Which of the following is the correct definition of equilibrium theory of island biogeography?

Effect of Area

The species–area relation, whereby the number of species in a spatial unit increases with that unit’s area, well predates the MacArthur and Wilson theory of island biogeography, having been documented for about 150 years. Two general kinds of models for this relation have been proposed. The first has number of species predicted from an assumed species–abundance distribution and the total number of individuals of all species combined (assumed proportional to area). The second develops species–area relations from MacArthur and Wilson’s species-equilibrium approach.

May’s paper coalesces the literature for the first sort of model. Two species–abundance distributions are of particular importance.

The first, a log-series distribution, has been used to describe light-trap data and other collections. It leads exactly to the following species–area relation:

[2]S=αln1+ρA/α

where α is a parameter of the abundance distribution, and where ρ is the density of individuals. For A sufficiently large, this can be written

[3]S≅αlnρ /α+αlnA

Notice that this is an exponential or semilog–linear relation of species to area, that is,

[4]S=c1+c2logA

as opposed to the log–log–linear relation that the lognormal implies (below), that is,

[5]logS=logc +zlogA⇒S=cAz

Note also that eqn [3] is inexact for small A (or S) and that S flattens out as A approaches zero.

Various more or less plausible ways to arrive at a log-series distribution from hypothetical biological processes have been given, perhaps the most common of which is not a biological mechanism but rather a property of the sampling procedure: species–area data in which samples of different areas are taken randomly from some homogeneous large area should have a semilog–linear plot for sample areas sufficiently large.

The second species–abundances distribution, the lognormal, is expected when (1) per-individual population growth rates vary randomly over some substantial period of time or (2) the relative abundances of each species is governed by many factors acting on the per-individual growth rate (and therefore, on the logarithm of population size) independently of one another. Both follow from the Central Limit Theorem of statistics. For Preston’s (the originator of this approach) one-parameter (‘canonical’) distribution, if we assume that J, the total number of individuals in all species combined divided by the number of individuals in the rarest species, is proportional to island area, then species number (S) increases as approximately the 0.26 power of area, that is, S = cA 0.26, a particular example of eqn [5]. However, the true relationship is not a power function but approaches one with power 0.25 as S gets large. For small S, the relation bends downward and approaches a linear relation of species to area (thus being quite different from the curves generated by the logseries distribution just discussed). Note this derivation assumes that something is constant about the shape of the distribution from small to large islands. Preston argues that what is constant is the number of individuals in the rarest species and the density of all individuals combined. It is fairly plausible that total number of individuals increases linearly with area for some well-defined taxon, although evidence bearing on this is not entirely supportive. While one study found that total density of birds increased with total species diversity, other results are more in accord with the assumption. On the other hand, while the assumption that number of individuals in the rarest species is constant is a natural one; given the mathematics of the distribution, it is perhaps less plausible biologically. For the two-parameter distribution, some other feature (e.g., standard deviation) also varies. However, the power of the species–area relation is fairly insensitive through the range of reasonable biological variation in the distribution (Engen has derived a species–area relation from yet a third species–abundance distribution, the broken stick; it is again a power function).

Which description is better, eqn [4] or [5]? Connor and McCoy interpret their review of 100 data sets to say that the two fit about equally. Clear examples of each of the two are given in Figure 5.

The second type of species–area mathematical theory explicitly takes into account the ingredients of the MacArthur–Wilson equilibrium model. The model of Schoener that assumes abundances at equilibrium are complementary (summing over all species to ρA, where ρ is the density of all individuals combined and A is island area), has d log S/d log A (the slope on a log–log plot) not constant but ranging from 0.5 to 0; the midpoint of this range is very much like that given by the lognormal distribution (z = 0.26). The equilibrium and lognormal models differ, however, in the curvature of the species–area plot.

The equilibrium species–area model also predicts that the greater the per-species immigration rate λA, the smaller the d log S/d log A. Indeed z is smaller for less remote islands within an archipelago. But far archipelagoes have smaller z’s than near archipelagos. This is probably because of a differentially high λA among birds that have been able to colonize such archipelagoes (Figure 6). Various additional evidence suggests that this model is on the right track. For example, the species–area slope for birds on islands of Burtside Lake, Minnesota (USA) is unusually high, but P is very large and the islands are very small.

A final form for the species–area relation has been suggested by Lomolino and others, one having essentially an S-shape, that is., a greater rate of increase for intermediate-sized islands than either for small or large islands; note that the low slope for the smallest islands is the feature of this concept that makes it very different from any of the species–area curves proposed so far, descriptive or mechanistical. Although some evidence for such a slope was known for special cases (e.g., plants on a Micronesian atoll, in which freshwater lenses are absent on islets below a certain area), a recent survey found that the initial flat portion of the species–area curve typically included a substantial portion of an archipelago’s islands. While the statistical significance of this result has yet to be evaluated, clearly its detection has proven more feasible than expected.

Although direct observation of species immigration is difficult, evidence for the target effect – larger islands intercept more immigrants – is also known from a variety of systems (e.g., Bahamian spiders, Australian sea-dispersed beach plants).

Synopsis

Island biogeography is determined by three processes: immigration, evolution, and extinction. These processes are determined by the area and isolation of islands such that smaller and more isolated islands have lower numbers of species than larger and less isolated islands. In the Anthropocene, human impacts are increasingly more important to island biogeography. Humans have increased immigration to islands by introducing species, caused rapid evolutionary change to native island species in the form of adaptations to human impacts, and precipitated island extinctions. Here, we review how island biogeography arose in the past and how it is now changing in the Anthropocene.

Tests of IBT

IBT provides clear predictions of the species richness of an island based on its area and isolation through the action of colonization, speciation, and extinction (Fig. 2). Scientific theories must be rigorously tested; however, rigorous experimental tests of IBT can be challenging due to the size of islands and the scale of the three biogeographic processes involved.

Manipulation experiments to test IBT have largely centered on the defaunation of small islands and recording whether the island returns to its predefaunation species richness. These studies explicitly test the concept of equilibrium species richness (Schoener, 2011). The first, and most well-known experiment, manipulated red mangrove (Rhizophora mangle) islands in the Florida keys (Simberloff and Wilson, 1970). Arthropod species richness was first estimated for six islands that varied in area and isolation, but all six were small with low isolation in general (max area, 0.003 ha; max isolation, 1.2 km). Arthropods on the islands were then removed through pesticide fumigation. The researchers surveyed the recolonization of arthropods to the islands and found that the islands recovered to their prefumigation species richness values such that larger islands still had more species than smaller islands and it took longer for the more isolated islands to return to their predefaunation species richness, providing support for equilibrium species richness determined by area and isolation as predicted by IBT (Fig. 3B). Other well-known tests of IBT have measured the colonization of species (e.g., spiders, plants, lizards) to islands following a major natural disturbance like a volcano or hurricane that removed existing species. In addition to island manipulations, other tests have used surveys through time to show that even though the identities of species may change on islands, the species richness of islands can be quite stable providing additional support for the concept of equilibrium species richness (Schoener, 2011).

However, the equilibrium species richness levels of islands may be changing in the Anthropocene. Other surveys of islands have not found stable equilibrium species richness values and have attributed this instability to climate change. For example, surveys of plant species richness on Bahamian islands in the 1990s and 2000s found that in the first decade of surveys, species richness was somewhat stable, but in the latter decade extinction rates greatly increased causing species richness to decline (Morrison, 2010). This change in species richness coincided with temperature warming and decreased rainfall across the region.

2.1 The Model

2.1.1 Explaining the TTIB With a Simple Example

The TTIB can be understood using a simple example consisting in five species (A, B, C, D, E), arranged in three trophic levels, with species C and E being basal species, species B and D primary consumers and species A the top predator (Fig. 2). The core idea of the TTIB is that colonization and extinction of species on the island obey the principle of “at least one prey species per predator”. In practical terms, this principle can be translated as follows:

Fig. 2. Simple food web used to illustrate the Trophic Theory of Island Biogeography. (a) The complete food web (on the mainland) consists in five different species (A, B, C, D, E), (b) subfood webs that species A can colonize and (c) subfood webs that species A cannot colonize.

1.

Colonization of a given species can only take place when at least one of its prey species is present (Fig. 3). This means that the colonization rate is now modulated by the probability that the island food web contains at least one prey species for the focal species;

Fig. 3. Restriction of colonization under the TTIB. Transitions among community states that do not include species A are depicted by dotted arrows, as in Fig. 1. Communities in grey represent communities that can be colonized by species A (i.e. the fraction hA−PXA=1 of the possible island communities). The associated species A-colonized communities (the “outer communities”, i.e. the fraction PXA=1 of the possible island communities) are linked to them with a thick dashed l.

2.

Extinction of a given species now depends not only on the single-species extinction rate of the focal species, but also on the rate at which the focal species gets caught in an “extinction cascade” (Fig. 4). Extinction cascades happen when a species “down”, or lower, in the local food web supports a whole portion of the food web and goes extinct (e.g. species C in the (A, B, C, D) community in Fig. 4).

Fig. 4. Increase in the extinction rate of species A as a result of cascading extinctions. Each of the panels represents one the community that includes species A (the “outer communities” in Fig. 3). Species in black dots are species that contribute to the additional extinction rate of species A. For instance, in the (A, B, C) community, if species B or species C goes extinct, species A must also go extinct. The mention under each panel is the extinction rate of species A in the configuration depicted in the matching panel, e.g. in the above mentioned example, the rate of extinction of species A is 3e because it goes extinct at its own rate plus that of species B and that of species C. In this particular case, the total extinction rate of species A can be deduced from that of species B because if species C goes extinct, then species B must also go extinct. Thus, in this instance, the extinction rate of A is simply that of species B plus e. However, this additivity of extinction rate is not always in place. For instance, in the (A, B, C, D) community, species B and species D both experience a “2e” extinction rate, but species A only experiences a “2e” extinction rate as well because the single extinction of either species B or D has no effect on A, while the extinction of C makes the whole food web collapse.

For a general idea of the TTIB dynamics, we can write that the probability of occurrence of a given species Z obeys the following differential equation (rewriting Eq. 16):

(17)d PXZ=1dt=chZ−PXZ=1−eZPXZ=1

where hZ is the probability that island community is hospitable to species Z (i.e. community contains at least one prey of species Z) and eZ is the effective extinction rate of species Z computed using e, the number of ways it can go extinct through a single-species extinction in the island food web and the weights associated with these extinction events (which are computed from the occurrence probabilities of species “down” the food web).

Let us start this example using the mainland food web given in Fig. 2a. Species A can only colonize a restricted set of island food webs (Figs 2b and 3). In other island food webs, it simply cannot settle because there is neither prey species B nor D (Fig. 2c). Once species A is on the island, the community must be in one of the “outer community” states of Fig. 3. The extinction rate of species A when established in one of these outer communities depends on how many species down the food web may provoke an extinction cascade affecting species A (Fig. 4). For instance, when only one species down the food web can provoke the extinction of species A through cascading extinction, then the extinction rate of species A is 2e; if two species can provoke such an extinction (e.g. if the community is (A, B, C)), then the extinction rate of species A is 3e.

Although the graphical representation of transitions among communities and colonization-prone communities for a focal species is useful to fully grasp the principles of the TTIB, a more quantitative approach can be obtained by focusing on the master equation behind food web dynamics. The following explanation starts with the corresponding master equation in the TIB and then introduces an equivalent formulation in the case of the TTIB.

The TIB model, as expressed using Eqs (1) and (2), does not distinguish species based on any feature. However, the underlying random variable describing the number of species present on the island, S, can be decomposed as a sum of indicator variables Xi which describe the presence/absence of species i, so that at all times:

(18)St=∑iXit

Under the TIB, each of the Xi(t) is a random variable the value of which changes from 1 to 0 with rate e and from 0 to 1 with rate c. The corresponding master equation for a single species is thus given by two coupled differential equations (indices i are omitted for the sake of clarity):

(19a)dPX=0dt=ePX=1−cPX=0

(19b)dPX=1dt=cPX=0−ePX=1

Noting PX=1=p and PX=0=1−p, we obtain the well-known equation for the occupancy of islands by a single species under MacArthur and Wilson's framework:

(20) dpdt=c1−p−ep

When compared with the framework set by Eqs (16) or (17), Eq. (20) means that: (i) there are no effects of network structure on any one of the three parameters of Eq. (16); and (ii) the probability that an island is hospitable to colonization is always 1 (i.e. there is no restriction to species colonization potential).

The stationary distribution of X following Eq. (19) is a Bernoulli distribution of parameter c/c+e, associated with the eigenvalue 0 of the matrix defining the process defined in Eq. (19). In other words, solving for the equilibrium of Eq. (19) is equivalent to finding the eigenvalues and eigenvectors of a 2 × 2 matrix, and the equilibrium is given by the eigenvector associated with the eigenvalue 0. The other eigenvalue, −c+e, is associated with the eigenvector −1,1 (i.e. any discrepancy in the probability of occurrence of the species from the stationary distribution of X), so that an initially absent species at time t = 0 has a probability of occurrence at time t equal to:

(21a)PXt=1|X0= 0=cc+e1−e−c+et

while an initially present species at time t = 0 has occurrence probability:

(21b)PXt=1|X0=1=cc+e+ec+ee−c+et

Now let us proceed with the simple four species community (B, C, D, E) given in Fig. 1 under the TIB, i.e. without using the principle of “at least one prey species per predator species” on the island. Each of the PX, where X now represents a community, obeys a differential equation similar to Eq. (19b), with losses due to both extinction of local species and colonization by new species, and gains due to “upwards” transitions from species-poor communities and “downwards” transitions from species-rich ones. For instance, the equation for the community (D, E) is:

(22)dPDEdt=cPD+PE+ePBDE+PCDE−2c+ePDE

More generally, noting P the vector of all PX, the master equation can be written as:

(23)dPdt=G⋅P

where G is a matrix describing all the coefficients of the master equation. In the case of the TIB acting on the food web described in Fig. 1a, matrix G is given in Table 1.

Table 1. Matrix G of Eq. (23) in the Case of the TIB Acting on the Food Web Presented in Fig. 1

		From
		Empty	B	C	D	E	BC	BD	BE	CD	CE	DE	BCD	BCE	BDE	CDE	BCDE
To	Empty	− 4c	e	e	e	e
B	c	− 3c − e				e	e	e
C	c		− 3c − e			e			e	e
D	c			− 3c − e			e		e		e
E	c				− 3c − e			e		e	e
BC		c	c			− 2(c + e)						e	e
BD		c		c			− 2(c + e)					e		e
BE		c			c			− 2(c + e)					e	e
CD			c	c					− 2(c + e)			e			e
CE			c		c					− 2(c + e)			e		e
DE				c	c						− 2(c + e)			e	e
BCD						c	c		c			− c − 3e				e
BCE						c		c		c			− c − 3e			e
BDE							c	c			c			− c − 3e		e
CDE									c	c	c				− c − 3e	e
BCDE												c	c	c	c	− 4e

Empty cells are equal to zero (omitted for clarity). Columns indicate “giver” community states, rows indicate “receiver” community states. The sum of each column equals zero because the sum of incoming and outgoing state transition rates must balance (the sum of the probability of all states must always be equal to 1). A single equation such as Eq. (22) can be retrieved by following the matching row of the matrix and adding/subtracting appropriate terms based on matrix coefficients on that row.

Solving the equation G⋅P=0 (i.e. finding a vector of sum equal to 1 associated with the eigenvalue 0 of matrix G) yields the probability of finding the food web in the different states. In the case of the TIB, the result is somehow easy to find without having to resort to the study of matrix eigenvalues and eigenvectors; Eq. (11) already gives the probability of finding a community with exactly S species present. Dividing this expression by the number of combinations of S species among T yields the following general formula:

(24)PX= cc+eXec+eT−X

where |X| is the cardinality of community X (i.e. its species richness). The probability that a single species, say C, is present on the island can be obtained by summing Eq. (24) over all communities that include species C:

(25)PXC=1=∑C∈XPX=∑k=0T∑C∈XX=kcc+ekec+eT−k=∑k=1T T−1k−1cc+ekec+eT−k=cc+e

We now shift to the case of the TTIB, using the example given in Fig. 1b, i.e. the same food web as the one used above, but with an intrinsic dependency between species occurrences due to the underlying TTIB principle. In this context, certain communities cannot exist, i.e. (B), (D), (B, D), (B, E), (B, D, E) (grey communities in Fig. 1b). The associated G matrix is given in Table 2.

Table 2. Matrix G of Eq. (23) in the Case of the TTIB Acting on the Food Web Presented in Fig. 1

		From
		Empty	C	E	BC	CD	CE	DE	BCD	BCE	CDE	BCDE
To	Empty	− 2c	e	e	e	e		e	e
C	c	− 3c − e		e	e	e
E	c		− 2c − e			e	e		e
BC		c		− 2(c + e)				e	e
CD		c			− 2(c + e)			e		e
CE		c	c			− 2(c + e)			e	e
DE			c				− c − 2e			e	e
BCD				c	c			− c − 3e			e
BCE				c		c			− c − 3e		e
CDE					c	c	c			− c − 3e	e
BCDE								c	c	c	− 4e

Empty cells are equal to zero (omitted for clarity). Interpretation of this table follows the same legend as Table 1.

Solving G⋅P=0 using the G matrix given in Table 2 yields complicated expressions. However, the same type of computations as the ones used to go from Eq. (24) to Eq. (25) can be applied to this stable distribution of community states to obtain the stable distribution of each species occurrence probability. For instance, one obtains that the probability of observing species B is given by:

(26)PXB=1=c2c+ec+2e

The food chain (B, C) being particularly simple (see also Section 2.2.1), this result is easy to interpret: the probability of occurrence of species B relies on species C being present (with probability c/c+e as species C is a basal species), and species B having colonized (rate c), and the whole food chain not collapsing (rate of species B extinction 2e).

Classical Theories of Island Biogeography: Predicted Patterns

The Theory of Island Biogeography (IBT) predicts a variation of species richness with island area and isolation (MacArthur and Wilson, 1967). According to the IBT, the species–area relationship (SAR) is due to larger habitat heterogeneity, that results on lower extinction rates and therefore, higher species richness maintenance. At the same time, such richness is expected to decrease as a function of island isolation, due to reduced immigration rates.

Further studies of island biogeography also pointed for an increase in species richness with island geological age due to longer times for species accumulation either by arrival of new immigrants or arise of a new species by speciation (Rosenzweig, 1995). The General Dynamic Theory of Oceanic Island Biogeography (GDM; Whittaker et al., 2008) also included island age as an important factor for predicting islands species richness, combined with island area. The explanation for the GDM also relies into the interaction between immigration, speciation and extinction rates. According to the GDM, species richness would increase linearly with island area, but would vary as a unimodal function of island age, due to the variation of habitat heterogeneity in the life cycle of an oceanic island. Such islands, which are mainly volcanic, tend to increase in area and height in their youth, due initially to volcanic activity and latter to erosion (that also increases habitat heterogeneity). An advanced stage of erosion leads to loss of habitats—increasing extinction rates—and, in older stages, the disappearance of the island, turning into an atoll or seamount, sinking into the sea.

Besides the influence of island area, age and isolation in species richness, it is also expected for those environmental variables to affect the level of endemism in islands. In the terrestrial realm, bigger islands are expected to show increased numbers of endemics, given the possibility of diversification driven by sympatric and ecological speciation—a process known as adaptive radiation. Older islands are also expected to show increased levels of endemism, due to longer times for cladogenesis. Notwithstanding, isolated islands shall exhibit increased percentage of endemic species as well, due to reduced gene flow.

The processes that influence biodiversity distributions on terrestrial and marine realms—i.e. immigration, speciation and extinction—although the same, interact differently and vary differently with such island physical features (area, isolation and age), leading to differences on island biogeography patterns.

Community theory

The theory of island biogeography postulates that species richness in isolated habitats is regulated by local extinction and colonization and should vary with habitat size and proximity to potential sources of colonizers. The intermediate disturbance hypothesis predicts high richness in communities subject to a moderate degree of disturbance or stress; according to this model, high stress leads to mortality in all but fast-growing individuals, and under low stress, inter- and intraspecific interactions such as competition and predation determine community structure. Other models look at resource and habitat partitioning/niche diversification, temporal offsets in life histories, and other mechanisms controlling community composition and structure. Studies of amphibians, plants, invertebrates, and algae in temperate woodland pools, Mediterranean temporary pools, Negev and Namibian desert pools, Scandinavian rockpools, Arctic snowmelt pools, and other areas show complex relationships between community composition and habitat variables such as size, hydroperiod, frequency of flooding, hydrologic predictability, distance from other waters, and salinity. The data suggest that community richness is related to both degrees of disturbance and the predictability of disturbance. Isolation is also important, with greater richness in waters that are connected to larger bodies (e.g., in floodplains) but also fewer taxa specifically adapted to temporary habitats. Species pools in individual water bodies are poor in comparison to the regional set of species (Table 6), and experimental assemblages comprised of larger subsets of available species function differently than the smaller natural communities.

Table 6. Regional species pools (β diversity) are greater than local species pools (α diversity), as illustrated by numbers of non-dipteran macroinvertebrates found in early spring from nine adjacent temporary pools on Cape Cod, Massachusetts, USA

Modified from figure 2 in Colburn EA (2004) Vernal Pools: Natural History and Conservation. Blacksburg, VA: McDonald and Woodward.

Island biogeography theory at the light of ecosystem principles

In general terms, the Island Biogeography Theory explains therefore why, if everything else is similar, distant islands will have lower immigration rates than those close to a mainland, and ecosystems will contain fewer species on distant islands, while close islands will have high immigration rates and support more species. It also explains why large islands, presenting lower extinction rates, will have more species than small ones. This theory forecasts effect of fragmenting previously continuous habitat, considering that fragmentation leads to both lower immigration rates (gaps between fragments are not crossed easily) and higher extinction rates (less area supports fewer species).

The Ecological Law of Thermodynamics equally provides a sound explanation for the same observations. Let us look in first place to the problem of the immigration curves. In all the three examples, the decline in immigration rates as a function of increasing isolation (distance) is fully covered the concept of openness introduced by Jørgensen (2000a). Once accepted the initial premise that an ecosystem must be open or at least non-isolated to be able to import the energy needed for its maintenance, islands' openness will be inversely proportional to its distance to mainland. As a consequence, more distant islands have lower possibility to exchange energy or matter and decreased chance for information inputs, expressed in this case as immigration of organisms. The same applies to fragmented habitats, the smaller the plots of the original ecosystem the bigger the difficulty in recovering (or maintaining) the original characteristics. After a disturbance, the higher the openness the faster information and network (which may express as biodiversity) recovery will be.

The fact that large islands present lower extinction rates and more species than small ones, as well as less fragmented habitats in comparison with more fragmented ones, also complies with the Ecological Law of Thermodynamics. All three examples can be interpreted in this light. Actually, provided that all the other environmental are similar, larger islands offer more available resources. Under the prevailing circumstances, solutions able to give the highest exergy will be selected, increasing the distance to thermodynamic equilibrium not only in terms of biomass but also in terms of information (i.e. network and biodiversity). Moreover, after a disturbance, like in the case of the Krakatau Island, the rate of re-colonization and ecosystem recovery will be a function of system's openness.

Island Biogeography Theory in the Light of Ecosystem Principles

In general terms, the Island Biogeography Theory explains therefore why, if everything else is similar, distant islands will have lower immigration rates with fewer species than those close to a mainland, while close islands will have high immigration rates and support more species. It also explains why large islands, presenting lower extinction rates, will have more species than small ones. This theory has been applied, for instance, in forecasting the effects of fragmenting previously continuous habitat, considering that fragmentation leads to both lower immigration rates (gaps between fragments are not crossed easily) and higher extinction rates (less area supports fewer species).

The Ecological Law of Thermodynamics equally provides a sound explanation for the same observations. Let us look in the first place to the problem of the immigration curves. In all the three examples, the decline in immigration rates as a function of increasing isolation (distance) is fully covered the concept of openness introduced by Jørgensen (2000). Once accepted the initial premise that an ecosystem must be open or at least nonisolated to be able to import the energy needed for its maintenance, islands' openness will be inversely proportional to its distance to mainland. As a consequence, more distant islands have lower possibility to exchange energy or matter and decreased chance for information inputs, expressed in this case as immigration of organisms. The same applies to fragmented habitats, the smaller the plots of the original ecosystem the bigger the difficulty in recovering (or maintaining) the original characteristics. After a disturbance, the higher the openness, the faster information and network (which may express as biodiversity) recovery will be.

The fact that large islands present lower extinction rates and more species than small ones, as well as less fragmented habitats in comparison with more fragmented ones, also complies with the Ecological Law of Thermodynamics. All three examples can be interpreted in this light. Provided that all the other environmental are similar, larger islands offer more available resources. Under the prevailing circumstances, solutions able to give the highest eco-exergy will be selected, increasing the distance to thermodynamic equilibrium not only in terms of biomass but also in terms of information (i.e., network and biodiversity). Moreover, after a disturbance, such as in the case of Krakatau Island, the rate of recolonization and ecosystem recovery will be a function of the system's openness.

Changes in Community Composition and their Consequences

Using as a model MacArthur and Wilson's theory of island biogeography, researchers studying islands of forest have predicted that smaller fragments would support lower numbers of species than large fragments. This prediction has held true in a broad variety of temperate and tropical sites, with fragments often containing only a limited subset of a region's biota. These reductions in diversity have shown to affect disparate groups of plants and animals, including birds (e.g., insectivores, frugivores, cavity nesters), insects (e.g., beetles, fruit flies, ants), and plants (e.g., herbs, forbs, shade-tolerant trees).

Two different mechanisms have been invoked to explain this general pattern. First, populations in fragments could have become locally extinct following fragment isolation. Alternatively, lower diversity in fragments could also result from differences in the initial species composition of the patches that were isolated. This may be especially common in tropical forests, where regional species diversity is very high but many species are locally rare or patchily distributed. In this case a species may be missing from a fragment not because it went locally extinct, but because it was absent when the fragment was originally isolated.

Species diversity is not always lower in fragments, however, and there are numerous cases in which it has actually been found to increase following fragmentation. Many amphibians, insects, small mammals, and plants are habitat generalists tolerant of a broad range of habitat types. In some cases species diversity even increases despite the loss of forest-interior species, because their absence is compensated by an influx of generalists from the surrounding matrix. Perhaps one of the best examples of this phenomenon is tropical pool-breeding frogs, of which disturbed-habitat specialists (e.g., Scinax rubra, Adenomera hylaedactyla) can be found in recently isolated forest fragments and on the edges of continuous forest. Similar results have also been documented for small terrestrial mammals (e.g., Oecomys spp.), perhaps due to their preference for foraging in sites with abundant leaf litter and fallen branches.

Shifts in community structure may also depend on what trophic level a species occupies. Top predators such jaguars (Panthera onca) and gray wolves (Canis lupus) are hypothesized to be particularly vulnerable to extinction because they are found at lower population densities, forage in large territories, or are dependent on prey that can also be detrimentally affected by fragmentation. When these species become locally extinct, medium-sized predators (also known as mesopredators) such as coyotes (Canis latrans) and opossum (Didelphis virginiana) may increase in abundance. As a result, the abundance of the species preyed upon by the mesopredators will in turn decrease.

One of the defining features of forest habitats is the myriad interactions in which resident species are involved. Predation, herbivory, competition, and mutualisms all play an important role in structuring forest communities and promoting evolutionary change. As a result, it is widely believed that the disruption of these interactions in fragmented landscapes, particularly mutualistic ones related to plant reproductions and establishment, could have major repercussions for ecosystem functioning. In fact some authors have gone so far as to suggest that fragmentation-related reductions of these interactions will lead to ‘ecological meltdown’ or ‘cascades’ of further extinctions in forest fragments.

Some interactions relating to plant recruitment can be substantially modified in fragmented areas. For instance, the pollination of plants can decrease in fragments, either because pollinators are less abundant, they visit plants less frequently, or because they transfer less pollen per visit. Interestingly, a number of studies have also documented the opposite effect – dramatic increases in pollination in both fragments and the intervening matrix. The increase in these cases is usually due to a superabundance in the disturbed areas of exotic pollinators, such as the African honeybee (Apis mellifera scutellata). Seed dispersal and predation can be modified as well, although results to date have been somewhat contradictory. The quantity and composition of the seed rain has been shown to vary in disturbed habitats, due to changes in the abundance, diversity, or diet of dispersing animals such as monkeys, bats, birds, and dung beetles. Once these seeds are successfully dispersed, an influx of predators from the habitat surrounding fragments, particularly rodents and insects, can rapidly depress the seed numbers. This may be why the abundance of seedlings of understory plants is frequently much lower in fragments than in continuous forest. However, seedling numbers can also be lower if herbivory is higher in fragments and near edges, as might be expected given the larger populations of generalist browsers such as white-tailed deer (Odocoileus virginianus) or meadow voles (Microtus pennsylvanicus) in these areas.

Abstract

The passing of the 50th anniversary of the theory of island biogeography (IBT) has helped spur a new wave of interest in the biology of islands. Despite the longstanding acclaim of MacArthur and Wilson’s (1963, 1967) theory, the breadth of its influence in mainstream ecology today is easily overlooked. Here we summarize some of the main links between IBT and subsequent developments in ecology. These include not only modifications to the core model to incorporate greater biological complexity, but also the role of IBT in inspiring two other quantitative theories that are at least as broad in relevance—metapopulation theory and ecological neutral theory. Using habitat fragmentation and life-history evolution as examples, we also argue that a significant legacy of IBT has been in shaping and unifying ecological schools of thought.