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Contributed by Larry Rockwood and James Lawrey
On August 27, 1883, Krakatau, an island about the size of Manhattan located between Sumatra and Java, underwent a series of volcanic eruptions releasing as much energy as 100 megatons of TNT (Wilson 1992). Magma, ash, and rock flew 5 km into the air and fell back into the sea, creating a tsunami 40 m in height, washing away villages in Java and Sumatra, killing 40,000 people. Waves were still a meter high when they came ashore in Sri Lanka. A total of over 18 cubic kilometers of rock and ash were thrown into the air with dust and sulfuric acid aerosol reaching 50 km in the stratosphere where its effects were seen as brilliant sunsets for several years thereafter. All this airborne material produced “darkness at noon” in areas near the former Krakatau.
Only the southern end of Krakatau remained. This island, which became known as Rakata, was covered by pumice 40m thick. The pumice had been heated to between 300 and 850o C, and all living things had been destroyed; Rakata was a sterile island. Yet living things soon began colonizing this lifeless rock. Nine months after the explosion a visitor found a small spider spinning its web. In the fall of 1884, a year after the eruption, biologists found a few shoots of grass. By 1886 there were 15 species of grasses and shrubs; by 1897 there were 49 species; and in 1928 300 species of plants were found. In 1919 there were patches of forest; by 1929 most of the island was forested, forcing the grasses into small pockets (Wilson 1992).
What Wilson described in the preceding paragraphs sounds like a typical successional sequence, proceeding from a community of colonizing species to a mature or “climax” forest. What we want to emphasize here is the two processes at work on Rakata. Obviously one of those processes is colonization. New species continuously arrive on this island from the nearby mainlands. The other process is local extinction. Many species that arrived on this island, and were recorded early in the 20th century, are no longer present. Again, this may not be surprising to students of succession. So called climax species are supposed to outcompete and eliminate earlier successional species. But is this what happened? At least one animal species, the reticulated python, that we would associate with the more mature community was present as early as 1933 but was gone by the 1980s. The bird community is more to the point. In 1908 13 species of birds were recorded on Krakatau; by 1920 there were 31 species; and by 1933 30 species were found. Wilson (1992) believed that an “equilibrium” number for Krakatau was approximately 30 species of birds, and that number had been reached by 36 years after the explosion. More importantly, the actual composition of the bird community has not remained stable. During the interval between the 1920 and 1933 surveys, five species of birds went extinct on Krakatau, to be replaced by four new species (MacArthur and Wilson 1967). For example, the bulbul (Pycnonotus aurigaster) and the gray-backed shrike (Lanius schach) had gone extinct on Rakata between 1920 and 1933.
The history of Krakatau illustrates two major points: 1) Local populations are continuously subject to the twin processes of colonization and extinction; and 2) communities are continuously changing. Even when the number of species in the community is static, the composition of the community is not.
Spatial Ecology
The natural world is increasingly fragmented due to human activities. Wildlife populations are now more likely to be small, restricted in distribution, and increasingly isolated from each other. Partially as a reaction to these realities and partially because of increasingly sophisticated theoretical developments, ecologists have begun stressing the importance of the spatial context in populations, communities, and ecosystems. What we can broadly call spatial ecology is the progressive introduction of spatial variation and complexity into ecological analysis, including changes in spatial patterns over time. Krakatau is an example of both temporal and spatial complexity. Not only has its communities and populations changed over time, but the community found on present day Krakatau is still very different from the nearby mainland forests of Java and Sumatra. The local community of Krakatau remains distinct from those of the mainland (Wilson 1992).
Spatial ecology is distinguished by two different approaches: 1) landscape ecology and 2) metapopulation ecology.
Landscape ecology usually focuses on a larger geographic scale than traditional ecological studies; it was founded largely by community or ecosystem-oriented ecologists, geographers, and landscape planners. Landscape ecology explicitly recognizes the heterogeneity or “patchiness” of the environment both spatially and over time. It provides a large-scale perspective that describes the physical structures of patchy environments as well as the movements of both individuals and resources among them. Generally, landscape ecologists focus at the community, as opposed to the population level. Furthermore, landscapes have a more complex structure than usually allowed in simple metapopulation models, with habitat suitability being on a continuous scale, rather than simply “suitable” or “unsuitable” (Hanski 1999). Landscape ecologists do not usually work on population dynamics (Turner et al. 2001), but much of their work is relevant to metapopulations. For example, both landscape and metapopulation models often attempt to incorporate the roles of edge habitats, movements of individuals between patches via habitat corridors, spatial location of the patches, habitat fragmentation, landscape disturbance, and spatial and temporal variation in the quality of the habitat.
The metapopulation approach begins by stressing that local populations are influenced by immigration/emigration and extinction, as well as by birth and death processes. Until the 1960s, the idea that populations might routinely go locally extinct was rarely discussed in the literature. However, the population geneticist, Sewall Wright (1940) as well as ecologists such as Andrewartha and Birch (1954) introduced the notions that populations are connected by migration and that local extinctions might be commonplace (Hanski 1999). The importance of immigration and emigration to the long-term persistence of a local population, however, was first emphasized by Levins (1970) who coined the term metapopulation. For Levins a metapopulation was a population consisting of many local populations. He asserted that all local populations have a finite probability of extinction, and long-term survival of a species was at the regional or metapopulation level (Hanski 1999). Beginning in the 1990s, as it became obvious that the natural world was becoming increasingly fragmented, the metapopulation approach became standard in the world of conservation biology. An understanding of metapopulations, the probabilities of local extinctions in different sized natural reserves, and the rates of immigration and emigration between these preserves, became one of the fastest growing research areas in population, community, landscape, and conservation biology. As currently defined, metapopulations are regional assemblages of plant and animal species with the long-term survival of the species depending on a shifting balance between local extinctions and re-colonizations in the patchwork of fragmented landscapes.
The spatial distribution of a species is based on environmental patchiness. However, the recognized patterns of spatial distribution (clumped, random or regular) only describe the current spatial pattern; they address neither the underlying causation of the pattern, nor the long-term persistence of the population at that site.
The term “metapopulation” has been used for any spatially structured population and “metapopulation dynamics” has been used to refer to any population dynamics involving spatial patterns (Hanski 1998). Furthermore, as Harrison (1994) has pointed out several different types of metapopulations exist: classical metapopulations, mainland-island metapopulations, non-equilibrium metapopulations, and patchy metapopulations.
As pointed out by Tilman and Kareiva (1997), we must recognize that an individual organism only interacts with its local environment and with the competitors and/or predators present in that local environment. Such realities have been largely ignored by ecologists in the past, particularly when deriving theoretical models for competition or predation. Both classical and modern studies of competition and predator-prey interactions can be easily integrated into a simple metapopulation (spatial) context. For example, envision the environment as a series of patches and apply the competitive exclusion principle. If we have a superior competitor that drives other species extinct on a given patch, the inferior competitors are only driven locally extinct. They can remain in the region if they can have a higher dispersal rate than extinction rate and there are empty habitat patches. Similarly, a predator may drive a prey species locally extinct, but the prey population remains regionally present if it continues to colonize empty habitat patches faster than its predator. Although this is an oversimplification, consider the following two examples.
Huffaker (1958) worked with orange mites and their predators in the laboratory. He found that coexistence of the two species was impossible on any given orange. Here one orange represents a small homogeneous habitat or patch. Through the addition of spatial complexity, however, as well as barriers to limit the rates of movements between patches, the orange mite and its predator co-existed in the laboratory for many months. A higher dispersal rate and environmental complexity allowed the prey species to remain regionally present, even though it was continually driven locally extinct on a given orange once the predator arrived. Notice the parallels to epidemiological and host-parasite interactions. An unoccupied, but suitable, habitat patch is the equivalent to an individual susceptible to a parasite, yet not infected. An infected individual is the equivalent of an occupied habitat patch.
Spatial complexity can also have important effects on competitive interactions. For example, spatial complexity can help explain the coexistence of more species than expected based on the theory that the number of coexisting species should not exceed the number of limiting resources (Hutchinson 1961). As pointed out by Lehman and Tilman (1997), usually there is a trade-off, often expressed in terms of energetic investments, between competitive ability and colonization ability. While a superior competitor may take over a given site, if the less competitive species is a better colonizer, it may simply escape to a new site before competitive exclusion can occur. For example, Hubbell et al. (1999) proposed that high tree diversity on Barro Colorado Island in Panama is due, at least in part, to the low dispersal ability in competitively dominant species. Through a combination of low local abundance, low dispersal, and chance events, many plant species are absent from the local neighborhood in which a tree is located. Many sites are colonized by “default” species that were not the best competitor for the site. For example, an individual tree sapling competes with only 6.3 neighbors on average. Thus, plants compete only with those individuals sufficiently nearby to shade them or whose roots overlap with theirs in the soil. To “win” locally, a tree must only compete with those species that have “shown up” in the local neighborhood. Inferior competitors “win” by default. Because winners are only the best competitors that happen to have colonized a specific site, this process can lead to an almost unlimited diversity (Tilman 1994, Hubbell et al. 1999).
While landscape ecology and metapopulation ecology have started at different scales and with different assumptions and traditions, these two branches both ask similar questions. Many landscape ecology courses include sections on metapopulations. An important future task will be the reconciliation of these two approaches and the establishment of common methodologies and principles.
MacArthur and Wilson and the equilibrium theory of island biogeography
Spatial ecology has its roots in the MacArthur and Wilson equilibrium (or dynamic) theory of island biogeography (1963, 1967). MacArthur and Wilson (1963, 1967) brought a quantitative theoretical framework to the study of biogeography. Islands and island examples have been of great importance in biology (e.g., the Galapagos and Darwin) and islands have been analyzed as natural laboratories and experimental systems. They are small, contained ecosystems in which certain species found in continental ecosystems may be missing. The lessons learned from examining islands can also be applied to those continental areas that are comparable to islands. That is, streams, lakes, tidal pools, caves, and mountaintops can be thought of as habitat islands in a -terrestrial sea.- The approach of island biogeography has also been applied to host animals as habitat patches for parasites. Finally, as noted above, the natural world is increasingly fragmented, surrounded by roads, agricultural crops, shopping malls, industrial sites, and urban development. As conservation biologists became increasingly aware that wildlife preserves were islands, a set of rules for the design of natural areas was inferred from the MacArthur and Wilson theory (Diamond 1975, Terborgh 1975, Wilson and Willis 1975, Willis 1984).
The basic principles derived from the MacArthur and Wilson theory are:
1) The relationship between habitat island area and the number of species found there (the species-area curve); 2) Local extinction is a normal, common occurrence, particularly on small islands with small populations; 3) Local diversity is based on an interplay between colonization from a “mainland” source of species and local extinction, resulting in an “equilibrium” number of species; 4) Island size and distance from the source of species will affect the “equilibrium” number of species. That is, large islands that are close to the mainland will have more species than small islands, far from the mainland.
The relationship between number of species on an island and the area of the island is one of cornerstones of island biogeography theory. The species area relationship has been discussed since the 19th Century, and MacArthur and Wilson (1967) proposed that the number of species on an island could be approximated by the equation:

S = the number of species on the island, A = the area of the island, C = a constant (the y-intercept, see below), and z = a constant which remains consistent within a taxonomic group and/or the types of islands being considered.
The above equation can be log transformed as follows:

This is an equation for a straight line with a slope = z, with log C as the y-intercept. Thus, if data are gathered on the area of islands of different sizes and on the number of species on each island, a regression of the log-transformed data will produce a linear equation with slope z. The slope is consistent within a taxonomic group but also depends on the type of island system. That is, the z-value depends on whether we are dealing with true oceanic islands, recently isolated islands (-land-bridge- islands), or habitat islands. According to MacArthur and Wilson (1967), z-values range from 0.20-0.40 for oceanic islands, 0.12-0.25 for arbitrary portions of the mainland, and greater than 0.26 for habitat islands (Gould 1979, Quinn and Harrison 1988). Preston (1962) showed that a z-value 0.26 is expected when the log of species abundance versus the number of species has a normal distribution. Gould (1979) pointed out that a slope of 0.25 is extremely common for species area curves. What is of interest are those z-values differing significantly from 0.25. When we simply sample larger and larger areas of habitats not isolated from each other, the z-values are theorized to be smaller than the expected of 0.25. When small areas are sampled, they often include several transient species passing through the area, raising the number of species. The result is a smaller than expected rise in the number of species with increasingly large sample areas. Thus, ants from non-isolated continental areas in New Guinea (Wilson 1961) have a z-value of 0.17, mammals from the Sierra Nevada have a z-value of 0.12 (Brown 1971), and birds from the Great Basin of the US a z-value of 0.17 (Brown 1978). By contrast, larger than expected z-values arise when islands contain great habitat diversity, with semi-isolated, unique biota encountered as sample areas are increased. Examples include terrestrial invertebrates found in caves (z = 0.72, Culver et al. 1973), mites on cushion plants (z = 0.42-0.69, Tepedino and Stanton 1976), and mammals on isolated mountain tops (z = 0.43, Brown 1971 and z = 0.33, Brown 1978). Lawrey (1991, 1992) has suggested that pollution, by reducing interspecific competition, produces larger than expected z-values for lichens species on rocks of differing sizes. Whereas z-values varied from 0.16-0.21 for six undisturbed sites, a site disturbed by air pollution near the Capital Beltway in Maryland yielded a species area curve with a z-value of 0.28.
Some scientists have asserted that as islands get larger the topography becomes more complex, there are more habitats, and therefore we have more species. In their study of red mangrove islands, however, Simberloff and Wilson (1969, 1970) found that species number increased with island size alone and was unrelated to habitat diversity.
The number of species found on an island, according to MacArthur and Wilson was due to two contrasting processes of A) Immigration and B) Extinction. Extinction was envisioned as a normal, locally common event, while new species were added through immigration form the mainland. Diversity was the result of the equilibrium between immigration and extinction. Furthermore, the theory indicated that once the -equilibrium- number of species was reached, the only constant was the number of species in the community, not the identity of the species involved (Figure 5.1). Since extinction is a locally common process, there should be a regular -turnover- in the species found on the island.
The expected number of species on an island is affected not only by the area of the island, but also by the distance of the island from the source of species. Immigration rates are lower on smaller islands and on islands farther from the -mainland- source of species. By contrast, immigration rates are higher on larger islands and on islands closer to the -mainland.- Extinction rates are expected to be higher on small islands, since average population sizes are smaller (Wilson 1992).
The rate at which new immigrant species establish themselves on the island falls as the number of species on the island increases. As more species become established on the island, fewer individual immigrants will belong to a species not already present; moreover, it will be harder for a new species to successfully colonize due to competition with the already established species. Species with high dispersal rates are those that arrive quickly, while those with lower dispersal rates arrive more slowly. Because of the proposed colonization-competition tradeoff, the species with lower dispersal rates are more competitively dominant.
The extinction curve rises as more species arrive on the island. The more species that are present, the more that can become extinct. But again, as more species are present, competition increases and the average population size per species declines, leading to an increased probability of extinction. Finally, if succession proceeds to a -climax- stage, the community will be saturated with species. At equilibrium, the number of species will be constant on the island, though some new species will continue to arrive while others will go extinct.
The MacArthur and Wilson equilibrium theory captured the imagination of ecologists, conservation biologists and biogeographers, making it the leading paradigm for the spatial dynamics of species during the 1980s. It shares much of the conceptual framework of metapopulation biology. Both view nature as subdivided into discrete fragments of suitable habitat; both view local populations as subject to stochastic processes and prone to extinction; and both stress the importance of movements of individuals between habitats (or islands). A key difference is that island biogeography stressed the community property of diversity rather than focusing on the dynamics of individual populations. Furthermore, island theory was developed to explain patterns at large spatial scales as opposed to fragmentation of landscapes at small scales (Hanski 2002).
The MacArthur and Wilson model is now categorized as a mainland-island metapopulation. There is a constant source of species, the mainland. The mainland population is seen as permanent, with no chance of extinction. Furthermore, dispersal is one-way. Species move from the mainland to the island; the reverse is not significant. Finally, no movement from one island to another is included in this type of metapopulation.
Data Analysis
The theory of island biogeography suggests that the species richness for a given type of organism on islands, including habitat islands, is a function of immigration and extinction rates. In turn, immigration and extinction rates are a function of island size and distance from the colonizing source. Because our rock -islands- are of various sizes and distributed patchily, we can readily determine whether a relationship exists between species richness and island area. Use the general equation (1) to describe the relationship between rock surface area and species richness.
(1) log(S) = log(C) + Z*log(A)
A plot of log(S) vs. log(A) should approximate a straight line that can be described with a linear regression. The y-intercept of this line is equal to log(C) and the slope is equal to Z.
Armesto and Contreras (1981) found a significant relationship between lichen species richness and rock habitat area in their study done in Chile. They calculated a Z value of 0.20, which compares well with other data from continental studies where immigration rates are high. However, it is much lower than values from studies done on oceanic islands where barriers to dispersal are more severe (Table 1). This suggests that lichens colonize the rocks very efficiently and rapidly reach an equilibrium situation.
Table 1. Some representative values of z that have been reported in the literature. Notice that high rates of dispersal yield low z-values. This is because both good and poor-dispersing organisms are equally likely to colonize large islands, but the poor dispersing organisms are less likely to colonize small islands.
Fauna or Flora Type of Island z
Land invertebrates Caves 0.72
Mites Cushions plants 0.42-0.69
Mammals Mountaintops 0.43
Beetles West_Indies 0.34
Land plants Galapagos 0.33
Lichens Rocks 0.20
Ants New Guinea 0.17
Mammals Sierra Nevada 0.12

Literature Cited
Andrewartha, H.G. and L.C. Birch. 1954. The distribution and abundance of animals. University of Chicago Press. Chicago, Illinois.
Armesto, J. J. and L.C. Contreras. 1981. Saxicolous lichen communities: nonequilibrium systems? American Naturalist 118:597-604.
Diamond, J.M. 1975. The island dilemma: lessons of modern biogeographic studies for the design of natural reserves. Biol. Conserv. 7: 129-146.
Gould, S.J. 1979. An allometric interpretation of species_area curves: the meaning of the coefficient. American Naturalist 114:335-343.
Hanski, Ilkka. 1998. Metapopulation dynamics. Nature 396: 41-49.
Hanski, Ilkka. 1999. Metapopulation Ecology. Oxford University Press, Oxford, UK.
Harrison, S. 1994. Metapopulations and conservation. Pages 111-128 in J.P. Edwards, R.M. May, and N.R. Webb, Editors. Large-scale ecology and conservation biology. Blackwell, London, UK
Hubbell, S.P., R.B. Foster, S.T. O’Brien, K.E. Harms, R. Condit, B. Wechsler, S.J.Wright and S. Loo de Lao. 1999. Light-gap disturbances, recruitment limitation, and tree diversity in a Neotropical Forest. Science 283: 554-7.
Hutchinson, G.E. 1961. The paradox of the plankton. Amer. Nat. 95: 137-47.
Lehman, C.L. and D. Tilman. 1997. Competition in spatial habitats. Pages 185-203 in D. Tilman and P. Kareiva, Editors. Spatial ecology. Princeton University Press, Princeton, N.J.
Levins, R. 1970. Extinction. Pages 77-104 in M. Gerstenhaver, Editor. Some Mathematical Problems in Biology. American Mathematical Society, Providence, R.I.
MacArthur, R.H., and E.O. Wilson. 1963. An equilibrium theory of insular zoogeography. Evolution 17: 373-387
MacArthur, R.H. and E.O. Wilson. 1967. The Theory of Island Biogeography. Princeton University Press, Princeton, N. J.
Preston, F.W. 1962. The canonical distribution of commonness and rarity. Ecology 43: 185-215.
Quinn, J.F. and S.P. Harrison. 1988. Effects of habitat fragmentation and isolation on species richness. Evidence from biogeographic patterns. Oecologia 75: 132-40.
Simberloff, D.S. 1974. Equilibrium theory of island biogeography and ecology. Annual Review of Ecology and Systematics. 24:161-182.
Terborgh, J. 1975. Faunal equilibrium and the design of wildlife preserves. Pages 369-380 in F. Golley, and E. Medina, Editors. Tropical ecological systems: trends in terrestrial and aquatic research. Springer, Berlin and New York, NY.
Tilman, D. 1994. Competition and biodiversity in spatially structured habitats. Ecology75: 2-16.
Tilman, D. and P. Kareiva. 1997. Spatial ecology. Princeton University Press, Princeton, N.J.
Willis, E.O. 1984. Conservation, subdivision of reserves, and the antidismemberment hypothesis. Oikos 42: 396-398.
Wilson, E.O. 1992. The diversity of life. Norton. New York.
Wilson, E.O. and E.O. Willis. 1975. Applied biogeography. Pages 523-534 in M.L. Cody and J.M. Diamond, Editors. Ecology and evolution of communities. Harvard University Press, Cambridge, MA.
Wright, S. 1940. Breeding structure of populations in relation to speciation. American Naturalist 74: 232-248