To achieve a coherent evolutionary theory, it is necessary to account for the effects of the environment on the process of development. Phenotypic plasticity is the change in the expressed phenotype of a genotype as a function of the environment. Various measures of plasticity exist, many of which can be united within the framework of a polynomial function. This function is the norm of reaction. For the special case of a linear reaction norm, genetic variation can be partitioned into portions that are independent and dependent on the environment. From this partition two heritability measures are derived which can be used, alternatively, to compare populations or make predictions about the response to selection. Genetically, plasticity is likely due both to differences in allelic expression across environments and to changes in interactions among loci; plasticity is not a function of heterozygosity. Plasticity responds to both artificial and natural selection. The evolution of plasticity is modeled in thre...

Genetics and Evolution of Phenotypic Plasticity

Constraints on phenotypic evolution can take a variety of forms. Constraints can arise from inheritance, selection, development, and design limits. Contemporary visions of the evolutionary process often focus on one or two of these varieties and ignore the others. A unifying framework that considers all four major varieties of constraint is emerging within the discipline of quantitative genetics. I attempt to sketch that emerging framework and summarize recent efforts toward unification. Although couched in the technical language of quantitative genetics, the ongoing search for a common framework promises a rapprochement among the approaches of optimality theorists, population geneticists, and developmental biologists.

Constraints on phenotypic evolution.

Our emphasis is on the genetic basis of quantitative variation, and its effects on the evolution of quantitative. Our review indicates that few experiments approach basic issues such as the number of loci that contribute to within-population variation, the rate of polygenic mutation, the extent of pleiotropy, the mechanisms that maintain additive variance, and the reasons for reduced fitness of extreme phenotypes

Evolutionary Quantitative Genetics: How Little Do We Know?

The connection between development and evolution has become the focus of an increasing amount of research in recent years, and heterochrony has long been a key concept in this relation. Heterochrony is defined as evolutionary change in rates and timing of developmental processes; the dimension of time is therefore an essential part in studies of heterochrony. Over the past two decades, evolutionary biologists have used several methodological frameworks to analyse heterochrony, which differ substantially in the way they characterize evolutionary changes in ontogenies and in the resulting classification, although they mostly use the same terms. This review examines how these methods compare ancestral and descendant ontogenies, emphasizing their differences and the potential for contradictory results from analyses using different frameworks. One of the two principal methods uses a clock as a graphical display for comparisons of size, shape and age at a particular ontogenic stage, whereas the other characterizes a developmental process by its time of onset, rate, and time of cessation. The literature on human heterochrony provides particularly clear examples of how these differences produce apparent contradictions when applied to the same problem. Developmental biologists recently have extended the concept of heterochrony to the earliest stages of development and have applied it at the cellular and molecular scale. This extension brought considerations of developmental mechanisms and genetics into the study of heterochrony, which previously was based primarily on phenomenological characterizations of morphological change in ontogeny. Allometry is the pattern of covariation among several morphological traits or between measures of size and shape; unlike heterochrony, allometry does not deal with time explicitly. Two main approaches to the study of allometry are distinguished, which differ in the way they characterize organismal form. One approach defines shape as proportions among measurements, based on considerations of geometric similarity, whereas the other focuses on the covariation among measurements in ontogeny and evolution. Both are related conceptually and through the use of similar algebra. In addition, there are close connections between heterochrony and changes in allometric growth trajectories, although there is no one-to-one correspondence. These relationships and outline links between different analytical frameworks are discussed.

Heterochrony and allometry: the analysis of evolutionary change in ontogeny

Consistent individual differences in boldness, reactivity, aggressiveness, and other 'personality traits' in animals are stable within individuals but vary across individuals, for reasons which are currently obscure. Here, I suggest that consistent individual differences in growth rates encourage consistent individual differences in behavior patterns that contribute to growth-mortality tradeoffs. This hypothesis predicts that behavior patterns that increase both growth and mortality rates (e.g. foraging under predation risk, aggressive defense of feeding territories) will be positively correlated with one another across individuals, that selection for high growth rates will increase mean levels of potentially risky behavior across populations, and that within populations, faster-growing individuals will take more risks in foraging contexts than slower-growing individuals. Tentative empirical support for these predictions suggests that a growth-mortality perspective may help explain some of the consistent individual differences in behavioral traits that have been reported in fish, amphibians, reptiles, and other animals with indeterminate growth.

Growth‐mortality tradeoffs and ‘personality traits’ in animals

We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.

https://www.genetics.org/content/genetics/124/4/979.full.pdf

Analysis of the inheritance, selection and evolution of growth trajectories.

We present a quantitative genetic model for the evolution of growth trajectories that makes no assumptions about the shapes of growth trajectories that are possible. Evolution of a population's mean growth trajectory is governed by the selection gradient function and the additive genetic covariance function. The selection gradient function is determined by the impact of changes in size on the birth and death rates at different ages, and can be estimated for natural populations. The additive genetic covariance function can also be estimated empirically, as we demonstrate with four vertebrate populations. Using the genetic data from mice, a computer simulation shows that evolution of a growth trajectory can be constrained by the absence of genetic variation for certain changes in the trajectory's shape. These constraints can be visualized with an analysis of the covariance function. Results from four vertebrate populations show that while each has substantial genetic variation for some evolutionary changes in its growth trajectory, most types of changes have little or no variation available. This suggests that constraints may often play an important role in the evolution of growth.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1558-5646.1992.tb00612.x

Measuring selection and constraint in the evolution of growth.

Growth trajectories differ from many other quantitative, characters in that they are characterized by a continuous function rather than by a finite number of discrete measurements. We review here recently developed methods for predicting the evolution of growth trajectories under the influence of natural or artificial selection. Using our method, analysis of genetic data from mice shows that the patterns of genetic variation arising from developmental processes impose constraints on evolution of growth trajectories. These constraints can be quantified to reveal the families of growth trajectories that can be produced by selection and those families that cannot. The data suggest there may be relatively few evolutionary degrees of freedom for growth trajectories despite the presence of abundant additive genetic variation to alter size and (or) growth rate at every age. The description of these constraints may be useful to both biologists who would like to determine the evolutionary options available to natu...

David Lofsvold

Papers

Analysis of the inheritance, selection and evolution of growth trajectories.

Measuring selection and constraint in the evolution of growth.

The evolution of growth trajectories and other complex quantitative characters.