Environmental Biology II: Population Ecology — Characteristics, Carrying Capacity, Growth and Regulation, Fluctuations, Dispersion and Metapopulations, r- and K-Species and Keystone Species — and Community Ecology, Interactions and Biological Invasions

With unlimited resources a population grows exponentially: dN/dt = rN, where r is the intrinsic rate of natural increase (birth rate minus death rate per individual), and Nt = N₀e^(rt). The doubling time is ln 2 ÷ r ≈ 0.693 ÷ r, or roughly 70 divided by the growth rate in per cent, so a population growing at 2% a year doubles in about 35 years. The curve is J-shaped. No real population can grow this way for long, because resources are finite. The carrying capacity, K, is the maximum population size that an environment can sustain indefinitely with the resources available.

The logistic model of Verhulst (1838), later revived by Pearl and Reed, builds that limit in: dN/dt = rN(1 − N/K). The term (1 − N/K) is the unused fraction of carrying capacity; it is close to 1 when the population is small, so growth is nearly exponential, and falls to 0 as N approaches K, so growth stops. The curve is S-shaped (sigmoid), and its steepest point, the inflection, is at N = K/2, where the growth rate reaches its maximum of rK/4. With r = 0.4 per year and K = 1,000, the population grows fastest at N = 500, by 0.4 × 1000 ÷ 4 = 100 individuals a year; at N = 250 it grows by 0.4 × 250 × (1 − 0.25) = 75. This is why the maximum sustainable yield of a fishery or forest is taken from a stock held near half its carrying capacity.

Regulation is density-dependent when a factor's effect per individual increases with density: competition for food and space, predation, parasitism, disease and stress all intensify in crowded populations and bring them back towards K. It is density-independent when the effect is the same whatever the density: a frost, a flood, a drought or a fire kills a similar proportion of a sparse or a dense population. Density-dependent factors regulate; density-independent factors cause fluctuations but cannot, by themselves, hold a population near an equilibrium.

Real populations fluctuate around K rather than settling on it. Some fluctuate irregularly with the weather; some irrupt, rising rapidly and then crashing, as locusts do; and some cycle with a regular period, the classic cases being the three-to-four-year cycles of lemmings and voles and the roughly ten-year cycle of the snowshoe hare and the Canada lynx, reconstructed from the fur records of the Hudson's Bay Company. Time lags in density-dependent feedback, predator-prey interactions and food supply all generate such oscillations.

Many species live not as one continuous population but as a metapopulation, a "population of populations": subpopulations in separate habitat patches linked by occasional dispersal, each liable to go extinct locally and to be recolonised from the others. Richard Levins (1969) modelled the proportion of occupied patches, p, as dp/dt = cp(1 − p) − ep, where c is the colonisation rate and e the local extinction rate. At equilibrium p* = 1 − e/c, so the metapopulation persists only if colonisation outpaces extinction; with c = 0.5 and e = 0.1, 80% of patches are occupied at equilibrium. The model explains why corridors, which raise c, and the protection of many patches, which spreads the risk of e, are central to conservation in fragmented landscapes.

The terms come from the two parameters of the logistic equation, as MacArthur and Wilson (1967) framed them: r-selection favours a high rate of increase, K-selection efficient competition near carrying capacity. Most species lie somewhere along the continuum. K-selected species are the ones most vulnerable to extinction, because their slow reproduction cannot make up for added mortality. A keystone species has an effect on its community far larger than its abundance would suggest. Robert Paine (1969) removed the predatory starfish Pisaster ochraceus from rocky shores in Washington State, and mussels took over, the number of species falling sharply. Other examples are sea otters, which keep sea urchins from destroying kelp forests; fig trees, which feed many tropical frugivores through lean seasons; elephants, which open woodland; and top predators such as the tiger. Ecosystem engineers such as beavers, which create habitat physically, are a related idea.

A community is an assemblage of populations of different species living and interacting in the same area. Clements saw it as an organismic unit, a "superorganism" whose parts develop together towards a climax; Gleason's individualistic concept (1926) saw it as a coincidental assemblage of species that happen to share tolerances, each distributed independently along gradients. Field studies of species along gradients have largely supported Gleason, though strong interactions do bind some species together. Communities are described by their dominant species, species richness and evenness, vertical stratification and trophic structure.

Predators respond to prey density in characteristic ways, described by Holling's functional responses: type I, a linear rise; type II, a rise that levels off as handling time limits intake; and type III, a sigmoid response when predators switch to abundant prey. Plants resist herbivores with physical defences such as spines and tough leaves and with chemical ones such as alkaloids, tannins and cyanogenic compounds, which herbivores in turn evolve to tolerate, an arms race called coevolution. Allelopathy, a term coined by Molisch in 1937, is the release by one plant of chemicals that inhibit the germination or growth of others; it helps invasive plants such as Parthenium and Lantana form dense stands.

A biological invasion occurs when a species introduced outside its native range establishes, spreads and causes harm. Invasion proceeds through transport, introduction, establishment and spread, and Williamson's "tens rule" suggests that only about one in ten species passes each stage. Invaders often succeed because they have escaped the natural enemies of their home range (the enemy release hypothesis), reproduce fast, tolerate a wide range of conditions and, among plants, may be allelopathic. Invasive alien species are counted among the leading drivers of biodiversity loss. In India the most damaging include Lantana camara in forests, Prosopis juliflora in drylands and grasslands, water hyacinth (Eichhornia crassipes) choking lakes and rivers, Parthenium hysterophorus ("congress grass"), which causes dermatitis and asthma as well as crop losses, Mikania micrantha in the north-east and the Western Ghats, and the African catfish Clarias gariepinus in fresh waters.