Answers: Exercise 10 Page 1 of 4
Answers to Exercise 10
Life Tables, Survivorship Curves, and Population Growth
1. We plot survivorship curves on semi-log graphs because lx is a proportion: the
proportion of the original cohort surviving to age x. The distance between points on a
logarithmic axis reflects their proportional relationship, and so a logarithmic scale is
appropriate.
This kind of graph also makes clear important differences between the three types of
survivorship curve. Note that on the linear graph, type II and type III curves have
qualitatively similar shapes, whereas on the semi-log graph they look quite different.
2. The keys to interpreting the shapes of survivorship curves are to look at their slopes
compared with the graphs of age-specific survival (gx). The type I curve begins with a
shallow slope, indicating low mortality among the young—that is, a high proportion
of individuals of each age survive to the next age throughout the early part of life. The
curve steepens at older ages, indicating increased mortality in old age. A type I curve
tells us that most individuals in this population survive a long time and die at old ages.
The graph of gx supports this interpretation: survival is high in the young, and drops
off with age. Inspect columns E and H to see these patterns numerically.
The type III curve reflects the opposite pattern of survival and mortality. The curve
begins with a steep slope, indicating low survival (and high mortality) among the
young. The shallow slope in middle and old ages indicates that most of the individuals
that survive their youth survive to old age. The graph of gx shows the same
thing—survival among the young is very low, and increases with age (until the oldest
age). Inspect columns F and I to see these patterns numerically.
The type II curve indicates a constant rate of survival across all ages (until the last).
Note that a straight line on a semi-log plot indicates change by a constant proportion.
The graph of gx (a horizontal line) also shows that survival is the same for all ages
(except the oldest). Inspect columns G and J to see these patterns numerically.
3. The type I curve of life expectancy is probably not surprising, as it shows that the
expected number of years of life remaining decreases with increasing age.
The type II curve may strike you as somewhat surprising. It indicates that an
individual can expect to live about 2 more years, regardless of age, up to about 6 years
of age. After this, life expectancy decreases, to 1 year at 10 years of age. How can this
be? A type II survivorship curve occurs when the same proportion of survivors die at
each age (in other words, when the risk of death is constant for all ages). In this
circumstance, life expectancy is the reciprocal of risk of death. If you look at the
spreadsheet, you will see that half of the survivors die at each age. The reciprocal of _
