Review
54.2 Life tables help predict how age-
54.4 Appropriate management and conservation of wild or commercial populations requires knowledge of their life history strategies and population dynamics.
Original Paper: Simpfendorfer, C. A. 2005. Demographic models: Life tables, matrix models and rebound potential. In J. A. Musick, and R. Bonfil, eds. Management techniques for elasmobranch fishes. FAO Fisheries Technical Paper 474: 143−153.
Many temperate shark species grow slowly, have a long life span, mature late, and produce few young. By contrast, the tropical Australian sharpnose shark is fast-
Management decisions about endangered shark populations require knowledge of how their population growth rates respond to mortality events such as predation, disease, and fishing (including bycatch mortality). Life tables can be used to predict how age-
The table is a static life table for the Australian sharpnose shark. It was constructed from shark catch data during a single fishing season (only female individuals were used in the analysis). The table is composed of survivorship (lx: the number of females that have survived within each age class) and fecundity (mx: the number of females born per adult female shark within each age class). Note that survivorship and fecundity at age 0 are for individuals just born into the population.
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| Age (x) | Survivorship of females (lx) |
Fecundity of female offspring (mx) |
lx mx | x lx mx |
|---|---|---|---|---|
| 0 | 1 | 0 | ||
| 1 | 0.32 | 1.98 | ||
| 2 | 0.19 | 2.59 | ||
| 3 | 0.11 | 2.81 | ||
| 4 | 0.06 | 2.89 | ||
| 5 | 0.03 | 2.92 | ||
| 6 | 0.02 | 2.93 | ||
| 7 | 0.01 | 2.93 | ||
| 8 | 0.005 | 2.93 | ||
| 9 | 0.003 | 2.93 | ||
| 10 | 0.002 | 0 |
Questions
Complete the fourth column of the table by calculating lx mx for each age class (x) of the population. Then, calculate the net reproductive rate (R0) for the population, and explain what this value represents.
Individual age values are shown in the table below. They are calculated by multiplying lx by mx for each age class. The net reproductive rate for the population is calculated as R0 = sum (lx mx), or 0 + 0.63 + 0.49 + 0.31 + 0.17 + 0.09 + 0.06 + 0.03 + 0.02 + 0.01 + 0 = 1.81. This represents the mean number of offspring produced by each reproductive individual in the cohort during her lifetime.
| Age (x) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| lx mx | 0 | 0.63 | 0.49 | 0.31 | 0.17 | 0.09 | 0.06 | 0.03 | 0.02 | 0.01 | 0 |
Given the value of R0 for the population, can you determine whether the shark population is increasing, decreasing, or not changing in size? Explain your answer.
The population is increasing. Because the life table adjusts for deaths at each year in the life cycle, death rates are built into the life table. If the value of R0 is greater than 1 (as this one is), the population is increasing.
Complete the final column of the life table by calculating x lx mx for each age class (x) of the population. Then, calculate the generation time, G, for the population.
The generation time is calculated by first multiplying the age class (x) by the reproductive rate for that age class (lx mx) to get x lx mx. The values are summed as G = sum (x lx mx), or 0 + 0.63 + 0.98 + 0.93 + 0.68 + 0.45 + 0.36 + 0.21 + 0.16 + 0.09 + 0 = 4.49.
| Age (x) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| x lxmx | 0 | 0.63 | 0.98 | 0.93 | 0.68 | 0.45 | 0.36 | 0.21 | 0.16 | 0.09 | 0 |
Using previous calculations of R0 and G, calculate an estimate of r, the per capita growth rate of the population.
The per capita rate of increase is calculated as r = (ln R0)/G. Thus r = (ln 1.81)/4.49 = 0.132.
Consider the life history differences between the Australian sharpnose shark versus the larger temperate sharks. Which shark populations do you think will have a higher r value? Given fishing pressures and life history characteristics, which shark populations do you think have a greater chance of being overfished? Explain your answer.
Sharpnose shark populations are more likely to have a higher r value than are populations of temperate sharks. Sharpnose sharks mature and reproduce early, so they produce offspring more rapidly than larger sharks, even though they have a shorter life span. Also, sharpnose sharks are small and not deliberately fished but are part of bycatch. Larger, temperate species, because of their slow growth, late maturity, and limited offspring, reproduce more slowly. If fishing pressure becomes intense, temperate sharks could be overfished.
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