Up to this point we have assumed that individuals within a population do not vary in their birth and death rates. This is a big assumption given that we know real populations are made up of individuals of different ages, sizes, and sexes, which vary in their capacity to reproduce or survive. For example, a newborn whale or human cannot reproduce immediately, but must mature to reproductive age. Likewise, the likelihood of death will vary depending on the age of the individual. Ecologists use a form of accounting, known as a life table, to keep track of how demography will affect the growth rate of the population. Life tables summarize how survival and reproductive rates vary with the age, size, or sex of the individuals within a population. These summaries can then be used to predict future population trends and develop strategies for managing populations of commercial or ecological value. They are also used by life insurance companies to determine how much to charge people of different ages for insurance policies.

Let’s consider an example of a life table from the literature. Table 54.1 shows a cohort life table using data from the acorn barnacle Balanus glandula on the shorelines of Scotland. A cohort life table uses a cohort—a group of individuals born within the same time frame—from the larger population to estimate growth rate. The two columns on the left show the number of individuals surviving and the number of offspring produced at different ages (x) through time. As the number of individuals within the cohort die, N_x decreases from 1 million barnacles to only 2 barnacles after 8 years. The proportion of individuals that survive, known as survivorship (l_x), can be calculated by simply dividing N_x by N₀, or the number of barnacles originally born into the cohort (represented by age 0). In addition, we can calculate the fecundity (m_x), or the mean number of barnacle offspring produced per surviving adult barnacle per age class, by dividing the total number of offspring (N_{x offspring}) by the number of individuals (N_x) that produce those offspring. Multiplying survivorship (l_x) by fecundity (m_x) gives us the number of offspring produced for individuals within a particular age class within the population. The sum of these values for all the age classes gives us the net reproductive rate, R₀, which is simply the mean number of offspring produced per individual in the cohort, adjusted for survival:

R₀ = sum (l_x m_x)                                                             (54.8)

If R₀ is greater than 1.0, there is a net increase in offspring produced each generation, and assuming the birth and death rates do not change over time, the population should increase exponentially. If R₀ is less than 1.0, and individuals are not replaced as they die, the population declines eventually to extinction. If R₀ is 1.0, then the births and deaths balance out and the population will not change in size.

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We can use R₀ to estimate the per capita growth rate, r, of a cohort by scaling R₀ to account for the generation time of the cohort. The generation time, G, is the average age of the parents of all the offspring produced within the cohort (see Table 54.1 for equation). To estimate r, we simply divide the natural log (ln) of R₀ by G and get

r = (ln R₀)/G                                                                (54.9)

Cohort life tables follow individuals from birth to death as a function of calendar year or life stage (e.g., eggs, larvae, pupae, and adults in insects). This is relatively easy to do if the organisms are easily followed—for example, if they are sessile and short-lived as we saw in the barnacle example. For organisms that are harder to track, a static life table can be constructed by sampling a population at a single slice of time. Here the numbers of individuals and their reproduction for different age classes are recorded at one time and used in a similar way to those data in Table 54.1 to calculate the net reproductive rate and per capita growth rate of the population.

The construction of life tables has allowed ecologists to observe common life history patterns, reflecting common solutions to ecological challenges, across a tremendous diversity of organisms. For example, the number of individuals surviving through each life stage (survivorship, l_x) can be taken from a life table and plotted graphically to construct a survivorship curve. Typically, a survivorship curve is constructed for a hypothetical cohort, usually of 1,000 individuals, by plotting the numbers of individuals expected to survive to reach each age category on a logarithmic scale.

Survivorship curves tend to take one of three general shapes:

Species survivorship curves help us classify how mortality plays out in populations over time, but many species have patterns of survivorship somewhere in between these extremes. For example, some organisms show a “stair-stepped” curve, with bouts of mortality during vulnerable periods of their life, followed by periods of relatively low mortality.