280 research outputs found
The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.
Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function
The biased evolution of generation time
Many life-history traits, like the age at maturity or adult longevity, are
important determinants of the generation time. For instance, semelparous
species whose adults reproduce once and die have shorter generation times than
iteroparous species that reproduce on several occasions. A shorter generation
time ensures a higher growth rate in stable environments where resources are in
excess, and is therefore a positively selected feature in this (rarely met)
situation. In a stable and limiting environment, all combination of traits (or
strategies) that produce the same number of viable offspring on average are
strictly neutral even when their generation times differ. We first study the
evolution of life-history strategies with different generation times in this
context, and show that those with the longest generation time represent the
most likely evolutionary outcomes. Indeed, strategies with longer generation
times generate fewer mutants per time unit, which makes them less likely to be
replaced within a given time period. This `turnover bias' inevitably exists and
favors the evolution of strategies with long generation times. Its real impact,
however, should depend on the strength and direction of other evolutionary
forces; selection for short generation times, for instance, may oppose turnover
bias. Likewise, the evolutionary outcome depends on the strength of such
selection and population size, comparably to other biases acting on the
occurrence of mutations.Comment: Now we also study the evolution of development duration, suggesting
that turnover bias is involved in the evolutionary dynamics of any trait
linked with the generation tim
Demographic Diversity and Sustainable Fisheries
Fish species are diverse. For example, some exhibit early maturation while others delay maturation, some adopt semelparous reproductive strategies while others are iteroparous, and some are long-lived and others short-lived. The diversity is likely to have profound effects on fish population dynamics, which in turn has implications for fisheries management. In this study, a simple density-dependent stage-structured population model was used to investigate the effect of life history traits on sustainable yield, population resilience, and the coefficient of variation (CV) of the adult abundance. The study showed that semelparous fish can produce very high sustainable yields, near or above 50% of the carrying capacity, whereas long-lived iteroparous fish can produce very low sustainable yields, which are often much less than 10% of the carrying capacity. The difference is not because of different levels of sustainable fishing mortality rate, but because of difference in the sensitivity of the equilibrium abundance to fishing mortality. On the other hand, the resilience of fish stocks increases from delayed maturation to early maturation strategies but remains almost unchanged from semelparous to long-lived iteroparous. The CV of the adult abundance increases with increased fishing mortality, not because more individuals are recruited into the adult stage (as previous speculated), but because the mean abundance is more sensitive to fishing mortality than its standard deviation. The magnitudes of these effects vary depending on the life history strategies of the fish species involved. It is evident that any past high yield of long-lived iteroparous fish is a transient yield level, and future commercial fisheries should focus more on fish that are short-lived (including semelparous species) with high compensatory capacity
An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density - Dependent Survival Probabilities.
Source at https://doi.org/10.1155/2017/8934295 .A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the
survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that
the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age
class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also
been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability
to instability goes through a supercritical Neimark
â
Sacker bifurcation, and it is further shown that when the population switches
from possessing a precocious to a delayed semelparous life history both stability properties and the possibility of periodic dynamics
become weaker
Stable Bifurcations in Semelparous Leslie Models
In this paper, we consider nonlinear Leslie models for the dynamics of semelparous age-structured populations. We establish stability and instability criteria for positive equilibria that bifurcate from the extinction equilibrium at R0=1. When the bifurcation is to the right (forward or super-critical), the criteria consist of inequalities involving the (low-density) between-class and within-class competition intensities. Roughly speaking, stability (respectively, instability) occurs if between-class competition is weaker (respectively, stronger) than within-class competition. When the bifurcation is to the left (backward or sub-critical), the bifurcating equilibria are unstable. We also give criteria that determine whether the boundary of the positive cone is an attractor or a repeller. These general criteria contribute to the study of dynamic dichotomies, known to occur in lower dimensional semelparous Leslie models, between equilibration and age-cohort-synchronized oscillations. © 2012 Copyright J.M. Cushing
The Evolution of Dispersal in Random Environments and The Principle of Partial Control
McNamara and Dall (2011) identified novel relationships between the abundance
of a species in different environments, the temporal properties of
environmental change, and selection for or against dispersal. Here, the
mathematics underlying these relationships in their two-environment model are
investigated for arbitrary numbers of environments. The effect they described
is quantified as the fitness-abundance covariance. The phase in the life cycle
where the population is censused is crucial for the implications of the
fitness-abundance covariance. These relationships are shown to connect to the
population genetics literature on the Reduction Principle for the evolution of
genetic systems and migration. Conditions that produce selection for increased
unconditional dispersal are found to be new instances of departures from
reduction described by the "Principle of Partial Control" proposed for the
evolution of modifier genes. According to this principle, variation that only
partially controls the processes that transform the transmitted information of
organisms may be selected to increase these processes. Mathematical methods of
Karlin, Friedland, and Elsner, Johnson, and Neumann, are central in
generalizing the analysis. Analysis of the adaptive landscape of the model
shows that the evolution of conditional dispersal is very sensitive to the
spectrum of genetic variation the population is capable of producing, and
suggests that empirical study of particular species will require an evaluation
of its variational properties.Comment: Dedicated to the memory of Professor Michael Neumann, one of whose
many elegant theorems provides for a result presented here. 28 pages, 1
table, 1 figur
Coexistence of competing stage-structured populations
This paper analyzes the stability of a coexistence equilibrium point of a model for competition between two stage-structured populations. In this model, for each population, competition for resources may affect any one of the following population parameters: reproduction, juvenile survival, maturation rate, or adult survival. The results show that the competitive strength of a population is affected by (1) the ratio of the population parameter influenced by competition under no resource limitation (maximum compensatory capacity) over the same parameter under a resource limitation due to competition (equilibrium rate) and (2) the ratio of interspecific competition over intraspecific competition; this ratio was previously shown to depend on resource-use overlap. The former ratio, which we define as fitness, can be equalized by adjusting organisms' life history strategies, thereby promoting coexistence. We conclude that in addition to niche differentiation among populations, the life history strategies of organisms play an important role in coexistence
Optimization of resource allocation can explain the temporal dynamics and honesty of sexual signals
In species in which males are free to dynamically alter their allocation to sexual signaling over the breeding season, the optimal investment in signaling should depend on both a maleâs state and the level of competition he faces at any given time. We developed a dynamic optimization model within a gameâtheoretical framework to explore the resulting signaling dynamics at both individual and population levels and tested two key model predictions with empirical data on threeâspined stickleback (Gasterosteus aculeatus) males subjected to dietary manipulation (carotenoid availability): (1) fish in better nutritional condition should be able to maintain their signal for longer over the breeding season, resulting in an increasingly positive correlation between nutritional status and signal (i.e., increasing signal honesty), and (2) female preference for more ornamented males should thus increase over the breeding season. Both predictions were supported by the experimental data. Our model shows how such patterns can emerge from the optimization of resource allocation to signaling in a competitive situation. The key determinants of the honesty and dynamics of sexual signaling are the condition dependency of male survival, the initial frequency distribution of nutritional condition in the male population, and the cost of signaling
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