Population growth, Lotka-Volterra, niche, competition, predation, trophic cascades, diversity indices.
Community Ecology
Population growth (exponential, logistic)
Exponential: dN/dt = rN (unlimited resources). Logistic: dN/dt = rN(1 − N/K) with carrying capacity K (Verhulst 1838). Real populations…
Lotka-Volterra equations
Predator-prey coupled ODEs: dx/dt = αx − βxy, dy/dt = δxy − γy. Produces neutrally-stable oscillations; phenomenological basis for…
Competitive-exclusion principle
Gause 1934: two species requiring identical resources cannot stably coexist; one will exclude the other. Resolution: niche differentiation,…
Ecological niche
N-dimensional hypervolume of environmental conditions + resource use allowing a species to persist (Hutchinson 1957). Fundamental…
Keystone species
Species whose removal disproportionately alters community structure. Paine 1966: Pisaster sea star in rocky intertidal. Sea otters, wolves,…
Trophic cascade
Top-down effects propagating through food web: predator removal → prey release → lower trophic-level depletion. Yellowstone wolves (1995) →…
Species diversity (Shannon, Simpson)
Shannon H' = −Σp_i·ln(p_i); Simpson D = Σp_i². Combine richness + evenness. Shannon weights rare species; Simpson weights dominant ones.
Mutualism
Reciprocally beneficial interaction (pollinator-plant, mycorrhiza, gut microbiome). Obligate vs facultative. Cheater stability problem…
Island biogeography theory
MacArthur & Wilson 1967: species richness = equilibrium between immigration (↓ with distance) + extinction (↓ with area). Foundational for…
Ecological succession
Directional community change: primary (bare substrate, e.g. glacier retreat) or secondary (post-disturbance). Pioneer → intermediate →…