No abstract

We consider a model of exploitation of a size-structured population when the birth, growth and mortality rates depend on the individual size and interspecies competition, while the exploitation intensity is a function of the size only. For a given exploitation intensity and under natural assumptions on the rates, we establish existence and uniqueness of a nontrivial stationary state of the population. In addition, we prove existence of an exploitation intensity which maximizes a selected profit functional of exploitation.

Sweden has the world's highest density of moose (Alces alces). Moose is not only a valuable game species; it also causes forest damages and traffic accidents. To avoid moose browsing, foresters respond by planting spruce (Picea abies) to an extent that reshapes the forest landscape with impacts on both production and biodiversity. To address this problem and maintain a healthy moose population in balance with the other interests, an adaptive management based on the knowledge and experiences of local hunters and landowners is advocated. However, the different stakeholders do not agree on what is an appropriate moose population, which leads to conflicts that are hard to resolve. A key problem is that it is very difficult to encompass and foresee long-term consequences of different options for moose hunting and forest management. This makes it challenging to form coherent strategies that integrate different sectorial interests at a national level. To address this issue, we have developed a systems analysis framework for integrated modeling of the moose population, forestry, and their interactions and consequences for biodiversity. We analyze the short and long-term consequences for multiple scenarios of moose hunting and forest management. Based on the results we elucidate and quantify the trade-offs and possible synergies between moose hunting and forest production. This analysis can be used to support better informed and more constructive discussions among the stakeholders in the Swedish forest sectors, and to support policies for long term sustainable forest and moose management.

We study the dynamics of a size-structured population with interacting species. For given exploitation intensities we establish the existence and uniqueness of a nontrivial stationary state. We also prove that there exists a family of exploitation intensities maximizing the profit functional of exploitation. Bibliography: 4 titles.

Dedicated to Vasilii Vasil'evich Zhikov on the ocassion of his 70th birthdayWe establish the global stability of a nontrivial stationary state of the size-structured population dynamics in the case where the growth rate, mortality, and exploitation intensity depend only on the size and certain conditions on the model parameters are imposed. We show that a stationary state maximizing the profit functional of population exploitation, exists and is unique. We also obtain a necessary optimality condition, owing to which this state can be found numerically. Bibliography: 3 titles.