Narrow Results

We have simulated the effect of the diversity of the late expressed genes in the genetic pool of population on the phenotypes of individuals in the late ages. Using Penna model based on the Monte Carlo method we have obtained for the oldest fractions of populations lower mortality rates than predicted by the exponential Gompertz function. Such deviations from the expected exponential increase of mortality are the characteristic for populations which are not in equilibrium with the environment, or if a relatively high probability of reversions was assumed, or if the population is heterogeneous. In such populations, the genes expressed in the late ages, are under the very weak selection pressure and thus, highly-polymorphic. As an effect, the probability of the genetically-determined death of the oldest organisms does not grow as fast as predicted by the Gompertz exponential curve describing mortality during earlier periods of life.

We propose a simple model describing the dynamics of a system of two populations — more numerous natives and less numerous immigrants. The immigrants' birth rate is higher than that of the natives. Several modifications of this model taking into account changes of the birth rates due to external factors and/or possibility of contacts between the populations, are also introduced. The model is studied within two approaches — by solving a set of differential equations and through a Monte Carlo simulations. We show that the question of which population will eventually dominate depends on such factors as the probability of producing offsprings of mixed origin, assimilation of the immigrants, the ratio of the birth rates, initial numbers of the populations and the average age of an individual. In all, but two extreme cases, both populations will survive.

In this paper we investigate the optimal harvesting problems of a single species with Gompertz law of growth. Based on continuous harvesting models, we propose impulsive harvesting models with constant harvest or proportional harvest. By using the discrete dynamical systems determined by the stroboscopic map, we discuss existence, stability and global attractivity of positive periodic solutions, and obtain the maximum sustainable yield and the corresponding optimal population level. At last, we compare the maximum sustainable yield of impulsive harvest with that of continuous harvest, and point out that proportional harvest is superior to constant harvest.

A single species fishery model has been developed using the Gompertz law of population growth and the CPUE (Catch-per-unit-effort) hypothesis. The dynamical and the bionomic steady states were determined and their natures were examined from the biological as well as economic view points. The optimal harvest policy is discussed by taking the fishing effort as a dynamic control variable. The results are compared with those of the Schaefer model [10].