BIOL 4120

Principles of Ecology

Phil Ganter

320 Harned Hall


The dead arm of the cactus above is home to populations of yeast, bacteria and insects but is a habitat that persists only for a short time.  How do species that live in temporary habitats persist?

Lecture 12 Metapopulations

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Overview - Link to Course Objectives


A region may contain more than one population of any given species.  A Metapopulation is the larger unit made up of a group of Subpopulations (local populations of one species).

  • Several organizational schemes for metapopulations exist:
    • Patchy Populations
      • A group of subpopulations interconnected through migration
      • Some subpopulations might go extinct, but the metapopulation persists and can recolonize empty patches
      • Metapopulation is stable through constant extinction-recolonization events
        • an equilibrium is reached which balances local extinction and recolonization
      • for this kind of metapopulation, the regulation of the metapopulation is not directly tied to the fate of any one subpopulation
    • Core/Satellite or Mainland/Island or Source/Sink metapopulations (terms are equivalents)
      • A large population with smaller, satellite populations founded from the big one
        • Notice that the large population is often treated here as a source (and is relatively unaffected by the satellites) and the satellites are affected by the core, but not by one another
      • for this kind of metapopulation, the regulation of the core population drives the long-term fate of the satellite populations
      • Rescue Effect - This concept is usually applied in Island Biogeography, a subset of metapopulation theory.  
        • When an island is close to its source of species, both the rate of colonization and the rate of extinction are affected
          • Colonization is affected by the proximity of the mainland
          • The rescue effect is a reduction in the extinction rate because a population on an island is replenished or re-colonized from the source (the mainland)
            • The rescue effect comes from the arrival of new members into a population already established on the island
            • These new arrivals increase the population size and decrease the probability that the population will go extinct.
    • Isolated, Nonequilibrium Populations
      • Like patchy populations, but there is no migration between patches so that once extinct, a subpopulation is lost
        • if the populations do not exchange migrants, each is a closed system and the population growth models we have discussed describe their dynamics
        • the changes in the species in the region would be the sum of changes in the independently changing populations in the region
      • Metapopulation is unstable, as subpopulations are lost but no new ones are established
      • for this kind of metapopulation, the possibility of local extinction implies the possibility of metapopulation extinction
      • Habitat Fragmentation by human activity can create metapopulations with isolated subpopulations from previously large local populations
        • fragments left by human activities may be too small to sustain breeding populations
        • fragments may be too far apart to allow sufficient migration
        • Checkerspot butterfly (Euphydryas editha) is an example of what can happen to species whose habitat has been affected by human activity
          • large source population and nine satellites (all on Jasper Ridge)
          • present on Jasper Ridge since at least 1934
          • In 1996, core population collapsed and eventually the species disappeared from Jasper Ridge
            • satellite populations did not persist long after core was lost

NOTE:  The book covers a famous example of insect metapopulations, the populations of the bay checkerspot butterfly, Euphydryas editha, near San Francisco, CA.  The populations occur on ridges composed of serpentine soil.  This does not mean soil with lots of snakes.  Serpentine soil is named for its parent rock, a group of minerals (collectively called serpentine minerals) that are hydrous iron magnesium phyllosilicates.  There are over 20 minerals in this group and the rocks made of mixtures of these minerals are called serpentinite.  They also contain other metals including chromium and cobalt.  The rocks are often greenish and, when polished, must have reminded someone of a snakeskin (hence the name may refer to snakes).  They are igneous rocks (actually, ultramafic) that are from the Earth's mantle and tend to occur at the surface as intrusions into the continental rock, which is the reason for the patchy occurence in the San Francisco area as ridges of serpentinite rock.  For our purposes, serpentine soils contain high percentages of serpentinite and the soil moisture will have high concentrations of the metals characteristic of the rock.  These metals are toxic at such high concentrations and many plants can not grow on serpentine soils.   Those that do occur there often occur only on serpentine soils, which are not common and so the plants found there are often rare and appear on lists of threatened or endangered species.

Extinction and Colonization

Patchy populations are of interest to ecologists because the metapopulation may persist even thought the local populations are guaranteed to go extinct.  The persistence of the metapopulation is truly an emergent property!

To see how this happens and to explore the dynamics of this situation, we will use a mathematical model.  The model will describe the outcome of the operation of two processes:

  • Extinction:  the loss of a local population for any reason (disease, visit by a predator, demographic stochasticity, etc.).  This is sometimes called Local Extinction because it refers to local populations.
  • Colonization:  The founding of new local populations from existing populations

A Model of Patchy Metapopulations

Before building the model, we need to state the assumptions built into the model

  • This model applies to patchy metapopulations, which implies that the habitat consists of discrete patches of suitable habitat surrounded by unsuitable habitat and that there is some degree of dispersal between patches.  From this second assertion, we can infer that suitable patches which are not occupied by a local population are subject to colonization from occupied patches.
  • Each local population has a non-zero chance that it will go extinct in a specified time interval
  • The changes in local populations are not synchronized or correlated.

Now we can build the model and analyze its output.  Which output is of interest?  Metapopulation size is one possibility but predicting size might be complicated as we would need to predict subpopulation sizes.  We can simplify local population size to one of two states:  occupied or not occupied.  This gets rid of lots of complications but we must assume that once occupied a patch puts out migrants at some constant rate until it becomes extinct.  With this simplification, we can focus on a simplified metapopulation size: the proportion of patches in a region that are occupied.  As it increases, metapopulation size increases.  Suppose we call P the proportion of patches that are occupied by a local population of the species of interest and e is the probability that a patch will go extinct within a specified time.  The rate of extinctions we expect during the time interval is :

The colonization rate depends on a probability of a migrant finding a patch, m, and the P, the proportion of patches that are occupied.  P affects the colonization rate in a direct and an indirect way.  The direct effect is that, as P increases, the number of dispersing individuals increases and indirectly because, as P increases, the number of unoccupied patches decreases and the chance of finding such a patch decreases.  Thus, the colonization rate is:

The rate of change in the proportion of patches occupied (DP/Dt) is the difference between the colonization rate and the extinction rate (= C - E) or, with a little substitution:

For any given probability of extinction and probability of colonization (m) and extinction (e), we can plot the extinction (E) and colonization (C) rates versus the proportion of occupied patches (P).

The extinction rate changes linearly (the more patches that are occupied, the more that go extinct) but the colonization rate is humped, with the highest values found in the middle, where neither the patches providing dispersers nor unoccupied patches are rare.

Where the lines cross, the extinction rate equals the colonization rate and there is no net change in the proportion of patches occupied (for each loss a new population is begun).  We can see that this does not have to happen (imagine a situation where the colonization hump is very low and the extinction line is very steep.  What determines where the two lines cross?  That is the point where the rate of change in P (DP/Dt) is zero.  To find this, we set DP/Dt = 0 and we solve the equation to find that the rate of change in P is zero when:

So, we have a prediction for how the rates of extinction and colonization can produce a stable metapopulation with a predictable proportion of patches occupied.  Note that the equation above will produce nonsense if we allow e to exceed m (we would get a negative proportion of patches occupied, whatever than means).  Thus, the model needs to specify that m > e if the metapopulation is to persist.  We will use this relationship below to understand how changes in m and e affect the proportion of patches occupied (P)

Patch Size and Isolation

Patches can change on many ways.   Some are high quality while others may be of lower quality.  Some may be large and some may be isolated.  We can explore how these changes might affect the metapopulation with the model.  We will focus on two factors:   patch size and patch isolation.

How would a change in patch size affect metapopulation dynamics?

  • Large patches should lead to large populations.  Large local populations should have a smaller chance of going extinct through due to demographic stochasticity.  This might even be true for more specific reasons for extinction.  Large populations would be more likely to have individuals resistant to a disease.  Large populations may exceed the ability of a predator to drive the local population to extinction.
  • There is no clear relationship between population size and colonization rate.

How would Isolation (distance between patches) affect metapopulation dynamics?

  • Since extinction rate is a local phenomenon, isolation will not affect it.
  • Greater distance between populations will affect the colonization rate by making it more difficult to find unoccupied patches.

These two forces will then change the proportion of patches occupied.  A diagram will make the differences easier to understand.  We can compare small to large patches by comparing the extinction rate line produced with a small e (= large populations) to a line produced by a larger e (= small populations).  On the same graph, we can compare isolated patches (= small m) with a metapopulation with close patches (= large m) and see how these things interact.  

You can see that a metapopulation with large, close patches will have a higher rate of patch occupancy than will a metapopulation with small, isolated patches.

  • Think of what such a conclusion might mean to a resource manager.  As development reduces patch size and increases patch isolation, the possibility of metapopulation extinction increases.

Remember that the comparisons above will work for any factors that increase or decrease m or e.  Patch size and isolation are only examples of factors that affect m and e.

Heterogeneity  variation in habitat quality over space (Spatial Heterogeneity) or time (Temporal Heterogeneity) can increase the probability of extinction

Weather is a factor which has great heterogeneity and it only takes one severe storm, severe drought or severe cold spell to doom local populations

In January, 2007, northern Florida was host to severe storms that generated tornados.  The storms killed 17 of the 18 whooping cranes (Grus americana) that had just established a winter population there.  These cranes are endangered and there is an intensive program to rescue them from extinction.  The species is migratory and overwintered in the southern US from Texas to Florida at one time.  Hunting and habitat alteration caused local extinctions.  They were almost extinct from nature (only 21 wild birds in 1941) but a breeding program in zoos preserved the species.  There are now over 300 in the wild and about 150 in zoos.   The young in the release program were kept innocent of human contact (keepers donned crane costumes when in the crane compound).  A successful population that breeds in Canada and overwinters in Texas has been established.  However, the conservation ecologists in charge of the project realized that a single event in Texas or Canada could be disastrous and wanted to establish a second population.  A second breeding population is now being attempted in Wisconsin with overwintering in Florida.  In 2001, a breeding population in Wisconsin were lead to overwintering sites in Florida by leading them with ultralight aircraft disguised as cranes.  In Fall of 2006, they lead 18 yearling birds to Florida to establish a second overwintering site but the prediction of disaster turned out to be too real.  Metapopulation ecology has moved out of academia and into the real world.

  • Spatial heterogeneity is the degree to patches vary in both quality and the arrangement of those patches (distance between)
    • Each subpopulation's maximal size depends on it's patch quality
    • Spatial heterogeneity important as a means of unlinking the fates of individual patches
      • this effect is called Spreading the Risk
      • can lead to stable metapopulations even though local subpopulations have a high probability of going extinct
    • Importance of spatial heterogeneity to stabilizing metapopulations has been demonstrated for laboratory systems
      • Huffaker demonstrated the importance of spatial heterogeneity in simplified predator-prey system
        • studied a predator-prey system consisting of a herbivorous mite (feeding on oranges) and a predacious mite that ate the herbivorous mite
          • on one orange, the predator always eliminated the prey and then died off itself
          • when an array of oranges was used, mite populations on each orange eventually suffered the fate of the populations in the single orange system
            • the extinction process took longer but still local extinction lead to metapopulation extinction
          • Huffaker increased spatial heterogeneity
            • made the system larger (more oranges)
            • made some patches suitable (oranges) and some unsuitable (rubber balls)
            • made migration more difficult with Vaseline barriers between oranges (that the predator could cross, although with difficulty)
            • herbivores used sticks in oranges as launch sites for "ballooning" to next orange
          • increased heterogeneity resulted in persistence of both predator and prey
            • also resulted in predator-prey cycles!
      • microbial predator-prey systems also demonstrated that increased spatial heterogeneity stabilized metapopulation size

Species Characteristics

It is to be expected that metapopulation dynamics are affected by the characteristics of the species under consideration and that the reverse is also true.  Species characteristics are affected by metapopulation dynamics.

the r-selected species vs. K-selected species distinction (or the ruderal - non-ruderal distinction drawn by Grime) reflects the importance that dispersal can have on general life history characteristics.  Ruderals and r-selected species both have life history characteristics linked to inhabiting ephemeral (persisting for only a short time) habitats, like forest openings caused by a fallen canopy tree or in habitats like those my yeast and flies inhabit (see picture at the top of the page). 

Some examples of the interactions among species characteristics and metapopulation dynamics:

  • High fecundity and high dispersal rates are often correlated.
    • Dispersal is dangerous and many young are needed if all disperse into a hostile environment.
  • Population size is correlated with body size, so that local populations are smaller for a species with a large body size compared with a similar species that has a smaller body size.
    • Population size is inversely correlated with the probability of extinction and will affect metapopulation dynamics for this reason.

Overview of Populations

We have examined populations from more than one perspective and it is good to integrate these varying views.  This integration can be done by viewing populations hierarchically.

  • Local populations consist of interacting individual organisms (whether modular or not) are the lowest level of the population hierarchy. 
    • Individuals experience similar conditions within the local population and so it is reasonable to summarize their response to these conditions in a Life Table, from which we can calculate such important population parameters as birth and death rates and population growth rate.
    • In an ideal situation, all individuals would occupy a single patch of suitable habitat.  While this is often so, real populations may not always conform but the assumption that the members of the population experience similar conditions must be met.
  • The next level of the hierarchy is the metapopulation, where dispersal links local populations.  This linkage gives rise to dynamics at the metapopulation level that cannot be seen at the local level (another of those emergent properties).
    • Metapopulation dynamics are affected to the degree to which changes in local populations are correlated from population to population.  As the correlation weakens, metapopulation dynamics become less and less predictable from the changes occurring in any single local population.
    • Because metapopulations are composed of populations that exchange individuals, however rarely, the gene flow will, under most conditions, be sufficient to promote genetic similarity among the local populations that comprise the metapopulation.
  • The next level is the Subspecies.  This is one or more metapopulations that are separated from other metapopulations of the same species by sufficient distance and/or experience sufficiently distinct conditions that gene flow is not sufficient to maintain genetic similarity.
    • There are two ways for this isolation to occur. 
      • If Geographic Barriers separate metapopulations, the boundary between subspecies can be abrupt.
      • If there are no effective geographic barriers but the distance between the farthest metapopulations is great, gene flow may be slow enough to allow divergence between subspecies, even if there is no gap between metapopulations.  This phenomenon is called Isolation by Distance.
          • The book has an example of such in the discussion of Ensatina escholtzii, a salamander from the west coast, found in chapter 2.
    • Subspecies may diverge through the spread of different adaptations linked to local conditions or may diverge through genetic drift if population size is small enough and/or there is sufficient time for divergence.
    • Not all species are organized into subspecies and, so, this level of population organization does not always exist.
  • The Species level, the final level of population organization, consists of all local populations that can, with some reason, be considered as members of the same species.
    • The geographic range here is often large and those who study entire species often consider their efforts properly placed in the subdiscipline of Biogeography.

Asexual organisms, although they can not recombine and the concept of a gene pool does not apply, can be understood using the hierarchy above.

  • Local populations, because of the requirement that individuals within the populations experience similar conditions, are kept genetically similar not by the spread of successful genes but by the replacement of less successful genotypes by more successful genotypes
  • Metapopulations experience genotype flow, not gene flow, and are kept similar through the same means.
  • Subspecies may arise under the same conditions as for sexual species
  • The problematic level may be the species level of population organization when there is no obvious criterion for deciding when differences among subspecies have become large enough to consider them to be new species.
    • If you have a solution for this conundrum, contact me.  You will be famous.


    Metapopulation, Subpopulation, Patchy Population, Core/Satellite, Mainland/Island, Source/Sink, Rescue Effect, Isolated, Nonequilibrium Populations, Habitat Fragmentation, Extinction, Local Extinction, Colonization, m, e, E, C, P, DP/Dt, Spatial HeterogeneityTemporal Heterogeneity, , Subspecies, Geographic Barriers, Isolation by Distance, Biogeography

Last updated February 10, 2007