The standard model of population growth is the Demographic Transition Model that shows how the population of a country is likely to change over time. This model is the cornerstone of much of the work on population.
However, the question mentions optimistic and pessimistic models which leads me to think we are looking to find out about Malthus as his theories relating to population growth.
Thomas Malthus was a British demographer (someone who studies populations) that published his theories in 1798. Although they were published over 200 years ago his views are still widely quoted in A-level texts.
Malthus believed that there was a finite population size in relation to food supply and that any increase in population beyond this size would result in war, famine and disease and a decline in the standards of living. His theory was based on two main principles, namely that:
- The human population grows at an exponential rate (i.e. 1, 2, 4, 8, 16, etc)
- Food supply grows at an arithmetic rate (i.e.1, 2, 3, 4, 5, 6, 7 etc). This was due to a limited amount of land and the fact that it wasnt possible to continue getting more and more out of the same amount of land.
He therefore believed that, at a certain point in time, the population would have reached its maximum size for the resources that were available to it. At this point, the population would then decrease by either positive or negative means (or a combination of the two).
Negative (or preventive) checks were ways of limiting the growth of the population, for example, by postponing marriage (remember in the 1790s children, as a rule, came after marriage, very rarely before). Positive checks were events that would happen to reduce the size of the population, for example, war (as people fought over food supplies), disease and famine. All of these would then reduce the size of the population and also limit growth as life expectancy would be shortened.
Malthus views were undoubtedly pessimistic but other people disagreed with him. They had a more optimistic view of the future that claimed that, as the population grew new developments and technologies would make it possible for us to produce more food. You could argue that this is valid as pesticides, fertilisers, GM crops; irrigation systems and increased mechanisation have all allowed food production to increase rapidly. Although it may not appear so when we see continuing famine in parts of Africa, it is possible to produce enough food in the world at the moment to feed everyone. The reason why we have famine at the moment is that the resources are not distributed properly.