Modularity, Noise, and Natural Selection

Abstract

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates.In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results. K E Y W O R D S :Adaptation, models/simulations, morphological evolution, pleiotropy, quantitative genetics, selection-natural.The study of biological systems and its component parts, whether molecules, cells, tissues, organisms and its forming parts, and even species and their interactions, is rapidly converging to the central theme of modularity. This refers to the connections among some of the component parts of a biological system (genes or morphological traits, for example) and the lack of such associations among other parts of the same system. (Olson and Miller 1958;Berg 1960;Wagner et al. 2007). The notion that interacting parts are not independent is intuitive and appears early in the history of Biology (see Mayr 1982). Therefore, modularity is quickly becoming one of the central questions in modern biology (Wagner et al. 2007;Klingenberg 2008) and a point of convergence of various specialties and areas (Mathematics, Statistics, Genetics and Genomics, Evolutionary Biology, Ecology, Biochemistry, and Physiology).In biology, several types of modules have been recognized, including (1) functional, consisting of characters or features that act together on performing a task or function and are quasiautonomous in relation to other functional sets; (2) developmental, which corresponds to parts of an embryo that are relatively autonomous with respect to pattern formation and differentiation, or an autonomous signaling cascade; (3) variational, composed of characters that vary together and are relatively independent of other such sets (Wagner et al. 2007).The study of modularity is centered on statistical estimation of association among traits (Olson and Miller 1958;Berg 1960). Whether such association is measured by correlation, covariance, or distance/similarity measures, i...

The evolution of phenotypic integration: How directional selection reshapes covariation in mice

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“…2009), and phenotypic divergence is frequently size related and aligned with the main axis of within‐population covariation, the genetic line of least resistance (Schluter 1996; Marroig and Cheverud 2010; Marroig et al. 2012; Porto et al. 2013).…”

Análise morfológica craniana de Xenartha atuais e extintos: inferências evolutivas e funcionais

“…Análises detalhadas sobre a evolução morfológica craniana dos mamíferos, embasadas na teoria da genética quantitativa, foram realizadas apenas com os marsupiais do novo mundo (Marsupialia; da Silva, 2010; Shirai e Marroig, 2010) e com os macacos do novo e do velho mundo (Euarchontoglires; Eutheria; Cheverud, , 1996Marroig e Cheverud, 2001Ackermann, 2002;Marroig et al, 2004aMarroig et al, , 2004bMarroig et al, , 2011Marroig et al, , 2012Oliveira et al, 2009). …”

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“…Em teoria a correlação média dessa matriz deveria ser zero, afinal, os caracteres são independentes. Na prática, no entanto, ela pode variar bastante da expectativa teórica, simplesmente devido ao erro associado à estimativa da matriz (Marroig et al, 2012). Inclusive, quanto menor for o tamanho da amostra em relação à quantidade de variáveis, mais pervasivo será este efeito (ver Figura 1B de Marroig et al, 2012).…”