Ecology
Metapopulation
Patches connected by migration — extinction-recolonization dynamics, source-sink, Levins 1969
A metapopulation is a set of local populations on discrete habitat patches connected by migration, where the regional persistence of the species depends on the balance between local extinctions and recolonizations. Richard Levins formalized it in 1969 with the equation dp/dt = cp(1 - p) - ep, giving the steady-state occupancy p* = 1 - e/c. Ilkka Hanski's incidence function model extended the idea to spatially explicit landscapes and was calibrated using ~25 years of mark-recapture on the Glanville fritillary butterfly across roughly 4000 meadow patches in the Åland Islands, Finland.
- CoinedLevins 1969
- Equationdp/dt = cp(1−p) − ep
- Persistencec > e (so p* > 0)
- Spatial modelHanski IFM 1994
- Empirical anchorGlanville fritillary, ~4000 Åland patches
- Source-sinkPulliam 1988
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Why metapopulation matters
- It explains how species persist in fragmented habitat. Habitat fragmentation has converted continuous landscapes into archipelagos of patches; Levins' c > e criterion is the simplest test for whether a species can survive that conversion. The Glanville fritillary in Åland persists across ~4000 patches with a long-run occupancy of roughly 15-25%, exactly what the model predicts.
- Extinction debt is a model output. When habitat loss drops colonization c below extinction e, regional extinction is inevitable but lags by decades. Tilman et al. (1994, Nature) showed prairie species can be 50-100 years past the threshold before population data reveal the decline.
- Reserve design is metapopulation-driven. SLOSS (Single Large Or Several Small) debates rest on patch-area scaling A^x and dispersal kernel exp(-alpha d). Connectivity-aware design beats scattered reserves of equal total area when dispersal is limited.
- Source-sink dynamics rescue marginal habitat. Pulliam's 1988 framework explains why species are routinely found where lambda < 1 — the population is subsidized by neighbors. Removing an apparent sink without recognizing this can cascade across the network.
- Calibrated models predict patch occupancy with ~70% accuracy. Hanski's incidence function model on the Åland fritillary produces patch-level occupancy probabilities used directly by Finnish conservation authorities to prioritize meadow restoration and grazing leases.
- It generalizes to non-spatial systems. The same patch-occupancy math applies to disease spread across host populations, plasmids across bacterial cells, and species across host trees in tropical forests. Levins' 1969 equation is structurally identical to the SI epidemic model.
- It is the unit of evolutionary rescue and adaptation. Differential success across patches plus migration generates the variance that fuels rapid adaptation; populations that look uniform across a region often hide locally adapted alleles maintained by between-patch heterogeneity.
Common misconceptions
- Every fragmented population is a metapopulation. Fewer than 25% of vertebrate species in fragmented landscapes show classical Levins dynamics. Most are mainland-island systems (one large source dominates), patchy populations (dispersal too high for independent extinction), or non-equilibrium declining systems where recolonization has effectively stopped.
- Patches and populations are the same thing. A patch is habitat; a local population is the individuals on it. Empty patches still count — the dynamics depend on how often empty patches get colonized, not just on how many are currently occupied.
- Sinks are bad and should be removed. A persistent sink can be a meaningful conservation asset because it stabilizes occupancy, hosts genetic diversity that doesn't survive in sources, and may flip to source status when conditions change. The Florida scrub-jay and northern spotted owl networks include critical sinks.
- Levins' p captures abundance. It captures the fraction of patches occupied, not the number of individuals. Two regions with the same p can have wildly different total population sizes if patch areas differ; that is exactly why Hanski's IFM brings A_i into the extinction term.
- The model assumes immigration from outside. No — colonization in Levins comes from currently occupied patches in the same metapopulation (the cp(1-p) term). External rescue, when added, is the "rescue effect" of Brown and Kodric-Brown 1977, a separate term that breaks the basic Levins symmetry.
- Higher dispersal is always better. Up to a point. Beyond it, patches synchronize (everyone goes extinct together because they share a bad year), genetic structure collapses, and local adaptation erodes. Empirical optima sit at intermediate dispersal — roughly when the inter-patch distance equals the species' typical dispersal scale 1/alpha.
How metapopulation dynamics work
The simplest model is one ordinary differential equation. Let p(t) be the fraction of habitat patches that are currently occupied. New colonizations arrive at rate proportional to the supply of immigrants (occupied patches, p) times the supply of empty target patches (1 - p), giving the bilinear cp(1 - p) term. Local extinctions remove occupied patches at per-patch rate e, giving -ep. The equation dp/dt = cp(1 - p) - ep has a stable equilibrium at p* = 1 - e/c whenever c > e, and at zero otherwise. The threshold c = e separates regional persistence from regional extinction. Levins wrote this in 1969 to model insect-pest control under spatially distributed pesticide application; the framework was generalized to conservation in the 1980s and 1990s, principally by Lande, Hanski, and Gilpin.
Real landscapes violate Levins' homogeneity assumption — patches differ in area, quality, and position. Hanski's spatially realistic incidence function model (IFM, 1994) replaces the global rates with patch-specific ones. Extinction probability for patch i over a unit time scales as E_i = min(e/A_i^x, 1): bigger patches go extinct less often. Colonization probability depends on connectivity S_i = sum over occupied j of exp(-alpha d_ij) A_j^b, giving C_i = S_i^2 / (S_i^2 + y^2). Five parameters (e, x, alpha, y, b) are fit by maximum likelihood to mark-recapture or repeat-survey data. Hanski's group fit this model to the Glanville fritillary on ~4000 dry meadow patches across a 50 by 70 km region of the Åland Islands, generating patch-level extinction-risk maps that are still used by Finnish conservation agencies for triage.
Pulliam's source-sink extension (1988) lets local growth rate lambda_i differ across patches: lambda > 1 sources export emigrants, lambda < 1 sinks would die out without immigration. The regional growth rate is a weighted average — sinks can be permanently full while contributing nothing or even sinking the metapopulation total. The mainland-island variant, where one source patch is so large its extinction probability is effectively zero, is the limiting case used to model continental species expanding into archipelagos and forms the bridge to MacArthur and Wilson's island biogeography.
Metapopulation vs panmictic vs island
| Feature | Metapopulation | Panmictic | Mainland-island |
|---|---|---|---|
| Patches | Many, all extinction-prone | One effectively continuous | One mainland + many islands |
| Local extinction | Common, asynchronous | Rare; equals regional extinction | Rare on mainland, common on islands |
| Recolonization | From other patches | Not applicable | From mainland source |
| Persistence rule | c > e (Levins) | Demographic stochasticity only | Mainland never goes extinct |
| Genetic structure | Strong (F_ST > 0.1 typical) | Negligible | Mainland-skewed |
| Example | Glanville fritillary, Åland | Most marine plankton | Sea birds on offshore islets |
Source vs sink patches
| Metric | Source patch | Sink patch |
|---|---|---|
| Local growth rate | λ > 1 | λ < 1 |
| Net migration | Net emigration (exporter) | Net immigration (importer) |
| Persistence without flow | Persists indefinitely | Goes extinct |
| Habitat quality | Birth rate > death rate | Death rate > birth rate |
| Density | Often near carrying capacity | Can appear full because of subsidy |
| Conservation priority | Critical — loss collapses network | Buffer; loss masked then catastrophic |
Famous case studies
- Glanville fritillary (Melitaea cinxia) in Åland. Hanski's group tracked roughly 4000 meadow patches across the Åland archipelago of southwest Finland for over 25 years. Mean occupancy ~15-25%, with ~100 local extinctions and ~100 colonizations per year. The longest-running test of metapopulation theory ever conducted, and the calibration source for the IFM software MetaPop.
- Bay checkerspot (Euphydryas editha bayensis) on Jasper Ridge, California. Paul Ehrlich's 50+ year study showed three demographically independent patches; two went extinct in drought years (1992-1998) and the system collapsed when recolonization failed. A textbook case of a metapopulation losing its capacity for rescue.
- Northern spotted owl in the Pacific Northwest. The 1990 listing decision under the US Endangered Species Act was the first explicit application of metapopulation theory to a vertebrate. Old-growth fragmentation lifted e and lowered c; predicted occupancy declined ~3% per year, consistent with later surveys.
- European pool frog (Pelophylax lessonae) in Sweden. A genuinely peripheral metapopulation persisting near the species' northern climatic limit, used to test whether range edges are inherently sink-dominated. Sjögren-Gulve (1994) found classic Levins dynamics with c only slightly above e — extinction debt evident.
- Tilman 1994 extinction debt for prairie plants. A theoretical paper combining the Levins model with competitive hierarchies showed that habitat destruction commits the best competitors to extinction first, with delays of decades to centuries — the empirical case for why species lists keep shrinking long after habitat loss stops.
Frequently asked questions
What exactly is a metapopulation?
A metapopulation is a population of populations — a set of local breeding populations occupying discrete habitat patches in a landscape, where each local population has a non-trivial probability of going extinct on a timescale relevant to the regional dynamics, and patches are connected by enough dispersal to permit recolonization but not enough to homogenize the patches into one panmictic unit. The hallmark signature is asynchronous turnover: patches blink occupied and empty over time, but the regional fraction occupied tends toward a steady state. Richard Levins coined the term in 1969 in a paper on pesticide-driven pest dynamics, framing the long-run survival of the species as a balance between local extinction rate e and colonization rate c.
What does the Levins 1969 equation say?
Levins wrote dp/dt = cp(1 - p) - ep, where p is the fraction of patches occupied, c is the per-patch colonization rate (proportional to occupancy because immigrants come from occupied patches), and e is the per-patch extinction rate. Solving for the steady state gives p* = 1 - e/c. Three regimes follow: if c > e the species persists with p* > 0; if c = e it is on the knife edge; if c < e it goes extinct globally even though every patch could in principle support it. The model is deliberately spatially implicit — it ignores patch position, area, and quality — which is its strength as a starting framework and its weakness for any specific real landscape.
How does the source-sink concept differ?
Pulliam's 1988 source-sink model relaxes the Levins assumption that all patches are equivalent. A source patch has birth rate exceeding death rate (lambda > 1) and exports surplus individuals; a sink patch has lambda < 1 and would go extinct without immigration. The sink can be permanently occupied if the source ships in enough emigrants to mask its negative intrinsic growth. This matters for conservation: removing what looks like a productive sink population can collapse a network if you didn't notice the surplus was being subsidized from elsewhere. It also explains why species are sometimes found in habitat that demographic data say is unsuitable — the patch is full because its neighbors keep refilling it.
What is Hanski's incidence function model?
Ilkka Hanski's incidence function model (IFM, 1994) is a spatially explicit stochastic patch occupancy model. For each patch i with area A_i and pairwise distances d_ij to other patches, extinction probability is E_i = e/A_i^x and colonization probability scales with connectivity S_i = sum over occupied j of exp(-alpha d_ij) A_j, giving C_i = S_i^2 / (S_i^2 + y^2). Five parameters (e, x, alpha, y, plus a dispersal exponent) fit by maximum likelihood to snapshot or turnover data predict long-run occupancy and extinction risk. Calibrated on the Glanville fritillary across ~4000 Åland meadows it forecasted patch-level occupancy with about 70% accuracy and is now standard practice in landscape conservation.
When is the metapopulation framing wrong?
When dispersal is so high that local populations are effectively one panmictic unit (no patch ever goes extinct independently), or so low that patches function as independent islands with no recolonization on relevant timescales. It is also misleading when a single source patch dominates regional persistence — that is more accurately a mainland-island system, a special case that Hanski distinguished from true Levins metapopulations. Habitat-tracking species like migratory birds that move continuously across a continuum, and species in continuous habitat without discrete patches, simply don't fit. Empirical estimates suggest fewer than 25% of vertebrate species in fragmented landscapes show classical metapopulation dynamics; most are mainland-island, patchy populations, or non-equilibrium declining systems.
Why does the framework matter for conservation?
Because regional extinction can be inevitable even when every existing local population looks healthy. If habitat loss pushes the colonization rate c below the extinction rate e, the steady-state occupancy p* = 1 - e/c crosses zero, and the species is committed to extinction even before any patch shows decline — the so-called extinction debt described by David Tilman in 1994. Calibrated metapopulation models predict the time lag (often decades to centuries) and identify which patches contribute most to connectivity. Reserve design therefore rewards maintaining several large patches close together over many small patches scattered widely, with corridors raising effective dispersal alpha, and identifying source patches whose loss would cascade across a network.