Applied ecology focused on biodiversity preservation: extinction risk, habitat fragmentation, invasive species, population viability analysis. Substrate of IUCN Red List assessments and reserve-design practice.
conservation-biology
Biodiversity
Variety of life at three nested scales: genetic diversity within populations, species diversity within communities (α, β, γ), and ecosystem…
Extinction risk (IUCN)
IUCN Red List categories: LC, NT, VU, EN, CR, EW, EX with quantitative triggers (≥80% decline in 10 y or 3 gen → CR under A2). Basis of…
Habitat fragmentation
Large contiguous habitat broken into isolated patches; reduces effective population size (edge effects, lower connectivity), often more…
Population viability analysis (PVA)
Stochastic simulation of small-population dynamics integrating demographic stochasticity, environmental variance, catastrophes, and…
Minimum viable population (MVP)
Smallest isolated population with >95% probability of persistence for 100 years (or 1000 years in stricter formulations). Empirical rule of…
Invasive species
Non-native species whose introduction causes ecological, economic, or human health harm. Tens-rule: ~1 in 10 introductions establish, ~1 in…
Reserve design (SLOSS)
Single-Large vs Several-Small debate; resolved pragmatically via systematic-conservation-planning algorithms (Marxan) that optimise…
Inbreeding depression
Reduced fitness in offspring of related individuals due to exposure of deleterious recessives and loss of heterozygote advantage.…
Levins metapopulation: dp/dt=c·p(1−p)−e·p; colonisation-extinction balance
Levins metapopulation framework — the canonical mean-field ODE model of patchy-habitat species persistence (Levins 1969; Hanski 1999…
Arrhenius species-area: S=c·A^z; power-law species-area relationship
Arrhenius species-area power-law framework — the canonical scaling law for biodiversity as a function of habitat area, underlying every…
Lande lognormal SDE: d(ln N)=(r−σ²/2)dt+σ·dW; population viability diffusion
Lande lognormal extinction SDE framework — the canonical stochastic-differential-equation model of environmental-stochasticity-driven…
Levins: dp/dt=c·p(1−p)−e·p; p_ss=(c−e)/c; λ_p0=c−e; at c=2,e=1: p_ss=1/2
Sympy-exact symbolic witness of the Levins metapopulation canonical form and persistence-threshold anchors. Setup: p, c, e — all positive…
SAR: S=A^z·c; dS/dA=A^(z−1)·c·z; elasticity=z exactly; S(2A)/S(A)=2^z
Sympy-exact symbolic witness of the Arrhenius species-area canonical form, elasticity identity, and log-log slope. Setup: c, A, z — all…
Lande SDE: Itô drift=r−σ²/2; critical r*=σ²/2; N_e(100,10)=200/11; drift-var=q(1−q)/(2T)
Sympy-exact symbolic witness of Lande lognormal extinction SDE drift correction, critical threshold, harmonic-mean effective size, and…
IUCN Red List (1964)
IUCN 1964+ Red List + modern 150,388 species 2024 + 42100 threatened; basis of conservation-prioritization.
MVP (Shaffer 1981)
M Shaffer 1981 minimum-viable-population; modern Frankham 50/500 rule + PVA population-viability-analysis.
Hotspots (Myers 2000)
N Myers 2000 36 biodiversity-hotspots; modern Mittermeier 2011 + conservation-prioritization frameworks.
Re-wilding (Soule-Noss 1998)
M Soule-R Noss 1998 re-wilding 3Cs cores-corridors-carnivores; modern Yellowstone + Oostvaardersplassen + Iberian-Lynx.
Deforestation (Laurance 2000)
W Laurance 2000 + Hansen 2013 Global Forest Watch; modern PADDD + REDD+ international policy responses.
Soulé (1985)
M Soulé 1985 'What is conservation biology?'; modern crisis-discipline + 1992 IUCN + 2010 Aichi-targets + 2030 Kunming-Montreal.
Species-area (Arrhenius 1921)
O Arrhenius 1921 species-area S=cA^z; modern Preston-1962 lognormal + Hubbell-2001 unified neutral theory.
MacArthur-Wilson (1967)
R MacArthur-E Wilson 1967 island-biogeography theory of-island-biogeography; modern habitat-fragment connectivity + meta-pop.
PVA (Shaffer 1981)
M Shaffer 1981 minimum-viable-population; modern stochastic-PVA + Lyapunov-exponent demography + climate-extinction-debt.
IUCN Red List (2001)
IUCN 2001 Red-List criteria A-E + LC/NT/VU/EN/CR/EW/EX; modern 150k species assessed + 2024 1M+ at-risk extinction estimate.
Planetary boundaries (Rockström 2009)
J Rockström 2009 + Steffen 2015 9 planetary boundaries; modern 6 transgressed including biosphere-integrity + biogeochemical.