Principles of Ecology
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
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).
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:
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?
How would Isolation (distance between patches) affect metapopulation dynamics?
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.
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.
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:
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.
Asexual organisms, although they can not recombine and the concept of a gene pool does not apply, can be understood using the hierarchy above.
Last updated February 10, 2007