[adegenet-forum] Interpreting results of sPCA

[Kelvin Gorospe]

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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