You are studying a closed population of beetles consisting of 3000 individuals. You register 400 births and 150 deaths during one month. Calculate r and lambda and predict the population size after 6 months.
You estimate the size of a flatworm population to be the following at five consecutive days: 100, 158, 315, 398 and 794 individuals. Plot the natural logarithm (i.e., to the base e, where e is Eulers number) of the population size and estimate r. You can plot the data by hand on a piece of paper, or by using EXCEL or R.
An isolated population of elk (a species of deer) in Washington state increased from 1975 to 1993 as follows:
\[ \begin{align*} 1975 &\,\,\,\,\, 8 & 1986 &\,\,\,\,\, 68 \\ 1976 &\,\,\,\,\, 13 & 1987 &\,\,\,\,\, 67 \\ 1977 &\,\,\,\,\, 14 & 1988 &\,\,\,\,\, 72 \\ 1979 &\,\,\,\,\, 15 & 1989 &\,\,\,\,\, 79 \\ 1981 &\,\,\,\,\, 20 & 1990 &\,\,\,\,\, 94 \\ 1982 &\,\,\,\,\, 21 & 1991 &\,\,\,\,\, 110 \\ 1983 &\,\,\,\,\, 27 & 1992 &\,\,\,\,\, 146 \\ 1984 &\,\,\,\,\, 40 & 1993 &\,\,\,\,\, 179 \\ 1985 &\,\,\,\,\, 54 && \end{align*} \]
Plot these data as function of time. What shape of population growth is shown by these data? Could one fit the logistic equation to these data? Use a discrete-time model to calculate the net reproductive ratio lambda for this population.
Suppose that a butterfly population shows logistic growth with K = 500 and r = 0.1 individuals/(individuals*month). What is the maximal population growth rate for this population?
A fisher is maximizing their fishing yield by maintaining a population of logistically growing lake trout at the density where the population growth rate is fastest. For the population in question this occurs at a density of 500 individuals. Predict the realized population growth rate after the population has been stocked with an additional 600 fish. Assume that for the trout \(r=0.005\) individuals/(individual*day).