Hal Caswell

A Stage‐Based Population Model for Loggerhead Sea Turtles and Implications for Conservation

Management of many species is currently based on an inadequate under- standing of their population dynamics. Lack of age-specific demographic information, particularly for long-lived iteroparous species, has impeded development of useful models. We use a Lefkovitch stage class matrix model, based on a preliminary life table developed by Frazer (1983a), to point to interim management measures and to identify those data most critical to refining our knowledge about the population dynamics of threatened log- gerhead sea turtles (Caretta caretta). Population projections are used to examine the sen- sitivity of Frazers life table to variations in parameter estimates as well as the likely response of the population to various management alternatives. Current management practices appear to be focused on the least responsive life stage, eggs on nesting-beaches. Alternative protection efforts for juvenile loggerheads, such as using turtle excluder devices (TEDs), may be far more effective.

DEMOGRAPHY AND DISPERSAL: CALCULATION AND SENSITIVITY ANALYSIS OF INVASION SPEED FOR STRUCTURED POPULATIONS

A fundamental characteristic of any biological invasion is the speed at which the geographic range of the population expands. This invasion speed is determined by both population growth and dispersal. We construct a discrete-time model for biological invasions that couples matrix population models (for population growth) with integrodifference equa- tions (for dispersal). This model captures the important facts that individuals differ both in their vital rates and in their dispersal abilities, and that these differences are often determined by age, size, or developmental stage. For an important class of these equations, we demonstrate how to calculate the populations asymptotic invasion speed. We also derive formulas for the sensitivity and elasticity of the invasion speed to changes in demographic and dispersal parameters. These results are directly comparable to the familiar sensitivity and elasticity of population growth rate. We present illustrative examples, using published data on two plants: teasel (Dipsacus sylvestris) and Calathea ovandensis. Sensitivity and elasticity of invasion speed is highly correlated with the sensitivity and elasticity of pop- ulation growth rate in both populations. We also find that, when dispersal contains both long- and short-distance components, it is the long-distance component that governs the invasion speed-even when long-distance dispersal is rare.

LIFE HISTORIES AND ELASTICITY PATTERNS: PERTURBATION ANALYSIS FOR SPECIES WITH MINIMAL DEMOGRAPHIC DATA

Elasticity analysis is a useful tool in conservation biology. The relative impacts of proportional changes in fertility, juvenile survival, and adult survival on asymptotic population growth λ (where ln(λ) = r, the intrinsic rate of increase) are determined by vital rates (survival, growth, and fertility), which also define the life history characteristics of a species or population. Because we do not have good demographic information for most threatened populations, it is useful to categorize species according to their life history characteristics and related elasticity patterns. To do this, we compared the elasticity patterns generated by the life tables of 50 mammal populations. In age-classified models, the sum of the fertility elasticities and the survival elasticity for each juvenile age-class are equal; thus, age at maturity has a large impact on the contribution of juvenile survival to λ. Mammals that mature early and have large litters (“fast” mammals, such as rodents and smaller carnivores) also...

PREDATOR-MEDIATED COEXISTENCE: A NONEQUILIBRIUM MODEL

There is now convincing evidence, from a variety of ecological systems, that predation is capable of maintaining coexistence among a set of competing prey species, some of which would be excluded in its absence. This interaction has been suggested as a major factor determining the structure of some communities, but attempts to incorporate it into the mathematical framework of population theory have been frustrating. Although the possibility of predator-mediated coexistence is easily shown, parameter-space studies of simple three-species models suggest that it is an improbable occurrence, requiring a very delicate balancing of parameter values. To attack this problem, I classify population systems as open or closed, and equilibrium or nonequilibrium. Closed systems consist of a single homogeneous patch of habitat; open systems, in their simplest form, are a collection of such patches (or cells) connected by migration. Equilibrium theories are restricted to behavior at or near an equilibrium point, while nonequilibrium theories explicitly consider the transient behavior of the system. Almost all of the work on predator-mediated coexistence has been limited to closed, equilibrium systems. In such studies conditions are sought which guarantee that predation results in a stable equilibrium at which all species are present. A general property of open systems is that transient, nonequilibrium behaviors may persist for extremely long periods of time. A model is presented which uses this fact to generate long-term, but nonequilibrial, coexistence among competitors under the impact of predation. The model is a discrete, or logical, model, in which presence and absence of each of two competitors and a predator is followed in a set of stochastically connected local population cells. The predator acts to open up new cells for nonequilibrium growth of the prey species. All forms of predator-mediated coexistence other than the open-system, nonequilibrium effect were purposely eliminated from the model. The results of the model clearly demonstrate the possibility of long-term predator-mediated coexistence in such a system. In spite of stacking the deck against it, the positive effect of the predator on coexistence is statistically highly significant. Moreover, a crude evolutionary analysis suggests that the effect is not only possible, but probable. These results can be generalized far beyond the highly abstracted framework of the model. Such generalizations suggest that this phenomenon may be of major importance in natural systems. The predictions of the model can be tested against the real world in several ways. First, it predicts the possibility of predator-mediated coexistence, which agrees with the numerous observations of that phenomenon. More importantly, it makes predictions (concerning the spatial and temporal organization of the predation process) that distinguish it from the other modes of predator-mediated coexistence. These predictions are corroborated by observations of a number of cases where predation has failed to generate coexistence. The distinction between closed and open, equilibrium and nonequilibrium, population systems has an important impact on the form and substance of ecological theory.

Structured-population models in marine, terrestrial, and freshwater systems

Part 1: Theory and methods. Structured-population models: many methods, a few basic concepts H. Caswell, S. Tuljapurkar, R. Nisbet, A. de Roos. Matrix methods for population analysis H. Caswell. Stochastic matrix population models S. Tuljapurkar. Delay-differential equations for structured populations R. Nisbet. A gentle introduction to physiologically structured population models A. de Roos. Nonlinear matrix equations and population dynamics J.M. Cushing. Part II: Applications. The relative importance of life-history stages to population growth: prospective and retrospective analyses C. Horvitz, D.W. Schemske, H. Caswell. Life history evolution and extinction S.H. Orzack. Population dynamics of Tribolium R. Desharnais. Evolutionary dynamics of structured populations J. Kumm, S. Mylius, D. Promislow. The effects of overlapping generations and population structure on gene-frequency clines O.E. Gaggiotti, C.E. Lee, G. Wardle. Dynamics of population with density-dependent recruitment and age structure L. Botsford. Models for marine ecosystems E. Hofmann. Frequency response of a simple food-chain model with time-delayed recruitment: implications for abiotic-biotic coupling B.C. Monger, J.M. Fischer, B.A. Grantham, V. Medland, B. Cai, K. Higgins. Stochastic demography for conservation biology C.S. Nations, M. Boyce. Sensitivity analysis of structured-population models for management and conservation P. Dixon, N. Friday, P. Ang, S. Heppel, M. Kshatriya. Nonlinear ergodic theorems and symmetric vs. asymmetric competition K.M. Crowe. The evolution of age-structured marriage functions: it takes two to tango C. Castillo-Chavez, S. Hsu Schmitz. Inverse problems and structured-population dynamics S.N. Wood . Nonlinear models of structured populations: dynamic consequences of stage structure and discrete sampling J. Val, F. Villa, K. Lika, C. Boe. Multispecies lottery competition: a diffusion analysis J.S. Hatfield, P.L. Chesson. About the authors. Index.

PROSPECTIVE AND RETROSPECTIVE PERTURBATION ANALYSES: THEIR ROLES IN CONSERVATION BIOLOGY

Demographic perturbation analysis explores how population statistics (especially population growth rate λ) respond to changes in the vital rates (survival, growth, development, reproduction, and so on). Perturbation analysis is used in two logically distinct ways. Prospective analyses (sensitivity and elasticity) explore the functional dependence of λ on the vital rates. They predict the changes in λ that would result from any specified change in the vital rates and are independent of previous patterns of variability of the vital rates. Retrospective analyses (life table response experiment [LTRE] methods and other kinds of variance decomposition) express observed variation in λ as a function of observed (co)variation in the vital rates. Their results are specific to the observed pattern of variation. Sensitivity and elasticity analysis can be used to identify potential management targets because changes in vital rates with high sensitivity or elasticity will produce large changes in λ. Sometimes that potential may not be realized because it is difficult or impossible to change those vital rates. Retrospective analyses cannot identify potential management targets because they compare the contributions of past changes in vital rates, not the effects of future changes. Just as the results of heritability analysis say nothing about the efficacy of clinical treatments, so the results of retrospective analysis say nothing about the efficacy of potential management tactics. Perturbation analysis is a powerful tool with important implications for conservation. It is important that perturbation analyses be applied properly.

A general formula for the sensitivity of population growth rate to changes in life history parameters.

This paper considers the sensitivity of population growth to small changes in birth, growth, survival, and migration probabilities for an arbitrary population classification (i.e., age, instar, size, developmental stage, age, and spatial location, etc.). The stage-specific life history parameters are expressed in a discrete-time system of linear difference equations, the dominant eigenvalue of which defines the population growth rate. The sensitivity of this eigenvalue to production of class i by class j individuals is shown to be proportional to the product of the reproductive value of stage i and the abundance of stage j in the stable stage distribution. This formula is readily computable, and several examples are presented. For the special case of age-structured populations, this formula reduces to those derived by Hamilton, Emlen, and Goodman.

Population Growth Rates and Age Versus Stage‐Distribution Models for Teasel (Dipsacus Sylvestris Huds.)

Mathematical models are developed to examine the population—level response of an herbaceous plant species (teasel, Dipsacus sylvestris Huds.) which was experimentally introduced into several habitats and monitored for 5 yr. Models based on morphological stages (size) rather than chronological age give more satisfactory results. Populations growth rates (λm) range from 0.63 to 2.60, which are likely typical for fugitive plants. Values are interpreted as responses to both external and internal factors. Grass litter, and the presence of other dicotyledonous species, and the overall primary productivity of the rest of the community are important factors determining the success or failure of an attempted colonization by teasel. Individual plant and population—level growth rates seem to be determined independently.

Diversity of ageing across the tree of life

Evolution drives, and is driven by, demography. A genotype moulds its phenotype’s age patterns of mortality and fertility in an environment; these two patterns in turn determine the genotype’s fitness in that environment. Hence, to understand the evolution of ageing, age patterns of mortality and reproduction need to be compared for species across the tree of life. However, few studies have done so and only for a limited range of taxa. Here we contrast standardized patterns over age for 11 mammals, 12 other vertebrates, 10 invertebrates, 12 vascular plants and a green alga. Although it has been predicted that evolution should inevitably lead to increasing mortality and declining fertility with age after maturity, there is great variation among these species, including increasing, constant, decreasing, humped and bowed trajectories for both long- and short-lived species. This diversity challenges theoreticians to develop broader perspectives on the evolution of ageing and empiricists to study the demography of more species.

Demography of the endangered North Atlantic right whale

Northern right whales (Eubalaena glacialis) were formerly abundant in the northwestern Atlantic, but by 1900 they had been hunted to near extinction. After the end of commercial whaling the population was thought to be recovering slowly; however, evidence indicates that it has been declining since about 1990 (ref. 1). There are now fewer than 300 individuals, and the species may already be functionally extinct owing to demographic stochasticity or the difficulty of females locating mates in the vast Atlantic Ocean (Allee effect). Using a data set containing over 10,000 sightings of photographically identified individuals we estimated trends in right whale demographic parameters since 1980. Here we construct, using these estimates, matrix population models allowing us to analyse the causes of right whale imperilment. Mortality has increased, especially among mother whales, causing declines in population growth rate, life expectancy and the mean lifetime number of reproductive events between the period 1980–1995. Increased mortality of mother whales can explain the declining population size, suggesting that the population is not doomed to extinction as a result of the Allee effect. An analysis of extinction time shows that demographic stochasticity has only a small effect, but preventing the deaths of only two female right whales per year would increase the population growth rate to replacement level.