Most phylogenetic comparative methods used for testing adaptive hypotheses make evolutionary assumptions that are not compatible with evolution toward an optimal state. As a consequence they do not correct for maladaptation. The "evolutionary regression" that is returned is more shallow than the optimal relationship between the trait and environment. We show how both evolutionary and optimal regressions, as well as phylogenetic inertia, can be estimated jointly by a comparative method built around an Ornstein-Uhlenbeck model of adaptive evolution. The method considers a single trait adapting to an optimum that is influenced by one or more continuous, randomly changing predictor variables.
"The procedure adds shifts one at the time and is therefore extremely efficient but the selection criteria is heuristic and has no theoretical grounding for that problem, where observations are correlated through the tree structure. Several extensions of the model without or with known shifts have also been proposed: Hansen et al. (2008) extended the original work of Hansen (1997) on OU processes to a two-tiered model where β(t) is itself a stochastic process (either BM or OU). Bartoszek et al. (2012) extended it further to multivariate traits whereas Hansen and Bartoszek (2012) introduced errors in the observations. "
[Show abstract][Hide abstract] ABSTRACT: Comparative and evolutive ecologists are interested in the distribution of
quantitative traits among related species. The classical framework for these
distributions consists of a random process running along the branches of a
phylogenetic tree relating the species. We consider shifts in the process
parameters, which reveal fast adaptation to changes of ecological niches. We
show that models with shifts are not identifiable in general. Constraining the
models to be parsimonious in the number of shifts partially alleviates the
problem but several evolutionary scenarios can still provide the same joint
distribution for the extant species. We provide a recursive algorithm to
enumerate all the equivalent scenarios and to count the effectively different
scenarios. We introduce an incomplete-data framework and develop a maximum
likelihood estimation procedure based on the EM algorithm. Finally, we propose
a model selection procedure, based on the cardinal of effective scenarios, to
estimate the number of shifts and prove an oracle inequality.
"Given this model form, there was weak evidence for a nonzero autocorrelation between the optima in different years t (DIC reduced by 3.29 for model 2 vs. 1, with ζ t AR1 or iid, respectively). We investigated whether the data showed evidence for non-stationarity, by fitting an alternative model where the optimum follows a random walk (discrete time equivalent of Brownian motion as modeled by Estes and Arnold (2007) and Hansen et al. (2008)) instead of AR1, but this increased the DIC by 1.4 (model 3 versus model 2). Fitting an alternative model with a linear trend in the optimum, equivalent to an environmental covariate x t = t, did not reduce the DIC either (models 4 and 5, with ζ t iid or AR1, respectively). "
[Show abstract][Hide abstract] ABSTRACT: Despite considerable interest in temporal and spatial variation of phenotypic selection, very few methods allow quantifying this variation while correctly accounting for the error variance of each individual estimate. Furthermore, the available methods do not estimate the autocorrelation of phenotypic selection, which is a major determinant of eco-evolutionary dynamics in changing environments. We introduce a new method for measuring variable phenotypic selection using random regression. We rely on model selection to assess the support for stabilizing selection, and for a moving optimum that may include a trend plus (possibly autocorrelated) fluctuations. The environmental sensitivity of selection also can be estimated by including an environmental covariate. After testing our method on extensive simulations, we apply it to breeding time in a great tit population in the Netherlands. Our analysis finds support for an optimum that is well predicted by spring temperature, and occurs about 33 days before a peak in food biomass, consistent with what is known from the biology of this species. We also detect autocorrelated fluctuations in the optimum, beyond those caused by temperature and the food peak. Because our approach directly estimates parameters that appear in theoretical models, it should be particularly useful for predicting eco-evolutionary responses to environmental change. This article is protected by copyright. All rights reserved.
This article is protected by copyright. All rights reserved.
"We propose the use of OU models to infer selection at the cis-regulatory level underlying lineage-specific TF binding, chromatin activity, or gene expression. The use of OU processes to compare evolutionary models such as random drift, stabilizing selection or lineage-specific selection for quantitative morphological traits was first applied to the evolution of morphological traits (Hansen 1997; Butler and King 2004; Hansen et al. 2008). Later, these same models were applied to study the evolution of gene expression. "
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