Steven Hecht Orzack

Population dynamics in variable environments I. Long-run growth rates and extinction

Abstract A model of population growth is studied in which the Leslie matrix for each time interval is chosen according to a Markov process. It is shown analytically that the distribution of total population number is lognormal at long times. Measures of population growth are compared and it is shown that a mean logarithmic growth rate and a logarithmic variance effectively describe growth and extinction at long times. Numerical simulations are used to explore the convergence to lognormality and the effects of environmental variance and autocorrelation. The results given apply to other geometric growth models which involve nonnegative growth matrices.

OPTIMALITY MODELS AND THE TEST OF ADAPTATIONISM

The use of optimality models in the investigation of adaptation remains controversial. Critics charge that advocates of the optimality approach assume that the traits they analyze are optimal. Advocates of the approach deny this but admit to assuming that the traits have adaptive explanations. This controversy is part of the ongoing debate about adaptationism. We believe that this controversy remains unresolved in part because of ambiguity in the definition of adaptationism. In this article, we clarify the thesis of adaptationism, show how the structure of optimality models relates to that thesis, and describe how the thesis of adaptationism is testable. In addition, we describe the types of analyses that are essential to a test of an optimality model if the optimality of the trait is to be assessed and if assessments of the success of specific models are to contribute to a test of adaptationism. These analyses allow one to distinguish between the hypothesis that natural selection has had some influence or an important influence on a trait and the hypothesis that the trait is optimal. At present, to our knowledge, there are only two sets of studies in evolutionary biology in which this critical distinction has been made.

Reproductive effort in variable environments, or environmental variation is for the birds

We analyze a model of life history evolution in which there is a temporally variable cost of reproduction. Analysis of the stochastic growth rate indicates that the optimal clutch size in a variable environment can be substantially increased or decreased relative to the optimal clutch size in a constant environment. This finding holds regardless of whether the cost of reproduction varies discretely or continuously. Our results also illustrate how two distinct optimal life histories can evolve in response to a given amount of environmental variability. One life history pays a cost of reproduction that is relatively fixed and small on average (by producing a small fixed clutch size); it can always produce an optimal clutch size but is unable to exploit highly favorable environments. The other pays a cost of reproduction that is variable and large on average (by producing a large fixed clutch size); it cannot always produce an optimal clutch size but is able to exploit highly favorable environments.

Dynamic heterogeneity and life history variability in the kittiwake

1. Understanding the evolution of life histories requires an assessment of the process that generates variation in life histories. Within-population heterogeneity of life histories can be dynamically generated by stochastic variation of reproduction and survival or be generated by individual differences that are fixed at birth. 2. We show for the kittiwake that dynamic heterogeneity is a sufficient explanation of observed variation of life histories. 3. The total heterogeneity in life histories has a small contribution from reproductive stage dynamics and a large contribution from survival differences. We quantify the diversity in life histories by metrics computed from the generating stochastic process. 4. We show how dynamic heterogeneity can be used as a null model and also how it can lead to positive associations between reproduction and survival across the life span. 5. We believe our approach to identifying the nature of among-individual heterogeneity yields important insights into the forces that generate within-population variation of life-history traits. It provides an alternative to claims that fixed individual differences are a major determinant of heterogeneity in life histories.

How (not) to test an optimality model

The controversy over the use of optimality models in the investigation of adaptation is long-standing. Nonetheless, little or no attention has been paid in this debate to the most important question to be asked about such models: how should the test of an optimality model be structured if the local optimality of the trait is to be assessed? Here we answer this question and describe how such a test can contribute to a test of adaptationism.

HOW TO FORMULATE AND TEST ADAPTATIONISM

Although Brandon and Rausher (1996, this issue) are highly critical of our article (Orzack and Sober 1994a), their approach differs little from ours. We find some of their suggestions to be reasonable; others reflect mischaracterization f our arguments in important ways. In our article and in another previous article (Orzack and Sober 1994b), we suggested that an adaptationist view of a trait T is best understood as the following proposition:

Life History Evolution and Population Dynamics in Variable Environments: Some Insights from Stochastic Demography

What are the evolutionary consequences of environmental fluctuations? In this paper, I present results from the theory of stochastic demography which provide a partial answer to this central question in the evolutionary analysis of life histories.

Common Ancestry and Natural Selection

We explore the evidential relationships that connect two standard claims of modern evolutionary biology. The hypothesis of common ancestry (which says that all organisms now on earth trace back to a single progenitor) and the hypothesis of natural selection (which says that natural selection has been an important influence on the traits exhibited by organisms) are logically independent; however, this leaves open whether testing one requires assumptions about the status of the other. Darwin noted that an extreme version of adaptationism would undercut the possibility of making inferences about common ancestry. Here we develop a converse claim—hypotheses that assert that natural selection has been an important influence on trait values are untestable unless supplemented by suitable background assumptions. The fact of common ancestry and a claim about quantitative genetics together suffice to render such hypotheses testable. Furthermore, we see no plausible alternative to these assumptions; we hypothesize that they are necessary as well as sufficient for adaptive hypotheses to be tested. This point has important implications for biological practice, since biologists standardly assume that adaptive hypotheses predict trait associations among tip species. Another consequence is that adaptive hypotheses cannot be confirmed or disconfirmed by a trait value that is universal within a single species, if that trait value deviates even slightly from the optimum. 1Two Darwinian hypotheses 2Logical independence 3How adaptive hypotheses bear on the tree of life hypothesis 4How the tree of life hypothesis bears on adaptive hypotheses 5What do adaptive hypotheses predict? 6Common ancestry and quantitative genetics to the rescue 7Conclusion

Liver physiology and sex ratio biology

will only lead to the discovery of plasticity genes by chance, or after exhaustive effort. The study of plasticity, and of plasticity genes, will be important and useful for our understanding of the response of organisms to the environment. At this early stage, where evidence is being drawn together from molecular, physiological, evolutionary and ecological research, we need to define clearly what we are hoping to explain and to be realistic about expectations for the results of our experiments.