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.
