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 →…
May food-web stability (Jacobian random-matrix)
May 1972: random S-species community matrix M with off-diagonal variance σ², connectance C is locally stable iff σ√(SC) < 1. Reframes…
MacArthur resource-utilisation niche overlap
MacArthur 1969 / Tilman 1982: species i resource utilisation u_i(R) on resource axis R; competition coefficient α_ij = ∫ u_i u_j dR / ∫…
Competitive exclusion (Gause 1934)
G F Gause 1934 Paramecium experiments: two species with identical niche cannot coexist indefinitely; one competitively excludes the other;…
Species-area relationship (Arrhenius 1921)
O Arrhenius 1921 + MacArthur-Wilson 1967: S = c A^z; z~0.25 island biogeography, z~0.15 mainland; basis of conservation-biology…
Trophic cascade (Paine 1966)
R Paine 1966 Pisaster keystone-species removal experiment; top-predator regulates lower trophic-levels; basis of food-web theory +…
Intermediate disturbance (Connell 1978)
J Connell 1978 hypothesis: maximum diversity at intermediate disturbance frequency/intensity; tropical-rainforest + coral-reef benchmarks;…
Metacommunity (Leibold 2004)
M Leibold 2004 metacommunity 4-paradigms: patch-dynamics, species-sorting, mass-effects, neutral; dispersal-limitation +…
Functional diversity (Petchey-Gaston 2002)
Petchey-Gaston 2002 FD: dendrogram-based summed-branch-lengths in trait-space; Cornwell 2006 convex-hull volume; basis of…
Lotka-Volterra (1926)
A Lotka 1925 + V Volterra 1926 predator-prey; modern modern foundational text + competition LV + 2024 modern coexistence-theory Chesson…
Niche overlap (MacArthur 1955)
R MacArthur 1955 + Levins 1968 niche-overlap; modern modern foundational + neutral-theory Hubbell 2001 + 2024 modern coexistence-theory.
Gause (1934)
G F Gause 1934 'The Struggle for Existence' competitive-exclusion; modern modern foundational text + 2024 microbial-coexistence stable.
Food web (Elton 1927)
C Elton 1927 'Animal Ecology' food-web; modern modern foundational text + Pimm 1982 + 2024 network-ecology + meta-food-web allometric.
Keystone (Paine 1969)
R Paine 1969 keystone-species Pisaster intertidal; modern modern foundational text + ecological-cascades + 2024 modern keystone-restoration.
Trophic cascade (Power 1992)
M Power 1992 + Carpenter-Kitchell 1985 trophic-cascade; modern modern foundational + Yellowstone-wolves 1995 + meta-analyses 2024.