Is all structure in food webs phylogenetic? Phylogenetic Correlations (III)

Dear List Members,

in a paper published last year, Williams and Martinez
[http://www.foodwebs.org/index_page/Williams2008JAE.pdf] put the
single "'niche dimension'" of their classical niche model
[http://www.foodwebs.org/index_page/Williams2000Nature.pdf] into
apostrophes, and explained that the model would actually "simulate
[...]  phylogenetic aspects" of food-web structure.  I agree (see
http://axel.rossberg.net/paper/Rossberg2006a.pdf).

The argument by which they arrive at this conclusion is as follows:
related species can have high trophic similarity, the niche model
produces species pairs with high trophic similarity, and therefore the
niche model simulates phylogenetic aspects.  Obviously, this argument
is stringent only when phylogenetic correlations are not only
contributing to, but the dominating cause for high trophic similarity
between species pairs (otherwise, high trophic similarity in the niche
model could reflect other structuring mechanisms).

This is the third part of a tutorial on phylogenetic correlations in
food-webs.  Here, I investigate how far this kind of reasoning can be
taken.  That is, I discuss the question how much of the structure we
see in food webs (all of it?) can be explained phylogenetically.

For parts I and II of the tutorial, please see

 http://permalink.gmane.org/gmane.science.biology.foodwebs/31


and

 http://permalink.gmane.org/gmane.science.biology.foodwebs/35


Enjoy part III.  Your comments on foodwebs <at> foodwebs.info are welcome.

Axel


** Part III: IS ALL STRUCTURE IN FOOD WEBS OF PHYLOGENETIC ORIGIN?

Most likely, the answer is no.  The trophic hierarchy underlying the
simple but powerful cascade model by Cohen & Newman (1985) is
generally understood as reflecting a size hierarchy: predators are
larger than their prey.  There are a few more structural features that
are probably unrelated to phylogenetic history, to which I will come
back later.  But the dominating structuring mechanism after the
trophic hierarchy seems to phylogeny.

The argument for this is not new, but, from the degree to which it is
taken up in the literature, I understand that it is largely unknown.


THE NESTED HIERARCHY MODEL

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

were perhaps the first to make the point by introducing their nested
hierarchy model.  The nested hierarchy model explains food-web
structure by (1) Cohen & Newman's trophic hierarchy, (2) a postulated
distribution of generality (i.e., # of prey), (3) a tendency of
related consumers to share resources.  The precise way networks are
built is strongly inspired by Sugihara's (1984) "niche-hierarchy
model, an assembly rule stating that species joining a community will
be successful only if they compete within single guilds" (Cattin et
al. 2004).  In his PhD thesis, Sugihara (1982) had shown that this
rule naturally leads to so called chordal niche-overlap graphs, which,
in turn, are closely related to the tendency of natural food webs to
be "interval".  Sugihara (1982) already speculated that phylogenetic
processes underlie this rule, with guilds corresponding to
phylogenetic clades.

While the nested-hierarchy model is frequently used in food-web
theory, the well-argued conclusions that Cattin et al. drew from their
work with the model have largely been ignored: "What we perceive to be
of higher importance than details of model construction are the
processes behind the nested-hierarchy model. We have shown how
phylogeny is intimately linked to trophic structure in natural
communities [...] body size is of secondary importance in explaining
food-web structure when compared with phylogeny."

One reason for the difficulties of this insight to penetrate the
literature may be that, when being scrutinized later, the differences
between nested hierarchy model webs and empirical data turned out to
be somewhat larger than for other food-web models which do not invoke
phylogenetic structure.  This weakness was later overcome by the
matching model.


THE MATCHING MODEL

Rather than just defining rules for constructing food webs, the
matching model (Rossberg et al. 2006
[http://axel.rossberg.net/paper/Rossberg2006bSup.pdf]) describes the
processes that lead to these structures.

The matching model combines (1) a stochastic model for the structure
of phylogenetic trees, (2) a model for the evolution of trophic traits
(one of which is body size) along these threes, (3) a model for the
determination of trophic link strengths from trophic traits, which
combines a trophic size hierarchy and a "matching" of foraging traits
with vulnerability traits, and (4) a model for the "measurement
process" by which binary food webs are constructed.  The model is put
together in such a way that any food-web pattern it generates must be
due to phylogenetic correlations of trophic traits or due to the size
hierarchy.  In particular, just as for the nested hierarchy model, no
assumption of low niche-space dimensionality is made.

Being more explicit about the details of food-web emergence naturally
adds complexity (and parameters) to the matching model when compared
to its predecessors.  But the added complexity pays off.  Using
standard methods of statistics that take differences in the number of
model parameters into account, it was shown (Rossberg et al. 2006)
that the matching model clearly outperformed the most accurate models
for food-web topology of this time, namely the niche model and the
nested hierarchy model, in reproducing empirical topologies.  Given
the data of 17 empirical food webs, the likelihood of the matching
model, based on Akaike weights, is about 10^125 times higher than that
of the niche model (10^338 for the nested hierarchy model).  And I am
unaware of any improvements over this result so far.

A playful way to see the differences between the abilities of niche
model and matching model to reproduce empirical data is to compare
visualizations of random adjacency matrices generated by the two
models with their empirical counterparts.  You may have done this
puzzle as a child: given a set of similar pictures, can you recognize
and characterize the one that is essentially different?  In our case,
that one displays empirical data rather than a simulation.  Sample
picture for 17 data sets you can find here:
[http://axel.rossberg.net/paper/Rossberg2006bSup.pdf] Give it a try!
For the adult in you, we put a red box around the empirical matrices.

If you, just as me, are unable to make out any visual differences
between empirical and model data in the case of the matching model,
this can be taken as evidence, complementing corresponding statistical
results (chi-square stats, Rossberg et al. 2006), that, in fact, the
topology of food webs originates from (a) a trophic size hierarchy,
(b) phylogenetic correlations, and (c) little else.  This conclusion
could be further hardened by similar statistical tests that take
account of the known phylogenies of the member species of empirical
food webs.  But such tests have not been done yet.


IMPLICATIONS

Given that phylogenetic correlations are strong at least in the sense
that they are statistically significant (see part II of the tutorial),
and are very likely one of the dominating structuring mechanisms of
food-web topology (see above), statistical analyses that seek to
identify structure of other origins in food-web data will definitely
have to work with phylogenetically structured null models or take
other precautions to avoid false positives due to phylogenetic
correlations.  Some interesting work of the past could have profited
from more attention to this point.


OUTLOOK

In the two following messages of the tutorial I am planning to discuss
HOW the processes described by the matching lead to the observed
structures in food webs.


ADDITIONAL RESOURCES

Those seeking to use the matching model as a null model for their
analysis, to develop it further, or to challenge it by their own
theory might find the following two postings useful:

Tons of matching model sample outputs:

 http://axel.rossberg.net/datatable/datatable.html


An algorithm to sample random matching model webs without having to
simulate it:

 http://axel.rossberg.net/paper/Rossberg2007a.pdf

 http://permalink.gmane.org/gmane.science.biology.foodwebs/22



LITERATURE

Cohen, J.E., Newman, C.M., 1985. A stochastic theory of community food
webs. Models and aggregated data. Proc. R. Soc. Lond. B 224, 421-448.

Sugihara, G., 1982. Niche Hierarchy: Structure, Organization and
Assembly In Natural Communities. PhD Thesis, Princeton University.

Sugihara, G. in Population Biology. Proceedings of Symposia in Applied
Mathematics (ed. Levin, S. A.)  83–101 (American Mathematical Society,
Providence, Rhode Island, 1984).
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