Usually individuals of the same type and exposed to the same environment are still not demographically equal; some are small, others large, some may be young, others old, with all these differences feeding through to their population dynamical behavior. Such diversity can be dealt with by introducing the idea of population structure. Here structure means that individuals are distinguished by their h(eterogeneity)-state. This h-state may be composed of a location in space and a physiological state. To classify as a state, (1) all population dynamical behavior of individuals at a particular point in time, be it dying, giving birth, or impinging on the environment, should be fully determined by the current state and environmental condition; (2) an individual's future states should be fully determined by its present state and the intervening environmental conditions. Fully determined should be interpreted here in a stochastic sense, that is, given the indicated information, the behavior or future states are independent of any further adducible information. Conditions (1) and (2) form a restriction on the combined choices for describing h-states and environments. Arriving at good h-state and environment descriptions is an essential step in the craft of translating from the real to the model world.
Populations in turn should be defined by the requirement that all individuals share the same environment. Populations living under spatially heterogeneous conditions may be accommodated by making spatial position a component of an individual's h-state and letting the environmental condition be a function ofspatial locations to local environmental conditions, with individuals only being affected by a local environmental condition singled out according to their h-state.
The definitions of population, h-state, and environment have as consequence that given the course of the environment individuals proceed through their lives independently. This conditional independence property forms the basis of all further deliberations.
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