REALISTIC MODELS IN POPULATION ECOLOGY
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the oscillation period “does not seem to fit any value of the life history
information and biodemographical data of N . vitripennis”. If individuals
in the N . vitripennis population behave similarly regardless of age, size
etc., a more complex total population model, whose form and parameters are based on the animals’ physiology and interaction with the
environment, may be realistic. McQueen (1971), for example, did
formulate a realistic model for two species of slime mold in competition
without distinguishing individuals in each of the populations, and
Tsuchiya et al. (1972) similarly modeled a predator-prey interaction of
amoeba and bacteria with excellent experimental agreement.
It is occasionally argued in the literature that total population models
are “general” and are therefore useful for drawing general conclusions or
proving theorems. In my opinion, these models are not general, only
simple, and in fact overly simplified. It is dangerous to draw conclusions
relative to, say, the competitive exclusion principle or stability in
complex communities based on such models, because the equations
themselves are usually inaccurate and have little or no relation to
reality. Furthermore, one can modify the equations to produce contradictory results. Instead, one should employ models which contain more
explicit representation of populations and are therefore more realistic.
Perhaps the single most important attribute of individuals in a population is their age and so the inclusion of age-structure is the first logical
step to increase the realism of population models.
111. AGE-SPECIFIC MODELS
To my knowledge the earliest model to include age-structure of a
population was formulated by Bailey (1931). The model was constructed
to characterize host-parasite interactions, but it also describes single
species dynamics if either the total parasite population or Bailey’s
interaction parameter is set equal zero. The model itself is in the form of
an integral equation.
Later, Lewis (1942) and Leslie (1945, 1948, 1959) independently
formulated algebraic models with age-structure. In these models the
population is divided into different age groups or cohorts, each of
which experiences a different death rate and contributes to the birth
rate in differing proportions depending on its age. In equal time
intervals those members of each cohort who do not die increakin age
to the next cohort. The algebraic equations describing the birth, death
and aging processes are conveniently written in matrix notation.
Subsequently, partial differential equation models including age-size
structure were proposed by Von Foerster (1959) and independently by
Hoyle (1963). (See also Trucco, 1965a, b for earlier references.) Both
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the oscillation period “does not seem to fit any value of the life history
information and biodemographical data of N . vitripennis”. If individuals
in the N . vitripennis population behave similarly regardless of age, size
etc., a more complex total population model, whose form and parameters are based on the animals’ physiology and interaction with the
environment, may be realistic. McQueen (1971), for example, did
formulate a realistic model for two species of slime mold in competition
without distinguishing individuals in each of the populations, and
Tsuchiya et al. (1972) similarly modeled a predator-prey interaction of
amoeba and bacteria with excellent experimental agreement.
It is occasionally argued in the literature that total population models
are “general” and are therefore useful for drawing general conclusions or
proving theorems. In my opinion, these models are not general, only
simple, and in fact overly simplified. It is dangerous to draw conclusions
relative to, say, the competitive exclusion principle or stability in
complex communities based on such models, because the equations
themselves are usually inaccurate and have little or no relation to
reality. Furthermore, one can modify the equations to produce contradictory results. Instead, one should employ models which contain more
explicit representation of populations and are therefore more realistic.
Perhaps the single most important attribute of individuals in a population is their age and so the inclusion of age-structure is the first logical
step to increase the realism of population models.
111. AGE-SPECIFIC MODELS
To my knowledge the earliest model to include age-structure of a
population was formulated by Bailey (1931). The model was constructed
to characterize host-parasite interactions, but it also describes single
species dynamics if either the total parasite population or Bailey’s
interaction parameter is set equal zero. The model itself is in the form of
an integral equation.
Later, Lewis (1942) and Leslie (1945, 1948, 1959) independently
formulated algebraic models with age-structure. In these models the
population is divided into different age groups or cohorts, each of
which experiences a different death rate and contributes to the birth
rate in differing proportions depending on its age. In equal time
intervals those members of each cohort who do not die increakin age
to the next cohort. The algebraic equations describing the birth, death
and aging processes are conveniently written in matrix notation.
Subsequently, partial differential equation models including age-size
structure were proposed by Von Foerster (1959) and independently by
Hoyle (1963). (See also Trucco, 1965a, b for earlier references.) Both