Population Dynamics: Probabilistic Extinction, Stability, and Explosion Theorems.

Book chapter, 2015

The relation between individual reproduction and the probability that populations die out is given. Populations that decrease on average will, of course, always die out, but populations whose expected sizes grow can also have a high probability of extinction. Malthus's law of exponential growth of populations, i.e., not dying out, holds in general, not only for populations of independently reproducing individuals, but also under some types of interaction. The stable age distribution and general stable composition, appearing as a consequence of exponential growth, are described. Finally, populations whose size and composition may influence individual reproduction are described.