## Survivorship curves

The pattern of mortality in the Phlox population is illustrated in Figure 4.7a using both qx and kx values. The mortality rate was fairly high at the beginning of the seed stage but became very low towards the end. Then, amongst the adults, there was a period where the mortality rate fluctuated about a moderate level, followed finally by a sharp increase to very high levels during the last weeks of the generation. The same pattern is shown in a different form in Figure 4.7b. This is a survivorship curve, and follows the decline of log10lx with age. When the mortality rate is roughly constant, the survivorship curve is more or less straight; when the rate increases, the curve is convex; and when the rate decreases, the curve is concave. Thus, the curve is concave towards the end of the seed stage, and convex towards the end of the generation. Survivorship curves are the most widely used way of depicting patterns of mortality.

The yy-axis in Figure 4.7b is logarithmic. The importance of using logarithms in survivorship curves can be seen by imagining two investigations of the same population. In the first, the whole population is censused: there is a decline in one time interval from 1000 to 500 individuals. In the second, samples are taken, and over the same time interval this index of density declines from 100 to 50. The two cases are biologically identical, i.e. the rate or probability of death per individual over the time interval (the per capita rate) is the same. The slopes of the two logarithmic survivorship curves reflect this: both would be — 0.301. But on simple linear scales the slopes would differ. Logarithmic survivorship curves therefore have the advantage of being standardized from study to study, just like the 'rates' qx, kx and mx. Plotting numbers on a logarithmic scale will also indicate when per capita rates of increase are identical. 'Log numbers' will therefore often be used in preference to 'numbers' when numerical change is being plotted. 