Modeling Phenotypic Plasticity in Growth Trajectories: A Statistical Framework

Abstract

Phenotypic plasticity, that is multiple phenotypes produced by a single genotype in response to environmental change, has been thought to play an important role in evolution and speciation. Historically, knowledge about phenotypic plasticity has resulted from the analysis of static traits measured at a single time point. New insight into the adaptive nature of plasticity can be gained by an understanding of how organisms alter their developmental processes in a range of environments. Recent advances in statistical modeling of functional data and developmental genetics allow us to construct a dynamic framework of plastic response in developmental form and pattern. Under this framework, development, genetics, and evolution can be synthesized through statistical bridges to better address how evolution results from phenotypic variation in the process of development via genetic alterations. K E Y W O R D S :Developmental trajectory, dynamic modeling, functional mapping, logistic growth curve, phenotypic plasticity.The capacity of an organism to alter its phenotypes in response to changing environment is known as phenotypic plasticity (Schlichting 1986;Sultan 2000). Because of its central role in evolution and speciation, an explosion of interest in studying the causes and consequences of this phenomenon has been enthused for over a century (Baldwin 1896;Waddington 1942;Scheiner 1993;Wu 1998;Agraval 2001;Pigliucci 2005;West-Eberhard 2005;Fusco and Minelli 2010;Nicotra et al. 2010;Pfennig et al. 2010; Sultan 2010;Beldade et al. 2011;Sommer and Ogawa 2011). Recently, mounting recognition has been gained for the fact that phenotypic plasticity may make an important contribution to the occurrence of complex human diseases (Bateson et al. 2004;Feinberg 2007;Burdge and Lillycrop 2010;Hochberg et al. 2011) and the response of biodiversity to climate change (Nicotra * These authors contributed equally to this work. et al. 2010), stimulating the mechanistic study of plastic changes at the molecular and pathway level (Gilbert and Epel 2009).The phenotypic plasticity of an organism arises from its genotype through programmed change in gene expression (Lewontin 2000;West-Eberhard 2005;Beldade et al. 2011). It has become increasingly clear that phenotypic plasticity is not only regulated by environmental factors, but also largely determined by endocrine hormones and epigenetic methylation that mediate various biological functions during development (Richards 2008;Sommer and Ogawa 2011). An emerging conceptual framework for studying phenotypic plasticity is to integrate it with development by viewing the phenotype as the outcome of complex synergistic developmental systems (Sultan 2000;Dmitriew et al. 2010;Love 2010;Beldade et al. 2011; Parsons et al. 2011). Fusco andMinelli (2010) assessed the value of taking the phenotypic plasticity of developmental processes into the picture to account for the evolution of life cycle. P E R S P E C T I V EUnlike static phenotypes at single time points, the phenotypic plasticity of development ...

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