Population and Community Ecology

Ecologists study life at several nested levels. A population is all the members of one species living in the same area at the same time, for example every snowshoe hare in a Canadian forest. A community is every population of every species living and interacting in that same area, so the community includes the hares, the lynx that hunt them, the plants the hares eat, and everything else sharing the space. Population ecology asks how a population's size changes over time. Community ecology asks how different species affect each other once they share the same space and resources. This sheet covers both, starting with how populations grow, then how species living together interact.

When a population has unlimited food, space, and no predators or disease, it grows at its maximum possible rate. This is called exponential growth, and it produces a J-shaped curve when population size is graphed against time. The population grows slowly at first, but the rate keeps accelerating because a bigger population produces even more new individuals per unit of time. Exponential growth is described by dN/dt = rN, where N is the population size, t is time, and r is the per capita growth rate (the birth rate minus the death rate for an average individual, ignoring migration for simplicity). dN/dt is the number of new individuals added per unit of time. Example: A bacterial culture has N = 100 cells and a per capita growth rate of r = 0.5 per hour. dN/dt = rN = 0.5 × 100 = 50 new cells added in that hour. As N grows, that number keeps climbing even though r stays the same.

In the real world, resources like food, water, nesting sites, and space run out. As a population grows, individuals compete more for those limited resources, and the growth rate slows down. The maximum population size that an environment can sustain long-term is called the carrying capacity, symbol K. This produces logistic growth, an S-shaped curve. Growth starts off close to exponential when the population is small compared to K, then slows as the population approaches K, and levels off once N reaches K. Logistic growth is described by dN/dt = rN(K − N)/K. The new part, (K − N)/K, is a brake. When N is small compared to K, (K − N)/K is close to 1, so growth is nearly exponential. When N gets close to K, (K − N)/K shrinks toward 0, so growth slows toward zero. Example: A pond can sustain K = 500 fish. The population is currently N = 400, with r = 0.2 per generation. dN/dt = rN(K − N)/K = 0.2 × 400 × (500 − 400)/500 = 0.2 × 400 × 0.2 = 16 fish added that generation.

A limiting factor is anything that keeps a population from growing indefinitely. Limiting factors fall into two categories based on whether their effect depends on how crowded the population already is. Density-dependent factors have a bigger effect as population density rises. Competition for food and space, predation, and the spread of disease all get more intense in a crowded population, because there is less food per individual and diseases pass more easily between individuals that are close together. These factors are what create the braking effect in logistic growth. Density-independent factors affect a population by roughly the same amount no matter how crowded it is. A wildfire, a hard freeze, or a drought kills a similar fraction of a population whether it has 50 members or 5,000.

Community ecology looks at how species affect each other. In predation, one species (the predator) kills and eats another (the prey). The predator benefits and the prey is harmed, so ecologists write this as a +/− interaction. Predator and prey populations often cycle together. The classic example is the snowshoe hare and the Canada lynx: as hares become abundant, lynx have more food and their population grows, but more lynx means more hares are eaten, so the hare population falls, which then causes the lynx population to fall from lack of food, and the cycle repeats roughly every 8 to 11 years. In competition, two organisms use the same limited resource, and both are harmed by the presence of the other, a −/− interaction. Intraspecific competition is between members of the same species, such as tree seedlings of the same species competing for sunlight. Interspecific competition is between different species, such as two lizard species competing for the same insect prey. The competitive exclusion principle states that two species cannot indefinitely occupy the exact same niche if a resource is limiting. One species will eventually outcompete and exclude the other, unless the species evolve or behave differently enough to divide up the resource, a pattern called resource partitioning. A well-studied example is several warbler species that all feed in the same spruce trees but forage in different parts of the tree, letting them coexist.

Three more interactions round out how species affect each other: In mutualism, both species benefit, a +/+ interaction. Bees gain nectar while pollinating flowers, and the flowers get pollinated in return. Nitrogen-fixing bacteria such as Rhizobium live in nodules on legume plant roots, giving the plant usable nitrogen while the bacteria receive sugars and shelter. In commensalism, one species benefits and the other is essentially unaffected, a +/0 interaction. Barnacles that attach to a whale's skin get transported to new feeding grounds while the whale is largely unaffected. Cattle egrets follow grazing cattle and eat the insects the cattle stir up, without helping or harming the cattle. In parasitism, one species (the parasite) benefits by living on or in another species (the host) and harming it, a +/− interaction, the same signs as predation. The key difference is that a parasite usually does not kill its host quickly and often lives on or inside a single host over an extended time. A tapeworm living in a host's intestine, and a tick feeding on a deer, are both parasites.

Every species interaction covered on this sheet can be classified by its effect on each species involved, using + for benefit, − for harm, and 0 for no significant effect.

1. A population is growing exponentially with r = 0.3 per year and N = 200 individuals. What is dN/dt right now? 2. A lake has a carrying capacity of K = 1,000 fish. Does the population grow faster when N = 200 or when N = 900? Why? 3. A severe drought kills a large fraction of a rabbit population no matter how many rabbits there were beforehand. Is drought acting as a density-dependent or density-independent factor here? 4. A cattle egret follows grazing cattle and eats insects the cattle stir up. The cattle are not helped or harmed. Classify this interaction and give its symbol. 5. Using kestrel-pond-population.csv, in which year does the population first reach carrying capacity, and what is that carrying capacity, K? 6. Calculate the percent increase in population from year 0 to year 1, and from year 3 to year 4, using percent change = (later − earlier) ÷ earlier × 100. 7. The pond gains more fish in raw numbers from year 3 to year 4 than it does from year 0 to year 1, yet your answer to Question 6 shows a smaller percent increase in the later interval. Using the (K − N)/K brake term from the logistic growth formula on this sheet, explain why. 8. At year 4, the population is N = 400. Using this sheet's logistic growth formula, dN/dt = rN(K − N)/K, with K = 500 and r = 0.2 per year, calculate dN/dt. 9. Using mark-recapture-survey.csv, estimate the population size at each of the 3 sites with the Lincoln-Petersen formula: N = (M × C) ÷ R, where M is the number marked and released, C is the total second-sample size, and R is the number recaptured that were already marked. Which site has the largest estimated population, and which has the smallest? 10. Suppose Meadow Pond's second sample had instead recaptured 25 marked animals (R = 25) instead of 20. Recalculate the Lincoln-Petersen estimate for Meadow Pond. Is the new estimate higher or lower than your answer in Question 9, and does that match what you'd expect when R increases in the formula?