The Theory of Island Biogeography


†† Island biogeography has been a subject of considerable interest to biologists and geographers since the time of Darwin, Wallace, and the less well-known Hooker. Hooker explored islands in the South Atlantic and South Pacific. Darwin and Wallace are more important in our current thinking, since these two were pioneers in the development of the theory of evolution. However, much of the theory of island biogeography was built on data which came from their studies of the Galapagos and East Indies respectively. Islands have been studied as natural experiments ever since, with varying levels of intensity. Oceanic islands are isolated and small enough to reveal processes and results too complex to interpret in mainland areas.


Islands are unique. Since they are isolated, evolutionary processes work at different rates - there is little or no gene flow to dilute the effects of selection and mutation. Endemism is rampant. However, both in theory and practice, that same isolation makes islands more vulnerable to habitat change and extinction. Introduction of a single predator or herbivore can have dramatic impact on the local community, as we have just seen with biota of the Hawaiian islands.


Islands, as natural experiments, have not been protected from damage and extinction through human activities. Since islands are isolated, and in many cases the species found on them are endemic, extinction has been particularly common on islands. 93% of the bird species whose extinction has been recorded since 1600 have been island species. Historical records suggest a mean extinction rate through the Pleistocene of approximately 1 species in 83.3 years. In 1980, that rate was one species every 3.6 years. Extrapolating the curve, an extinction rate of one island species per year can be predicted for the immediate future.


One of the reasons islands are important in the more general structure of ecology, biogeography, and conservation biology is that islands, as at least relatively isolated areas, are excellent natural laboratories to study the relationship between area and species diversity. When we fully understand the relationship, it will be applicable to fragments of habitat that human activities protect. We all know those sanctuaries are important, but we need to know what and how much we can protect in them.


Species-Area Relationships


†† One of the immediately obvious characteristics of islands is the number of species resident there, a number much lower and therefore more countable than the diversity on a continental mainland. Such counts can reveal interesting relationships. For example, Great Britain has 44 species of mammals, yet Ireland, only approximately 20 miles further removed from mainland Europe into the Atlantic, has only 22 species. Is 20 miles a sufficient distance to increase isolation and decrease mammalian immigration by half? If so, then flying mammals (bats) should show similar numbers of species on both islands, since immigration and isolation would be significantly less severe to a bat species. The number of bats is not similar. Only 7 of the 13 bat species resident in Great Britain breed in Ireland. What factor accounts for the difference? The single factor which provides the best explanation is island area (though it is not the only contributing factor). There is a classic curve originally drawn by Darlington, and reprinted in every biogeography chapter since then, which depicts the relationship between area and the number of reptilian species in the West Indies.


†† Figure - A curve relating island area to reptilian diversity in the West Indies.


†† As a log-log plot it is not a 'curve', but a straight line. From it a 'rule-of-thumb' can be formulated which says that increasing the area of an island by a factor of 10 (or, more correctly, counting the number of species on a nearby island 10 times larger) would approximately double the number of reptile species present. That relationship is called a power function. For islands it is written as:


††††††S = C Az


†† where:


S is the number of species present,

C is a constant which varies with the taxonomic group under study (taxa which consist of good dispersers (these species also typically have rapid population growth) will logically accumulate more species on an isolated island, all else being equal),

A is the area of the island, and the exponent z has been shown to be fairly constant for most island situations.


Geographic variation in C has been observed and 'loosely' reflects the isolation of island groups typically studied due, for example, to the presence or absence of major air or water circulation pathways nearby (islands located along the Gulf Stream would be more likely to accumulate species than those located in the doldrums of the Sargasso Sea) and also to effects of gross climatic difference (i.e. C is higher in the tropics than for islands at high arctic latitudes). C can also be regarded as a scaling factor. In terms of the graph of a species-area relationship, z determines the 'shape' of the curve, which is raised or lowered as a whole by the value of C. The meaning of z, in an all out treatment, is related to the distribution of abundances of species, i.e. to the number of species expected if the total number of individuals increases (as it would on a larger island) and those species follow a Preston log-normal distribution of abundance (see May 1975 for a full treatment). However, there is a simpler level of meaning for the z, revealed by manipulating

the equation. The graph of the basic equation would show an exponential rise in the number of species as area increased. If we take the logarithms of both sides of the equation, we get something that should look easier to work with:


††††††† log S = log C + zlogA


If we conveniently forget that the equation has logs as its terms, then you can see that this is the equation for a line, with the basic formula:


††††††† Y = b + mx


So that if we plot the log of the number of species against the log of island area, we get a straight line, and the slope of the line is the coefficient z. The z, establishes the characteristic relationship between the number of species and area for all taxa. It is a general characteristic, and fittingly, it is related to the most basic hypotheses about the way species are put together in communities. There is variation in z, but it reflects, in theory at least, general patterns of isolation involved in the studies. Study of taxa in mainland 'islands' less isolated from their surroundings will give a lower z value (though much higher total species numbers) than would parallel studies of the same taxa on oceanic islands. It is argued this results from species that could not live indefinitely within the 'island' being observed as transients in mainland habitat 'islands', though they would never be observed on oceanic islands. Is z really as independent of autecological characteristics of species and effects of real world disturbance as this view might lead you to think? The answer, at least from modeling studies to be considered below, is a clear no. The value of z seems to vary with the growth characteristics of species and with the frequency and intensity of disturbance (Villa et al. 1992).


Species-area curves have been generated for a large variety of places and taxa, and the range of z values is remarkably small. The data in the table below fit fairly closely with what would be predicted based upon the theory of species abundance distributions. May (1975) gave an extended treatment of the mathematical relationships among observed and theoretical abundance and diversity patterns. Here the treatment will be limited to a more compact form (derived from a chapter on patterns in multi-species communities in May (1976)). The most commonly observed distribution of the relative abundance of species is a log normal. This means that a plot of the logs of species abundance against the number of species (i.e. a histogram) follows a bell shape. Sampled distributions usually have what is called a 'veil line'.


Figure - Lognormal abundance distribution for moth samples.


†† Figure - The theoretical Preston log-normal species abundance distribution


†† The curves indicate the presence of a few common species (the right hand end of the curve) and a larger number of species of intermediate abundance. We don't usually see the left hand end of the curve (the very rare species) because we rarely sample enough individuals to capture even one. A larger total sample moves the veil line to the left, taking in more of the total curve. Preston used other data, a log-normal species abundance distribution for birds in Maryland, to develop the log normal.


Theoretically, the Preston log-normal the z value should be 0.263.May says that the problem is that z doesn't really tell us much, since within the constraints as S varies from 20 to 10,000 species, the z value changes only from 0.29 to 0.13. It really turns out that z is largely a mathematical property of the log-normal, and doesn't tell us much about communities. If they are log-normal, then z will be at least close to .263. Nevertheless, there is still some interest in patterns in z. To indicate that briefly, here's a short table of some species-area relationships:


†† Group††††††††††††††††††††† Location†††††††††††††††††††† value



†† beetles††††††††††††††††††† West Indies††††††††††††††† 0.34


†† reptiles and†††††††††††† West Indies††††††††††††††† 0.30

†† amphibians

†† birds††††††††††††††††††††††† North America-Great 0.17


†† Birds††††††††††††††††††††††† West Indies††††††††††††††† 0.24

†† land vertebrates†††† Lake Michigan†††††††††† 0.24


†† ants††††††††††††††††††††††††† Melanesia††††††††††††††††† 0.30

†† birds††††††††††††††††††††††† East Indies†††††††††††††††† 0.28

†† land plants†††††††††††††† Galapagos†††††††††††††††† 0.33

†† dipterans†††††††††††††††† Cincinnati parks††††††† 0.24

†† mammals††††††††††††††† North America†††††††††† 0.1-0.2


†††† The values of z for mainland areas are clearly lower, e.g. both diptera in parklands and mammals over North America generally, than the values for isolated islands. As mentioned above, the explanation for these lower values is the inclusion of transients in species counts from small 'islands'. Consider a badger, with a home range of 200 square km, or a wolf with a home range of 400 square km, or even larger areas for seasonal migrants like caribou or large predatory birds. These animals could easily be included in counts from 'island' areas much smaller than their home ranges, i.e. they could be present in a 'patch' of mainland area considered as an 'island' transients. They could not survive in such small areas if isolated by significant barriers, but sampling larger areas more comparable to their home ranges would then not add them to species lists as if new; they are already on the species list from being present as transients in the smaller areas. Oceanic islands do not contain such transients. Thus we get measurements of species numbers which are 'too high', include transients, in small mainland sample areas, and too few additions as larger areas are sampled. The slope of the graph relating the number of species to island area, i.e. the z, is lowered. The theory underlying the log normal and island biogeography implicitly assumes that all species counted could be resident permanently within the 'island' area, this may not be the case with some mainland species. Compare the slopes for bird species numbers on islands in the East and West Indies, both >0.2, with that for boreal forest birds in the Great Basin of western North America (0.16). All three values are for habitat islands, but on mainland the slope is lower, and the likely reason is the presence of some 'transient' birds in species counts within small habitat islands in the Great Basin. That may also explain the low value for mammals, but what about the low value for Cincinnati flies? Are they likely to be transients? The explanation here more likely lies in the assumption that islands are truly isolated; immigration onto an island requires a jump dispersal, i.e. the intervening habitat is assumed to be inhospitable. The same sampling artifacts that led to low values for mammals do also apply here. Models assume island populations are numerically self-sustaining, and have increasing probabilities of extinction on the island as they become rarer. Other green areas, garbage, etc. may sustain fly populations (and even permit reproduction!) in habitats between park 'islands' in the urban area, permitting high rates of re-immigration, so that populations which might not otherwise be sustained in a park remain. That 'rescue' is much less likely for oceanic island populations.


†† Figure - Species-area curves for ants on New Guinea (relatively, a mainland) and the isolated islands nearby. The island curve is steeper (a higher z) than the New Guinea curve, as explained above.


Is the relationship between species and area linear?


There are theoretical reasons to expect a z of 0.263. However, in doing so we are accepting that species-area curves are linear. There are some points to consider:


Given apparent differences in what you might expect, is the linear equation predicting z logical? There is at least one study that questions the assumption of linearity (Crawley and Harral, 2001). They sampled Berkshire and the East Berks in England in nested, contiguous quadrats, at 100 and 25km2, also 456 km2 contiguous quadrats and replicates (not contiguous) from 0.01 m2 to 110 ha in Silwood Park. Initial results, averaging the values obtained, don't differ significantly from the theory.They found z=0.302 for samples from the Silwood research estate, and z= 0.267 for samples over the larger area of Berkshire and all of Great Britain.


†† An important point about effects of area on species diversity may have slid by here. The biological question is why does area affect species numbers? There are two schools of thought:


1) The Preston canonical log normal distribution can be used to suggest that area determines the total population size of the collection of species living there. Area is the direct determinant of diversity, since the multiplicity of factors which determine relative abundance and species diversity are prescribed, and independent of the specific island of area being studied.


2) The alternative school suggests that area is of only indirect importance. Area fits because area is a good indicator of the amount of habitat diversity present on an island. It is really the 'number of niches' that determines the number of species, but there is no established method for counting, or even estimating the number of niches in an environment. Instead, physical variables are usually measured. The assumption is made that the two measures should be highly correlated.


Letís look at some of the basic data used to verify the basic relationship between species numbers and island areas. One of the frequent approaches is the use of multiple regression models to determine what factors account for differences in species diversity on islands. Jared Diamond (1973; Diamond and Mayr 1976) used this method to study the distribution of bird species on New Guinea and its satellite islands. The data were first fit to the basic equation; for these bird data the equation then reads:


††††††† S = 15.1 A22


†† for the satellite islands near New Guinea, and this relationship accounted for 81% of the variation in the number of bird species among islands studied. When Diamond instead measured the numbers of species in montane habitat islands on New Guinea proper, only the constant changed, to 12.3. Figure 4 shows the numbers of species and the locations of montane habitat islands. The central 'line' of New Guinea is a mountain backbone, and forms the largest single island. Diamond discerned that a part of the effect of increasing area was due to an increase in the maximum elevation observed on larger (even habitat) islands, and the concommitant differences in the number of habitats resulting from a greater range of elevations, which cause differences in climate.


Figure - A map of the montane areas of New Guinea and the diversity of montane birds in those areas. Variation in species numbers is correlated with variation in altitude.


†† In addition to the number of species accounted for by area alone, each 1000m of elevation 'caused' an increase of 2.7% in bird species diversity on New Guinea satellite islands (and 8.9% in New Guinea habitat islands) on average. After the entry of this term, the regression equation reads:


††††††† S = 15.1 (1 + .027L/1000) A22


†† Diamond realized that the number of species on islands also reflected the degree to which the islands were isolated by distance from source populations. The more distant from the New Guinea source of species, the smaller the number of species when islands similar in size and elevation were compared. The decrease is approximately exponential with distance, and the number decreases by half for each 2600 Km on average. Thus, Pitcairn Island (the place where the Bounty's mutineers ended up) is about 8000 Km from New Guinea, and has about 1/8 or 12.5% of the bird species numbers on a similar area of New Guinea. When this factor in incorporated into the multiple regression equation, the result is:


††††††† S = 15.1 (1 + .027L/1000) (e-D/3750) A22


The following figures show you how some of the data look, and why the distance relationship is exponential. Figure 5 shows the basic species-area relationship for the satellite islands around New Guinea.


Figure - Species-area relationship for birds of oceanic islands around New Guinea. Differences in isolation are evident both in absolute numbers of species and in different slopes for islands in different distance ranges.


Figure compares some of the data for satellite islands to the curve for areas of the New Guinea mainland (called a saturation curve). The slope is clearly steeper for the islands than for mainland areas of similar habitats. The open circles are points for islands relatively near New Guinea, the filled circles for more distant islands. More distant islands have fewer species for the same area.


Figure looks at that relationship. Each island diversity is assessed as the fraction of the number of species expected in a mainland habitat of the same area. This % saturation is plotted against distance from New Guinea.


Other data sets have been analyzed using the same basic approach, but one can significantly add to our understanding of the biology underlying island diversity patterns. In a study of bird species diversity on the Channel Islands off Santa Barbara, California, Power (1972) worked backwards from the physical variables to the biological variables which correlated most closely with bird species diversity, using a method called path coefficient analysis. The method begins with a multiple regression analysis paralleling the study of New Guinea satellite islands. Power first found the factor which explained the largest portion of the total variation in bird species diversity, entered it into the model equation, then determined the factor which explained the largest portion of the variation which remained after applying the model equation. That factor enters second, and forms part of a new model equation. Subsequent factors are entered in order of importance, using the variation about the model equation fitted using factors already incorporated. In order of importance, Power found the number of plant species on islands was the best single predictor variable, accounting for 67% of the total variation in bird species diversity. Island area, on the other hand, accounted for only 33% of variation if considered alone. It seems logical that habitat heterogeneity (or diversity) for bird species would be measured by the biotic diversity of their residences, food sources, or residences of their food resources, i.e. the diversity of the plant community.


Having used plant species diversity as the first factor entered stepwise into the model, what was the next most important factor? Not area! Once effects on plant species diversity are removed, area doesn't even account for a significant fraction of remaining variation, let alone be the most important factor in residual variation. Only one factor is significant in explaining residual variation of a model including plant species diversity. That factor is isolation (distance), which accounts for 14% of total variance when entered as the second factor in the stepwise model equation. The remaining 19% of variance is unexplained variation, called error variance; no other factor accounts for a significant portion of variation out of this residual. This is a solid indication that measures of habitat heterogeneity (diversity) are the critical predictors of island species diversity.


Power, however, went further. Since plant species diversity, used as a predictor variable (or factor) is itself a biological variable, he asked what, in turn, explains plant species diversity. Using the same stepwise regression method, Power found 3 factors were significant, and they were 3 factors that correspond closely to those which Diamond found significant in explaining bird species diversity in the New Guinea satellite islands: 1) area accounts for the largest proportion of plant species diversity, 68%; 2) latitude accounts for 15% of the variance. Latitude effects are detectable only after effects of area have been removed, especially since the latitudes of the Channel Islands don't differ by much. This factor apparently measures position of islands relative to North-South air and water currents off the California coast, rather than a direct impact of latitude itself. 3) Isolation, or distance from the nearest source pool, with the islands all at similar distances from mainland, accounted for only 3%, but was significant. The remaining 14% of variation was unexplained, i.e. error variance. Taking this analysis at face value, we can see the origin of path coefficients. It suggests that the underlying factors which explain bird species diversity on the California Channel Islands are abiotic, the same factors which Diamond found in his studies, particularly area and factors important in assessing isolation, but that the proximal factors important to the birds are biological as well. A statistical path then takes the following form:


area††† ---->†† plant species diversity

latitude††††††††††† island area†† ††††††††††† ----> bird species

distance††† †††† isolation†††††††††††††††††††† †††††††††††† diversity


†† At this point it should be clear that a major group of biogeographers believe that island area is an excellent, though indirect, indicator of island species diversity.


While we may be accustomed to thinking of islands strictly in 'geological' terms, it is clear that islands take many forms, including lakes, forest patches in agricultural lands, or even zebra mussels colonies. The key aspect of islands is that they are favourable habitat surrounded by inhospitable habitat. Looking at how zebra mussel colonies on soft sediments in Lake Erie can be 'islands', Bially and MacIsaac (2000) looked at invertebrate species diversity in relation to island area. A very clear image emerged. Small islands (10 cm2) host only about 8 species, on average, while midsize islands (100 cm2) supported ~13, and large islands (70,000 cm2) supported about 20 taxa. The invertebrates utilize gaps between mussel shells as habitat, and mussel feces and pseudofeces as food.


The Basic Model of Island Biogeography


The model is one of a dynamic equilibrium between immigration of new species onto islands and the extinction of species previously established. There are 2 things to note immediately: 1) this is a dynamic equilibrium, not a static one. Species continue to immigrate over an indefinite period, not all are successful in becoming established on the island. Some that have been resident on the island go extinct. The model predicts only the equilibrium number of species, will remain 'fixed'. The species list for the island changes; those changes are called turnover. 2) The model only explicitly applies to the non-interactive phase of island history. Initially, at least, we will consider only events and dynamics over an ecological time scale, and one which assumes ecological interactions on the island occur as a result of random filling of niches, without adaptations to the presence of interacting species developing there. Evolution is clearly excluded.


The variables used in the basic model are Is, the immigration rate, which is clearly indicated by the subscript to be species specific, i.e. to be dependent on the number of species already present on the island. Here we're not counting noses, but rather the rate at which new species (those not already present on the island) immigrate. Phrased explicitly, it is the number of species immigrating per unit time onto an island already occupied by S species. Also Es, the extinction rate, measured in species lost per unit time from an island occupied by S species. Finally, we need to know the size of the pool of species in the source area available to colonize the island.


The immigration rate Is must certainly decrease monotonically (on average) as the number of species on the island increases, since as S increases there are fewer and fewer species remaining to immigrate from the pool P of potential immigrants at the source. If all species were equally likely to immigrate successfully (i.e. had equal dispersal capabilities), but actual immigrations were chance events, then the relationship between Is and S would be linear, the probability of a new species immigrating would be directly proportional to the number of species left to arrive. There are, however, considerable differences in the dispersal abilities of species in source areas. Those with the highest dispersal capacities are likely to colonize an island rapidly (have a higher immigration rate), and later, on average, those with lower dispersal capacities will follow. They will not only immigrate later, but the rate at which they immigrate will be lower because they have lower dispersal capacities. The rate at which species accumulate on islands is, therefore, initially rapid and then slower. Also, among those species with lower dispersal capacities the successful immigration of any one species should have less effect on the immigration rates of species remaining in the source pool (we have not removed a likely immigrant from the pool) than would the earlier immigration of a highly dispersible species. Therefore, this part of the curve should be 'flatter'; the rate of immigration should be little affected by the arrival of one of these poor dispersers. The result is an observed immigration rate curve which is concave. The actual (or theoretical) curve for any island is dependent on its isolation. For any source pool, the observed rate, while similar in shape, will be lower for more distant islands than for closer ones. Immigration rates are graphed from the left hand edge of figure 1, declining from the y axis with an increasing number of species already present.


Figure - The basic graphical model of equilibrium in the MacArthur-Wilson model. Figure from Brown and Gibson -Biogeography.


The extinction rate Es should be, from parallel reasoning, a monotonically increasing function of S. If area, for example, acts only through its effects on population sizes, and extinctions are the chance result of small population sizes and demographic stochasticity, then as the number of species increases, the number of species with small populations and subject to chance extinctions increases in proportion, i.e. the relationship would be linear. However, if we consider a more realistic biological scenario, then as the number of species increases, depressant interactions within and between species (competition, predation, parasitism) are more likely to occur, and extinctions are more likely as a result. Remember that these are not species that have evolved adaptations to interactions. Effects are direct and unmoderated. Since any extinctions resulting from interaction are in addition to those resulting from demographic stochasticity, the more realistic shape for the extinction curve is concave upwards. The extinction rate begins at 0 when there are no species on the island, then increases as species accumulate. At least for purposes of simplicity in looking at the basic implications of the model, the extinction curve can be thought of as a mirror image of the immigration curve.


We now have all the information to produce the basic graphical model. That model predicts that there is some value of S, which is called Ŝ, for which immigration rate and extinction rate are in balance; there is a dynamic equilibrium. At that diversity on the island species are immigrating at a rate equal to disappearances due to extinction. The result is constant change in the species list on the island; that change in names occurs at a rate called x, the turnover rate. The length of the species list, however, should remain constant. This is a stable equilibrium since, should something happen, and the number of species on the island be perturbed, the imbalance between immigration and extinction rates at the new S would tend to return island diversity toward its equilibrium value. Below Ŝ additional species accumulate; immigration rate is larger than extinction rate. Above Ŝ the reverse is true, extinctions exceed immigrations and the number of species declines to Ŝ.


Tests of the Model

To test the model, an important piece of evidence is a carefully designed manipulative experiment studying the fauna which colonize 'islands'. One of Wilson's students, Dan Simberloff, tested the model using islands which consist of mangrove mangles in the Florida Keys. Simberloff's Ph.D. thesis had consisted of measurements of the re-colonization of these islands following 'defaunation' (he had encased individual mangles in giant plastic bags, sprayed them with short acting, low persistence insecticides, then followed the rates, numbers, and species which immigrated onto them after exposure). Re-equilibration, i.e. reaching a stable number of species, had occurred within 3 years of fumigation in his earlier experiments. In a second series of studies (Simberloff 1976), the manipulations were equally inventive.After the islands had been censused, and an equilibrium number of species determined for each island (a 'control' diversity), crews moved in with chain saws, handsaws and hatchets, and each island was split into 2 or more smaller parts, with water gaps of 1m between. To the insects, apparently this 1m gap was sufficient to make crossing from one sub-island to another a jump dispersal. The smaller, sub-islands were then censused repeatedly over a time interval sufficient to permit re-equilibration to find out how species numbers changed with island area. Remember, the area censused had been part of a previous island, and should contain all habitats (plant parts, vertical structures) in the same proportions as before (i.e. the same habitat heterogeneity, however measured). Alterations were only quantitative, in the form of area reduction, no unique feature was removed.


The results were clear-cut. Each island reduced in size re-equilibrated at a lower insect diversity. Considering all the experimental islands in developing a model for the pattern in reduction, the diversity change fit a log-log relationship (i.e. a power function) between diversity and area. Thus, Simberloff's data fit the original species-area relationship. Area was the key determinant. The process of re-equilibration, however, involved extinction of species from islands supersaturated due to their reduction in size. We have already encountered the underlying biological cause of those extinctions: population sizes of 'marginal' species, that is those whose populations were already small before reduction in area, were decreased to the point where chance extinction due to demographic stochasticity became likely, and re-colonization unlikely. Such extinctions are an important component of the equilibrium model of island biogeography.


Figure - Effect of island fragmentation on insect diversity in mangrove mangles. Simberloff (1976).


There are few islands that have been studied over long enough periods to test the hypothesis of equilibrium with turnover, i.e. the occurrence of a stable but dynamic equilibrium. Among those few are the California Channel Islands. The interpretation of these data is a source of continuing controversy. That's important, because the crux of the equilibrium theory is proof (or documentation) of insular turnover at equilibrium. A paper (Gilbert 1980) found 25 attempts to document turnover at equilibrium, and found few (basically just mangrove island studies by Simberloff) acceptable without question. In Simberloff's original defaunation studies, for example, one island supported 7 species of Hymenoptera prior to fumigation and 8 after equilibrium had been re-established about one year later. However, only two of these species were present both before and after fumigation. This sort of experimental study is designed to allow for rapid re-equilibration.


The Channel Island studies represent an interesting attempt to deal with the problems of scale (here time) when dealing with most real ecosystems. Recognizing that there may be difficulties (the initial, historical survey of species presences on the island used breeding records collected over many years, rather than a single survey at one time), Diamond's studies of turnover on the Channel islands are still regularly cited (Diamond 1969).


Initial data reported collections and observations indicating the fauna of individual islands in 1917. Diamond compared those species lists with a survey he did in 1968. Over the 51 years between censuses the numbers of species on islands remained almost perfectly constant, but turnover was as high as 62%, i.e. as much as 62% of the original list had been replaced by new species. The islands had the following characteristics:


Island†††† †††††††††††††††† 1917††††††††††††††††† 1968 Extinctions ††† Immigrations %turnover

Los Coronados†††††† 11††††† ††††††††††††††† 11†††††† 4†††††††††† †††††††††† 4†††††††††††† †††††††† 36

San Nicholas†††††††††† 11††††††††††††††††††† 11†††††† 6†††††††† †††††††††††† 6†††††††††††† †††††††† 50

San Clemente†††††††† 28††††† ††††††††††††††† 24†††††† 9†††††††††† †††††††††† 5††††††††††† ††††††††† 25

Santa Catalina††††††† 30††††† ††††††††††††††† 34†††††† 6†††††††††† †††††††††† 10††††††††††† ††††††† 24

Santa Barbara†††††† 10††††† †††††††††††††††† ††6††††††† 7†††††††††† †††††††††† 3†††††††††††† †††††††† 62

San Miguel†††† †††††††† 11††††† ††††††††††††††† 15††††† 4†††††††††† †††††††††† 8†††††††††††† †††††††† 46

Santa Cruz†††† ††††††††† 36††††† ††††††††††††††† 37†††††† 6†††††††††† †††††††††† 7†††††††††††† †††††††† 17

Anacapa††††††† ††††††††† 15††††† ††††††††††††††† 14†††††† 5†††††††††† †††††††††† 4†††††††††††† †††††††† 31


These data seem initially to fit the equilibrium theory quite well. Numbers remain almost constant while turnover occurs in a significant number of species. However, the theory also suggests, as you will soon see, that turnover should be related to island area (through effects of area on extinction rates) and/or isolation (through effects on immigration rates. Neither was the case; instead turnover was approximately inversely proportional to the number of species present. That is not forecast by the model.


Figure - The number of species in censuses of 3 of the California Channel Islands.


Figure - % turnover in species numbers on California Channel Islands. (a) for nine of the islands. (b) for Anacapa as a function of time between pairs of surveys.


Why should turnover be related to island area or isolation? Consider first 2 islands at equal distance from the source, but differing in area. Long distance (jump) dispersal is generally assumed to be a chance event, not directed or goal oriented. In that case, dispersal probabilities and immigration rates onto the 2 islands should be the same. Area, however, does affect the extinction rate of colonists. The larger island should have 1) higher habitat heterogeneity, 2) decreased intensity of interactions due to reduced niche overlaps resulting from habitat heterogeneity and 3) larger population sizes making chance extinctions less likely.


These factors should be operative, at least in a relative way, independent of the number of species present. Therefore, the extinction curves should have similar shape, but have lower values for the larger island. Putting this comparison on a graph, but using a linearized version of immigration and extinction curves, we find a larger equilibrium number of species on the larger island, but also a lower turnover rate on that island.


To assess the effects of isolation consider 2 islands of equal size, but located at differing distances from the source. With identical sizes we assume that habitat heterogeneity, population sizes and interactions on the islands are quantitatively identical, and thus they have the same extinction rate curves. Immigration rates onto the more distant island should, however, be lower at any S since the probability of a successful dispersal decreases (possibly exponentially) with distance. We can go further, and suggest that the decrease should be most noticeable for species which tend to be among the first colonists. Later immigrants with lower dispersal capacities have only a slim chance anyways, and depend on rare, special conditions like storms for successful immigration. For these species a change in distance should mean less in shifting immigration rates. Once more we turn these suggestions into a comparison on the graph. The more distant island has a lower equilibrium number of species, but also a lower turnover rate at equilibrium than an island closer to the source.


Figure - Multiple immigration and extinction curves indicating effects of differences in size and isolation on equilibria and turnover rates. Brown and Gibson (1983).


These comparisons can be combined in various interesting and complicated ways. Rather than document the possibilities, it is probably more valuable to attempt to list the assumptions and predictions of the basic MacArthur-Wilson model. Some of the ideas in this list will not be fully examined until later in this section.


Under What Conditions Does the Model Apply?

†††† 1) Islands are real isolates (rescue effect, discussed below, not important)

†††† 2) Islands have comparable habitat heterogeneity (complexity). There are no gross environmental changes over the time period of colonization

†††† 3) Species counted on islands are residents

†††† 4) There is a definable mainland species pool


What Are the Characteristics of the Equilibrium?

†††† 1) It is dynamic

†††† 2) It is approached asymptotically

†††† 3) The process is inherently stochastic

†††† 4) The model and the equilibrium are describing processes in ecological time


What Are the Characteristics of Turnover?

†††† 1) The process is not successional

†††† 2) Species replacements occur frequently

†††† 3) Immigration rates decrease with increasing species numbers. Extinction rates increase with increasing species numbers


What Influences the Equilibrium Number of Species?

†††† 1) Influenced by area through extinction rates

†††† 2) Influenced by isolation through immigration rates

†††† 3) Varies faster with area on distant islands (see below)

†††† 4) Varies faster with isolation on small islands (see below)


With this summary in mind, we return to problems. With regard to Diamond's data, no combination of size and isolation leads to the prediction that turnover rate is inversely (or in any other sense) proportional to the number of species on an island.


Since the data are repeatedly cited and classic, it's worth trying to understand why this anomalous result was reported. There are a number of possible answers, and arguments in the literature could be described by indicating that 'the fur has definitely flown'. For one thing, the interval between the censuses was very long. That may have had significant effect on the measured turnover. If the time interval is long enough it becomes likely that some of the species which had gone extinct at some time between the censuses also re-immigrated during that interval (or the converse). In either case the measured turnover would underestimate actual rates. To attempt to correct for that possibility, Diamond and his collaborators went back to the Channel Islands annually during the early 1970's, and also used thorough data gathered for Farnes Island off Great Britain. The result of differences in the interval between censuses is evident in Fig.8 (and reported in Diamond and May 1978). The result for the Farne Islands is parallel. In either case the apparent turnover decreases rapidly as the census interval increases. To show you why, consider what happened to the meadow pipit on Farnes between 1946 and 1974 (May and Diamond 1977). The pipit bred for 2 years, went extinct in the 3rd, then went through 5 more cycles of immigration and extinction over the remainder of the period. From annual census records that indicates 11 turnover events in 29 years, where a census after 30 years would have recognized only a single extinction, as well as a constant diversity of 6 species on the island. The same basic pattern applies to the Channel Islands. Instead of turnover rates ranging from 17-62% (or .34-1.24% per year), annual censuses indicate actual turnover rates of 1-10% per year, and are about an order of magnitude larger than indicated by to 51 year interval for most islands.


That's not the only corrective surgery which has been suggested for the theory. It is also evident that monotonic rate functions (particularly the immigration rate curve) may be overly simplistic. That should be evident by drawing a parallel between accumulation of species on an island and primary succession. When an island is newly formed (frequently volcanic) it has no organic content in (and frequently no) mineral soil. The first plants must be special sorts that have no requirement for nutrients from the soil (or possibly no requirement for soil at all); instead they are soil formers, leaving behind their nutrients extracted from the rock (as well as their bodies) to improve conditions for later arrivals. Krakatoa, East of Java, was not only a B movie, but a real historical event in the 1880's. What kind of immigration curve described the relationship between immigration rate and the number of species on Krakatoa after its formation. Depending on our definition of immigration (does it end with landing on the island, or require initial growth to be counted) and extinction (does a species have to reproduce at least once on an island before we consider its loss an extinction?) either immigration rate or extinction rate curves could be modified. For simplicity we'll include the modifications in the immigration rate curve.Now it isn't monotonic decreasing; instead it may have an initial rising phase representing the additional immigration possible with the formation of soil. That is the naive logic. Reality isn't quite so simple. Over the first 50-60 years since eruption (1883) the 'curves' of the number of species accumulated over time for various plant groups seem virtually straight lines; there is no decrease in rate of immigration over this time. Similar arguments could be advanced, producing a similar curve shape, with respect to other trophic levels. Equilibrium diversity and turnover rates can be affected by these modifications.


Figure - Colonization rates for vascular plants on Krakatau measured in terms of total number of species (labeled 13), immigration and extinction rates (14), and as functions of the number of species present (15). From Thornton et al. (1993).


Since Diamond's data from the Channel Island studies suggested an appropriate relationship between turnover and area-isolation effects, but could not quantify them, an appropriate experimental test became important. Jim Brown and his wife Astrid attempted such a test (Brown and Brown 1977).They studied the colonization of thistle plants by assorted insects and spiders by repeated census following defaunation. Almost everything fit the basic MacArthur-Wilson model, but... The turnover rate should be inversely related to island distance (isolation) according to the theory. If we look at just distance effects on the same island (i.e. area), the nearer island should have a higher turnover rate. That's not what the Browns found. Instead, whether plant 'islands' were large or small the turnover rates were higher on more distant islands.


†††††††††††††††††† †††††††††††††††† Site 1†††††† †††††††††††††††††††††††††††††††††††††††††††††††††††††† Site 2


†††††††† ††# of plants†† Mean # speciesturnover rate†† # of plants Mean # species††† turnover rate

††††††††††††† ††††††††† †††††††††††††††††††††††††††††††††††††††††††††††††††††††††††

††††††††††††††††† †††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††

large-††††† 16††††† ††††††††† 3.82††††† ††††††††† 0.67††††††† ††††††† 9†††††† †††††††††††††† 5.25††† ††††††††††† 0.29



large-††††† 7†††††† †††††††††† 3.78††††† ††††††††† 0.78††††††† ††††††† 9†††††† †††††††††††††† 4.44††† ††††††††††† 0.42



small-††††† 56††††† †††††††† 1.89††††† ††††††††† 0.78††††††† ††††††† 21††††† ††††††††††††† 2.21††† ††††††††††† 0.69



small-††††† 3†††††† †††††††††† 1.33††††† ††††††††† 1.00††††††† ††††††† 11††††† ††††††††††††† 0.80††† ††††††††††† 0.91



Based upon a 5 day census interval (remember what Diamond's data ended up showing about the importance of census interval), turnover rates were consistently higher on the more isolated plants. This reversal of the expected pattern is explained as resulting from the effect of repeated immigration of species onto near islands. The original model was psychologically, if not explicitly, concerned with a degree of isolation which made such repeated immigrations unlikely. Under real conditions repeated immigration may be likely, particularly on near islands. Addition of a new immigrant member into a small population reduces the probability of extinction. This repeated immigration is, therefore, termed the 'rescue effect'. It could, as I've just suggested, be presented as affecting immigration or extinction, but since the key effect is on extinction rates, making extinction less likely on near islands, that's where the curves are usually adjusted for rescue. When the rescue effect occurs, turnover rates will tend to be directly proportional to distance. The effect may be evident in data sets as divergent as these studies of plant 'islands' and Diamond's New Guinea satellite island avifaunas.


Figure - How the rescue effect modifies curves of immigration, extinction, and turnover as a function of distance.


From predictions of rescue effect occurrence we can make some general, graphical predictions of how distance effects immigration, extinction and turnover. Note that we are here graphing these rates against distance, not against species numbers. The immigration rate declines exponentially with distance, as we've previously seen in a variety of data. The extinction rate was previously considered as depending on island area, and unrelated to distance; it would have been a straight horizontal line on this graph before we considered rescue. Now we recognize that the rescue effect bends the extinction curve down at low distances. When we combine these curves to estimate turnover as a function of distance, it has an intermediate peak; turnover is highest at those distances when both immigration and extinction rates are high. Very close to the source extinction rates are low; at large distances immigration rates are low.


The next correction to the simple model is one which questions the validity of the species-area relationship. Are projections of area-dependent extinction valid for the total range of island areas studied? Of course, I wouldn't be suggesting the question unless something were amiss. There is a problem on very small islands. MacArthur and Wilson recognized that possibility in presenting the basic theory, and suggested such islands were unstable, should have very high turnover rates, and probably not have area-dependent extinction curves. Basically, they thought any area effects would be masked by the instability of the islands. The figure in the original monograph showed a split curve for extinction rates, i.e. an unpredictable area effect. The original data used to construct that graph was drawn from studies of the ecology of the Kapingamarengi atoll system in the Carolina Islands in Micronesia (Niering 1963). These small outcrops appeared to show a threshold in the species-area relationship at about 3.5 acres in area. It was suggested that the instability was not habitat destruction by physical forces, but instability in the presence of fresh water. Below the threshold area the water table on the island is saline; fresh water availability depends totally on frequent rains. Above the threshold area there is a permanent 'lens' of fresh water, and extinction of plant and animal species dependent on fresh water becomes much less likely.


Figure - Predictions of extinction rate characteristics on very small islands. From MacArthur and Wilson (1967)


Modeling Effects of Disturbance on the Equilibrium Theory


†† It is apparent that disturbance can have important consequences for observed equilibria or the lack thereof. What is difficult is the fact that disturbance has effects on the survival and/or reproductive success of individuals. A disturbance, unless extraordinarily massive, does not affect every member of a population. Modeling on an individual basis has been difficult or impossible until recently. An Italian group (Villa et al. 1992) attempted to evaluate the effect of regular disturbance at differing intensities on the equilibrium. The following were their conditions:


1) Island habitats were equally distant from the 'source', but differed in size, from 50 'cells' (each cell was a potential site for an individual) to 1100.

2) There were 64 species. Each had its own mean lifespan, interval between reproduction, and a range of clutch sizes from minimum to maximum, i.e. a life history. Each species also has a relative dispersal capacity.

3) A colonization species pool with relative abundances in the pool set.

4) Colonization occurs by randomly allowing individuals to disperse according to a negative exponential distribution (but distributions are affected by relative dispersal distance). They are successful if they land on an empty cell. If so their life histories determine whether the population grows or goes extinct.

5) Disturbances occur periodically. Intensity varied from 0%-75%, where this probability was applied to each individual, and determined the likelihood of the individual being killed by the disturbance.


Some results of this simulation seem about as you might have predicted. Some are 'strange'. The two figures below show you some of the key results. Figure 11 shows you their eyeball estimates of the conditions which resulted in equilibrium. Over the 120 time intervals their simulation ran, slow-growing organisms never reached equilibrium on large islands, but did on small ones when there was no disturbance (indicated by 0 on the x-axis). They could not reach equilibrium on any islands at higher levels of disturbance. Fast growing organisms (on the right) could reach equilibrium on any size island in the absence of disturbance, and with the larger population size possible on very large islands, could even reach equilibrium in the face of moderate disturbance levels (i.e. levels 2 and 3).


Figure - indications of relative equilibrium (thick lines) in 10 simulation runs for islands with different numbers of cells (the y-axis) and different intensities of disturbance (the x-axis: 0-no disturbance, 1-10% effect, 2-25% effect, 3-40% effect, 5-75% effect). Part a is for organisms with 'slow' growth (low clutch size, longer interval between reproduction, longer lifespan) and part b for 'fast' growing individuals.


Figure - Species-area relationships for a) slow-growing and b) fast-growing organisms affected by disturbance. The 3 curves are for no disturbance (top curves), 25% disturbance effect (middle curves) and 75% disturbance (bottom curves).


Evident in the above Figure is the community level effect of disturbance. Disturbance lowers the overall number of species resident, but if there is sufficient time for equilibrium to have been reached, life history makes a difference. At low levels of disturbance, the slow-growing species attain a higher diversity. At high levels of disturbance, species are not able to remain around long, and a greater diversity can be achieved by being a good colonizer (a weed, rapid population growth, etc.). Counter-intuitively, when the actual fitting values for these curves are assessed, the steepness of the species area curve increases when disturbance is present, even though overall diversity decreases. What all this tells us is we need to know more about the effects of disturbance in real communities. The real world is affected by disturbance on a more-or-less frequent basis, and conservation models based on an equilibrium paradigm need to be re-considered to incorporate some indication of the effects of disturbance.



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