Biomedical subjects

Stephen P Ellner

Publications and source records attributed to Stephen P Ellner.

13 recordsLinked to original sources

PubMed2006

Stochastic stable population growth in integral projection models: theory and application.

Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative properties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population structure. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, University of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411-440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325-344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple traits (size, age and a latent "quality" variable), which would be difficult to accommodate in a classical matrix model. We use the model to explore the evolution of size- and age-dependent flowering using an evolutionarily stable strategy (ESS) approach. We find close agreement between the observed flowering behavior and the predicted ESS from the stochastic model, whereas the ESS predicted from a deterministic version of the model is very different from observed flowering behavior. These results strongly suggest that the flowering strategy in O. illyricum is an adaptation to random between-year variation in vital rates.

Ecosystem↗

PubMed2006

Why animals lie: how dishonesty and belief can coexist in a signaling system.

We develop and apply a simple model for animal communication in which signalers can use a nontrivial frequency of deception without causing listeners to completely lose belief. This common feature of animal communication has been difficult to explain as a stable adaptive outcome of the options and payoffs intrinsic to signaling interactions. Our theory is based on two realistic assumptions. (1) Signals are "overheard" by several listeners or listener types with different payoffs. The signaler may then benefit from using incomplete honesty to elicit different responses from different listener types, such as attracting potential mates while simultaneously deterring competitors. (2) Signaler and listener strategies change dynamically in response to current payoffs for different behaviors. The dynamic equations can be interpreted as describing learning and behavior change by individuals or evolution across generations. We explain how our dynamic model differs from other solution concepts from classical and evolutionary game theory and how it relates to general models for frequency-dependent phenotype dynamics. We illustrate the theory with several applications where deceptive signaling occurs readily in our framework, including bluffing competitors for potential mates or territories. We suggest future theoretical directions to make the models more general and propose some possible experimental tests.

Animal Communication↗

PubMed2006

Prey evolution on the time scale of predator-prey dynamics revealed by allele-specific quantitative PCR.

Using rotifer-algal microcosms, we tracked rapid evolution resulting from temporally changing natural selection in ecological predator-prey dynamics. We previously demonstrated that predator-prey oscillations in rotifer-algal laboratory microcosms are qualitatively altered by the presence of genetic variation within the prey. In that study, changes in algal gene frequencies were inferred from their effects on population dynamics but not observed directly. Here, we document rapid prey evolution in this system by directly observing changes in Chlorella vulgaris genotype frequencies as the abundances of these algae and their consumer, Brachionus calyciflorus, change through time. We isolated a group of algal clones that we could distinguish by using microsatellite-DNA markers, and developed an allele-specific quantitative PCR technique (AsQ-PCR) to quantify the frequencies of pairs of clones in mixed culture. We showed that two of these genotypes exhibited a fitness tradeoff in which one was more resistant to predation (more digestion-resistant), and the other had faster population growth under limiting nitrogen concentrations. A fully specified mathematical model for the rotifer-algal population and evolutionary dynamics predicted that these two clones would undergo a single oscillation in clonal frequencies followed by asymptotic fixation of the more resistant clone, rather than the recurrent oscillations previously observed with other algal clones. We used AsQ-PCR to confirm this prediction: the superior competitor dominated initially, but as rotifer densities increased, the more predator-resistant clone predominated.

Alleles↗

PubMed2006

Integral projection models for species with complex demography.

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross-classification by several attributes (e.g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/elasticity analysis for density-independent models, local stability analysis in density-dependent models, and optimal/evolutionarily stable strategy life-history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6-year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods.A zip archive of R scripts illustrating our suggested methods is also provided.

Biological Evolution↗

PubMed2006

Ecology: mechanisms for consumer diversity.

A variety of mechanisms can theoretically produce competitive coexistence in nature, making it hard to identify a single explanation for the maintenance of diversity in any particular system. Based on laboratory experiments with a consumer-resource system of crustacean Daphnia eating algae, Nelson et al. suggest that maintenance of genetic diversity in the consumer populations they studied depends only on the dynamics of the population structure of the consumer. We suggest that the differences in Daphnia genetic diversity that they find for different experimental treatments could equally be explained by a simple, well known mechanism: the number of coexisting competitors cannot exceed the number of shared resources. Here we confirm this possibility by using a simple mathematical model and suggest that more than one mechanism may account for the maintenance of genetic diversity observed by Nelson et al. in their system.

Aging↗

PubMed2004

Evolutionary trade-off between defence against grazing and competitive ability in a simple unicellular alga, Chlorella vulgaris.

Trade-offs between defence and other fitness components are expected in principle, and can have major qualitative impacts on ecological dynamics. Here we show that such a trade-off exists even in the simple unicellular alga Chlorella vulgaris. We grew algal populations for multiple generations in either the presence ('grazed algae') or absence ('non-grazed algae') of the grazing rotifer Brachionus calyciflorus, and then evaluated their defence and competitive abilities. Grazed algae were better defended, yielding rotifer growth rate 32% below that of animals fed non-grazed algae, but they also had diminished competitive ability, with a growth rate under nutrient-limiting conditions 28% below that of non-grazed algae. Grazed algae also had a smaller cell size and were more concentrated in carbon and nitrogen. Thus, C. vulgaris genotypes vary phenotypically in their position along a trade-off curve between defence against grazing and competitive ability. This genetic variation underlies rapid algal evolution that significantly alters the ecological predator-prey cycles between rotifers and algae.

Animals↗

PubMed2004

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model.

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, lambda(s). We use lambda(s) to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, lambda(s), which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(lambda(s)) can be used to calculate elasticities.

Asteraceae↗

PubMed2004

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system.

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358-1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802-815; Yoshida et al., 2003, Nature, 424, 303-306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to 'management': externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.

Animals↗

PubMed2003

Evolution of complex flowering strategies: an age- and size-structured integral projection model.

We explore the evolution of delayed age- and size-dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step-function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering-threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (lambda) of the survival-growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general size- and age-dependent integral projection models are presented.

Adaptation, Biological↗

PubMed2003

Rapid evolution drives ecological dynamics in a predator-prey system.

Ecological and evolutionary dynamics can occur on similar timescales. However, theoretical predictions of how rapid evolution can affect ecological dynamics are inconclusive and often depend on untested model assumptions. Here we report that rapid prey evolution in response to oscillating predator density affects predator-prey (rotifer-algal) cycles in laboratory microcosms. Our experiments tested explicit predictions from a model for our system that allows prey evolution. We verified the predicted existence of an evolutionary tradeoff between algal competitive ability and defence against consumption, and examined its effects on cycle dynamics by manipulating the evolutionary potential of the prey population. Single-clone algal cultures (lacking genetic variability) produced short cycle periods and typical quarter-period phase lags between prey and predator densities, whereas multi-clonal (genetically variable) algal cultures produced long cycles with prey and predator densities nearly out of phase, exactly as predicted. These results confirm that prey evolution can substantially alter predator-prey dynamics, and therefore that attempts to understand population oscillations in nature cannot neglect potential effects from ongoing rapid evolution.

Animals↗

PubMed2003

Evolution as a critical component of plankton dynamics.

Microevolution is typically ignored as a factor directly affecting ongoing population dynamics. We show here that density-dependent natural selection has a direct and measurable effect on a planktonic predator-prey interaction. We kept populations of Brachionus calyciflorus, a monogonont rotifer that exhibits cyclical parthenogenesis, in continuous flow-through cultures (chemostats) for more than 900 days. Initially, females frequently produced male offspring, especially at high population densities. We observed rapid evolution, however, towards low propensity to reproduce sexually, and by 750 days, reproduction had become entirely asexual. There was strong selection favouring asexual reproduction because, under the turbulent chemostat regime, males were unable to mate with females, produced no offspring, and so had zero fitness. In replicated chemostat experiments we found that this evolutionary process directly influenced the population dynamics. We observed very specific but reproducible plankton dynamics which are explained well by a mathematical model that explicitly includes evolution. This model accounts for both asexual and sexual reproduction and treats the propensity to reproduce sexually as a quantitative trait under selection. We suggest that a similar amalgam of ecological and evolutionary mechanisms may drive the dynamics of rapidly reproducing organisms in the wild.

Animals↗

PubMed2003

Pair-edge approximation for heterogeneous lattice population models.

To increase the analytical tractability of lattice stochastic spatial population models, several approximations have been developed. The pair-edge approximation is a moment-closure method that is effective in predicting persistence criteria and invasion speeds on a homogeneous lattice. Here we evaluate the effectiveness of the pair-edge approximation on a spatially heterogeneous lattice in which some sites are unoccupiable, or "dead". This model has several possible interpretations, including a spatial SIS epidemic model, in which some sites are occupied by immobile host-species individuals while others are empty. We find that, as in the homogeneous model, the pair-edge approximation is significantly more accurate than the ordinary pair approximation in determining conditions for persistence. However, habitat heterogeneity decreases invasion speed more than is predicted by the pair-edge approximation, and the discrepancy increases with greater clustering of "dead" sites. The accuracy of the approximation validates the underlying heuristic picture of population spread and therefore provides qualitative insight into the dynamics of lattice models. Conversely, the situations where the approximation is less accurate reveals limitations of pair approximation in the presence of spatial heterogeneity.

Algorithms↗

PubMed2002

Energy storage and the evolution of population dynamics.

We explore the mutual dependence of life history evolution and population dynamics by modeling a structured rotifer population that preys on a dynamic food supply. We focus on the ecological role of energy storage. A physiologically based submodel describes how individual predators allocate assimilated energy among growth, reproduction, and storage. We use invasibility analyses to predict evolutionary stable strategies for energy allocation. Various proxy measures of fitness based on measurable biological quantities, such as average population size or average per-capita fecundity, fail to predict evolutionary stable strategies. The predicted strategies indicate that selection strongly favors storage allocation for juveniles, but only for adults when prey densities are high. With the evolution of energy storage, population dynamics can shift from aperiodic to stable cycles without any need to invoke group selection.

Animals↗