Study guide & lexicon

The Ecological Theater

Core theory for the comprehensive exam in ecology and wildlife science: a companion to the narrated program.
42:15 running time9 chapters128 lexicon terms104 references

Each chapter lists the key equations, the landmark studies an examiner is likely to cite, every numbered lexicon term from the video (with the time it appears), and practice prompts. Work the prompts aloud and sketch each graph from memory: isoclines, rate curves, phase planes. Timestamps match the video and the interactive player.

I

Population Dynamics

How, and why, do populations change in size?
video 0:43–7:10
0:51 Exponential & geometric growth · 1:58 Logistic growth & density dependence · 3:05 Time lags, cycles & chaos · 4:08 Life tables & matrix models · 5:33 Stochasticity, viability & life history

Key equations

Exponential growth
dN/dt = rN,   N(t) = N0ert,   r = b − d,   td = ln 2 / r
Geometric growth
Nt+1 = λNt,   λ = er
Logistic growth
dN/dt = rN(1 − N/K);   MSY = rK/4 at N = K/2
Delayed logistic (Hutchinson)
dN/dt = rN(t)[1 − N(t − τ)/K]: monotonic if rτ < 1/e; damped if 1/e < rτ < π/2; limit cycle if rτ > π/2
Logistic map (May)
xt+1 = rxt(1 − xt): 2-cycle at r = 3, 4-cycle at ≈ 3.449, chaos beyond ≈ 3.57
Life table
R0 = Σ lxmx;   G = Σ x lxmx / R0;   r ≈ ln R0 / G
Matrix model
n(t+1) = A n(t); λ = dominant eigenvalue; w = stable stage distribution; v = reproductive values; sensitivity sij = viwj/⟨v,w⟩; elasticity eij = (aij/λ)sij
Variable environments
λG = (Π λt)1/T ≤ λ̄;   ln λG ≈ ln λ̄ − σ2/(2λ̄2)

Landmark studies

StudySystemKey finding
Hutchinson 1948TheoryTime lags in density dependence can generate oscillations.
May 1976Logistic mapSimple deterministic models produce period doubling and chaos.
Crouse, Crowder & Caswell 1987Loggerhead sea turtleλ most elastic to large-juvenile survival; supported turtle excluder devices over egg protection alone.
Shaffer 1981Minimum viable populationDefined MVP via a persistence probability and time horizon (e.g., 99% for 1000 years).
Gilpin & Soulé 1986Extinction vortexGenetic and demographic processes reinforce declines in small populations.
Grime 1977Plant strategiesC-S-R triangle of competitors, stress-tolerators, and ruderals.

Lexicon

No. 0010:52
Intrinsic rate of increase (r)
Instantaneous per-capita growth rate, b − d, under ideal conditions; units of 1/time.
No. 0021:19
Finite rate of increase (λ)
Ratio of population sizes in successive time steps, N(t+1)/N(t); λ = e^r.
No. 0031:41
Density independence
Per-capita birth and death rates that do not change with population density.
No. 0041:59
Density dependence
Per-capita birth or death rates that change with population density; the basis of population regulation.
No. 0052:15
Carrying capacity (K)
Equilibrium density at which per-capita births equal deaths.
No. 0062:15
Maximum sustainable yield
Largest harvest a population can sustain indefinitely; at N = K/2 in the logistic model.
No. 0072:29
Compensation & overcompensation
Recruitment that saturates (Beverton–Holt) versus recruitment that declines at high density (Ricker).
No. 0082:47
Allee effect
Positive density dependence at low density; a strong Allee effect produces an extinction threshold.
No. 0093:06
Time lag
Delay between a change in density and the resulting change in per-capita growth.
No. 0103:16
Limit cycle
A self-sustaining oscillation of fixed amplitude that trajectories approach from any start.
No. 0113:34
Period-doubling bifurcation
Abrupt doubling of a cycle’s period as a parameter increases: 1 → 2 → 4 → … → chaos.
No. 0123:53
Deterministic chaos
Bounded, aperiodic dynamics from a deterministic rule, with sensitive dependence on initial conditions.
No. 0134:09
Survivorship (lₓ)
Proportion of a cohort surviving from birth to age x.
No. 0144:41
Net reproductive rate (R₀)
R₀ = Σ lₓmₓ: expected lifetime offspring per individual; growth per generation.
No. 0154:54
Leslie & Lefkovitch matrices
Projection matrices of age- or stage-specific survival and fecundity; dominant eigenvalue = λ.
No. 0164:54
Stable stage distribution
Constant proportions among stages approached under fixed vital rates (right eigenvector).
No. 0175:13
Elasticity
Proportional change in λ per proportional change in a vital rate; elasticities sum to 1.
No. 0185:34
Demographic stochasticity
Chance variation in individual births and deaths; strongest in small populations.
No. 0195:34
Environmental stochasticity
Temporal variation in vital rates that affects all individuals together; catastrophes are extreme cases.
No. 0205:55
Geometric mean growth
Long-run λ under variability; always ≤ the arithmetic mean, so variance reduces growth.
No. 0216:12
PVA & minimum viable population
Projection of extinction risk; MVP = smallest population with an acceptable persistence probability.
No. 0226:32
Extinction vortex
Mutually reinforcing genetic and demographic declines in small populations (Gilpin & Soulé 1986).
No. 0236:45
r- and K-selection
Life-history strategies favored at low density and high variability (r) versus near carrying capacity (K).

Exam prompts

  1. Derive maximum sustainable yield from the logistic model. Why is harvesting at MSY risky when the environment varies?
  2. Show with a numerical example why variance in λ lowers long-run growth even when mean λ exceeds 1.
  3. Distinguish sensitivity from elasticity. How did elasticity analysis change sea turtle conservation?
  4. How does a strong Allee effect change the logic of minimum viable population size?
II

Niche Theory

Where can a species live, and what does it do there?
video 7:10–12:04
7:18 Three ideas of the niche · 8:23 Fundamental & realized niches · 9:23 Partitioning & limiting similarity · 10:50 The modern niche

Key equations

MacArthur–Levins overlap
αij = Σk pikpjk / Σk pik2   (p = proportional use of resource k)
Pianka overlap
Ojk = Σ pijpik / √(Σ pij2 Σ pik2)
Limiting similarity
coexistence requires roughly d/w ≳ 1 (separation of means / utilization width)
Requirement niche (ZNGI)
the set of resource levels where (1/N) dN/dt = f(R1, R2) − m = 0

Landmark studies

StudySystemKey finding
Grinnell 1917California thrasherNiche as the habitat conditions a species requires.
Elton 1927Animal EcologyNiche as functional role: relations to food and enemies.
Hutchinson 1957TheoryNiche as an n-dimensional hypervolume; fundamental vs realized niches.
Connell 1961Barnacles, Isle of CumbraeCompetition from Balanus sets the lower limit of Chthamalus; desiccation sets Balanus’s upper limit.
MacArthur 1958Spruce-woods warblersFive congeners partition foraging zones and behavior within trees.
Lack 1947; Grant & Grant 2006Darwin’s finchesCharacter displacement in beak size in sympatry.
Chase & Leibold 2003TheoryNiche = requirements (ZNGIs) + impacts (consumption vectors).
Soberón & Peterson 2005Distribution modelingBAM diagram: Abiotic, Biotic, and Movement constraints on distributions.

Lexicon

No. 0247:19
Grinnellian niche
The habitat and environmental conditions a species requires; the basis of distribution modeling.
No. 0257:36
Eltonian niche
A species’ functional role: what it eats, what eats it, and its effects on the community.
No. 0267:52
Hutchinsonian niche
The n-dimensional hypervolume of conditions and resources permitting a species to persist.
No. 0278:24
Fundamental niche
Conditions under which a species can persist given abiotic tolerances alone, without enemies or competitors.
No. 0288:24
Realized niche
The portion of the fundamental niche a species actually occupies, given biotic interactions.
No. 0299:24
Niche partitioning
Division of resources, space, or time among coexisting species, reducing competition.
No. 0309:42
Niche overlap
Shared use of resources by two species, measured as overlap of utilization curves.
No. 0319:58
Limiting similarity
The maximum similarity in resource use compatible with stable coexistence (MacArthur & Levins 1967).
No. 03210:18
Character displacement
Evolutionary divergence of traits where competing species co-occur (sympatry) but not apart (allopatry).
No. 03310:37
Ghost of competition past
Connell (1980): present niche differences produced by past competition, now no longer observable.
No. 03410:51
Requirement & impact niches
Chase & Leibold (2003): conditions allowing zero or positive growth, and the species’ per-capita effects on them.
No. 03511:07
ZNGI
Zero net growth isocline: resource levels at which a population’s growth exactly balances its losses.
No. 03611:30
Species distribution model
Statistical model relating occurrences to environmental predictors to map habitat suitability.
No. 03711:30
BAM diagram
Soberón & Peterson: occupied area = overlap of Abiotic suitability, Biotic interactions, and Movement.
No. 03811:51
Niche construction
Modification of the environment by organisms, altering selection on themselves and others.

Exam prompts

  1. Compare Grinnellian, Eltonian, and Hutchinsonian niches. Which does a species distribution model estimate, and why?
  2. Design an experiment that separates the fundamental from the realized niche of two plants along a moisture gradient.
  3. What evidence would distinguish character displacement from alternative explanations (cf. Schluter & McPhail 1992)?
  4. Explain how requirement and impact niches together predict the outcome of competition.
III

Competition

What happens when species need the same things?
video 12:04–18:13
12:12 Kinds of competition · 13:52 Lotka–Volterra competition · 15:25 Resource competition & R* · 16:36 Modern coexistence theory

Key equations

Lotka–Volterra competition
dN1/dt = r1N1(K1 − N1 − α12N2)/K1;   dN2/dt = r2N2(K2 − N2 − α21N1)/K2
Outcomes
species 1 wins: K1 > K2/α21 and K1/α12 > K2 · species 2 wins: reverse · stable coexistence: K1 < K2/α21 and K2 < K1/α12 (α12 < K1/K2, α21 < K2/K1) · unstable (priority effects): K1 > K2/α21 and K2 > K1/α12
Resource competition (Tilman)
dN/dt = N[f(R) − m]; R* solves f(R*) = m; with Monod uptake f = μmaxR/(Ks + R), R* = m Ks/(μmax − m)
Modern coexistence (Chesson)
coexistence when ρ < κ1/κ2 < 1/ρ; niche difference = 1 − ρ; fitness ratio = κ1/κ2; invasion criterion: r̄i > 0 when rare

Landmark studies

StudySystemKey finding
Gause 1934ParameciumCompetitive exclusion in laboratory cultures.
Park 1954Tribolium flour beetlesClimate-dependent outcomes and priority effects.
Tilman 1977Freshwater diatomsPhosphate and silicate ratios predicted competitive outcomes (R* and resource ratios).
Wedin & Tilman 1993Prairie grassesLowest R* for soil nitrogen predicted the winner.
Schoener 1983Review of field experimentsCompetition common in field experiments; six mechanisms of competition.
Holt 1977TheoryApparent competition through a shared predator.
Janzen 1970; Connell 1971Tropical treesSpecialist enemies near parents promote diversity (Janzen–Connell).
Chesson 2000TheoryStabilizing vs equalizing mechanisms; storage effect; relative nonlinearity.
Hutchinson 1961PhytoplanktonParadox of the plankton.

Lexicon

No. 03912:13
Intra- vs interspecific competition
Competition within a species (the source of density dependence) versus between species.
No. 04012:30
Exploitative vs interference
Indirect competition through resource depletion versus direct prevention of resource use.
No. 04112:48
Allelopathy
Chemical interference: release of compounds that inhibit competitors (e.g., juglone of black walnut).
No. 04213:08
Scramble vs contest
Even division of resources so all suffer, versus winners taking enough and losers none (Nicholson 1954).
No. 04313:08
Asymmetric competition
Unequal per-capita effects between competitors; e.g., size-asymmetric competition for light.
No. 04413:34
Apparent competition
Indirect negative interaction between prey species mediated by a shared predator (Holt 1977).
No. 04513:53
Competition coefficient (α)
Per-capita effect of one species on another’s growth, relative to intraspecific effects.
No. 04614:13
Zero-growth isocline
All combinations of densities at which a species’ growth rate is zero.
No. 04714:28
Competitive exclusion principle
Gause: complete competitors cannot coexist indefinitely; one excludes the other.
No. 04814:50
Priority effect
When arrival order or initial abundance determines the outcome of interactions.
No. 04915:26
R*
Minimum resource level at which a population can persist; with one limiting resource, lowest R* wins.
No. 05016:19
Supply point
Resource availability in the absence of consumers; locates the outcome on the two-resource plane.
No. 05116:19
Resource-ratio hypothesis
Tilman: the ratio of limiting resources supplied determines which species dominate or coexist.
No. 05216:37
Mutual invasibility
Coexistence criterion: each species has a positive growth rate when rare in the other’s presence.
No. 05316:52
Stabilizing mechanism
Niche difference causing stronger intra- than interspecific limitation; favors species when rare.
No. 05416:52
Equalizing mechanism
Reduction in average fitness differences between species; cannot by itself stabilize coexistence.
No. 05517:27
Janzen–Connell effect
Specialist enemies concentrated near parent trees reduce recruitment of conspecifics nearby.
No. 05617:27
Storage effect
Fluctuation-dependent coexistence: species-specific responses to environment plus buffered population growth.
No. 05717:53
Paradox of the plankton
Hutchinson (1961): many phytoplankton coexist on few resources, defying competitive exclusion.

Exam prompts

  1. Draw the four Lotka–Volterra isocline configurations and state the condition for each outcome.
  2. Why does the species with the lowest R* win? Which assumptions does the rule require?
  3. Distinguish stabilizing from equalizing mechanisms, with a field example of each.
  4. How would you test for apparent competition in a field system?
IV

Predation

How do consumers and their victims shape each other?
video 18:13–24:23
18:19 Predator–prey cycles · 19:32 Functional & numerical responses · 20:49 Optimal foraging · 21:39 Enrichment & stability · 22:49 Keystones, cascades & fear

Key equations

Lotka–Volterra predator–prey
dN/dt = rN − aNP;   dP/dt = caNP − mP;   isoclines N* = m/(ca), P* = r/a
Functional responses (Holling)
Type II: f(N) = aN/(1 + ahN) → 1/h as N → ∞;   Type III: f(N) = aN2/(1 + ahN2)
Rosenzweig–MacArthur
dN/dt = rN(1 − N/K) − aNP/(1 + ahN);   dP/dt = caNP/(1 + ahN) − mP
Nicholson–Bailey
Ht+1 = λHte−aPt;   Pt+1 = cHt(1 − e−aPt)
Marginal value theorem
leave when g′(t*) = g(t*)/(τ + t*), the long-term average intake rate including travel time τ
Diet model
add prey type i (ranked by E/h) if Ei/hi > Σj<i λjEj / (1 + Σj<i λjhj)

Landmark studies

StudySystemKey finding
Gause 1934Paramecium & DidiniumPredator eliminated prey unless refuges or immigration were added.
Huffaker 1958Mites on orangesPersistence required spatial complexity and dispersal barriers.
Holling 1959Functional responsesTypes I–III; the disc equation and handling time.
Rosenzweig 1971TheoryParadox of enrichment.
Krebs et al. 1995; Sheriff et al. 2009Snowshoe hare, Kluane (Yukon)Food and predation jointly drive the cycle; predator-induced stress lowers reproduction.
Paine 1966, 1969Pisaster, Washington coastKeystone predation maintains diversity (15 → 8 species after removal).
Hairston, Smith & Slobodkin 1960TheoryGreen world hypothesis: predators limit herbivores.
Estes et al. 1998Aleutian kelp forestsOrca predation on otters released urchins and collapsed kelp.
Crooks & Soulé 1999Southern California scrubCoyote loss led to mesopredator release and bird declines.
Zanette et al. 2011Song sparrowsPredator playback alone reduced annual offspring by ~40%.
Charnov 1976TheoryMarginal value theorem for patch residence.

Lexicon

No. 05818:20
Lotka–Volterra predator–prey model
dN/dt = rN − aNP; dP/dt = caNP − mP: exponential prey, linear functional response.
No. 05918:53
Neutral cycles
Closed orbits whose amplitude depends only on initial conditions; structurally unstable.
No. 06019:11
Population cycle
Regular multi-year oscillation in abundance, e.g., the ~10-year snowshoe hare–lynx cycle.
No. 06119:33
Functional response
Per-predator consumption rate as a function of prey density (Holling Types I, II, III).
No. 06219:43
Handling time (h)
Time to pursue, subdue, and consume one prey item; caps intake at 1/h in a Type II response.
No. 06320:04
Prey switching
Disproportionate attack on whichever prey type is most common; one cause of Type III responses.
No. 06420:33
Numerical response
Change in predator density with prey density, via reproduction or aggregation.
No. 06520:33
Total response
Functional × numerical response: total prey killed per unit time.
No. 06620:50
Optimal foraging theory
Predicts foraging decisions that maximize net energy intake rate.
No. 06721:00
Profitability
Energy gained per unit handling time (E/h) for a prey type; the basis of diet ranking.
No. 06821:19
Marginal value theorem
Charnov (1976): leave a patch when its marginal intake rate falls to the habitat-wide average.
No. 06921:40
Rosenzweig–MacArthur model
Predator–prey model with logistic prey and a Type II functional response; hump-shaped prey isocline.
No. 07022:08
Paradox of enrichment
Rosenzweig (1971): raising prey carrying capacity destabilizes predator–prey dynamics.
No. 07122:26
Nicholson–Bailey model
Discrete host–parasitoid model with diverging oscillations; stabilized by aggregation or refuges.
No. 07222:26
Prey refuge
Habitat or condition protecting part of the prey population, which tends to stabilize dynamics.
No. 07322:50
Keystone species
A species whose impact on its community is disproportionately large relative to its abundance (Paine).
No. 07423:33
Trophic cascade
Alternating indirect effects of predators down a food chain, e.g., otters → urchins → kelp.
No. 07523:33
Top-down vs bottom-up
Regulation of populations by consumers above them versus by resources below them.
No. 07623:33
Mesopredator release
Increase in smaller predators after loss of an apex predator (Crooks & Soulé 1999).
No. 07723:55
Non-consumptive effects
Effects of predation risk on prey behavior, physiology, and demography without killing.
No. 07823:55
Landscape of fear
Spatial variation in prey-perceived predation risk that shapes habitat use.

Exam prompts

  1. Why is the Lotka–Volterra predator–prey model structurally unstable? List modifications that stabilize it.
  2. Explain the paradox of enrichment with the Rosenzweig–MacArthur isocline diagram.
  3. Contrast consumptive and non-consumptive effects of predators. How could you separate them experimentally?
  4. Under what conditions should a trophic cascade propagate to primary producers?
V

Island Biogeography

Why do islands hold the species they do?
video 24:23–29:01
24:32 The species–area relationship · 25:32 The equilibrium theory · 26:47 Experiments & refinements · 27:55 Habitat islands & conservation

Key equations

Species–area relationship
S = cAz;   log S = log c + z log A;   islands z ≈ 0.20–0.35, mainland nested samples ≈ 0.12–0.17
Linear equilibrium model
I(S) = I0(1 − S/P), E(S) = E0S/P  ⇒  Ŝ = I0P/(I0 + E0),   turnover T = I0E0/(I0 + E0)
Darlington’s rule
with z ≈ 0.3, a tenfold loss of area leaves 10−0.3 ≈ 0.5 of the species

Landmark studies

StudySystemKey finding
MacArthur & Wilson 1963, 1967TheoryEquilibrium theory: richness balances immigration and extinction.
Simberloff & Wilson 1969Mangrove islets, Florida KeysArthropods recolonized to near pre-defaunation richness within ~1 year, with turnover.
Brown & Kodric-Brown 1977Arthropods on thistlesRescue effect: immigration lowers extinction on near islands.
Lomolino 1990Mammals on islandsTarget-area effect: larger islands receive more immigrants.
Diamond 1975; Simberloff & Abele 1976Reserve designThe SLOSS debate.
Newmark 1987Western North American parksMammal extinctions since establishment, greatest in small parks.
Whittaker et al. 2008Oceanic islandsGeneral dynamic model: island age, area, and in-situ speciation.

Lexicon

No. 07924:33
Species–area relationship
S = cA^z: species richness increases as a power function of area.
No. 08024:59
z-value
Slope of log S vs. log A; ~0.2–0.35 for islands, ~0.12–0.17 for mainland samples.
No. 08125:33
Equilibrium theory of island biogeography
MacArthur & Wilson: island richness is a dynamic balance of immigration and extinction.
No. 08225:50
Source pool (P)
The set of species on the mainland available to colonize an island.
No. 08326:12
Turnover
Replacement of species at equilibrium: extinction of residents balanced by new arrivals.
No. 08426:25
Distance & area effects
Isolation lowers immigration; small area raises extinction.
No. 08526:48
Defaunation experiment
Simberloff & Wilson (1969): removing island arthropods to watch recolonization reach equilibrium.
No. 08627:11
Rescue effect
Immigration that bolsters small populations and lowers extinction rates (Brown & Kodric-Brown 1977).
No. 08727:11
Target effect
Larger islands intercept more dispersers, raising immigration rates.
No. 08827:36
In situ speciation
On remote islands, new species arise within the archipelago, adding to richness beyond immigration.
No. 08927:56
Habitat fragmentation
Breaking of continuous habitat into smaller, isolated patches within a matrix of altered land.
No. 09027:56
Relaxation
Decline of species richness in a newly isolated fragment toward a lower equilibrium (faunal collapse).
No. 09128:16
Extinction debt
Future extinctions already committed by past habitat loss or isolation.
No. 09228:34
SLOSS debate
Single large or several small reserves of equal total area: which conserves more species?

Exam prompts

  1. Draw the MacArthur–Wilson diagram for near/far and large/small islands; predict richness and turnover for each.
  2. What did the Simberloff–Wilson defaunation experiment demonstrate, and what were its limitations?
  3. Define extinction debt and explain how you would estimate it for a fragmented landscape.
  4. Argue both sides of SLOSS for a reserve network in your own study system.
VI

Metapopulations

How does a species persist when every local population winks out?
video 29:01–33:06
29:09 The Levins model · 30:17 Habitat loss & the extinction threshold · 31:12 Kinds of spatial populations · 32:17 Spatially realistic metapopulations

Key equations

Levins model
dp/dt = cp(1 − p) − ep;   p* = 1 − e/c; persistence requires c > e
Habitat destruction
dp/dt = cp(1 − D − p) − ep;   p* = 1 − D − e/c; extinction threshold at D = 1 − e/c
Incidence function model (Hanski)
Ji = Ci/(Ci + Ei − CiEi);   Ei = min(1, e/Aix);   Ci = Si2/(Si2 + y2)
Connectivity
Si = Σj≠i pj e−αdij Ajb
Source–sink
sources: λ > 1 (net exporters); sinks: λ < 1 (persist only with immigration)

Landmark studies

StudySystemKey finding
Levins 1969Agricultural pestsMetapopulation concept and patch-occupancy model.
Harrison 1991ReviewTypes: classic, mainland–island, patchy, nonequilibrium.
Pulliam 1988TheorySources, sinks, and population regulation.
Hanski 1994, 1998Glanville fritillary, ÅlandIncidence function model; occupancy predicted by area and connectivity.
Moran 1953Canadian lynxCorrelated weather synchronizes separate populations (Moran effect).
Tilman, May, Lehman & Nowak 1994TheoryHabitat destruction and extinction debt; best competitors lost first.
Schlaepfer, Runge & Sherman 2002ReviewEcological and evolutionary traps.

Lexicon

No. 09329:10
Metapopulation
A set of local populations in discrete patches linked by dispersal, with local extinction and recolonization.
No. 09429:28
Patch occupancy (p)
Fraction of habitat patches occupied; the state variable of the Levins model.
No. 09529:47
Equilibrium occupancy (p*)
p* = 1 − e/c in the Levins model; the metapopulation persists only if c > e.
No. 09630:31
Extinction threshold
Level of habitat loss at which a metapopulation collapses although suitable habitat remains: D = 1 − e/c.
No. 09730:46
Unoccupied suitable habitat
Empty patches capable of supporting a population; essential to colonization–extinction dynamics.
No. 09831:13
Mainland–island metapopulation
A large persistent population supplies colonists to small, extinction-prone satellite populations.
No. 09931:13
Patchy population
Patches linked by such frequent dispersal that they function as one population.
No. 10031:38
Source–sink dynamics
Pulliam (1988): surplus from habitats with λ > 1 sustains populations in habitats with λ < 1.
No. 10131:56
Ecological trap
Low-quality habitat that animals prefer because once-reliable cues have become decoupled from quality.
No. 10232:18
Incidence function model
Hanski (1994): patch occupancy probability as a function of patch area and connectivity.
No. 10332:18
Connectivity
Distance-weighted influence of the surrounding occupied patches, scaled by their areas (Hanski’s Sᵢ).
No. 10432:48
Spatial synchrony
Correlated fluctuations among local populations, raising the risk of simultaneous extinction.
No. 10532:48
Moran effect
Synchrony among populations induced by correlated environmental variation such as shared weather.

Exam prompts

  1. Derive p* for the Levins model and explain why a species can vanish while suitable habitat remains.
  2. Distinguish the main metapopulation types and give a real example of each.
  3. Why can abundance mislead about habitat quality? Include ecological traps in your answer.
  4. How does spatial synchrony affect metapopulation persistence, and what causes it?
VII

Metacommunities

How do local communities connect across a region?
video 33:06–36:26
33:13 Scale & diversity · 34:24 Four paradigms · 35:30 Dispersal & diagnosis

Key equations

Whittaker’s partition
γ = ᾱ × β (multiplicative); additive form γ = ᾱ + βadd
Turnover vs nestedness (Baselga)
βSOR = βSIM (turnover) + βSNE (nestedness-resultant)
Variation partitioning
[a] environment only + [b] shared + [c] space only + [d] unexplained = 1 (adjusted R2 from RDA)

Landmark studies

StudySystemKey finding
Whittaker 1960, 1972Siskiyou Mountains vegetationIntroduced α, β, and γ diversity.
Tilman 1994TheoryCompetition–colonization trade-off permits regional coexistence.
Leibold et al. 2004SynthesisMetacommunity concept; four paradigms.
Mouquet & Loreau 2003TheoryLocal diversity peaks at intermediate dispersal; β declines with dispersal.
Cottenie 2005Meta-analysis of 158 datasetsVariation partitioning across metacommunities; species sorting most common.
Kraft et al. 2015CritiqueCompetition can masquerade as environmental filtering.

Lexicon

No. 10633:14
Metacommunity
A set of local communities linked by dispersal of multiple potentially interacting species (Leibold et al. 2004).
No. 10733:28
Alpha, beta & gamma diversity
Local richness, among-site compositional variation, and regional richness; γ = α × β (Whittaker).
No. 10833:47
Turnover vs nestedness
Beta diversity from species replacement versus from poorer sites holding subsets of richer ones.
No. 10934:01
Environmental filtering
Exclusion of species unable to tolerate local abiotic conditions during community assembly.
No. 11034:25
Patch dynamics
Paradigm of identical patches where coexistence arises from a competition–colonization trade-off.
No. 11134:25
Competition–colonization trade-off
Better competitors are poorer colonizers, allowing fugitive species to persist regionally.
No. 11234:43
Species sorting
Paradigm in which environmental heterogeneity and niche differences determine local composition.
No. 11334:59
Mass effects
Paradigm in which high dispersal sustains species in sink patches, decoupling composition from environment.
No. 11435:31
Dispersal limitation
Failure of species to reach all suitable sites, leaving composition spatially structured.
No. 11535:49
Variation partitioning
Dividing explained compositional variation into pure environmental, pure spatial, and shared fractions.

Exam prompts

  1. Contrast the four metacommunity paradigms by their assumptions about environmental heterogeneity and dispersal.
  2. Why is local diversity predicted to peak at intermediate dispersal rates?
  3. What can, and cannot, variation partitioning tell you about metacommunity processes?
  4. Partition γ into α and β for three sites with species {A,B,C}, {B,C,D}, and {D,E}.
VIII

Neutral Theory

What if species differences didn’t matter at all?
video 36:26–40:08
36:34 Ecological equivalence · 37:46 θ, m & abundance distributions · 39:06 Tests & legacy

Key equations

Fundamental biodiversity number
θ = 2JMν (metacommunity size × speciation rate); equals Fisher’s α at equilibrium
Log-series (metacommunity)
expected species with n individuals: Sn = θxn/n, with x close to 1
Ewens sampling formula
E[S] = Σk=0J−1 θ/(θ + k)
Immigration
m = probability a local death is replaced by an immigrant; Etienne’s I = m(J − 1)/(1 − m)

Landmark studies

StudySystemKey finding
Kimura 1968Molecular evolutionNeutral theory of molecular evolution; drift of neutral alleles.
Fisher, Corbet & Williams 1943Butterflies, mothsLog-series distribution and Fisher’s α.
Preston 1948, 1962Birds, mothsLognormal distribution in octaves; veil line.
Hubbell 2001Barro Colorado Island forestUnified neutral theory; θ, m, zero-sum multinomial.
Condit et al. 2002Tropical forests, Panama and AmazoniaDistance decay of similarity tested against dispersal limitation.
McGill 2003; Volkov et al. 2003BCI and othersDebate over whether neutral SADs outperform the lognormal.
Comita et al. 2010Barro Colorado IslandConspecific negative density dependence varies among species.
Scheffer & van Nes 2006TheoryEmergent neutrality: clumps of similar species.

Lexicon

No. 11636:51
Ecological equivalence
Identical per-capita rates of birth, death, dispersal, and speciation for all individuals of all species.
No. 11737:05
Zero-sum dynamics
A community of fixed size J in which each death is matched by one birth or immigrant.
No. 11837:05
Ecological drift
Random change in species’ relative abundances due to demographic stochasticity.
No. 11937:29
Monodominance
Fixation of a single species, the inevitable endpoint of drift in a closed neutral community.
No. 12037:47
Fundamental biodiversity number (θ)
θ = 2 × metacommunity size × speciation rate per birth; equals Fisher’s α at equilibrium.
No. 12138:13
Immigration probability (m)
Probability that a local death is replaced by an immigrant from the metacommunity.
No. 12238:32
Species abundance distribution
Frequency distribution of species’ abundances; log-series, lognormal, or zero-sum multinomial forms.
No. 12338:32
Preston’s veil line
Sampling limit that hides the rarest species, truncating the left side of a lognormal SAD.
No. 12438:51
Zero-sum multinomial
Hubbell’s neutral SAD for a dispersal-limited local community.
No. 12539:07
Distance decay of similarity
Decline in compositional similarity between communities with geographic distance.
No. 12639:40
Null model
A model that excludes the process of interest, providing a baseline for detecting it.
No. 12739:40
Emergent neutrality
Scheffer & van Nes (2006): clusters of similar species coexisting near-neutrally within niches.

Exam prompts

  1. List the assumptions of neutral theory. Which are most often violated, and does that matter?
  2. What is θ, how is it estimated, and how does it relate to Fisher’s α?
  3. Why is fitting a species abundance distribution weak evidence for neutrality?
  4. Explain neutral theory’s value as a null model, with an example from your field.
IX

Synthesis

How do the theories fit together?
video 40:08–42:15
40:14 Four high-level processes · 41:22 Exam rehearsal

Four processes

ProcessPopulation-genetics analogueWhere it appears
SelectionNatural selectionNiches, competition, predation, stabilizing and equalizing mechanisms, species sorting
Ecological driftGenetic driftDemographic stochasticity, small populations, neutral theory, island extinction
DispersalGene flowIsland colonization, rescue effect, metapopulations, mass effects
SpeciationMutationPoint speciation (θ), in-situ radiation on remote islands, regional pool

Lexicon

No. 12840:15
Vellend’s four processes
Selection, ecological drift, dispersal, and speciation: the high-level processes of community dynamics.

Rehearsal answers

Why is a Type II functional response destabilizing?

Per-capita predation risk, f(N)/N = a/(1 + ahN), falls as prey density rises, so predation weakens as prey increase: inverse density dependence that amplifies fluctuations.

Why does the species with the lowest R* win?

At equilibrium each consumer holds the resource at its own R*. The species with the lower R* depresses the resource below the other’s break-even level, so the competitor’s growth becomes negative (single limiting resource, well-mixed, equilibrium conditions).

Why don’t empty patches mean habitat is unimportant?

In colonization–extinction dynamics a fraction of suitable patches (e/c in the Levins model) is always empty. Those patches are needed for recolonization; destroying them lowers p* and can cross the extinction threshold.

Stabilizing vs equalizing mechanisms?

Stabilizing mechanisms (niche differences) make intraspecific limitation exceed interspecific limitation and give rare species an advantage. Equalizing mechanisms shrink average fitness differences. Only stabilizing mechanisms create a rare-species advantage.

How do the four paradigms differ?

Patch dynamics: homogeneous patches, competition–colonization trade-off. Species sorting: heterogeneous patches, moderate dispersal, composition tracks environment. Mass effects: heterogeneous patches, high dispersal, source–sink spillover. Neutral: equivalent species, drift and dispersal limitation.

What does θ measure?

θ = 2JMν, the product of metacommunity size and speciation rate. It sets regional richness and evenness under neutrality and equals Fisher’s α of the log-series.

References