Although both empirical and theoretical approaches to scientific research are essential to scientific progress, the interactions between the two practices seems to be problematic in the biological scientific community citep{fusco2015new}. In an apology for “non-mathematical biology,” E.O. Wilson (2013) went so far as to asses that “The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail.” Not subscribing to Wilson’s point of view and in an attempt to put a bridge between our theoretical and empirical studies in evolutionary biology, we tried to formulate some risky theoretical predictions to test on real biological data. The problem in the genomic era is the difficulty to extract full value from the large amounts of data becoming available. It seems easier to keep doing what we are doing on a larger and larger scale than to try and think critically and ask deeper questions.

Given the already available huge amount of genomic data for a vast array of taxa representing a broad spectrum of the biological diversity, to test our predictions, we adopted a comparative approach based on phylogeny citep{garland1993phylogenetic, blomberg2002tempo,blomberg2003testing}.The Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages (phylogenies) to test evolutionary hypotheses. The comparative method has deep roots in evolutionary biology; In “The Origin of Species” Charles Darwin used differences and similarities between species as a major source of evidence. The process of descent with modification result in the fact that closely related lineages share many traits and trait combinations meaning that lineages are not independent. Accordingly, the development of explicitly phylogenetic comparative methods are needed citep{felsenstein1988phylogenies}. These methods were primarily developed to control for phylogenetic history when testing for adaptation citep{pagel2002accounting} . Although most studies that employ PCMs focus on extant organisms, many methods can also be applied to extinct taxa and can incorporate information from the fossil record citep{Fusco:2012aa}.

Phylogenetic comparative approaches can complement other ways of studying adaptation, such as studying natural populations, experimental studies, and mathematical models as used in this particular case. Making interspecific comparisons allow to assess the generality of evolutionary phenomena by considering independent evolutionary events. Such an approach is particularly useful when there is little or no variation within species.Felsenstein (cite{felsenstein1988phylogenies}) proposed the first general statistical method in 1985 for incorporating phylogenetic information, i.e., the first that could use any arbitrary topology (branching order) and a specified set of branch lengths. The logic of the method is to use phylogenetic information (and an assumed Brownian motion like model of trait evolution) to transform the original tip data (mean values for a set of species) into values that are statistically independent and identically distributed.Successively other methods were developed such as the Phlylogenetic Generalized least-squares model (PGLS), used in this work, which is now probably the most commonly used PCM citep{grafen1989phylogenetic}.

This approach is used to test whether there is a relationship between two (or more) variables while accounting for the fact that lineage are not independent. The method includes the generalized least squares (GLS or OLS) as a special case, and as such the PGLS estimator is also unbiased, consistent, efficient, and asymptotically normal. The PGLS consider the V matrix of expected variance and covariance of the residuals given an evolutionary model and a phylogenetic tree. Therefore, it is the structure of residuals and not the variables themselves that show phylogenetic signal. A number of models have been proposed for the structure of V such as Brownian motion citep{felsenstein1988phylogenies} Ornstein-Uhlenbeck, citep{hansen1997stabilizing} and Pagel’s lambda model.

citep{pagel2002accounting}(see article IV for detailed descriptions). When a Brownian motion model is used, PGLS is identical to the independent contrasts estimator citep{grafen1989phylogenetic}. It is important to mark that also the GLS is a specific PGLS assuming a Brownian motion and a star phylogeny. In this case the phylogenetic signal is absent and the PGLS is a normal GLS (OLS). In PGLS, the parameters of the evolutionary model are typically co-estimated with the regression parameters.PGLS can only be applied to questions where the dependent variable is continuously distributed.

In the following article we used evolutionary models to fit our data and detect the phylogenetic signal. Successively we adopted the PGLS method to verify our theoretical predictions on the relationships between couples of continuous variables on a genomic dataset.


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