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Concept explainers
To analyze:
The net reproductive rate (R0) for population and investigate its value.
Given:
An incomplete cohort life table is provided in Table 1, from which the components given in columns 4 and 5 are to be calculated.
Table 1: A life table of Australian sharp nose shark showing survivorship and fecundity.
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 |
Introduction:
A cohort life table shows demographic changes in a population. The table provides information about rate of reproduction, generation time, fecundity, rate of survival of the individuals and all information required to study a population in detail.
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Explanation of Solution
The survivorship (lx) of Australian sharpnose shark is calculated by dividing number of surviving individuals by number of individuals that were present at the time of birth (N0). The fecundity (mx) of an individual female is calculated by dividing the number of female offspring (Nx) by the number of females who have produced these offspring (Nx offspring).
A number of offspring per age class are calculated by simply multiplying lx with mx. The value of lxmx for the age class 1 is calculated as follows:
The values of lxmx for the subsequent age classes can be calculated by using a similar method.
Table 2: A complete life table of Australian sharpnose shark.
Age (x) | Survivorship of females (lx) | Fecundity of female offspring (mx) | lx mx |
0 | 1 | 0 | 0 |
1 | 0.32 | 1.98 | 0.63 |
2 | 0.19 | 2.59 | 0.49 |
3 | 0.11 | 2.81 | 0.31 |
4 | 0.06 | 2.89 | 0.17 |
5 | 0.03 | 2.92 | 0.08 |
6 | 0.02 | 2.93 | 0.06 |
7 | 0.01 | 2.93 | 0.03 |
8 | 0.005 | 2.93 | 0.014 |
9 | 0.003 | 2.93 | 0.008 |
10 | 0.002 | 0 | 0 |
From Table 2 net reproductive rate (R0) of the shark population can be calculated by using,
The net reproductive rate for the shark population is 1.792 that is greater than 1. So, it represents a net increase in the number of offspring in each generation. The population growth here is exponential.
Therefore, it can be concluded that reproductive rate of the shark population is 1.792, which indicates the exponential population growth and increase in offspring in each generation.
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Chapter 54 Solutions
LIFE: THE SCIENCE OF BIOLOGY
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