FURTHER STUDIES
MATHEMATICS P2
Module 16: Modelling
INTRODUCTION TO MODELLING
MALTHUSIAN POPULATION MODEL
The Malthusian population model is based on compound growth.
FURTHER STUDIES MATHEMATICS P2 1
, When calculating growth rates from population indicators, remember the following:
LOGISTIC POPULATION MODEL
In the Malthusian model, which is based on the compound growth formula, the
population
continues to grow exponentially. Although this may be an accurate model in the early
stages of a
growing population, it is unrealistic in the long term. As the population continues to
increase, the
growth rate is likely to decrease due to food shortages, space constraints, increased
levels of
disease and predation etc.
Our new model, the logistic model, is based on the premise that as the population
grows the birth
rate decreases – i.e. that the growth rate is density dependent – and that the
population will
ultimately level off at a carrying capacity, the maximum population that can be
sustained by the
system. As a result, logistic models produce a characteristic S-shaped curve for the
population
over time:
FURTHER STUDIES MATHEMATICS P2 2
MATHEMATICS P2
Module 16: Modelling
INTRODUCTION TO MODELLING
MALTHUSIAN POPULATION MODEL
The Malthusian population model is based on compound growth.
FURTHER STUDIES MATHEMATICS P2 1
, When calculating growth rates from population indicators, remember the following:
LOGISTIC POPULATION MODEL
In the Malthusian model, which is based on the compound growth formula, the
population
continues to grow exponentially. Although this may be an accurate model in the early
stages of a
growing population, it is unrealistic in the long term. As the population continues to
increase, the
growth rate is likely to decrease due to food shortages, space constraints, increased
levels of
disease and predation etc.
Our new model, the logistic model, is based on the premise that as the population
grows the birth
rate decreases – i.e. that the growth rate is density dependent – and that the
population will
ultimately level off at a carrying capacity, the maximum population that can be
sustained by the
system. As a result, logistic models produce a characteristic S-shaped curve for the
population
over time:
FURTHER STUDIES MATHEMATICS P2 2
