An optimal hunting policy for a stochastic logistic model

1979 ◽  
Vol 16 (2) ◽  
pp. 319-331 ◽  
Author(s):  
Andris Abakuks

A stochastic version of the logistic model for population growth is considered, and the general form of an optimal policy is found for hunting the population so as to maximise the long-term average number of captures per unit time. This optimal policy is described by a critical population size x∗such that it is optimal to hunt if and only if the population size is greater than or equal to x∗. Methods of determining x∗for given parameter values are provided, and some properties of the optimal policy as the population size tends to infinity are proved.

1979 ◽  
Vol 16 (02) ◽  
pp. 319-331 ◽  
Author(s):  
Andris Abakuks

A stochastic version of the logistic model for population growth is considered, and the general form of an optimal policy is found for hunting the population so as to maximise the long-term average number of captures per unit time. This optimal policy is described by a critical population size x∗such that it is optimal to hunt if and only if the population size is greater than or equal to x∗. Methods of determining x∗for given parameter values are provided, and some properties of the optimal policy as the population size tends to infinity are proved.


1989 ◽  
Vol 26 (04) ◽  
pp. 873-879 ◽  
Author(s):  
E.G. Kyriakidis ◽  
Andris Abakuks

This paper is concerned with the problem of controlling a simple immigration–birth process, which represents a pest population, by the introduction of catastrophes which, when they occur, reduce the population size to zero. The optimality criterion is that of minimising the long-term average cost per unit time of the process. Firstly, an optimal policy is found within a restricted class of stationary policies, which introduce catastrophes if and only if the population size is greater than or equal to some critical value x. The optimality of this policy within the wider class of all stationary policies is then verified by applying the general results of Bather (1976).


2018 ◽  
Vol 45 (3) ◽  
pp. 195 ◽  
Author(s):  
Rebecca J. Hobbs ◽  
Lyn A. Hinds

Context Fertility control is seen as an attractive alternative to lethal methods for control of population size and genetic diversity in managed animal populations. Immunocontraceptive vaccines have emerged as the most promising agents for inducing long-term infertility in individual animals. However, after over 20 years of scientific testing of immunocontraceptive vaccines in the horse, the scientific consensus is that their application as a sole management approach for reducing population size is not an effective strategy. Aims The purpose of this review is to evaluate currently available non-lethal fertility-control methods that have been tested for their contraceptive efficacy in Equidae, and to assess their suitability for effective management of wild (feral) horses in an Australian setting. Key results (1) Fertility-control agents, particularly injectable immunocontraceptive vaccines based on porcine zona pellucida (PZP) or gonadotrophin-releasing hormone (GnRH), can induce multi-year infertility (up to 3 years) in the horse. Some formulations require annual or biennial booster treatments. Remote dart delivery (on foot) to horses is possible, although the efficacy of this approach when applied to large numbers of animals is yet to be determined. (2) The proportion of females that must be treated with a fertility-control agent, as well as the frequency of treatment required to achieve defined management outcomes (i.e. halting population growth in the short term and reducing population size in the long term) is likely to be >50% per annum. In national parks, treatment of a large number of wild horses over such a broad area would be challenging and impractical. (3) Fertility control for wild horses could be beneficial, but only if employed in conjunction with other broad-scale population-control practices to achieve population reduction and to minimise environmental impacts. Conclusions In Australia, most populations of wild horses are large, dispersed over varied and difficult-to-access terrain, are timid to approach and open to immigration and introductions. These factors make accessing and effectively managing animals logistically difficult. If application of fertility control could be achieved in more than 50% of the females, it could be used to slow the rate of increase in a population to zero (2–5 years), but it will take more than 10–20 years before population size will begin to decline without further intervention. Thus, use of fertility control as the sole technique for halting population growth is not feasible in Australia.


1990 ◽  
Vol 12 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Samuel Hollander

In his Presidential address to the American Economic Association, Gary Becker alludes to Thomas Malthus's “great contribution” (1988, p. 1) in a prologue to a wider exploratory discussion of some of the implications for macroeconomics flowing from recent programs in family economics. The content of the contribution as represented here (p. 2) includes diminishing returns to increases in employment “when land and other capital are fixed;” population growth positively related to the wage, the lower population growth at low wages turning on reduced birth rates (the preventive check) and increased death rates (the positive check); and a long-run equilibrium wage at which population is constant at a level determined by the production function. Becker emphasizes the stability of the equilibrium wage in the face of disturbances. A catastrophic reduction in population size (eg. the Black Death) and consequently a wage increase will be followed by positive population growth which restores both the wage and population size to their respective equilibrium levels. In the event of increases in the amount of usuable land, population size will become permanently higher with the wage ultimately reduced to its original long-run level. Becker represents Malthus as reaching “much more pessimistic conclusions about the long-term economic prospects of the average family” than, for example, Godwin and Condorcet who had maintained that the economic position of mankind will continue to improve over time.


1989 ◽  
Vol 26 (4) ◽  
pp. 873-879 ◽  
Author(s):  
E.G. Kyriakidis ◽  
Andris Abakuks

This paper is concerned with the problem of controlling a simple immigration–birth process, which represents a pest population, by the introduction of catastrophes which, when they occur, reduce the population size to zero. The optimality criterion is that of minimising the long-term average cost per unit time of the process. Firstly, an optimal policy is found within a restricted class of stationary policies, which introduce catastrophes if and only if the population size is greater than or equal to some critical value x. The optimality of this policy within the wider class of all stationary policies is then verified by applying the general results of Bather (1976).


2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yilun Shang

We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.


Author(s):  
Daniel Ochieng Achola

Objectives: To develop a mathematical model that incorporates genetic defect in estimating the growth rate of roan antelopes in Ruma National Park,Kenya.Methodology: This study has developed an improved Oksendal and Lungu’s stochastic logistic model to estimates population growth rate of roans by incorporating genetic defect that were not considered by Magin and Cock. Appropriate adjustments were made to Vortex version 9.99 a computer simulation programme to simulate the extinction process.Results: There is a high-level impact between inbreeding and population growth(survival) in small populations. Supplementation of both juvenile and adult roans ensured population survival for longer period.Conclusion: Due to unpredictable consequences to the ecosystem and conflict with wildlife management policies in protected areas, this paper recommends supplementation instead of predator control to curb inbreeding which is a major threat to small populations. Supplementation should be done in phases without causing disruption to social groups.


2019 ◽  
Vol 10 (1) ◽  
pp. 21-28
Author(s):  
Aniela Bălăcescu ◽  
Radu Șerban Zaharia

Abstract Tourist services represent a category of services in which the inseparability of production and consumption, the inability to be storable, the immateriality, and last but not least non-durability, induces in tourism management a number of peculiarities and difficulties. Under these circumstances the development of medium-term strategies involves long-term studies regarding on the one hand the developments and characteristics of the demand, and on the other hand the tourist potential analysis at regional and local level. Although in the past 20 years there has been tremendous growth of on-line booking made by household users, the tour operators agencies as well as those with sales activity continue to offer the specific services for a large number of tourists, that number, in the case of domestic tourism, increased by 1.6 times in case of the tour operators and by 4.44 times in case of the agencies with sales activity. At the same time, there have been changes in the preferences of tourists regarding their holiday destinations in Romania. Started on these considerations, paper based on a logistic model, examines the evolution of the probabilities and scores corresponding to the way the Romanian tourists spend their holidays on the types of tourism agencies, actions and tourist areas in Romania.


Author(s):  
L.V. Vetchinnikova ◽  
◽  
A.F. Titov ◽  
◽  

The article reports on the application of the best known principles for mapping natural populations of curly (Karelian) birch Betula pendula Roth var. carelica (Mercklin) Hämet-Ahti – one of the most appealing representatives of the forest tree flora. Relying on the synthesis and analysis of the published data amassed over nearly 100 years and the data from own full-scale studies done in the past few decades almost throughout the area where curly birch has grown naturally, it is concluded that its range outlined in the middle of the 20th century and since then hardly revised is outdated. The key factors and reasons necessitating its revision are specified. Herewith it is suggested that the range is delineated using the population approach, and the key element will be the critical population size below which the population is no longer viable in the long term. This approach implies that the boundaries of the taxon range depend on the boundaries of local populations (rather than the locations of individual trees or small clumps of trees), the size of which should not be lower than the critical value, which is supposed to be around 100–500 trees for curly birch. A schematic map of the curly birch range delineated using this approach is provided. We specially address the problem of determining the minimum population size to secure genetic diversity maintenance. The advantages of the population approach to delineating the distribution range of curly birch with regard to its biological features are highlighted. The authors argue that it enables a more accurate delineation of the range; shows the natural evolutionary history of the taxon (although it is not yet officially recognized as a species) and its range; can be relatively easily updated (e.g. depending on the scope of reintroduction); should be taken into account when working on the strategy of conservation and other actions designed to maintain and regenerate this unique representative of the forest tree flora.


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