Abstract
This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies.
Highlights
The motivation behind this research is the interest in developing new classes of mathematical models to describe the demographic dynamics of complex biological systems
In order to describe the demographic dynamics for this class of biological systems, we introduce the sequence {Xn }∞
We shall prove that such a stochastic sequence can be studied under the general setting provided by the theory on Multitype Branching Processes, with the corresponding types being all the possible combinations among populations and types of individuals in the biological system
Summary
The motivation behind this research is the interest in developing new classes of mathematical models to describe the demographic dynamics of complex biological systems. Branching processes are mathematical models with theoretical and practical interest They are simple to analyze and have wide applicability as models for a great variety of phenomena, especially for biological phenomena, playing a crucial role in studies on population dynamics. Multitype branching processes are stochastic models describing the dynamics of populations where several types of individuals coexist and each individual, independently of the rest, can produce new individuals of all the types The theory about such processes has been widely developed, see e.g., monograph [8].
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