Phylogenetic Correlations (II)

Dear Foodwebs List Members

this is the second part of a tutorial on phylogenetic correlations in
food-webs.  The first part discussed the question what phylogenetic
correlations are, and can be found here:

 http://www.mail-archive.com/foodwebs-meEmJjl1h1Ek+I/owrrOrA <at> public.gmane.org/msg00024.html

Here, I discuss the question how strong these correlations are.

Enjoy,

Axel

** Part II: HOW STRONG ARE PHYLOGENETIC CORRELATIONS IN FOOD-WEB TOPOLOGIES? 

PHYLOGENETIC CORRELATIONS IN HISTORICAL FOOD-WEB DATA

It is well known, and easily understood, that phylogenetic
correlations in data sets become the clearer the finer the taxonomic
resolution of the data sets is:  If there are more pairs of closely
related species, the similarities of these species become more
obvious.  For food webs, a theoretical analysis of this effect can be
found here http://axel.rossberg.net/paper/Rossberg2007a.pdf.

Historical food-web data sets, such as that compiled in Joel Cohen's
book "Community Food Webs" from 1990, are rather small and often have
comparatively low taxonomic resolution. This may explain why
phylogenetic correlations historically received little attention in
the field.

Rather than in the adjacency matrices, indications for phylogenetic
correlations can be found in the node descriptions of old food webs.
Cohen's web #50 ("Sand Beach, California" from J.W.Nybakken 1982), for
example, describes trophic links between (1) debris, (2) plankton, (3)
amphipods, (4) Blepharipoda, (5) Emerita analoga, (6) Tivela
stultorum, (7) Donax, (8) Olivella, (9) Thoracophelia, (10) Nepthys,
(11) Policines, (12) sea otter, (13) birds, and (14) fishes.  Thus, of
the 14 nodes, 9 refer to taxonomic units higher than species,
apparently because the member species of each of these taxa have
trophic roles sufficiently similar to warrant grouping them together.
The pattern is not always this clear.  In other webs one find nodes
defined by trophic role or body size.  Yet, of the 113 webs Cohen's
1990 collection, there are, by my count, at most 13 that do not
contain nodes referring to higher taxa.  The other 100 do.

QUANTIFYING THE STRENGTH OF PHYLOGENETIC CORRELATIONS IN FOOD WEBS

I will, in the following, nevertheless, concentrate on explicitly
reported food-web topologies, and ask if and how the strength of
phylogenetic correlations can be measured.  

This question poses itself more vigorously here than in other parts of
ecology, where it is sufficient to understand how to eliminate the
statistical effect of correlations from the data.  For the complex
statistics that we use to characterize food webs, this approach to
identify structure beyond phylogeny might be difficult to carry out.
Rather, one would try to build null models that explicitly exhibit
phylogenetic correlations, and would compare these with the data.  But
for this the strength of the correlations needs to be known.

Some care must be taken when asking how strong phylogenetic
correlations are, because the answer may depend on the taxonomic
resolution of the data set (s.a.), its taxonomic scope (a broader
scope shift weights to more distantly related species pairs), and its
spacial scope (over larger distances spacial correlations may
dominate).  Let me distinguish the following three kinds of measures:
"local" measures, for the degree by which correlation decay in time
after two species shared their last common ancestor, "global" measures
for the overall degree of correlations in a food web, and measures
comparing the strengths of different effects, where at least one
relates to phylogenetic correlations.

Cattin et al. 2004:
(http://www.unifr.ch/biol/ecology/bersier/publications/Nature_Cattin+_2004.pdf)

I sketched the method of Cattin in Part I already.  Regressions
between the taxonomic distance and the trophic similarity for all
species pairs in a data set were computed.  The slopes of these
regressions could serve as measures of the "local" kind.  But,
unfortunately, these slopes were not reported, since the point to be
made at this time was just to establish that phylogenetic correlations
are measurable at all.  And this was quite clear: "There was a strong
relationship (all P-values < 0.001) [...]"  So clear, perhaps, that
this important fact ultimately did not receive enough attention.  In a
sense, this result can be seen as a "global" characterization of
phylogenetic correlations in food webs.

Rossberg et al. 2006:
(http://axel.rossberg.net/paper/Rossberg2006b.pdf) 

We fitted a model for purely phylogenetically structured food webs (to
be described in Part III) to empirical data.  This produced, among
others, estimates for two model parameters p_v and p_f that
characterize the heredity of trophic traits on the time scale
separating speciations.  The model distinguishes between the heredity
(1-2 p_v) of traits characterising vulnerability to predation, and the
heredity (1-2 p_f) of traits determining foraging strategies and
capabilities.  These parameters could again serve as "local" measures
for the strength of correlations.  But care has to be taken, because a
"speciation" here is a separation of two "species" at the level of
taxonomic resolution of the fitted food-web data set (which varies
greatly even within data sets).  The numbers are therefore not
directly comparable between data sets.  Yet, the values of p_v and p_f
from the same fitted data set can be compared, and this comparison
yields an interesting result: usually, p_v << p_f, that is, evolution
of foraging traits is much faster than of vulnerability traits.  The
median of the ratio p_v/p_f over all fitted data sets was 0.039, and
0.0179 when excluding sets with many parasites and pathogens.  This
suggests that vulnerability traits evolve by a factor 25 to 60 slower
than foraging traits.

>From the fitted model, it might also be possible to derive a "global"
measure for the strength of phylogenetic correlations in a community,
such as the average degree of phylogenetic correlation between two
species selected randomly from the community (with replacement).  To
my understanding, such a measure would not depend on taxonomic
resolution, but only on the taxonomic and spacial scope.  But a
technical complication of the model (the phylogenetic tree is not
fully represented), so far prevented us from doing this.

Bersier & Kerli, 2007:
(http://dx.doi.org/10.1016/j.ecocom.2007.06.013)

These authors performed an analysis similar to that by Cattin et
al. discussed above, but now distinguishing between trophic
similarities with respect to foraging and with respect to
vulnerability.  To some degree, the analysis confirmed that
correlations between vulnerability traits (or consumer sets) are
stronger than between foraging traits (or resource sets), but some
uncertainty remained.  Here, too, the slopes of the regression lines
(and their measurement error) unfortunately remained unreported.  It
might be interesting to extend this work by determining the specific
functional relationship between taxonomic distance and phylogenetic
correlation.

Rossberg, this tutorial:

Since still no satisfactory measure for the "local" degree of
phylogenetic correlation seems to exist, I made here yet another
attempt: From diet tables of 25 fish species from the Bering Sea
(http://doc.nprb.org/web/03_prjs/), I extracted all pairs of distinct
diet items of the same consumer that (1) are resolved to species level
and (2) belong to the same genus.  For each pair, let f_1 and f_2
denote the proportions of biomass that the two species contribute to
the consumer's stomach content.  I took the logarithms of these
values, l_1=log_10(f_1), l_2=log_10(f_2), and plotted the points
(l_1,l_2) and (l_2,l_1) into a graph.  The result you can see here
http://axel.rossberg.net/paper/genus_pairs.pdf.  Apparently, the log
diet contributions of resource pairs from the same genus typically
differ by less then one: the RMS difference is 0.86, corresponding to
a spread by a factor 10^.86=7.2 in intake.  (Similar results are
obtained when deleting all points in the lower left 2x2 square of the
graph to avoid selection biases.)  Much of this difference may be
attributable to differences in prey abundance.  The actual differences
in trophic link strengths to related resources may be smaller.
Repeating this analysis with corrections for prey abundance may be
worthwhile.

OUTLOOK

In the next message, I will have a closer look at our phylogenetically
structured food-web model mentioned above.