Consider a population with the following numbers of individuals over time. year 1: 10
Year 2: 25
Year 3: 30
If the population size in year 4 is determined by a logistic model with delayed density dependence from a 1-year time lag and K = 50 individuals, what value of r would lead the population size to exceed carrying capacity in year 4?

Question

Quizplus · Accepted Answer

We can use the logistic equation with delayed density dependence to determine the population size in year 4, given the population sizes in years 1-3: Nt = K / [1 + (K / N(t-1)) * e^(-rt)] Plugging in the values given, we get: N4 = 50 / [1 + (50/30) * e^(-r)] To find the value of r that leads to the population exceeding carrying capacity in year 4, we need to solve for N4 > 50: 50 / [1 + (50/30) * e^(-r)] > 50 This simplifies to: 1 + (50/30) * e^(-r) < 1 e^(-r) < -20/50 r > ln(50/20) r > 0.916 The only answer choice that satisfies this inequality is D, r = 2.0. Therefore, choice D is the correct answer.

Consider a Population with the Following Numbers of Individuals Over