Sensitivity Of Population Growth Rate Research Articles

Population Research Priorities for Black Terns Developed from Modeling Analyses

-Black Tern (Chlidonias niger) populations are threatened in several regions of North America and are increasingly the subject of monitoring and research efforts. To focus future studies on critical information needs, I used a population model to determine the sensitivity of population growth rate (r) of Black Terns to reproductive and survival estimates commonly measured in field studies, and developed research priorities based on these results and a review of the literature. Sensitivity was estimated by two methods: 1) percent change in rresulting from a 10% increase in a parameter's value and 2) percent change in r resulting from an increase in the value of a parameter by an increment equal to 10% of the range of field estimates for that parameter. For 10% changes in baseline rates, rwas more sensitive to adult (168% increase in r) and sub-adult survival (62%) rate than to reproductive estimates (4-31%) as expected; however, when sensitivity was examined relative to variation in estimates for wild populations, adult survival, chick survival and nest success had similar effects (33-38%). Clutch size, hatchability, renesting rate, proportion of 2-year-old terns breeding, and longevity had relatively less influence on r (4-10%). Adult and chick survival rates should be high priorities for future study because adult rates are important for evaluating breeding success data and chick survival rates are needed to estimate productivity. Sub-adult survival is important, but will be difficult to study in small populations. Clutch size and hatchability information should have lower priorities. Although sensitivity to renesting rate was low, the lack of information justifies a greater emphasis. For nest success, the research emphasis needs to change from monitoring rates to quantifying limiting factors. Received 19 April 2000, ac-

Using elasticity analysis of demographic models to link toxicant effects on individuals to the population level: an example

1. A simple two‐stage population model was applied to data from a previously published life‐table response experiment (LTRE), which examined the toxicity of 4‐n‐nonylphenol to life‐history traits of the polychaete Capitella sp. I. Population growth rates (λ) and the relative sensitivities (= elasticities) of λ to changes in each of the individual life‐history traits were calculated. 2. In the present study, the life‐history parameters measured in laboratory‐reared individuals were manipulated to simulate potential effects of competition and predation on fecundity, time to reproductive maturity and juvenile survival to explore how such factors might influence the sensitivity of population growth rate to toxicant‐caused changes in individual life‐history traits. 3. Dramatic changes in elasticity patterns among simulations indicate that population growth rates may respond very differently to toxicant exposure depending on the extent to which other demographically limiting factors (e.g. competitors and/or predators) are operating on the population. 4. Effectively predicting the population‐level consequences arising from toxicant effects measured on individuals can be improved by exploring the elasticity pattern of λ for the population over a range of realistic ecological situations.

Selection pressures on vital rates in density–dependent populations

For density–independent populations, the sensitivity of population growth rate to changes in individual vital rates indicates the strength of selection on different parts of the life history. Here I show how this approach may be extended to any density–dependent and/or stochastic population model, including those that show cyclic, quasi–periodic and chaotic dynamics. One calculates the influence of individual vital rates on the outcome of competition between two almost identical life histories. The outcome of this competition is determined by the invasion exponent ϑ introduced by Rand. This is the Lyapunov exponent of the linearized system describing the invasion of a population with one life history by a variant type with another. Demographic sensitivities are given by the partial derivatives of ϑ with respect to the individual vital rates of the invading type. The density–independent analysis is a special case of this general framework. Sensitivities can often be obtained analytically when the population has a stable equilibrium point, and can be calculated by numerical differentiation in other cases. One can also use the methodology to examine selection pressures on the parameters describing density dependence and, if there are trade–offs between vital rates, it can be used to determine optimal life histories. A two age–class example shows that the occurrence of nonlinear dynamics can markedly alter selection pressures on a life history from those which operate when the population has a stable equilibrium point.

Spatiotemporal variation in predispersal seed predation intensity.

The effect of predispersal seed predation by Bruchus atomarius (Bruchidae, Coleoptera) on individual performance and population dynamics of the perennial forest herb, Lathyrus vernus (Leguminosae), was investigated in 11 permanent plots over 4 years. Seed predation and parameters describing intra-specific neighbour distance, plant size, inflorescence size, flowering phenology and current and previous herbivore damage were measured on all plants. In addition, demographic information from all plots was analysed using transition matrix population models in order to estimate the influence of seed predation on population growth rates. Predispersal seed predation rates differed significantly among years. Plot averages ranged from 0 to 83.7%. However, most of the variation occurred among individuals. Within individuals there was no consistency in predation rates among years. Exposure to herbivory, plant size and flowering phenology did not affect predation rates but individuals with larger inflorescences suffered from significantly higher predation. Seed predation in L. vernus was not influenced by neighbour distances of individual plants but it was positively correlated with the average density of seeds within plots, suggesting that seed predation is density dependent at the patch level. The reduction in population growth rate due to seed predation ranged from 0 to 7.6%. The sensitivity of population growth rate to reductions in seed production varied considerably among years and plots. This variation was mainly due to differences in the reproductive value of seeds and seedlings. The intensity of seed predation over the range found was not correlated with changes in population growth rate. The results of this study suggest that the influence of external factors, like seed predation, on population growth rate largely depends on the demographic transition rates in the investigated population.

Stem Dynamics of the Shrub Alnus Incana SSP. Rugosa: Transition Matrix Models

We constructed transition matrices from observed rates of sprout production and stem growth in two New York state populations of a clonal shrub, Alnus incana ssp. rugosa. The largest real eigenvalue of the transition matrix, l, summarized current population rates of growth. An old—field alder thicket showed slow population decline over all 3 yr of study. The other population, in an undisturbed natural swamp, showed decline in each year but overall increase when data from all 3 yr were combined. Sensitivity matrices were calculated from the stable size distributions and reproductive value vectors for each 3 yr matrix. Sensitivity of population growth rates to specific transitions was illustrated by changing values of the matrix elements and calculating resultant 1 values. Population growth rates were least affected by changes in survivorship of small stems, and most affected by altering sprout production rates and large stem survivorship. Annual variations in demographic rates, and comparisons between actual stem size class distributions and the stable distributions predicted by the matrix models, confirmed the inadequacy of assuming constant transition probabilities. In such a case, transition matrix models are best viewed not as projections of long—term population behavior, but as indicators of current demographic trends.

Transient Behavior and Life History Analysis of Teasel (Dipsacus Sylvestris Huds.)

A transient behavior analysis of the population dynamics of an herbaceous plant species (teasel, Dipsacus sylvestris Huds.) was developed to contrast with the long—term limiting response analysis of an earlier study. Following the arrival of a cohort of seeds at a site, there is typically an immediate increase in the rate of growth of rosette cover and the rate of seed production, followed by a decline several years later. This decline, caused by shifts in the stage structure of the population, may be critical in determining success or failure of a colonization episode. Simple calculations of the rate at which a population of Dipsacus might expand in space show that density effects on numbers of adult plants will become important in 15—20 yr. This conclusion supports the use of transient analysis in addition to the standard limiting behavior analysis, which assumes a constant environment over long time intervals. The reproductive value of Dipsacus increases exponentially from one stage to the next, and as a power function of accumulated biomass. A hint of a sigmoid response of reproductive value to biomass suggests that the transition from the vegetative rosette to the flowering stage may have evolved in response to the rate of accumulation of reproductive value as plant biomass increases. The response of Dipsacus to a variety of hypothetical changes in life history parameters was examined. A general method of calculating the sensitivity of population growth rate (lamda)_m was developed; when applied to the teasel model it showed that (lamda)_m is most sensitive to changes in the growth and reproduction of early stages. Delayed seed germination is not important to long—term population growth; the complete elimination of delayed germination from the model caused no more than a 4% decrease in (lamda)_m. It may be much more important in terms of transient behavior; elimination of delayed germination depressed the initial decline in rosette cover by up to 72%. If this decline delays the colonization process, the most important populational effect of delayed germination would be an increase in the probability that an attempted colonization will be successful. We also examined the optimality of the current biennial life history of Dipsacus, relative to both annual and perennial alternatives. The shift to an annual strategy is rendered suboptimal by the low probability of germination and survival of seeds relative to the probability of survival of rosettes, and by the high growth potential of rosettes. This growth potential increases the energy available for seed production by an order of magnitude over the hypothetical annual strategy, greatly increasing the reproductive value of the biennial flowering plants. The switch to a perennial habit is suboptimal because of the cost, in annual reproductive output, of maintaining a perennial flowering plant. This effect is greatest in rapidly growing populations. There seem to be no important differences between the transient and the limiting behavior analyses of life history optimality. Our direct, rather than inferred, demonstration of the optimality of teasel's life history supports the development of current theory based on optimality assumptions

The sensitivity of population growth rate to pertubations in the life cycle components

A discrete model representing the age distribution of a population in terms of the birth rate and death rate of different age groups is described. Applying this model, we derive inequalities that (1) order the sensitivity of the growth rate with respect to perturbations in (a) fecundity of each age class, and (b) probability of survival from one age class to the next; (2) compare for each class the sensitivity of the growth rate with respect to variations in (a) and (b). Interpretations of these results as regards strategies for colonizing species are discussed.