Chapter 9: Problem 4

How can the value of net reproductive rate for a population $\left(R_{0}\right)$ be used to assess whether a population is increasing or declining?

Short Answer

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Answer: The net reproductive rate (R0) is the average number of female offspring that each female in a population is expected to produce in her lifetime. It helps determine whether a population is increasing, decreasing, or stable by calculating the sum of age-specific survival rates multiplied by fecundity rates. If R0 > 1, the population is increasing; if R0 < 1, the population is declining; and if R0 = 1, the population is stable. This information can be used for implementing conservation or management measures.

Step by step solution

Understanding Net Reproductive Rate (R0)

Net reproductive rate, denoted as $R_0$, is the average number of female offspring that each female in a population is expected to produce in her lifetime. It's a crucial quantity in population ecology and helps in assessing whether the population is increasing, decreasing, or stable.

Calculation of R0

To calculate $R_0$, we need to know the age-specific fecundity rates and the survival rates for females in the population. R0 can be calculated using the following formula: $$R_0=\sum_{x=0}^{\infty}(l_x \times m_x)$$ Where: - $l_x$ denotes the probability of surviving from birth to age $x$. - $m_x$ denotes the average number of female offspring produced by an individual of age $x$.

Interpretation of R0

The value of $R_0$ helps us determine whether a population is increasing, decreasing, or stable. 1. If $R_0$ > 1, the population is increasing as each female, on average, is producing more than one female offspring in her lifetime. 2. If $R_0$ < 1, the population is declining as each female, on average, is producing less than one female offspring in her lifetime. 3. If $R_0$ = 1, the population is stable, implying that each female, on average, is producing exactly one female offspring in her lifetime. By calculating and analyzing the net reproductive rate ($R_0$), we can assess whether a population is increasing or declining and implement necessary conservation or management measures accordingly.

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How can the value of net reproductive rate for a population \(\left(R_{0}\right)\) be used to assess whether a population is increasing or declining?

Short Answer

Step by step solution

Understanding Net Reproductive Rate (R0)

Calculation of R0

Interpretation of R0

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