Age-structured population growth rates in constant and variable environments: a near equilibrium approach (original) (raw)
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The importance of growth and mortality costs in the evolution of the optimal life history
Journal of Evolutionary Biology, 2006
A central assumption of life history theory is that the evolution of the component traits is determined in part by trade-offs between these traits. Whereas the existence of such trade-offs has been well demonstrated, the relative importance of these remains unclear. In this paper we use optimality theory to test the hypothesis that the trade-off between present and future fecundity induced by the costs of continued growth is a sufficient explanation for the optimal age at first reproduction, a, and the optimal allocation to reproduction, G, in 38 populations of perch and Arctic char. This hypothesis is rejected for both traits and we conclude that this trade-off, by itself, is an insufficient explanation for the observed values of a and G. Similarly, a fitness function that assumes a mortality cost to reproduction but no growth cost cannot account for the observed values of a. In contrast, under the assumption that fitness is maximized, the observed life histories can be accounted for by the joint action of trade-offs between growth and reproductive allocation and between mortality and reproductive allocation (Individual Juvenile Mortality model). Although the ability of the growth/mortality model to fit the data does not prove that this is the mechanism driving the evolution of the optimal age at first reproduction and allocation to reproduction, the fit does demonstrate that the hypothesis is consistent with the data and hence cannot at this time be rejected. We also examine two simpler versions of this model, one in which adult mortality is a constant proportion of juvenile mortality [Proportional Juvenile Mortality (PJM) model] and one in which the proportionality is constant within but not necessarily between species [Specific Juvenile Mortality (SSJM) model]. We find that the PJM model is unacceptable but that the SSJM model produces fits suggesting that, within the two species studied, juvenile mortality is proportional to adult mortality but the value differs between the two species.
Life-history dynamics: damping time, demographic dispersion and generation time
2020
Transient dynamics are crucial for understanding ecological and life-history dynamics. In this study, we analyze damping time, the time taken by a population to converge to a stable (st)age structure following a perturbation, for over 600 species of animals and plants. We expected damping time to be associated with both generation time T c and demographic dispersion σ based on previous theoretical work. Surprisingly, we find that damping time (calculated from the population projection matrix) is approximately proportional to T c across taxa on the log-log scale, regardless of σ. The result suggests that species at the slow end of fast-slow continuum (characterized with long generation time, late maturity, low fecundity) are more vulnerable to external disturbances as they take more time to recover compared to species with fast life-histories. The finding on damping time led us to next examine the relationship between generation time and demographic dispersion. Our result reveals that the two life-history variables are positively correlated on a log-log scale across taxa, implying long generation time promotes demographic dispersion in reproductive events. Finally, we discuss our results in the context of metabolic theory and contribute to existing allometric scaling relationships. Main In a constant environment, (st)age-structured populations tend towards a
Population dynamic consequences of delayed life-history effects
Trends in Ecology & …, 2002
Many aspects of population fluctuations can be captured with reasonable precision using simple, nonstructured models of the population renewal process . Such models include the familiar logistic equation, Ricker models and linear and nonlinear autoregressive models. Another frequently used class of models is age-or stage-structured models (e.g. matrix models ) that split the life history into relevant age or stage components. A common feature among these model types is that life-history traits, such as survival and fecundity, do not vary with time. The predicted dynamics of a model population are thus dependent only on the initial specification of the survival and fecundity rates.
Unexpected discontinuities in life-history evolution under size-dependent mortality
Proceedings of the Royal Society B: Biological Sciences, 2003
In many organisms survival depends on body size. We investigate the implications of size-selective mortality on life-history evolution by introducing and analysing a new and particularly flexible life-history model with the following key features: the lengths of growth and reproductive periods in successive reproductive cycles can vary evolutionarily, the model does not constrain evolution to patterns of either determinate or indeterminate growth, and lifetime number and sizes of broods are the outcomes of evolutionarily optimal life-history decisions. We find that small changes in environmental conditions can lead to abrupt transitions in optimal life histories when size-dependent mortality is sufficiently strong. Such discontinuous switching results from antagonistic selection pressures and occurs between strategies of early maturation with short reproductive periods and late maturation with long reproductive cycles. When mortality is sizeselective and the size-independent component is not too high, selection favours prolonged juvenile growth, thereby allowing individuals to reach a mortality refuge at large body size before the onset of reproduction. When either component of mortality is then increased, the mortality refuge first becomes unattractive and eventually closes up altogether, resulting in short juvenile growth and frequent reproduction. Our results suggest a new mechanism for the evolution of life-history dimorphisms.
Journal or Theoretical Biology, 1988
An "increasing mortality with increasing chronological age in populations in the wild" (IMICAW) is a phenomenon shown by many species, and the greater or smaller (or non existent) IMICAW has an adaptive value, since it reduces the "mean duration of life" (ML). As Leopold (1961) pointed out, a smaller ML brings about a greater spreading velocity, within the species, of any advantageous mutation. However, this is an argument of group selection and is, therefore, inadequate to demonstrate that within a species a C gene causing IMICAW is stable compared with a C' allele not having this effect. The problem may be solved if we consider the inclusive fitness of C with the hypothesis that the dead individuals are replaced by kin individuals. In such a case, even with low values of the coefficient of relationship (Hamilton, 1971) of the substituting individuals, C tends to be stable and favoured by the selective mechanism as compared with C'. When the preferential replacement by kin individuals does not happen and/or when the turnover of generations is swift enough, C is not favoured and hence IMICAW loses its hypothesized adaptive value. In such cases, survival curves must be of type II or III of Pianka's classification (1970). It is discussed if IMICAW might be a consequence of the action of many harmful genes that express themselves tardily in the course of life.
Ecology, 1998
Interactive effects of one species on another may simultaneously influence mortality, growth, and fecundity. To quantify the strength of an interaction between two species, we must therefore use techniques that integrate these various responses into estimates of overall effect. Demographic models of populations provide such a framework. Here we develop a demographic model describing the life history of a hemimetabolous insect to evaluate the relative importance of predator effects on mortality and growth of damselflies (Enallagma boreale) in fishless ponds and mayflies (Baetis bicaudatus) in trout streams. Previous experiments have shown that dragonfly predators in fishless ponds inflict direct mortality and cause reduced growth rates in Enallagma damselflies. Parameterization of the demographic model from these data show, however, that only the direct mortality effects of dragonflies should significantly influence damselfly population dynamics. This is because damselfly size at emergence does not influence adult female fecundity, so the effects of dragonflies on damselfly larval growth do not influence adult fecundity. Likewise, both trout and stonefly predators inflict mortality on larval Baetis mayflies and cause decreases in growth rates. However, our demographic analyses indicate that the growth effects of both predators should dominate the population-dynamic effects on Baetis. This is because size at emergence translates directly into adult fecundity in mayflies. We also present data suggesting that developmental responses to changes in environmental conditions (e.g., predator abundances, resource availabilities) differ between species depending on these same life history parameters. The biological significance of lethal vs. sublethal predator impacts must be evaluated in a demographic framework to identify whether alterations in growth rate, and the timing of and size at metamorphosis, significantly influence population dynamics. The demographic model used for any particular organism must be tailored to its life history, but the various impacts of interactions with other species can all be integrated into estimates of projected population growth that can then be readily compared among species with different life histories.
Fitness versus longevity in age-structured population dynamics
Journal of Mathematical Biology, 2002
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the fitness and age characteristics exhibit counter-intuitive behavior as a function of the mutational bias. By analytical and numerical study of the underlying rate equations, we show that if deleterious mutations are favored, the average fitness of the population reaches a steady state, while the average population age is a decreasing function of the average fitness. When advantageous mutations are favored, the average population fitness grows linearly with time t, while the average age is independent of the average fitness. For no mutational bias, the average fitness grows as t 2/3 .
Evolutionary perturbations of optimal life histories
Evolutionary Ecology, 1995
An optimal age-structured life history is perturbed by increasing the mortality factors specific to an agek. These can be density dependent (DD) or independent (DI), avoidable or unavoidable. The last two refer to whether their effect on any individual depends or not on how much energy it devotes to defence. Agespecific trade-offs between the allocation of energy to defence and fecundity exist: survival probabilities through each agex, P x, are concave decreasing functions of the fecundity per unit size at that age,b x. These are constraints for the optimal life history. The changes induced by perturbation are evaluated by equations that predict whether some extra energy is diverted towards survivorship at the expense of fecundity or vice versa. The model predicts that for DI environments the degree of avoidability of the mortality source perturbed, is a decisive factor for the strategy selected at agek, but not for any other age class. DD environments are more complex since all ages are simultaneously embedded in density effects. The perturbations not only act directly — as in the DI situation — but also indirectly through their effect on equilibrium density,N *. When any kind of mortality source becomes more intense at agek, N * always decreases and all ages react in consequence according to the effect of density on each age-specific trade-off. Either coincidental or opposing reactions can be expected from direct and indirect effects. The resultant strategy for any age would be a matter of magnitude comparisons. Some possible general patterns are discussed.
Evolutionary perturbations of optimal life histories _Hernandez, Leon (1985) Evol Ecol
Evolutionary Ecology, 1995
An optimal age-structured life history is perturbed by increasing the mortality factors specific to an age k. These can be density dependent (DD) or independent (DI), avoidable or unavoidable. The last two refer to whether their effect on any individual depends or not on how much energy it devotes to defence. Agespecific trade-offs between the allocation of energy to defence and fecundity exist: survival probabilities through each age x, Px, are concave decreasing functions of the fecundity per unit size at that age, b x. These are constraints for the optimal life history. The changes induced by perturbation are evaluated by equations that predict whether some extra energy is diverted towards survivorship at the expense of fecundity or vice versa. The model predicts that for DI environments the degree of avoidability of the mortality source perturbed, is a decisive factor for the strategy selected at age k, but not for any other age class. DD environments are more complex since all ages are simultaneously embedded in density effects. The perturbations not only act directly -as in the DI situation -but also indirectly through their effect on equilibrium density, N*. When any kind of mortality source becomes more intense at age k, N* always decreases and all ages react in consequence according to the effect of density on each age-specific trade-off. Either coincidental or opposing reactions can be expected from direct and indirect effects. The resultant strategy for any age would be a matter of magnitude comparisons. Some possible general patterns are discussed.