Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

• Published in: PloS one Vol. 9; no. 6; p. e98746
• Main Author: Oizumi, Ryo
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 19.06.2014; Public Library of Science (PLoS)
• Subjects: Age; Animal reproduction; Animals; Biodiversity; Biology; Biology and Life Sciences; Breeding; Computer and Information Sciences; Control theory; Demographics; Demography; Ecology and Environmental Sciences; Economic models; Economists; Ecosystem; Environment; Food intake; Formulations; Growth rate; Integral equations; Iteroparity; Laplace transforms; Life Cycle Stages; Life history; Linear Models; Mathematical analysis; Mathematical models; Matrix methods; Optimal control; Partial differential equations; Physical Sciences; Population Dynamics; Population growth; Randomness; Resource utilization; Semelparity; Species diversity; Stochastic Processes; Stochasticity; Studies
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0098746

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.