Variation decomposition is a zombie idea?

Jan 10, 2013 4 min read

Another post as a response to something written by Jeremy Fox! I think it becomes time that I meet him in person so that I can address him by “Jeremy” instead of “Dr. Fox”, “Fox”, or “the author”. I tried to remove all the salesmanship from my response, though, because I wanted to make sure that 1) I summarized his blog post correctly, and 2) expressed my thoughts as clearly as possible. This will make it easier for others to point out my logical mistakes, and thus to correct my thinking, and my understanding of ecology.

Original argument by Dr. Fox

correlation does not equal causation
e.g. abundance in species over time

data

2 species, abundances not correlated
species abundances correlated with weather

naive conclusion

no density dependence
weather important

Dr. Fox’s conclusion: this is wrong

correlation is not prediction of density dependence (example from economics)

implication

zombie idea: “misinterpreting correlations, and lack of correlations, among variables as evidence for or against causality when those variables are affected by density-dependent feedbacks”
in community ecology: “Given that there’s intra- and interspecific density dependence within sites, I doubt that you can reliably infer the causes of metacommunity structure just by looking for statistical associations between environmental and geographic variables, and species abundances.”

My initial response

after reading that last quote, I thought that Dr. Fox made this conclusion:

so “correlations, partial correlations, variance partitioning, multiple regression, structural equation modeling, or related statistical methods” become useless in ecology, since this is probably a density-dependent dynamical system
because of this zombie idea dismissing general statistical techniques as tools to “infer how causality works in a density-dependent dynamical system” seems a bridge too far. I think that this could become a zombie idea in itself if lots of ecologists would follow this advice.

but I doubt that this is the intent of the blog post. The key word being “reliably”; he probably added this for people like myself to the sentence. Without it, it would seem that Dr. Fox is negating the scientific method; with this word, you can talk about observational versus experimental approaches, weak and strong tests of certain hypotheses etc.
I thus read the whole blog post again in more detail, followed by coming up with a second response.

My second response

I do think that Dr. Fox pulls a sleight of hand:

Dr. Fox’s conclusion and example only deals with pointing out that correlation is not a good prediction for density dependence
but the data do provide evidence for the hypothesis that weather influences population abundances through food availability etc.

so my conclusion for the data from Dr. Fox outlined above

there is evidence that weather is important
not a good test for whether density dependence is important or not, so not possible to make any conclusion on this aspect

implications of this for variation decomposition as a method to detect metacommunity processes

any statistical method is only as good as the prediction and associated hypothesis it is testing

not good to test for density dependence
could be for testing e.g. effects of environment on species abundances

statistical methods have their limitations (see indeed Gilbert and Bennett 2010, as pointed out by Dr. Fox)

thus observational data should be accompanied by experimental studies
see e.g. my PhD work (from a long time ago, observational study using variation decomposition, and experimental study)

my 2005 publication should thus only be seen as a starting point

there is lots of evidence for species sorting in response to environmental condition in general in these potentially dynamic systems (in 73% of the data sets)
it is difficult, but not impossible, to include for instance competition or density dependence or time or evolution into these analyses.
we should explore more interesting or detailed predictions, and some of these could use variation decomposition (e.g. generalist versus specialist species or body size)

The real problem would be that the zombie idea of testing density dependence with correlation could somehow make the correlations between species abundances and weather invalid.

I maybe missed this explanation in the blog post, but I could not find how density dependence could make not significant external drivers significant (but if I am wrong, let me know)
maybe this is addressed in Ziebarth et al. 2010, and is implicitly suggested by Dr. Fox?

My conclusions

Dr. Fox convincingly illustrates that correlation is not a good prediction for the hypothesis of density dependence, and there exist better predictions and tests.
My 2005 article is flawed, but I do not think that this zombie idea of density dependence is the most important one (we are working on a follow article, though).
Writing blog posts are fun, especially if you have a skilled writer as Dr. Fox giving you starting points. I just have to take care that when somebody writes to get a reaction (which is part of the appeal of Fox’s writing, and which he suggests in this and this post), that I read and react to the actual points made, and try to “read around” the salesmanship aspect of the writing.