Overfishing reduced food availability for sea lions in California, causing a decline in their population size. In 1972, under the US Endangered Species Act, fishing was banned from sea lion foraging areas. Subsequently, the population of sea lions increased in a logistic form as shown in the figure.The per capita growth rate is highest in the interval ______ and the population growth rate is highest in the interval ____.
Show Hint
Distinguish \textbf{pathogens} (disease-causing organisms) from \textbf{vectors} (organisms that transmit them). For avian malaria, the pathogen is \emph{Plasmodium}; the mosquito is only the vector.
Step 1: Recall the logistic-growth model.
Logistic growth is described by
\[
\frac{dN}{dt}=rN\!\left(1-\frac{N}{K}\right),
\]
where \(N\) is population size, \(r\) the intrinsic rate of increase, and \(K\) the carrying capacity.
Step 2: Per-capita growth rate.
Per-capita (per individual) growth is
\[
\frac{1}{N}\frac{dN}{dt} \;=\; r\!\left(1-\frac{N}{K}\right).
\]
This decreases linearly with \(N\) and is maximal when \(N\) is smallest. On the S-shaped curve, the smallest \(N\) is in the early phase (interval I).
\(\Rightarrow\) \emph{Per-capita growth rate highest in I.}
Step 3: Total population growth rate.
Total growth \(\frac{dN}{dt}=rN(1-N/K)\) is a quadratic function of \(N\) with a maximum at \(N=K/2\). Graphically this is the steepest part of the logistic curve—its midsection—corresponding to interval II.
\(\Rightarrow\) \emph{Population growth rate highest in II.}
Step 4: Conclude.
Per-capita growth: I; total growth: II. Hence option (A) I, II.
