6.1 Population Ecology
Key Takeaways
- Exponential growth (dN/dt = rN) produces a J-curve under unlimited resources; logistic growth (dN/dt = rN(K-N)/K) produces an S-curve that levels off at carrying capacity K
- Maximum population growth in the logistic model occurs at N = K/2, not at K, where (K-N)/K is largest while N is still substantial
- r-selected species produce many small offspring with little parental care and follow Type III survivorship; K-selected species produce few large offspring with high care and follow Type I survivorship
- Density-dependent factors (disease, competition) intensify with population size; density-independent factors (floods, fires, freezes) act regardless of population size
- The demographic transition model describes four stages of human population change, with rapid growth occurring in Stage 2 when death rates fall before birth rates
Why Population Ecology Matters for the Praxis Biology Exam
Population ecology is one of the most heavily quantitative areas of the Praxis Biology: Content Knowledge (5236) exam. Expect questions that test growth-model recognition, simple rate calculations, and interpretation of survivorship and age-structure graphs. The exam consistently asks you to distinguish exponential from logistic growth, to read carrying-capacity scenarios, and to classify species as r-selected or K-selected from a short life-history description.
A population is a group of individuals of the same species living in the same area at the same time and capable of interbreeding. Three properties describe any population:
- Population size (N) - total number of individuals
- Population density - individuals per unit area or volume (N / area)
- Dispersion pattern - how individuals are spatially arranged
Dispersion Patterns
| Pattern | Description | Typical cause | Classic example |
|---|---|---|---|
| Clumped | Individuals grouped in patches | Patchy resources, social behavior, herding | Elephants at a waterhole, wolves in packs |
| Uniform | Evenly spaced individuals | Territoriality, allelopathy | Nesting penguins, creosote bush |
| Random | No predictable spacing | Neutral interactions, abundant resources | Dandelions in a field, oak seedlings |
Clumped dispersion is by far the most common pattern in nature because most resources are not evenly distributed.
Exponential Growth (J-Curve)
When resources are unlimited, populations grow exponentially. The differential equation is:
dN/dt = rN
where r is the intrinsic rate of increase (per-capita birth rate minus per-capita death rate). The curve is shaped like the letter J and assumes no resource limits, no predators, and no disease. Exponential growth describes bacteria in fresh medium, invasive species during initial colonization, and reintroduced species in suitable habitat.
Quick calculation
If a population of 100 mice has r = 0.5 per year, the instantaneous growth rate is:
dN/dt = 0.5 x 100 = 50 mice per year at that moment.
Logistic Growth (S-Curve)
Real populations face resource limits. The logistic model introduces carrying capacity (K), the maximum population size the environment can sustain indefinitely:
dN/dt = rN((K - N)/K)
The curve is shaped like the letter S. Three regions of the curve matter for the exam:
- Early phase (N << K): the (K - N)/K term is close to 1, so growth is nearly exponential.
- Inflection point (N = K/2): growth rate is maximum in absolute terms.
- Approach to K (N close to K): (K - N)/K approaches 0, so growth rate approaches zero.
At N = K, births equal deaths and the population is at equilibrium. If N briefly overshoots K, growth becomes negative until the population returns to K.
Density-Dependent vs Density-Independent Factors
- Density-dependent factors intensify as population density rises: competition for food, disease transmission, predation efficiency, accumulation of waste.
- Density-independent factors act regardless of density: floods, fires, volcanic eruptions, unusually cold winters, droughts.
The Praxis often presents a vignette and asks which type of factor is at work. The trigger word is whether the effect scales with density.
Life-History Strategies
r-selected and K-selected are endpoints of a continuum, not strict categories.
| Trait | r-selected | K-selected |
|---|---|---|
| Number of offspring | Many | Few |
| Parental care | Little or none | Substantial |
| Offspring size | Small | Large |
| Time to maturity | Short | Long |
| Lifespan | Short | Long |
| Mortality | High, often density-independent | Lower, often density-dependent |
| Typical habitat | Unstable, disturbed | Stable, predictable |
| Examples | Insects, weeds, frogs, most fish | Elephants, whales, humans, oak trees |
Survivorship Curves
A survivorship curve plots the proportion of a cohort surviving against age (log scale on the y-axis). Three idealized shapes are tested:
- Type I - low juvenile mortality, most deaths late in life. Humans, large mammals, K-selected species.
- Type II - constant mortality across all ages. Many birds, small mammals, lizards.
- Type III - very high juvenile mortality, survivors live long. Most fish, oysters, plants with many seeds. Classic r-selected pattern.
Age Structure and the Demographic Transition
Age-structure diagrams (population pyramids) show the proportion of individuals in pre-reproductive, reproductive, and post-reproductive classes. A broad base predicts future growth; a narrow base predicts decline.
The demographic transition model describes how human populations change through four stages as a country industrializes:
- Stage 1 - Pre-industrial: high birth and death rates, slow growth.
- Stage 2 - Transitional: death rate falls (sanitation, medicine), birth rate still high, rapid growth.
- Stage 3 - Industrial: birth rate falls (urbanization, education), growth slows.
- Stage 4 - Post-industrial: low birth and death rates, near-zero growth or decline.
According to the U.S. Census Bureau and United Nations Population Division, most developed countries are in stage 4, while many sub-Saharan African nations remain in stage 2 or early stage 3.
A bacterial population of 1,000 cells grows under unlimited resources with an intrinsic rate of increase r = 0.8 per hour. Using the exponential growth equation dN/dt = rN, what is the instantaneous growth rate at this moment?
A deer population on an island has a carrying capacity K = 400. Wildlife managers count 380 deer. According to the logistic growth model dN/dt = rN(K - N)/K, what will happen to the population growth rate as N approaches K?