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Population dynamics: single species: age class: separate compartments

Model : popdyn2
Simile version : 3.1+
Date added : 2003-06-20
Keywords : Population dynamics ; Age-class modelling ; Disaggregated population ; Single-species population dynamics ;

Description

This models the dynamics of a population divided into three age classes: young, mature and elderly. Each age class is represented by a single compartment, whose value is the number of individuals in that class.

The flows between the age classes represent the ageing process: the movement of individuals from one class to the next as the grow older. The flows into the first age class represents reproduction. This depends on the number of mature females, which is a fraction of the number of mature individuals. The flow out of the third age class represents mortality: in this model, we assume that only the old individuals die.

Simple proportional relationships are used for all flows:

• a certain proportion of each class age each year;
• a certain proportion of the females reproduce each year;
• a certain proprtion of the elderly individuals die each year.

The model uses a time step of 1 year.

Source: Andrew Ford (1999): Modelling the Environment, p.28

Files

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p028.sml

Diagram

Equations

Compartments:
	elderly
		Initial value = 20
		Rate of change =  aging - deaths
		Comments: Number of elderly, millions

	mature
		Initial value = 30
		Rate of change =  maturation - aging
		Comments: Number of mature, millions

	young
		Initial value = 50
		Rate of change =  births - maturation
		Comments: Number of young, millions
Flows:
	aging = aging_rate*mature
	Comments: Number maturing, millions per year

	births = births_per_mature_female_per_year*mature_females
	Comments: Births, millions per year

	deaths = death_rate*elderly
	Comments: Number dying, millions per

	maturation = maturation_rate*young
	Comments: Number maturing, millions per year

Variables:
	mature females = female_fraction*mature
	Comments: Number of mature females, millions

Parameters:
	aging rate = 0.1
	Comments: Proportion aging, per year

	births per mature female per year = 0.5
	Comments: Number of births per female per year

	death rate = 0.2
	Comments: Proportion dying, per year

	female fraction = 0.5
	Comments: Proportion of females in the population

	maturation rate = 0.1
	Comments: Proportion of young maturing, per year

Results

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References

Ford, A (1999) Modeling the Environment.
Island Press. p.28

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