Optimal Population Level Research Articles

Optimal impulsive harvesting strategy of a stochastic Gompertz model in periodic environments

This research focuses on optimal impulsive harvesting strategy of a stochastic Gompertz model with periodic coefficients. By investigating the associated Hamilton function, the explicit expressions of the optimal impulsive effort, the maximum annual yield and the expectation of the optimal population level are provided. The theoretical results are also utilized to investigate the optimal impulsive harvesting strategy of scallop (Pecten maximus) fishery in the Saint Brieuc Bay, France.

Probability pooling for dependent agents in collective learning

The use of copulas is proposed as a way of modelling dependencies between different agents' probability judgements when carrying out probability pooling. This is combined with an established Bayesian model in which pooling is viewed as a form of updating on the basis of probability values provided by different individuals. Adopting the Frank family of copulas we investigate the effect of different assumed levels of comonotonic dependence between individuals, in the context of a collective learning problem in which a population of agents must reach consensus on which of two mutually exclusive and exhaustive hypotheses is true. In this scenario agents receive evidence from two sources; directly from the environment and also from other agents in the form of probability judgements. They then apply Bayesian updating to the former and probability pooling to the latter. We carry out multi-agent simulation experiments and show that optimal population level performance is obtained under the assumption of some degree of comonotonicity between agents, and consequently show that the standard assumption of agent independence is suboptimal. This is found to be particularly true of scenarios where there is a large amount of noise and very low amounts of direct evidence. Finally, we investigate dynamic environments in which the true state of the world changes and show that identifying the optimal level of agent dependency has an even greater effect on performance than for static environments in which the true state remains constant.

Expansion, Exploitation and Extinction: Niche Construction in Ephemeral Landscapes

We aim to understand general consequences of niche construction on metapopulation dynamics in ephemeral landscapes. To this effect, a contact process-like stochastic spatial model is introduced where local populations colonize and go extinct on a dynamic landscape of habitable and destroyed patches. In contrast to previous models, where the extinction threshold is a consequence of available niche rendered by global rates of patch destruction/renewal, here we investigate how the metapopulation persists when they are the sole generators of their own niche. Niche construction is full-filled by localized populations through the transformation of destroyed patches in their neighborhood to viable habitat for future colonization. With this theoretical framework we are able to address the dual nature of niche construction by investigating the ephemerality of the landscape (destruction rate) and the continuum of population level strategies, where construction comes at a cost to colonization. Using mean field theory and Monte Carlo simulations of the model, we are able to quantify optimal population level strategies in a wide range of ephemeral landscapes. Interestingly, we observe qualitative differences at the extinction threshold between analytic and numeric results. Investigating this discrepancy further, we find that increasing niche construction neighborhood in the spatial model leads to two interrelated effects i) an increased rate in range expansion ii) a loss in resiliency and return of the discontinuous transition at the extinction threshold. Furthermore, in the discontinuous regime of the model, spatial clustering prior to a critical transition disappears. This is a significant finding as spatial clustering has been considered to be an early warning signal before ecosystems reach their ‘tipping point’. In addition to maintaining stability, we find local niche construction strategies have an advantage when in scramble competition with an exploiter strategy because of their ability to monopolize the constructed niche due to spatial adjacency. As the niche construction neighborhood expands this advantage disappears and the exploiter strategy out-competes the niche constructor. In some cases the exploiter pushes the niche constructor to extinction, thus a tragedy of the commons ensues leading to ‘ecological suicide’ and a collapse of the niche.

Asymptotically periodic solution and optimal harvesting policy for Gompertz system

In this paper, the single species modelled by (asymptotically) periodic Gompertz equation is investigated. It is shown that the (asymptotically) periodic system has a unique (asymptotically) periodic solution which is globally asymptotically stable for the positive solution. When the nonautonomous Gompertz equation is subject to harvesting, we study the optimal harvesting policy for the periodic system and obtain the corresponding optimal population level and the maximum sustainable yield. Further, when the functions in the exploited Gompertz system are stably bounded functions, we study the ultimately optimal harvesting policy. By choosing the average limiting maximum sustainable yield as management objective, the corresponding optimal population level is determined.

A multi-level examination of school programs, policies and resources associated with physical activity among elementary school youth in the PLAY-ON study.

BackgroundGiven the decline in physical activity (PA) levels among youth populations it is vital to understand the factors that are associated with PA in order to inform the development of new prevention programs. Many studies have examined individual characteristics associated with PA among youth yet few have studied the relationship between the school environment and PA despite knowing that there is variability in student PA levels across schools.MethodsUsing multi-level logistic regression analyses we explored the school- and student-level characteristics associated with PA using data from 2,379 grade 5 to 8 students attending 30 elementary schools in Ontario, Canada as part of the PLAY-Ontario study.ResultsFindings indicate that there was significant between-school random variation for being moderately and highly active; school-level differences accounted for 4.8% of the variability in the odds of being moderately active and 7.3% of the variability in the odds of being highly active. Students were more likely to be moderately active if they attended a school that used PA as a reward and not as discipline, and students were more likely to be highly active if they attended a school with established community partnerships. Important student characteristics included screen time sedentary behaviour, participating in team sports, and having active friends.ConclusionFuture research should evaluate if the optimal population level impact for school-based PA promotion programming might be achieved most economically if intervention selectively targeted the schools that are putting students at the greatest risk for inactivity.

A Multi-Level Examination of the Association Between Older Social Models in the School Environment and Overweight and Obesity Among Younger Students

Few studies have examined how school characteristics are associated with obesity. The purpose of this study was to examine the student- and school-level characteristics associated with being overweight and obese among 12,049 students in grades 9 and 10 (junior students) attending 76 secondary schools in Ontario, Canada. The sample was 49.2% female and the average age was 14.7years. Overall, 15.0% of the sample was considered overweight and 6.3% of the sample was considered obese. Multi-level regression analysis revealed significant between-school random variation for the likelihood of a junior student (grade 9 or 10) being overweight or obese. For each 1% increase in the prevalence of obese senior students (grade 11 and 12) at a school, the odds of a junior student at that school being overweight or obese increased significantly. Important student-level characteristics included physical activity, screen time sedentary behaviour (e.g., watching television), participation in varsity sports and gender. Future research should evaluate if the optimal population level impact for school-based obesity prevention programming might be achieved by targeting the schools that are putting students at the greatest risk.

Optimal environmental and industrial policies and imperfect agglomeration effects

AbstractThis paper examines a simple general equilibrium model that considers problems related to agglomeration, technology, and the environment. First, it is shown that the manufactured goods sector converts from classical technology with constant returns to scale to modern technology with increasing returns to scale as the regional population increases. The optimal pollution level might be an inverted‐U shape with respect to population if optimal environmental policy is adopted. Second, the optimal population level of conversion is not attained in the market economy. The labour that is devoted to the manufactured goods sector in the market economy is too small. So, we derive the optimal subsidy rates to the manufactured goods sector to make resource allocation optimum. Third, we consider migration using the two‐region model. One region becomes a large city and the other region becomes a rural area if the total population is large. The industrial policy tends to extend the population difference between city and rural areas. On the other hand, if the total population is small, a symmetric point will be stable equilibrium.

Demographic and Technological Growth in the Tourism Market

This paper examines, in a differential game framework, demographic and technological growth in the tourism market. The number of tourists is assumed to follow a logistic growth, being influenced by demographic and technological factors, as well as the size of the market and investment in the tourism industry. The market for tourism is an oligopoly with differentiated products. In the steady-state equilibrium, the optimal population level of tourists is directly proportional to optimal investments in infrastructure, and they increase with demographic and technological factors and the size of the market and decrease with the number and diminished differentiation of destinations, production costs for tourism service and investment and the impatience of the tourism authority.

Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.

OPTIMAL IMPULSIVE HARVESTING OF A SINGLE-SPECIES WITH GOMPERTZ LAW OF GROWTH

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.

Optimal impulsive control in periodic ecosystem

In this paper, the impulsive exploitation of single species modelled by periodic Logistic equation is considered. First, it is shown that the generally periodic Kolmogorov system with impulsive harvest has a unique positive solution which is globally asymptotically stable for the positive solution. Further, choosing the maximum annual biomass yield as the management objective, we investigate the optimal harvesting policies for periodic logistic equation with impulsive harvest. When the optimal harvesting effort maximizes the annual biomass yield, the corresponding optimal population level, and the maximum annual biomass yield are obtained. Their explicit expressions are obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. In particular, it is proved that the maximum biomass yield is in fact the maximum sustainable yield (MSY). The results extend and generalize the classical results of Clark [Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, 1976] and Fan [Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165–177] for a population described by autonomous or nonautonomous logistic model with continuous harvest in renewable resources.

Optimal harvesting policies for periodic Gompertz systems

In this paper, we study the periodic Gompertz system with harvesting. First, we analyze the system with continuous harvesting and obtain the maximum annual-sustainable yield, the optimal harvesting effort and the optimal population level for such a system. Then, the harvesting is assumed to occur at fixed moments every year, and we establish the Gompertz system with impulsive perturbation. And we investigate the impulsive harvesting policy to maximize the annual yield and to keep the population sustainable development. At last, the optimal results of the impulsive harvesting system are compared with those of the continuous harvesting system.

Optimal harvesting policy for single population with periodic coefficients.

In this paper, we examine the exploitation of single population modeled by time-dependent Logistic equation with periodic coefficients. First, it is shown that the time-dependent periodic Logistic equation has a unique positive periodic solution, which is globally asymptotically stable for positive solutions, and we obtain its explicit representation. Further, we choose the maximum annual-sustainable yield as the management objective, and investigate the optimal harvesting policies for constant harvest and periodic harvest. The optimal harvest effort that maximizes the annual-sustainable yield, the corresponding optimal population level, the corresponding harvesting time-spectrum, and the maximum annual-sustainable yield are determined, and their explicit expressions are obtained in terms of the intrinsic growth rate and the carrying capacity of the considered population. Our interesting and brief results generalize the classical results of Clark for a population described by the autonomous logistic equation in renewable resources management.

A stochastic model for the economic management of a renewable animal resource

An optimal economic harvesting policy, which maximizes the present value of an animal population, capable of renewing itself, is discussed. It is assumed that, unhindered, the successive population levels, X n , form a Markov chain, with transitions X n+1=ƒ(X n) + ϵ nƒ(X n) , where f is the recruitment function, and {ϵ n } is an iid sequence of random shocks. When a positive set-up cost is present an optimal policy is of the ( S, s) type. The optimal population level is compared with that of an equivalent deterministic model. Bioeconomic conditions, which imply the optimality of conservation, or extinction are investigated.

Effects of Weather, Nitrogen and Population on Corn Yield Response1

AbstractThe effects of rainfall and temperature on the yield and response of corn (Zea Mays L.) to plant population and nitrogen application rates were estimated from experimental data collected at three Missouri sites over an 8‐year period. The growing season from May through August was divided into 15‐day periods to test for the effect of rainfall and temperature on corn response to several nitrogen and planting rates. Preseason rainfall and total rainfall during the growing season also were included as variables. Both temperature and rainfall variables affected yield significantly with the first half of August being most significant with respect to rainfall and the second half of May with respect to temperature. The economic optimum inputs at the mean rainfall for the growing season were 41,850 plants/ha and 163 kg N/ha. The optimal input of nitrogen was relatively sensitive to the rainfall level with the optimal population level less affected.