Leslie Matrix Model Research Articles

The ultimate-sustainable-yield problem in nonlinear age-structured populations

The Beverton-Holt theory of harvesting a multicohort fishery subject to constant recruitment, and the Leslie matrix harvesting model modified to include a nonlinear stock-recruitment relationship, are extended and shown to be related through the ultimate-sustainable-yield problem for an age-structured population. The well-known result that the optimal harvesting policy for the Leslie matrix model is bimodal is shown to hold for the Leslie matrix model modified to include an arbitrary stock-recruitment relationship. This conclusion extends a recent result of Reed (1979), who proved biomodality of the optimal harvesting strategy for the Leslie matrix model modified to include only compensatory stock-recruitment relationships. The paper concludes with a numerical example which demonstrates how the ultimate sustainable yield can be used as a standard of comparison for any sustainable-yield harvesting policy.

A development of the Leslie matrix formulation for restructuring and extending an ecosystem model: The infestation of stored wheat by Sitophilus oryzae

The basis for this study is a published model (J. Appl. Ecol., 15: 65–87) that simulates the temporal behavior of a population of rice weevils ( Sitophilus oryzea, L.) reared in small cells of wheat, and the environmental changes associated with population growth. This model was conceived and defined solely in terms of a FORTRAN algorithm. Such a structure was found to be flexible, and hence convenient, in the early stages of model development; in later stages, however, the mass of detail incorporated in the computer algorithm limited the model's development and made a full and comprehensible description of the model impossible. Thus we attempted to separate as much as possible of the underlying mathematical model from the computer algorithm. In order to facilitate this we extended the classical Leslie matrix model to describe the temporal behavior both of the weevil population and of relevant aspects of the environment. This model structure allowed a full and comprehensive statement of the complex algorithmically-defined model, and facilitated its extension from simulating a homogeneous to simulating a heterogeneous environment. The extended model was used to look at the effectiveness of various degrees of gas-tightness, for various initial temperatures and initial weevil densities, during winter storage of wheat in an underground granary.

Applications of transition matrix models in forest dynamics: Araucaria in Papua New Guinea and Nothofagus in New Zealand

This paper describes the application of the Leslie matrix model to single species populations, and a similar transition matrix model to communities of more than one species. Examples are drawn from populations of Araucaria spp. in tropical rainforest in Papua New Guinea, and from Nothofagus fusca stands in temperate montane forest in New Zealand. Both species generally had λ values close to 1.0 (r, the intrinsic rate of natural increase ≃ 0) and in both cases predicted trends were consistent with other ecological information from the stands or elsewhere. Various possible sources of error and empirical tests of the sensitivity of the single species model and the accuracy of its predictions are described. It is concluded that, despite certain limitations, with careful interpretation these models constitute an important tool for the investigation of forest dynamics. The basic model may be modified in various ways, for example, to include vegetative reproduction, or put to use in practical problems such as defining a harvesting strategy for a forest tree species. In studies of succession involving long-lived species these models are particularly valuable, not only for predicting the magnitude and direction of future changes, but also because they suggest a time scale for the trends, and this can then be evaluated in the light of other knowledge about the communities in question. Moreover, the variability of λ values obtained for differen species relates to their life cycle strategies, so that by the use of Leslie matrices it may be possible objectively to rank the species of a community along the continuum of r to k strategies.

The Sensitivity of the Stationary Age Class Distribution o Changes in the Life History Components

AbstractThe influence of the various components of the life history on the stationary age class distribution of a population was studied by applying the Leslie matrix model and then considering the single age class frequencies as well as the average age and the cumulative age class distribution in the stationary state.Since, for fixed survival probabilities, the effects of the (age specific) fecundities were shown to be already expressed by the (ultimate) growth rate, this investigation was concentrated on the influence of the survival probabilities and the growth rate. After having supplemented some useful details concerning the dependence of the growth rate on the life history and introduction of the shift concept as an interpretation of cumulative distributions, the mathematical results could be given a biologically intelligible meaning:An increase in the growth rate for fixed survival probabilities is followed by a shift of all age class frequencies to earlier ages. Whereas age specific changes in fecundity do not result in age specific changes in the stationary age class distribution, increases in survival up to and including age k, say, do exhibit such changes in that they cause a shift of age class frequencies at least from those ages exceeding k to earlier ages.

Population growth with stochastic fluctuations in the life table

Monte Carlo simulations with the Leslie matrix and similar population models show that as the variance in survivorship or fecundity increases, the expected population growth rate decreases. This is attributed to Jensen's inequality with the observation that the rate of increase is a concave function of age-specific survivorship and fertility rates. Applications of this observation are advised for demographic studies, population simulation, optimal harvest strategies, and natural selection for variance in fertility and survivorship rates.

Le modele matriciel deterministe de Leslie et ses applications en dynamique des populations

The Leslie matrix model (Leslie, 1945) for discrete population growth has been modified and used several times in population dynamics. A review is given of the basic model (nt + 1 = Ant) and of its principal modifications. The modifications relating to the influences of ‘internal’ or ‘external’ factors to the population are studied with greater detail. The same applies to models where the population is divided in stages rather than in age classes.

Use of the Leslie Matrix for Assessing Environmental Impact with an Example for a Fish Population

The Leslie matrix model for discrete population theory is examined for the assessment of the effects of environmental alterations on a species population using an eigenvalue analysis. This analysis provides estimates of population growth rate and stable age distribution. A sensitivity analysis is conducted for changes in elements of the population matrix and the resultant effect on population growth rate and stable age distribution. An example of this technique is presented for the cunner (Tautogolabrus adspersus). This example considers the effect of entrainment of cunner eggs and larvae at the intakes of power stations.

356. Note: Optimum Age Specific Harvesting of a Population

SUMMARY The problem of maximizing the sustainable yield from a population of constant size by altering the age composition of a crop is investigated using a simple extension of the Leslie matrix model. The cropping strategy that maximizes this yield is found to involve the complete removal of one age class, effectively reducing the age of maximum longevity of the population, and a partial removal of a second age class. A simple algorithm to find the optimum cropping strategy is described, and its application to typical demographic data is given.