Age-pattern of death shapes population growth rate

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Schindler S, Tuljapurkar S, Gaillard JM, & Coulson T (2012). Linking the population growth rate and the age-at-death distribution. Theoretical population biology, 82 (4), 244-52 PMID: 23103877

The age at which we die determines how fast our population grows. Recent work shows how to predict the growth rate of a population from the age-at-death distribution.

A gravestone dated 1673 in Bochum, Germany (c) Markus Schweiss / Wikimedia Commons / Public Domain

A gravestone dated 1673 in Bochum, Germany (c) Markus Schweiss / Wikimedia Commons / Public Domain

The rate at which a population grows is determined by the birth and death rates of its members. The birth rate captures the number of births per age class, whereas the death rate captures the number of deaths per age class. If the per-capita birth rate exceeds the death rate, the population grows, otherwise it shrinks.

Both rates are connected by a trade-off whose underlying mechanism is not yet fully understood. “Trade-off” because it is impossible to maximise the birth rate and minimize the death rate at the same time, which both might result in a bigger evolutionary success. But empirical and lab experiments show that an increase in fertility is followed by a lower survival probability.

So far, there is no formula to calculate the population growth rate exactly. It has to be approximated and for this the birth and death rates are multiplied. They enter the approximation as a combination and therefore, the effects of the rates on population growth cannot be studied separately.

Our team of researches from the UK, US, and France has made a step forward to disentangle the effects of fertility and mortality on the population growth rate. We have shown that the distribution of the age-at-death, that is the relative frequency of life length, yields already some information about the growth rate.

We have derived a formula to approximate the population growth rate where the mean age-at-death and its variance enter. This enables us to predict how changes in both measures affect the growth rate. If the mean age-at-death gets bigger then the population growth rate decreases, so the population either grows slower in numbers or shrinks faster. If the variance of age-at-death gets larger, the growth rate increases.

The main virtue of this new approximation is that it separates the effects of the age-pattern of death from fertility. However, as our approximation also contains a compound term of both fertility and mortality, there is still future work to be done to fully disentangle the effects of both rates.