Island biogeography and metapopulations: stable counts can hide constant turnover

Species richness is a count, not a list of identities

Equilibrium island biogeography balances immigration from a larger source pool with local extinction. As an island contains more of the possible species, fewer absent species remain available to arrive; the model’s extinction flow can rise with richness. Their balance can stabilise the count while still replacing which species are present.

The island biogeography model has a pool of one hundred possible species and explicit immigration and extinction functions. MacArthur and Wilson’s foundational book provides the research framework. The Modic curve is an expected-richness teaching calculation, not a forecast for a named island. It omits species identities, speciation and habitat differences, so an equilibrium count must not be presented as evidence that community composition is unchanged.

Patch occupancy asks whether a regional network persists

A metapopulation concerns local populations connected by dispersal. A local extinction can be followed by recolonisation if occupied patches supply enough colonists and suitable empty habitat remains. Regional persistence therefore differs from the survival of every individual patch population.

In the Levins metapopulation activity, occupied fraction p changes through cp(1−p) minus ep. Colonisation requires both an occupied source and an empty destination in the mean-field account. Levins’s original population-model paper gives primary context. The continuous fraction is not a literal census of a few patches. Spatial isolation, differences in patch quality and finite chance can matter greatly outside the homogeneous deterministic approximation.

Worked example: interpret two equilibria without mixing their units

Keep the two teaching models separate while comparing their logic. One describes species richness on an island; the other describes the fraction of habitat occupied by a particular population. Neither set of coefficients is an empirical estimate.

1. In island biogeography, set maximum immigration six and maximum extinction three. The equilibrium richness is one hundred times six divided by nine, about 66.67, with expected immigration and extinction both equal to two.
2. In the metapopulation model, set colonisation 0.5 and local extinction 0.2. The positive equilibrium occupied fraction is one minus 0.2 divided by 0.5, or 0.6, describing occupancy rather than a species count.
3. Raise local extinction above colonisation and inspect the loss of positive occupancy equilibrium in that model. Do not transfer this threshold to the island model or assume it directly measures a real habitat’s extinction risk.

Interactions can change a state without acting on it directly

The trophic cascade experiment adds another distinction. A top predator affects herbivores directly, and changing herbivores can alter plants indirectly. Looking only at the species directly eaten by the predator would miss part of that mechanism. The plant, herbivore and predator curves are population indices, which differ again from richness and occupancy.

Compare runs from the same initial plant and herbivore values over matching time horizons, changing only the initial top-predator presence. The fixed equations are chosen to make an interaction inspectable, not to claim that every food web responds identically. Alternative prey, behaviour, migration and habitat can alter a real cascade. Use the model to name a possible pathway and an observation to collect, rather than treating the curve’s shape as evidence that the pathway operates in a particular ecosystem.

Define persistence before evaluating an ecological change

A conservation discussion can sound contradictory when participants use the same word for different outcomes. A stable richness count, high occupied fraction and a large local population can move in different directions. Write the state variable and observation process first, then ask how the proposed intervention changes the mechanism governing that variable.

• Specify whether the outcome is species richness, identities, occupied fraction or population abundance.
• Separate a stable total from turnover among the members contributing to that total.
• Identify what connects local patches and whether colonisation can reach the places that become empty.
• Compare matching initial conditions and time horizons when isolating a proposed interaction.
• List missing spatial, behavioural and stochastic processes before interpreting a deterministic equilibrium as security.

Turn the model into a question for evidence

Suppose a monitoring programme reports an unchanged annual species count. A useful follow-up asks whether the same species remain, whether arrivals replace losses and whether the count masks changes in abundance. If the programme tracks occupancy, ask which patches can recolonise and which remain isolated. The data needed depend on the claim, not on which curve looks reassuring.

A good model also clarifies what would change the interpretation. If dispersal is too spatially restricted for mean-field mixing, the occupancy calculation needs a different structure. If species interactions drive vegetation changes, a richness total alone may miss the response. The practical value of these experiments is therefore a clearer measurement plan: define persistence, identify the mechanism and choose observations capable of distinguishing stability from replacement or temporary compensation.