Stephen P. Ellner

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.

Coexistence of plant species with similar niches

In the context of a simple mathematical model, we derive several mechanisms whereby plant species can coexist in a community without differing in their trophic niches (their relations with habitats, resources and exploiters). The model is based on the dynamics of species turnover in microsites, and incorporates localized competition, non-uniform seed dispersal and aspects of spatiotemporal environmental heterogeneity. These factors, which are not included in most standard competition models, allow stable coexistence of trophically equivalent species due to: (a) Differences in life-history ‘strategy’. (b) Input of seeds from nearby habitats (spatial Mass Effect). (c) Differences in demographic responses to environmental fluctuations (temporal Mass Effect). (d) Turnover in species composition between different habitat patches.

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. A zip archive of R scripts illustrating our suggested methods is also provided.

WHY DO POPULATIONS CYCLE? A SYNTHESIS OF STATISTICAL AND MECHANISTIC MODELING APPROACHES

Population cycles have long fascinated ecologists. Even in the most-studied populations, however, scientists continue to dispute the relative importance of various potential causes of the cycles. Over the past three decades, theoretical ecologists have cataloged a large number of mechanisms that are capable of generating cycles in population models. At the same time, statisticians have developed new techniques both for characterizing time series and for fitting population models to time-series data. Both disciplines are now sufficiently advanced that great gains in understanding can be made by synthesizing these complementary, and heretofore mostly independent, quantitative approaches. In this paper we demonstrate how to apply this synthesis to the problem of population cycles, using both long-term population time series and the often-rich observational and experimental data on the ecology of the species in question. We quantify hypotheses by writing mathematical models that embody the interactions and forces that might cause cycles. Some hypotheses can be rejected out of hand, as being unable to generate even qualitatively appropriate dynamics. We finish quantifying the remaining hypotheses by estimating parameters, both from independent experiments and from fitting the models to the time-series data using modern statistical techniques. Finally, we compare simulated time series generated by the models to the observed time series, using a variety of statistical descriptors, which we refer to collectively as “probes.” The model most similar to the data, as measured by these probes, is considered to be the most likely candidate to represent the mechanism underlying the population cycles. We illustrate this approach by analyzing one of Nicholson’s blowfly populations, in which we know the “true” governing mechanism. Our analysis, which uses only a subset of the information available about the population, uncovers the correct answer, suggesting that this synthetic approach might be successfully applied to field populations as well.

ROLE OF OVERLAPPING GENERATIONS IN MAINTAINING GENETIC VARIATION IN A FLUCTUATING ENVIRONMENT

Population genetics theory suggests that temporally fluctuating selection on phenotypes can act to maintain genetic variance only under very restrictive conditions. However, this conclusion is based on models with discrete nonoverlapping generations. We propose here that temporally fluctuating selection can indeed contribute significantly to the maintenance of genetic variation when the effects of overlapping generations and age-specific or stage-specific selection are considered. We develop a simple model for a population with overlapping generations, experiencing stabilizing selection with a temporally fluctuating optimum, and subject to repeated invasions by mutants with alternative phenotypes. We find that an evolutionarily stable population must have positive genetic variance maintained by selection so long as the product (variance of fluctuations) times (amount of generation overlap) times (selection intensity) is sufficiently high. This result applies to haploid, diploid, single-locus, or multilocus inheritance, and it does not depend on any form of heterozygote advantage to maintain genetic variance. However, it depends on the map between genotype and phenotype being constrained. If a single genotype can produce an arbitrary distribution of phenotypes, then genetic variance is not maintained by selection.

Chaos in a long-term experiment with a plankton community

Mathematical models predict that species interactions such as competition and predation can generate chaos. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web was isolated from the Baltic Sea, and consisted of bacteria, several phytoplankton species, herbivorous and predatory zooplankton species, and detritivores. The food web was cultured in a laboratory mesocosm, and sampled twice a week for more than 2,300 days. Despite constant external conditions, the species abundances showed striking fluctuations over several orders of magnitude. These fluctuations displayed a variety of different periodicities, which could be attributed to different species interactions in the food web. The population dynamics were characterized by positive Lyapunov exponents of similar magnitude for each species. Predictability was limited to a time horizon of 15–30 days, only slightly longer than the local weather forecast. Hence, our results demonstrate that species interactions in food webs can generate chaos. This implies that stability is not required for the persistence of complex food webs, and that the long-term prediction of species abundances can be fundamentally impossible.

Simple methods for calculating age-based life history parameters for stage-structured populations

Stage—classified matrix models are important analytical and theoretical tools for the study of population dynamics; in particular, these models may be appropriate for populations in which survivorship and fecundity are dependent on size or developmental stage, populations in which the age of individuals is difficult to determine, and populations in which there are multiple types of newborns. Nevertheless, methods for analyzing the implications of a populations stage—transition matrix have been limited in comparison to methods available for age—structured models (life tables or Leslie matrices). In this paper we show that all of the standard age—based measures of life history traits can be derived from a stage—transition model. By decomposing the transition matrix into separate birth, survival, and fission matrices we derive simple, direct formulas for age—based life history traits such as the discrete survivorship function, lx, maternity function, fx, mean age at maturity, and net reproductive rate, Ro, and also population parameters, including the stable age distribution, age—specific reproductive value, and generation time. These provide a common set of parameters for comparing age—structured and stage—structured populations or comparing populations with differently structured life cycles. In addition, we define four measures of age and life—span that summarize the relationship between stage and age in a stage—structured population: age distribution and mean age of residence for each stage class, expected remaining life—span for individuals in each stage class, and total life—span conditional on reaching a given stage class. We illustrate the use of our methods to address specific ecological questions by applying them to several previously published demographic data sets. These questions include: (1) what are the demographic effects of crowding on the tropical palm Astrocaryum mexicanum?; (2) how important is the initial rosette size in determining life history of teasel, Dipsacus sylvestris?; and (3) how old are reproducing adults in a stage—classified population of pink ladys—slipper, Cypripedium acaule? Our results may also be useful for evaluating the adequacy of a given stage—transition model.

SCALING UP ANIMAL MOVEMENTS IN HETEROGENEOUS LANDSCAPES: THE IMPORTANCE OF BEHAVIOR

Two major challenges of spatial ecology are understanding the effects of landscape heterogeneity on movement, and translating observations taken at small spatial and temporal scales into expected patterns at greater scales. Using a combination of computer simulations and micro-landscape experiments with Tribolium confusum beetles we found that conventional correlated random walk models with constant parameters severely underestimated spatial spread because organisms changed movement behaviors over time. However, a model incorporating behavioral heterogeneity between individuals, and within individuals over time, was able to account for observed patterns of spread. Our results suggest that the main challenge for scaling up movement patterns resides in the complexities of individual behavior rather than in the spatial structure of the landscape.

WHEN IS IT MEANINGFUL TO ESTIMATE AN EXTINCTION PROBABILITY

Recently Don Ludwig has shown that calculations of extinction probabilities based on currently available data are often meaningless due to the large uncertainty accompanying the estimates. Here we address two questions posed by his findings. Can one ever calculate extinction probabilities accurately? If so, how much data would be necessary? Our analysis indicates that reliable predictions of long-term extinction probabilities are likely to require unattainable amounts of data. Analytic calculations based on diffusion approximations indicate that reliable predictions of extinction probabilities can be made only for short-term time horizons (10% to 20% as long as the period over which the population has been monitored). Simulation results for unstructured and structured populations (three stage classes) agree with these calculations.

Habitat structure and population persistence in an experimental community.

Understanding spatial population dynamics is fundamental for many questions in ecology and conservation. Many theoretical mechanisms have been proposed whereby spatial structure can promote population persistence, in particular for exploiter–victim systems (host–parasite/pathogen, predator–prey) whose interactions are inherently oscillatory and therefore prone to extinction of local populations. Experiments have confirmed that spatial structure can extend persistence, but it has rarely been possible to identify the specific mechanisms involved. Here we use a model-based approach to identify the effects of spatial population processes in experimental systems of bean plants (Phaseolus lunatus), herbivorous mites (Tetranychus urticae) and predatory mites (Phytoseiulus persimilis). On isolated plants, and in a spatially undivided experimental system of 90 plants, prey and predator populations collapsed; however, introducing habitat structure allowed long-term persistence. Using mechanistic models, we determine that spatial population structure did not contribute to persistence, and spatially explicit models are not needed. Rather, habitat structure reduced the success of predators at locating prey outbreaks, allowing between-plant asynchrony of local population cycles due to random colonization events.