Population Dynamics Based on Individual Stochasticity

This book demonstrates that population structure and dynamics can be reconstructed by stochastic analysis. Population projection is usually based on age-structured population models. These models consist of age-dependent fertility and mortality, whereas birth and death processes generally arise from states of individuals. For example, a number of seeds are proportional to tree size, and amount of income and savings are the basis of decision making for birth behavior in human beings. Thus, even though individuals belong to an identical cohort, they have different fertility and mortality. To treat this kind of individual heterogeneity, stochastic state transitions are reasonable rather than the deterministic states. This book extends deterministic systems to stochastic systems specifically, constructing a state transition model represented by stochastic differential equations. The diffusion process generated by stochastic differential equations provides statistics determining population dynamics, i.e., heterogeneity is incorporated in population dynamics as its statistics. Applying this perspective to demography and evolutionary biology, we can consider the role of heterogeneity in life history or evolution. These concepts are provided to readers with explanations of stochastic analysis.

Proposes that a diffusion process representing life history can govern population structure and its dynamics Discusses the roles of individual differences in population dynamics and evolution, Uses semelparity to aid in understanding the framework concerning adaptive reproduction timing and foraging strategies

Autorentext

Ryo Oizumi, National Institute of Population and Social Security Research

Inhalt

Introduction : Stochasticity in Demography.- 1. Deterministic and Stochastic Population Models.- 2. Linear Structured Population based on SDE.- 3. Nonlinear Structured Population Models.- 4. Life-History Evolution and Adaptive Stochastic Controls.- 5 Application to External Stochasticity.- Epilogue: Population Dynamics from Perspective of Individual Diversity.