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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

Just a note

Take a population of 1000 individuals which dropped to 900 after one month. This is a monthly finite mortality of 10% (0.1). If we divided that month into 1000 intervals, what would be the mortality in each interval?

We have already shown that you cannot just multiply (or divide) finite mortality rates to get the rate over a longer or shorter period. In fact, if you did this, and decreased the number by (0.1/1000) a thousand times, you would find that after 1000 time periods the number surviving will have dropped to 904.8 animals - not 900 animals.

In terms of survival, if 100 animals die in a month, 900, or 0.9 of the population survive. Therefore, if s is the survival in 1/000th of a month, s1000=0.9 Rearranging which we find that s=0.91/1000 or 0.999895 - which would make the mortality in 1/1000th of a month 1-0.999895 or 0.000105

Clearly therefore, if we make the time interval very small we are going to end up with survival rates approaching 1 - and mortalities approaching zero. As a result, the only way to cope with the problem is to consider the rate the population is changing at any one instant, and sum (or integrate) their effects over finite periods of time.
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