| Let's start by ignoring competition. We'll add that effect
later. |
| What part of the current generation will be present in the next
generation? Some will die, so the population decreases by its
death rate D. |
| In addition, some will be born, so the population
increases by its birth rate B. |
| That is, |
| Pn+1 = (1 + B - D)⋅Pn. |
| (The 1 in the parentheses is there to account for the fact that the
population will not change if there are no births and no deaths.) |
| This is just Malthus' model, and the future is easy to predict. |
| If B - D < 0, then 1 + B - D < 1 and
the population decreases to extinction. |
| If B - D > 0, then 1 + B - D > 1 and
the population grows until ... |
|
| the model loses its validity, for example,
the competition factors cannot be
ignored, or |
| (according to the gloomy Malthus) war, disease, and famine bring the
growth within bounds. |