Population ecology studies how populations change in size, density, and distribution over time. This cheat sheet helps students connect growth models, limiting factors, and species interactions to real biological patterns. It also supports genetics units by showing how allele frequencies can be used to test whether a population is evolving.
These ideas are important for ecology, evolution, conservation biology, and data-based exam questions.
The core population formulas include growth rate, exponential growth, logistic growth, and carrying capacity. Hardy-Weinberg equilibrium uses p + q = 1 and p^2 + 2pq + q^2 = 1 to predict genotype frequencies in a non-evolving population. If observed genotype frequencies do not match expected values, one or more evolutionary forces may be acting.
Students should be able to calculate allele frequencies, interpret graphs, and explain how natural selection, mutation, migration, genetic drift, and nonrandom mating change populations.
Key Facts
- Population size is the total number of individuals in a population, while population density is calculated as density = number of individuals / area or volume.
- Population growth rate can be estimated with r = (births + immigration - deaths - emigration) / initial population size.
- Exponential growth occurs when resources are unlimited and follows the pattern dN/dt = rN, where N is population size and r is growth rate.
- Logistic growth slows as a population nears carrying capacity and is modeled by dN/dt = rN((K - N) / K), where K is carrying capacity.
- In Hardy-Weinberg equilibrium, allele frequencies add to 1, so p + q = 1 for two alleles.
- Hardy-Weinberg genotype frequencies are p^2 + 2pq + q^2 = 1, where p^2 is homozygous dominant, 2pq is heterozygous, and q^2 is homozygous recessive.
- A population is in Hardy-Weinberg equilibrium only if there is no mutation, no migration, no natural selection, random mating, and a very large population size.
- Evolution is defined as a change in allele frequencies in a population over generations.
Vocabulary
- Population
- A population is a group of individuals of the same species living in the same area at the same time.
- Carrying capacity
- Carrying capacity is the maximum population size an environment can support over time with its available resources.
- Limiting factor
- A limiting factor is any resource or condition that restricts population growth, such as food, space, predators, or disease.
- Allele frequency
- Allele frequency is the proportion of a specific allele among all copies of a gene in a population.
- Hardy-Weinberg equilibrium
- Hardy-Weinberg equilibrium is a condition in which allele and genotype frequencies remain constant from generation to generation.
- Genetic drift
- Genetic drift is a random change in allele frequencies, especially strong in small populations.
Common Mistakes to Avoid
- Confusing allele frequency with genotype frequency is wrong because p and q describe alleles, while p^2, 2pq, and q^2 describe genotypes.
- Using the recessive phenotype frequency as q instead of q^2 is wrong because the recessive phenotype represents the homozygous recessive genotype frequency.
- Assuming every population is in Hardy-Weinberg equilibrium is wrong because real populations often experience selection, migration, mutation, drift, or nonrandom mating.
- Treating carrying capacity as a fixed number is wrong because K can change when resources, climate, disease, or human impacts change.
- Ignoring immigration and emigration in population growth is wrong because movement into or out of a population can change population size and allele frequencies.
Practice Questions
- 1 A pond has 240 frogs in an area of 60 square meters. What is the population density in frogs per square meter?
- 2 In a population, the recessive phenotype frequency is 0.16. Assuming Hardy-Weinberg equilibrium, find q, p, p^2, 2pq, and q^2.
- 3 A population begins with 500 rabbits. In one year there are 90 births, 20 deaths, 15 immigrants, and 35 emigrants. What is the growth rate r for that year?
- 4 A small island population loses many individuals after a hurricane, and rare alleles become common in the next generation. Explain which Hardy-Weinberg condition was violated and why this can cause evolution.
Understanding Population Ecology and Hardy-Weinberg
Population patterns are shaped by feedback. When a herd becomes crowded, food may run out faster, disease can spread more easily, and predators may find prey more often. These density dependent factors become stronger as density rises.
Other limits affect populations regardless of their density. A drought, hurricane, wildfire, or sudden freeze can reduce a population even when few individuals are present. Real populations rarely form a smooth curve because weather, seasons, competition, and chance cause repeated rises and falls.
Carrying capacity is therefore better understood as a changing range than as one fixed number. A pond may support many fish after a wet season but far fewer during a dry summer.
Age structure helps explain why two populations with the same total size can have very different futures. A population with many young individuals may grow quickly as they reach reproductive age. A population made mostly of older individuals may shrink, even if conditions are good.
Ecologists use survivorship curves to show the chance that individuals remain alive at each age. Humans and many large mammals often survive through early and middle life, then mortality rises late in life.
Many fish, insects, and plants produce huge numbers of offspring, but most die young. These patterns reveal tradeoffs between producing many offspring and investing more care in each one.
Species interactions change population size through linked effects. Predation can prevent one prey species from becoming too common. Competition occurs when organisms need the same limited resource, such as nesting space, light, water, or prey.
In mutualism, both species gain a benefit, as with flowering plants and many pollinators. A change in one species can spread through a food web. If a predator disappears, its prey may increase and consume more plants.
This can affect insects, soil organisms, and other animals that depend on those plants. Conservation work uses these connections when deciding which species or habitats need protection.
Hardy-Weinberg calculations provide a baseline, not a description of most natural populations. A recessive trait can be rare in appearance while its allele remains hidden in heterozygous individuals. For example, if one percent of a population shows a recessive phenotype, that one percent represents the frequency of the recessive homozygous genotype.
Students first find the square root to estimate the recessive allele frequency. They subtract that value from one to find the other allele frequency. Expected genotype frequencies can then be compared with observed counts.
A meaningful mismatch suggests that the population does not meet at least one equilibrium condition. Small populations are especially important because random events can change allele frequencies sharply. This genetic drift can make an allele common or eliminate it without any survival advantage.
Natural selection differs because individuals with certain inherited traits leave more offspring on average. When reading a problem, separate random change, movement between populations, mating patterns, and differences in reproductive success before choosing an explanation.