Chapter 11 Solutions — Organisms and Populations

For exponential growth the integral equation is:

Nₜ = N₀ eʳᵗ

Given: the population doubles in t = 3 years, so Nₜ = 2N₀.

Substituting:

2N₀ = N₀ × eʳˣ³

2 = e³ʳ

Taking the natural logarithm of both sides:

ln 2 = 3r

r = ln 2 / 3

r = 0.6931 / 3

r ≈ 0.231 per year

The ecological principle behind biological control is predation — specifically, the ability of a natural predator to regulate the population density of its prey.

In predation, a predator kills and feeds on its prey, thereby keeping the prey population under check. When a pest insect (prey species) causes damage in a crop or an ecosystem, introducing or encouraging its natural predator (or parasitoid) can reduce the pest population to economically acceptable levels.

A classic example: the prickly pear cactus (Opuntia) introduced into Australia in the 1920s spread uncontrollably over millions of hectares because its natural predator was absent. When a cactus-feeding moth (its natural predator from its native habitat) was introduced, the cactus population was brought under control.

The key ecological insight is that predators in nature are 'prudent' — they do not drive their prey to extinction because that would also lead to their own extinction. Properly chosen biological control agents regulate pest populations sustainably without the side-effects of chemical pesticides.

Population:

A population is a group of individuals of the same species that live together in a well-defined geographical area, share or compete for similar resources, and potentially interbreed. Although interbreeding implies sexual reproduction, groups resulting from asexual reproduction are also considered populations for ecological studies. Examples: all cormorants in a wetland, all rats in an abandoned dwelling, all lotus plants in a pond.

Community:

A community (or biotic community) is an assemblage of populations of different species living together and interacting in a defined geographical area. It includes all the plants, animals, and microorganisms of an area. Communities are characterised by their species composition, species diversity, and the various interspecific interactions (competition, predation, parasitism, mutualism, commensalism, amensalism) among the constituent populations. No species in nature lives in isolation — all form part of a community.