there
> is a small, but still significant relationship between genetics and space
> as well as genetics and depth on a very small scale (the reef covered an
> area of only about 1300m^2 with depths of between 1 and 4m).
>
> Next, I wanted to visualize these structures using sPCA. So first I
> constructed two connection networks: both neighbor by distance connections,
> but one based on depth measurements (0,z) and one based on spatial
> coordinates (x,y). The distance limit (d2) for each network was based on
> inspecting correlograms for genetics vs. depth and genetics vs. space and
> using the extent of positive autocorrelation as the upper limit (d2) for
> defining neighbors in each of the connection networks. After performing
> sPCA I then plot the PCs using the spatial (x,y) coordinates to visualize
> the spatial arrangement of genetic relatedness. The sPCA based on spatial
> coordinates show a patchy reef, groups of similar PC scores clumping
> together throughout the reef. The sPCA based one depth coordinates,
> however, show a depth cline, with corals in the center of the reef (the
> shallow part) having distinct PC scores from corals on the outer slopes of
> the reef (the deeper part).
>
> Here are my questions:
> 1. For the sPCA based on spatial (not depth) coordinates, the barplot of
> eigenvalues shows the typical pattern of PC3 > PC4 > PC5, but if you look
> at the screeplot (the graph of PC score variance vs spatial
> autocorrelation), PC5 accounts for a larger amount of variance than PC3 and
> 4. This seems contradictory to me. Does anyone have an explanation?
>
> 2. Next, to do more exploratory analyses, I wanted to see how robust these
> results were for different distance limits (d2) in constructing the
> connection network. I noticed that when I pick an arbitrary number, like
> d2=12 for the sPCA using spatial (not depth) coordinates, the spatial
> patchiness disappears and instead there now appears to be a cline.  Because
> sPCA decomposes both genetic and spatial variance, is it possible for the
> spatial variance to swamp out the genetic variance, particularly if you
> define a connection network too arbitrarily? In other words, by defining
> d2=12, does the sPCA miss the finer scale spatial patchiness that was found
> when I defined my connection network with a more "sensible" d2?
>
> 3. Clearly depth and space are autocorrelated with each other. Based on
> the partial mantel tests, both are significantly, but only weakly
> correlated with genetic relatedness. Are there any general guidelines for
> interpreting low Mantel r values? As I understand it, Mantel r is not the
> same as a correlation r, because Mantel tests are based on distances and
> not raw data. I've seen other studies commenting on how small Mantel r's
> are often reported, but so far, I have not come across any studies that
> report values as small as mine.
>
> I've also tried to attach some graphs to this email, but I'm not sure if
> the list serve allows attachments. But hopefully my descriptions of my
> results were still good enough to get some feedback. Any input would be
> greatly appreciated! Thanks everyone!
>
>
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