Ecology I: Fundamental Concepts, Population Ecology and Species Interactions

An ecosystem has abiotic components — light, temperature, water, soil, nutrients, pH, salinity — and biotic components: producers, consumers and decomposers, and the interactions among them. Ecology is organised in levels: the individual, the population (individuals of one species in one place), the species, the community (the populations of all species that co-occur), the ecosystem (the community with its abiotic environment and the fluxes of energy and matter between them) and the biome (a large region defined by its climate and its dominant vegetation form). Each level has properties the level below does not: a birth rate belongs to a population, not to an individual; diversity belongs to a community.

The habitat is the place where an organism lives; the niche is its role and its requirements, so two species can share a habitat and differ in niche. Connell’s barnacles on the Scottish coast are the classic demonstration of the realised niche: Chthamalus can live across the whole intertidal zone, but is confined to the upper zone because Balanus outcompetes it lower down; removing Balanus extended Chthamalus downwards. Functional traits are measurable features of an organism that affect its performance or its effect on the ecosystem — specific leaf area, wood density, seed mass, body size, thermal tolerance — and they let ecologists compare communities by what their species do rather than by their names.

Ecophysiology asks how organisms cope with their abiotic environment. Homeostasis holds the internal state steady: regulators (mammals and birds for temperature, freshwater fish for osmotic balance) keep it constant at a cost, conformers let it follow the environment. Acclimation (acclimatisation in the field) is a reversible physiological adjustment within one individual’s lifetime, such as the rise in red-cell count at altitude; adaptation is a heritable change across generations produced by selection. The temperature sensitivity of a rate is summarised by Q₁₀ = (R₂/R₁)^{10/(T₂ − T₁)}: a respiration rate that rises from 2 to 5 units between 15 °C and 25 °C has Q₁₀ = 2.5. Physiological responses to a gradient are hump-shaped performance curves with a tolerance range, and Shelford’s law of tolerance says the distribution of a species is set by the factor it tolerates least well.

With unlimited resources a population grows exponentially: dN/dt = rN, so N(t) = N₀e^rt, where r = b − d is the intrinsic rate of increase (per-capita births minus deaths per unit time). The doubling time is t_d = ln 2 / r = 0.6931/r; a population with r = 0.05 per day doubles every 13.86 days. In discrete generations the model is N_t+1 = λN_t, with λ, the finite rate of increase, related to r by λ = e^r and r = ln λ. λ = 1.2 per year means 20 % growth per year and r = ln 1.2 = 0.182 per year. The population grows if r > 0 (λ > 1), is stationary at r = 0 (λ = 1) and declines if r < 0 (λ < 1).

Resources run out, and the logistic model adds a brake: dN/dt = rN(1 − N/K), where K is the carrying capacity. Its solution is the S-shaped curve N(t) = K / [1 + ((K − N₀)/N₀)e^−rt]. The per-capita growth rate (1/N)dN/dt = r(1 − N/K) falls linearly with N, from r at N → 0 to zero at N = K. The population growth rate dN/dt = rN − rN²/K is a downward parabola in N; setting its derivative r − 2rN/K to zero gives the maximum at N = K/2, where dN/dt = rK/4. This is the basis of maximum sustainable yield: with r = 0.4 per year and K = 1000, the fastest growth is 100 individuals per year at N = 500.

Density-dependent factors change the per-capita birth or death rate as density changes — competition for food or nest sites, disease transmission, predation that intensifies on a common prey — and can regulate a population towards an equilibrium. Density-independent factors act with the same per-capita force whatever the density — a frost, a flood, a drought — and cause fluctuations but cannot regulate. Delayed density dependence (a time lag between density and its effect, as in discrete-time models with large r) can turn a smooth approach to K into damped oscillations, cycles or chaos.

Population size is rarely counted directly. In mark–recapture, M animals are caught, marked and released; later a sample of n is caught, of which m are marked. If marked animals mix randomly, m/n = M/N, giving the Lincoln–Petersen estimate N̂ = Mn/m. Marking 120 fish, then catching 150 of which 30 are marked, gives N̂ = 120 × 150/30 = 600. The estimate assumes a closed population (no births, deaths or migration between samples), marks that are not lost and do not change behaviour, and equal catchability. For small samples Chapman’s form N̂ = (M + 1)(n + 1)/(m + 1) − 1 reduces the bias.

A cohort life table follows a group born at the same time. From the number alive at the start of each age class, nₓ, everything else follows: survivorship lₓ = nₓ/n₀; deaths dₓ = nₓ − nₓ₊₁; age-specific mortality qₓ = dₓ/nₓ; the average number alive during the interval Lₓ = (nₓ + nₓ₊₁)/2; the total individual-intervals still to be lived Tₓ = Σ Lₓ from x onwards; and life expectancy eₓ = Tₓ/nₓ. With the age-specific fecundity mₓ (female offspring per female in age class x) the table gives the net reproductive rate R₀ = Σ lₓmₓ, the average number of daughters a newborn female produces in her lifetime, and the generation time T = Σ x lₓmₓ / R₀. Then r ≈ ln R₀ / T.

From the table: R₀ = 0 + 1.0 + 0.6 + 0.1 = 1.7, so each female replaces herself 1.7 times and the population grows. Σ x lₓmₓ = 1 × 1.0 + 2 × 0.6 + 3 × 0.1 = 2.5, so T = 2.5/1.7 = 1.47 years, and r ≈ ln 1.7/1.47 = 0.531/1.47 = 0.36 per year. Life expectancy at birth is e₀ = 1250/1000 = 1.25 years; at age 1 it is e₁ = 500/500 = 1.00 year. Notice that q rises with age here, which is a Type I pattern in the later classes.

The Leslie matrix projects an age-structured population: n(t + 1) = L n(t), where the top row holds the fecundities Fₓ and the sub-diagonal the survival probabilities Pₓ from class x to x + 1. With L = [[0, 2, 1.5], [0.5, 0, 0], [0, 0.4, 0]] and n(0) = (100, 50, 20): the new first class is 0 × 100 + 2 × 50 + 1.5 × 20 = 130; the second is 0.5 × 100 = 50; the third is 0.4 × 50 = 20, so n(1) = (130, 50, 20), total 200. One step more gives (2 × 50 + 1.5 × 20, 0.5 × 130, 0.4 × 50) = (130, 65, 20), total 215. Repeated projection converges to a stable age distribution (the dominant eigenvector) in which every class grows by the same factor each step, the dominant eigenvalue λ; λ > 1 means growth.

A metapopulation is a population of populations: local populations in discrete habitat patches, each of which can go extinct and be recolonised by dispersers from occupied patches. In Levins’ model the fraction of occupied patches p changes as dp/dt = c p(1 − p) − e p, colonisation of empty patches at rate c by occupied ones, minus extinction at rate e. At equilibrium p* = 1 − e/c; with e = 0.2 and c = 0.5 per year, 60 % of patches are occupied. The metapopulation persists only if c > e, and it can persist regionally even though every local population is doomed — persistence is a property of the network, not of any patch.

• Source–sink dynamics: in a source habitat births exceed deaths (λ > 1) and surplus individuals emigrate; a sink (λ < 1) persists only through immigration. A sink can hold many individuals, so abundance is not a reliable guide to habitat quality.
• Rescue effect: immigration into a declining local population lowers its extinction risk, so extinction rate falls as the fraction of occupied patches rises.
• The Glanville fritillary butterfly on the Åland islands of Finland, studied by Hanski and colleagues, is the textbook metapopulation: hundreds of meadow patches with frequent local extinction and recolonisation.
• Conservation corollary: destroying a fraction e/c of patches — even empty ones — can push the whole network to extinction, because empty patches are the targets of colonisation.

"Symbiosis" in its broad, de Bary sense means any intimate living-together and so includes parasitism as well as mutualism; in many textbooks it is used for close mutualisms such as lichens. The Lotka–Volterra competition model gives each species logistic growth reduced by the other: dN₁/dt = r₁N₁(K₁ − N₁ − αN₂)/K₁ and dN₂/dt = r₂N₂(K₂ − N₂ − βN₁)/K₂, where α is the per-capita effect of species 2 on species 1 measured in species-1 equivalents. The zero-growth isoclines are straight lines: N₁ = K₁ − αN₂ and N₂ = K₂ − βN₁. Their relative positions give four outcomes: species 1 always wins, species 2 always wins, a stable coexistence equilibrium, or an unstable equilibrium where the winner depends on the starting numbers.

Solving the two isoclines together gives the interior equilibrium N₁* = (K₁ − αK₂)/(1 − αβ) and N₂* = (K₂ − βK₁)/(1 − αβ). Coexistence is stable when α < K₁/K₂ and β < K₂/K₁ — each species limits itself more than it limits its competitor. With K₁ = 500, K₂ = 400, α = 0.5 and β = 0.6: α < 1.25 and β < 0.8, so both conditions hold; 1 − αβ = 0.7; N₁* = (500 − 200)/0.7 = 428.6 and N₂* = (400 − 300)/0.7 = 142.9. Gause’s competitive exclusion principle — complete competitors cannot coexist — is the limiting case in which the niches do not differ.

The Lotka–Volterra predator–prey model is dN/dt = rN − aNP for prey and dP/dt = baNP − mP for predators, with attack rate a, conversion efficiency b and predator death rate m. Setting each to zero: prey stop changing when P* = r/a, predators when N* = m/(ba). With r = 0.6, a = 0.01, b = 0.1 and m = 0.2: P* = 60 and N* = 0.2/0.001 = 200. The model produces neutral cycles — predator peaks lag prey peaks by a quarter cycle and the amplitude is set by the starting point — which is structurally unstable; adding prey density dependence damps the cycles. The functional response (prey eaten per predator against prey density) is Holling’s Type I (linear), Type II (saturating, set by handling time) or Type III (sigmoid, which can stabilise prey at low density through prey switching or refuges).

Effects also travel indirectly through food webs. In a trophic cascade a top predator suppresses herbivores and so releases plants: sea otters eat sea urchins, and where otters were hunted out, urchins grazed kelp forests into barrens. Keystone species have effects far out of proportion to their abundance — Paine’s removal of the starfish Pisaster from rocky shores let mussels monopolise space and cut the number of species. Apparent competition arises when two prey share a predator: more of one prey feeds more predators, which then eat more of the other, so the two prey harm each other without ever competing for a resource. Top-down (consumer) and bottom-up (resource) control both operate, and their relative strength differs between systems.