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 three ways: optimality models, quantitative genetic models, and gametic models. All models make similar predictions about the conditions that will favor plasticity. In need of further development are the extension of quantitative genetic models, and structured population models; also needed are data on the true shapes of reaction norms and genetic variation and covariation for nonlinear reaction norm parameters and multiple environments.

Understanding the relationship between species richness and productivity is fundamental to the management and preservation of biodiversity. Yet despite years of study and intense theoretical interest, this relationship remains controversial. Here, we present the results of a literature survey in which we examined the relationship between species richness and productivity in 171 published studies. We extracted the raw data from published tables and graphs and subjected these data to a standardized analysis, using ordinary least‐squares (OLS) regression and generalized linear‐model (GLIM) regression to test for significant positive, negative, or curvilinear relationships between productivity and species diversity. If the relationship was curvilinear, we tested whether the maximum (or minimum) of the curve occurred within the range of productivity values observed (i.e., was there evidence of a hump?). A meta‐analysis conducted on the distribution of standardized quadratic regression coefficients showed that the average quadratic coefficient was negative (i.e., the average species richness–productivity relationship was curvilinear and decelerating), and that the distribution of standardized quadratic regression coefficients was significantly heterogeneous (i.e., the studies did not sample the same underlying species richness–productivity relationship). Looking more closely at the patterns of productivity–diversity relationships, we found that, for vascular plants at geographical scales smaller than continents, hump‐shaped relationships occurred most frequently (41–45% of all studies). A positive relationship between productivity and species richness was the next most common pattern, and positive and hump‐shaped relationships co‐dominated at the continental scale. For animals, positive, negative, and hump‐shaped patterns were common at most geographical scales, and no one pattern predominated. For both plants and animals, hump‐shaped curves were relatively more common in studies that crossed community boundaries compared to studies conducted within a community type, and plant studies that crossed community types tended to span a greater range of productivity compared to studies within community types. Sample size and plot size did not affect the probability of finding a particular productivity–diversity relationship (e.g., positive, hump‐shaped, etc.). However, hump‐shaped curves were especially common (65%) in studies of plant diversity that used plant biomass as a measure of productivity, and in studies conducted in aquatic systems.

Understanding the relationship between species richness and productivity is fundamental to the management and preservation of biodiversity. Yet despite years of study and intense theoretical interest, this relationship remains controversial. Here, we present the results of a literature survey in which we examined the relationship between species richness and productivity in 171 published studies. We extracted the raw data from published tables and graphs and subjected these data to a standardized analysis, using ordinary least-squares (OLS) regression and generalized linear-model (GLIM) regression to test for significant positive, negative, or curvilinear relationships between productivity and species diversity. If the relationship was curvilinear, we tested whether the maximum (or minimum) of the curve occurred within the range of productivity values observed (i.e., was there evidence of a hump?).A meta-analysis conducted on the distribution of standardized quadratic regression coefficients showed that the average quadratic coefficient was negative (i.e., the average species richness-productivity relationship was curvilinear and decelerating), and that the distribution of standardized quadratic regression coefficients was significantly heterogeneous (i.e., the studies did not sample the same underlying species richness-productivity relationship).Looking more closely at the patterns of productivity-diversity relationships, we found that, for vascular plants at geographical scales smaller than continents, hump-shaped relationships occurred most frequently (41-45% of all studies). A positive relationship between productivity and species richness was the next most common pattern, and positive and hump-shaped relationships co-dominated at the continental scale. For animals, positive, negative, and hump-shaped patterns were common at most geographical scales, and no one pattern predominated. For both plants and animals, hump-shaped curves were relatively more common in studies that crossed community boundaries compared to studies conducted within a community type, and plant studies that crossed community types tended to span a greater range of productivity compared to studies within community types. Sample size and plot size did not affect the probability of finding a particular productivity-diversity relationship (e.g., positive, hump-shaped, etc.). However, hump-shaped curves were especially common (65%) in studies of plant diversity that used plant biomass as a measure of productivity, and in studies conducted in aquatic systems.

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The use of structural equation modeling (SEM) is often motivated by its utility for investigating complex networks of relationships, but also because of its promise as a means of representing theoretical concepts using latent variables. In this paper, we discuss characteristics of ecological theory and some of the challenges for proper specification of theoretical ideas in structural equation models (SE models). In our presentation, we describe some of the requirements for classical latent variable models in which observed variables (indicators) are interpreted as the effects of underlying causes. We also describe alternative model specifications in which indicators are interpreted as having causal influences on the theoretical concepts. We suggest that this latter nonclassical specification (which involves another variable type—the composite) will often be appropriate for ecological studies because of the multifaceted nature of our theoretical concepts. In this paper, we employ the use of meta‐models to aid the translation of theory into SE models and also to facilitate our ability to relate results back to our theories. We demonstrate our approach by showing how a synthetic theory of grassland biodiversity can be evaluated using SEM and data from a coastal grassland. In this example, the theory focuses on the responses of species richness to abiotic stress and disturbance, both directly and through intervening effects on community biomass. Models examined include both those based on classical forms (where each concept is represented using a single latent variable) and also ones in which the concepts are recognized to be multifaceted and modeled as such. To address the challenge of matching SE models with the conceptual level of our theory, two approaches are illustrated, compositing and aggregation. Both approaches are shown to have merits, with the former being preferable for cases where the multiple facets of a concept have widely differing effects in the system and the latter being preferable where facets act together consistently when influencing other parts of the system. Because ecological theory characteristically deals with concepts that are multifaceted, we expect the methods presented in this paper will be useful for ecologists wishing to use SEM.

Macroecological studies infer ecological processes based on observed patterns. An often used measure of pattern is the species‐area curve. Insufficient attention has been paid to the variety of methods used to construct those curves. There are six different methods based on different combinations of: (1) the pattern of quadrats or areas sampled (nested, contiguous, noncontiguous, or island); (2) whether successively larger areas are constructed in a spatially explicit fashion or not; and (3) whether the curve is constructed from single values or mean values. The resulting six types of curves differ in their shapes, how diversity is encapsulated, and the scales encompassed. Inventory diversity (α) can either represent a single value or a mean value, creating a difference in the focus of the measure. Differentiation diversity (β) can vary in the extent encompassed, and thus the spatial scale, depending on the pattern of quadrat placement. Species‐area curves are used for a variety of purposes: extrapolation, setting a common grain, and hypothesis testing. The six types of curves differ in how they are used or interpreted in these contexts. A failure to recognize these differences can result in improper conclusions. Further work is needed to understand the sampling and measurement properties of the different types of species‐area curves.

We present a general quantitative genetic model for the evolution of reaction norms. This model goes beyond previous models by simultaneously permitting any shaped reaction norm and allowing for the imposition of genetic constraints. Earlier models are shown to be special cases of our general model; we discuss in detail models involving just two macroenvironments, linear reaction norms, and quadratic reaction norms. The model predicts that, for the case of a temporally varying environment, a population will converge on (1) the genotype with the maximum mean geometric fitness over all environments, (2) a linear reaction norm whose slope is proportional to the covariance between the environment of development and the environment of selection, and (3) a linear reaction norm even if nonlinear reaction norms are possible. An examination of experimental studies finds some limited support for these predictions. We discuss the limitations of our model and the need for more realistic gametic models and additional data on the genetic and developmental bases of plasticity.