Elasticity analysis as an important tool in evolutionary and population ecology

Individual effects of estrogens on a marine fish, Cunner (Tautogolabrus adspersus), extrapolated to the population level

Endocrine-disrupting chemicals (EDCs) in the environment may alter the population dynamics of wildlife by affecting reproductive output. This study describes a matrix modeling approach to link laboratory studies on endocrine disruption with potential ecological effects. The experimental model used is cunner (Tautogolabrus adspersus), which inhabit estuarine and marine areas where sewage treatment and other discharges containing estrogenic EDCs are likely. To test the effects of estrogenic exposures on fecundity, reproductively active cunner were exposed in three separate experiments by implanting 17beta-estradiol, estrone, or 17alpha-ethynylestradiol subcutaneously in a slow-release matrix at 0.05, 0.5, and 2.5 mg/kg. Egg production per gram female and egg viability were determined daily for a 1-week preexposure period and then for a 2-week exposure period. The mean number of eggs produced per gram female and egg viability (%) were calculated for the initial preexposure period and the 2-week exposure period for each experiment. Significant changes were observed in egg production per gram female in the high-17beta-estradiol treatment (P = 0.07) and high-17alpha-ethynylestradiol treatment (P = 0.04). A significant increase was observed in egg viability (%) in the low-17alpha-ethynylestradiol treatment (39.0%; P < or = 0.05). Cunner population response was projected using an age-structured matrix population model parameterized with published survival and fecundity estimates. By incorporating reproductive response data from laboratory exposures, model projections were used to describe how reproductive changes by estrogen treatment could alter cunner population growth rate (lambda). Published by Elsevier Inc.

Elasticity analyses of size-based red and white abalone matrix models: management and conservation

Prospective elasticity analyses have been used to aid in the management of fished species and the conservation of endangered species. Elasticities were examined for deterministic size-based matrix models of red abalone, Haliotis rufescens, and white abalone, H. sorenseni, to evaluate which size classes influenced population growth (lambda) the most. In the red abalone matrix, growth transitions were determined from a tag recapture study and grouped into nine size classes. In the white abalone matrix, abalone growth was determined from a laboratory study and grouped into five size classes. Survivorship was estimated from tag recapture data for red abalone using a Jolly-Seber model with size as a covariate and used for both red and white abalone. Reproduction estimates for both models used averages of the number of mature eggs produced by female red and white abalone in each size class from four-year reproduction studies. Population growth rate (lambda) was set to 1.0, and the first-year survival (larval survival through to the first size class) was estimated by iteration. Survival elasticities were higher than fecundity elasticities in both the red and white matrix models. The sizes classes with the greatest survival elasticities, and therefore the most influence on population growth in the model, were the sublegal red abalone (150-178 mm) and the largest white abalone size class (140-175 mm). For red abalone, the existing minimum legal size (178 mm) protects the size class the model suggests is critical to population growth. Implementation of education programs for novice divers coupled with renewed enforcement may serve to minimize incidental mortality of the critical size class. For white abalone, conservation efforts directed at restoring adults may have more of an impact on population growth than efforts focusing on juveniles. Our work is an example of how prospective elasticity analyses of size-structured matrix models can be used to quantitatively evaluate research priorities, fishery management strategies, and conservation options.

A hierarchical matrix model to assess the impact of habitat fragmentation on population dynamics: an elasticity analysis

To better understand the role of habitat quality and boundaries on population dynamics at the landscape scale, we develop a model combining a spatially implicit approach, a spatial population Leslie-type model and an implicit model of habitat fragmentation. An original approach of elasticity permits to identify which types of element and boundary influence the most population viability according to the wood fragmentation degree. The studied species is a corridor forest insect sensitive to fragmentation (Abax parallelepipedus, Coleoptera, Carabidae). We show that a single large patch of wood is better than several small patches for the population viability.

The Many Growth Rates and Elasticities of Populations in Random Environments

Despite considerable interest in the dynamics of populations subject to temporally varying environments, alternate population growth rates and their sensitivities remain incompletely understood. For a Markovian environment, we compare and contrast the meanings of the stochastic growth rate (lambdaS), the growth rate of average population (lambdaM), the growth rate for average transition rates (lambdaA), and the growth rate of an aggregate represented by a megamatrix (shown here to equal lambdaM). We distinguish these growth rates by the averages that define them. We illustrate our results using data on an understory shrub in a hurricane-disturbed landscape, employing a range of hurricane frequencies. We demonstrate important differences among growth rates: lambdaS<lambdaM, but lambdaA can be < or > lambdaM. We show that stochastic elasticity, ESij, and megamatrix elasticity, EMij, describe a complex perturbation of both means and variances of rates by the same proportion. Megamatrix elasticities respond slightly and stochastic elasticities respond strongly to changing the frequency of disturbance in the habitat (in our example, the frequency of hurricanes). The elasticity EAij of lambdaA does not predict changes in the other elasticities. Because ES, although commonly utilized, is difficult to interpret, we introduce elasticities with a more direct interpretation: ESmu for perturbations of means and ESsigma for variances. We argue that a fundamental tool for studying selection pressures in varying environments is the response of growth rate to vital rates in all habitat states.

Equivalence relationships between stage-structured population models

Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters (Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred.

Emerging Issues in Population Viability Analysis

Population viability analysis ( PVA) has become a commonly used tool in endangered species management. There is no single process that constitutes PVA, but all approaches have in common an assessment of a population's risk of extinction (or quasi extinction) or its projected population growth either under current conditions or expected from proposed management. As model sophistication increases, and software programs that facilitate PVA without the need for modeling expertise become more available, there is greater potential for the misuse of models and increased confusion over interpreting their results. Consequently, we discuss the practical use and limitations of PVA in conservation planning, and we discuss some emerging issues of PVA. We review extant issues that have become prominent in PVA, including spatially explicit modeling, sensitivity analysis, incorporating genetics into PVA, PVA in plants, and PVA software packages, but our coverage of emerging issues is not comprehensive. We conclude that PVA is a powerful tool in conservation biology for comparing alternative research plans and relative extinction risks among species, but we suggest caution in its use: (1) because PVA is a model, its validity depends on the appropriateness of the model's structure and data quality; (2) results should be presented with appropriate assessment of confidence; (3) model construction and results should be subject to external review, and (4) model structure, input, and results should be treated as hypotheses to be tested. We also suggest (5) restricting the definition of PVA to development of a formal quantitative model, (6) focusing more research on determining how pervasive density-dependence feedback is across species, and (7) not using PVA to determine minimum population size or (8) the specific probability of reaching extinction. The most appropriate use of PVA may be for comparing the relative effects of potential management actions on population growth or persistence.

Population viability analyses in plants: challenges and opportunities

This review of 95 plant population viability analyses (PVAs) reveals that most studies consider one species, only a few populations and are based on data collected for less than five years. Only five studies referred to themselves as PVAs. Plants offer numerous challenges, such as seed banks and periodic recruitment, but these can be answered with suitable data collection and modeling. New approaches, such as metapopulation models, inclusion of disturbance cycles, and integration of genetics and demography, are producing more realistic PVAs. Although exact solutions are fraught with limitations, plant PVAs can be useful in comparing management regimes, populations and microhabitats, and in using these results to guide conservation and management.