individuals, and it decreases by half to 500 in one time interval, then this decrease looks more dramatic on a graph like Figure 4.9a than a decrease from 50 to 25 individuals later in the season. Yet the risk of death to individuals is the same on both occasions. If, however, lx values are replaced by log(lx ) values, that is, the logarithms of the values, as in Figure 4.10b (or, effectively the same thing, if lx values are plotted on a log scale), then it is a characteristic of logs that the reduction of a population to half its original size will always look the same. Survivorship curves are, therefore, conventionally plots of log(lx ) values against cohort age. Figure 4.10b shows that for the marmots, there was a steady, more or less constant rate of decline until around the eighth year of life, then three further years at a slightly higher rate (until breeding ceased), followed by a brief period with effectively no mortality, after which the few remaining survivors died.
Figure 4.10 Representations of the survival of a cohort of the yellow‐bellied marmot (Table 4.2). (a) When lx is plotted against cohort age, it is clear that most individuals are lost relatively early in the life of the cohort, but there is no clear impression of the risk of mortality at different ages. (b) By contrast, a survivorship curve plotting log(lx ) against age shows a virtually constant mortality risk until around age eight, followed by a brief period of slightly higher risk, and then another brief period of low risk after which the remaining survivors died.
a classification of survivorship curves
Life tables provide a great deal of data on specific organisms. But ecologists search for generalities – patterns of life and death that we can see repeated in the lives of many species – conventionally dividing survivorship curves into three types in a scheme that goes back to 1928, generalising what we know about the way in which the risks of death are distributed through the lives of different organisms (Figure 4.11).
Figure 4.11 Classification of survivorship curves plotting log(lx) against age, above, with corresponding plots of the changing risk of mortality with age, below. The three types are discussed in the text.
Source: After Pearl (1928) and Deevey (1947).
In a type 1 survivorship curve, mortality is concentrated toward the end of the maximum life span. It is perhaps most typical of humans in developed countries and their carefully tended zoo animals and pets. A type 2 survivorship curve is a straight line signifying a constant mortality rate from birth to maximum age. It describes, for instance, the survival of buried seeds in a seed bank. In a type 3 survivorship curve there is extensive early mortality, but a high rate of subsequent survival. This is typical of species that produce many offspring. Few survive initially, but once individuals reach a critical size, their risk of death remains low and more or less constant. This appears to be the most common survivorship curve among animals and plants in nature.
These types of survivorship curve are useful generalisations, but in practice, patterns of survival are usually more complex. We saw with the marmots, for example, that survivorship was broadly type 2 throughout much of their lives, but not at the end (Figure 4.10b). Similarly, with the dinosaurs we will meet in the next section, survivorship followed the typical type 3 pattern until they reached sexual maturity, but again failed to conform to such a simple classification thereafter (see Figure 4.13). More generally, we see examples approximating to each of the three types in the survey in Figure 4.2, but also more examples where the shape changes as individuals pass through the different phases of their lives.
APPLICATION 4.2 The survivorship curves of captive mammals
Opinions naturally differ regarding both the ethics and the practical benefits of keeping wild animals in captivity in zoos, but the current reality is that zoos play an integral role in the conservation of many species, especially those, like many mammals, that are large and inherently attractive to the general public. Hence, in managing these animals, we need to understand their patterns of survivorship, and to know in particular if there are general rules organising these patterns that would not only describe the species for which we have good data, but also allow us to predict patterns for similar or related species when currently available data are sparse. Lynch et al. (2010) therefore reviewed what was known about the survivorship of captive mammals – 37 species, including primates, artiodactyls (cattle, sheep, deer, etc.), carnivores, bats, seals and the giant panda – and some of their results are summarised in Figure 4.12. They were more interested in the shapes of the survivorship curves (and for example whether they were type 1, 2 or 3) than in absolute values, and all data sets were therefore scaled to the maximum longevity of the species concerned. They then fitted all datasets to a general survivorship function with two shape parameters, α and β, which allowed the different curves to be classified and either grouped together or distinguished (Figure 4.12). Broadly speaking, with increasing values of α/β, mortality shifted towards being more evenly distributed throughout life, rather than being concentrated at the start; and with decreasing values of αβ, mortality shifted towards including senescence – a period of increased mortality at the end of life – rather than decreasing steadily with age.
Figure 4.12 Distribution of the shapes of survivorship curves for 37 species of animals kept in zoos. (For a full list of species names, see the original text.) A generalised survivorship function with two parameters, α and β was fitted to all datasets, allowing each to be located in logα–logβ space. The shapes themselves are illustrated in the insets, referring to the four starred locations, as survivorship on linear and semilogarithmic scales (solid and dashed lines, respectively; see Figure 4.11) and as distributions of mortality (histograms) between
