The theory of optimal reproductive strategies has traditionally been studied in two ways: formal analysis of simple models that neglect the effects of age structure, and computer studies of complex life histories. Each of these approaches has disadvantages. The consequences of simple models sometimes dependmore on the nature of the simplifying assumptions than on the biological issues in question. On the other hand, computer simulations are only as general as the examples considered. The present study seeks to extend the formal analysis of optimal life histories to complex cases. I show that an optimal life history maximizes for each age class the expected fecundity at that age plus the sum of all future expected parameters. This result enables us to determine, at least inthe case of a three—stage life history, the manner in which the optimal reproductive effort at each age depends on the efforts made at the other ages, and thus, the coevolution of the various age—specific efforts. Three cases are distinguished: (1) If fertility and post—breeding survival and growth are concave functions of reproductive effort (i.e., have second derivatives that areeverywhere negative) there is a single set of age—specific reproductive rates towhich the system evolves regardless of initial conditions. This set of reproductive rates corresponds to an iteroparous life history (repeated breeding at different ages). (2) On the other hand, if fertility and subsequent growth and survival are convex functions of effort (positive second derivatives), semelparity (a single, herculean reproductive effort, followed by death) will most often evolve. However, an alternative, iteroparous life history sometimes exists, although stability considerations suggest that it may be transitory. (3)More realistic fertility and growth survival functions can generate alternative reproductive strategies that are stable since each represents a local maximum infitness. Often one of these alternatives corresponds to semelparity, the second to repeated reproduction. In such cases, the evolutionary outcome depends on initial conditions. This suggests that related species, with similar ecologies, may have very different life histories, the differences resulting from historical accidents that have trapped each on a different adaptive peak. The Salmonid genera, Salmo and Oncorhynchus, are suggested as possible examples.

No abstract

No abstract

In the mid-1970s, theoretical ecologists were responsible for stimulating interest in nonlinear dynamics and chaos. Ironically, the importance of chaos in ecology itself remains controversial. Proponents of ecological chaos point to its ubiquity in mathematical models and to various empirical findings. Sceptics maintain that the models are unrealistic and that the experimental evidence is equally consistent with stochastic models. More generally, it has been argued that interdemic selection and/or enhanced rates of species extinction will eliminate populations and species that evolve into chaotic regions of parameter space. Fundamental to this opinion is the belief that violent oscillations and low minimum population densities are inevitable correlates of the chaotic state. In fact, rarity is not a necessary consequence of complex dynamical behaviour. But even when chaos is associated with frequent rarity, its consequences to survival are necessarily deleterious only in the case of species composed of a single population. Of course, the majority of real world species (for example, most insects) consist of multiple populations weakly coupled by migration, and in this circumstance chaos can actually reduce the probability of extinction. Here we show that although low densities lead to more frequent extinction at the local level, the decorrelating effect of chaotic oscillations reduces the degree of synchrony among populations and thus the likelihood that all are simultaneously extinguished.

Whereas case rates for some childhood diseases (chickenpox) often vary according to an almost regular annual cycle, the incidence of more efficiently transmitted infections such as measles is more variable. Three hypotheses have been proposed to account for such fluctuations. (i) Irregular dynamics result from random shocks to systems with stable equilibria. (ii) The intrinsic dynamics correspond to biennial cycles that are subject to stochastic forcing. (iii) Aperiodic fluctuations are intrinsic to the epidemiology. Comparison of real world data and epidemiological models suggests that measles epidemics are inherently chaotic. Conversely, the extent to which chickenpox outbreaks approximate a yearly cycle depends inversely on the population size.

No abstract

In this paper variations in life history data among local populations of Atlantic salmon have been examined. The following patterns emerge: (1) The mean age of first spawning increases with the difficulty of upstream migration as estimated by the distance the fish ascend into freshwater. Other indices of river harshness yield similar results. (2) The effect of commercial fishing has been to eliminate larger and older fish from the run. Available evidence suggests that this has selected for an early age of first return on the Miramichi River and that the frequencies of genes coding for different ages of first spawning have been altered. (3) The mean age of first spawning is positively correlated with marine growth rates after the grilse stage. Rapid growth at sea subsequent to the grilse stage is associated with delayed reproduction; slower growth with an earlier age of first breeding. This result suggests different paths of high—seas migration. (4) The variability about the mean age of first spawning first increases and then decreases as one moves north over the salmon's range from Maine to Ungava. In addition, we have observed that these results are in accord with predictions made by recent theoretical analyses of the optimal reproductive response to differing environmental conditions. We, therefore, conclude that the observed patterns of variation in life history are adaptive. We further take the agreement between theory and nature as a validation of the hypothesis that populations will in general differ from each other in the manner of their respective optima.

No abstract