Biodiversity: An Equilibrium Theory

In considering the latitudinal gradient in diversity, some factors increased local diversity (habitat heterogeneity and structural complexity), some decreased local diversity (competition), and some could act in either direction (predation).

Like population growth models with birth rate balancing death rate at equilibrium, there could be a similar model for local diversity, with some processes adding new species and others causing local extinctions of species.

That equilibrium theory was developed in 1967 in a seminal book (The Theory of Island Biogeography) by Robert MacArthur (of the warblers) and E.O. Wilson (of the ants).

They proposed that many communities occur in islands of habitat, surrounded by inhospitable habitats where the component species could not live. Such a situation is clearly the case with oceanic islands.

They proposed that the equilibrium diversity is determined by the balance between immigration of new species onto the island and extinction of species already established there. Here is the simple model:

Both immigration and extinction are curves. Why?

The immigrants must arise from a mainland (source) pool that includes all species resident there. Some are very good dispersers, others quite poor. The good dispersers likely arrive first at a rate that reflects their dispersal ability.

After they’ve reached the island, what is left is poorer dispersers, and their rate of arrival will be even lower than simply proportional to the number of species left to immigrate because of their lesser dispersal ability. Thus the concave curve.

For extinction we begin with a simple proportionality that says extinction is more likely when there are more species that could go extinct. That would produce a straight line.

However, with more species the probability of some being close competitors with others on the island increases, and the probability of species having smaller population sizes also increases. With both, the probability of extinction occurring increases. Thus extinction rises faster than simple proportionality, and is a curve.

What other factors influence these curves?

1. Distance of the island from a source of immigrants. The rate of immigration will be lower onto more distant islands.

2. The area of the island. Population size will logically be smaller on smaller islands, so that the extinction curve will rise more rapidly.

Here are the curves:

Immigration fromnear and far islands

Extinction on large and small islands

The theory was tested in numerous studies from its initial publication until around 1990, when metapopulation concepts began to replace the island model.

Among the first tests were Jared Diamond’s measurement of bird species diversity on islands surrounding New Guinea. He found the predicted relationships of species numbers with distance fromNew Guinea and with island area…

The basic equation for the equilibrium species numbers on islands includes only a few terms:

S cA zS is the equilibrium number of species

c is a constant that reflects the dispersal capability of the group of species under study (birds obviously have a higher c than worms)

A is the area of an island

z is a constant that measures how rapidly the number of species increases with area

But we know that there are other influences…

Diamond quantified the simple distance and area relationships, and recognized that habitat heterogeneity on islands might also be important. The full model equation he developed included:

1. Island area – the basic model - here he found a power function best fit his data. This equation was:

S = 15.1 A0.22

2. Then he added distance to the model…S = 15.1 e-D/3750 A0.22

3. Finally, he added island elevation – elevation is an indicator of spatial heterogeneity. For every 1000m of maximum elevation on an island, bird species diversity increased 2.7% on average.

S = 15.1 (1 + 0.027L/1000) e-D/3750 A0.22

Complicated though that equation is, it accounts for almost 90% of the observed bird species diversity among those islands.

A second test was not passive observation, but a manipulative experiment. It was Dan Simberloff’s Ph.D. research.

He selected mangrove mangles (small islands of mangrove) at different distances from the ‘mainland’ (the Florida coastline), and of differing size. He collected the insects from them to establish a baseline diversity. Some he kept as controls; others he covered with plastic sheet and fumigated with insecticide. He then followed the re-colonization of the ‘islands’ and the recovery of diversity on them. Here is how he defaunated ‘islands’:

And here is what he found, measuring recolonization afterislands had been cleared of insects by fumigation:

E2 was the nearest island. It returned to a diversity of 43 species within about 1 year.E1 was the farthest island. It had 24 species before defaunation, and recovered to ~20 species over the two years. Nearer islands recovered faster than farther ones.

Another important thing to recognize about the island model: The equilibrium is a dynamic one. Over time there is turnover, the replacement of one species by another in a list of species that remains relatively constant in size.

Also note the broad applicability of the model; it applies to a broad spectrum of situations where islands of suitable habitat are separated in a matrix of unsuitable habitat. That isn’t only true for oceanic islands.

What about mountains? Forests? Lakes?

The vegetation in zones along the slopes of mountains differs a lot with elevation. A plant (or an animal associated with it) from zone 2 is quite isolated by unsuitable habitat between the mountains from the nearest other area with zone 2-type vegetation.

Jim Brown made predictions about mammal diversity on mountaintops, and how much might be lost through climate changes that caused vegetation zones to shift in elevation. The extinctions he predicts are severe.

For an arboreal, forest-dwelling bird, the grassland habitat between patches of forest is unsuitable.

There are some remarkable examples of birds unwilling to cross fairly narrow separations. No birds have been observed to cross the 100-200m separating Barrow Colorado Island in Panama from the Mainland.

For aquatic species living in lakes, the terrestrial environments between lakes are clearly inhospitable. Studies have shown the same distance and area relationships in the diversity of species like snails in the lakes of New York State.

Review of island biogeography

The features of islands that most influence diversity are island area and distance from source(s) of species.

The simple rule for the effect of area is that a 10-fold increase in area will double the number of species. This rule is usually converted into a simple equation:

log S = log C + x log A

On a log-log plot, this equation shows you will see a straight line.

log S

log A

x is the slope of the line

C is the Y-intercept

The observed values of x fall into a small range, from ~0.2 to ~0.33.

We might expect the slope to be different on ‘mainlands’ and on islands. Mainlands will support more species, but add fewer as you look at a larger area (x is lower). This results from transients being counted from smaller areas on mainland, thus not being added as area increases.

Number ofSpecies

Area (km2)

Z = 0.12 - 0.17

Z = 0.24 - 0.34

Mainland

Island

As islands increase in size, they become more like the mainland

That is the relationship. Why does area increase diversity?

a) Increased habitat diversity on larger islands support more species

b) Larger populations of each species lowers chances of extinction

c) There may be sufficient area (and thus population size) to support (feed) an additional, higher trophic level

Distance reduces island species diversity. Why?

a) Differences in dispersal capacity makes it less likely that poorer dispersers can reach distant islands. This is evident even among good dispersers like birds with distance across the Pacific from Australia and New Guinea as sources…

Birds Australia Solomons Fiji Samoa Tonga Society

Pelicans +Quails,Owls + +Crows + + +Hawks + + + +Ducks + + + + +Pigeons + + + + + +Starlings + + + + + +

Solomons

Fiji

Samoa

Society Isl.

Tonga

New Guinea

Distance from release point

The notion works in many different settings. For mosquitos released in an urban area…

Number ofMosquitos

From Wolfenbarger 1975

Immigration and Extinction are the processes that determine island diversity. How do they occur, what constitutes an

immigrant?

1. ImmigrationImmigration has two components:

dispersal to the island, which may be:active (flight, walking) orpassive (carried on the wind, rafting)

establishing a breeding population on the island.

2. Extinction The causes of extinction include:

random events (environmental uncertainty, demographic uncertainties like the Allee effect),

loss of genetic diversity, or deterministic events like predation and competition.

These events are more likely to cause extinction of small populations than large ones.

Humans are responsible for a large fraction of extinctions occurring today and in the recent past.

Let’s consider evidence of what we’ve done…

In the last century there have been 42 extinctions of mammalian species; all have been on islands.

There have been 53 extinctions of bird species; 50 have occurred on islands. Approximately 93% of bird species extinctions between 1600 and 1980 were island occurrences.

In some cases we can tie those extinctions closely to humans. Steadman (1995) documented the loss of bird species on tropical islands following colonization of those islands by humans. He used a combination of fossil records and archaeological information on the islands.

The islands I used to show distance effects were among those he studied.

Samoa, Tonga and the Society Islands were colonized by Polynesians about 3500 years ago.

By 1000 years ago, human populations were widespread on Pacific Islands in this area.

Taken in total, he estimated that 2000 species or subspecies of birds were lost from Pacific islands over the 3500 years since human colonization. That loss represents about 20% of current global bird species diversity.

It was not always direct interaction with humans; frequently it was inexperience with species carried along – dogs and rats particularly.

Here’s details of the data for one island group, the Kingdom of Tonga…

Period Bird Diversity

Pre-human (>3000 years ago) 28 species

At the time of settlement (~1500 years ago) 21 species

200 years ago 10 species

Today 9 species

The largest percentage of losses occurred in conjunction with or after the arrival of Polynesian people.

Back to the main notion – extinction and is causes…

Extinction increases as the diversity of species on an island increases because:

1. there are more species to go extinct

2. Population sizes decrease as the number of species increases. Smaller populations have a higher likelihood of extinction.

3. Species interactions (competition, predation) may hasten extinctions. They are more likely to occur as the number of species present increases.

From the graphical model, we also know that extinction rate at any diversity is higher on a smaller island.

There is evidence for that…

Stuart Pimm (1991) found that bird extinction rates on European islands were strongly related to island area…

Extinction rate(species/yr)

1 100 10000 Area (km2)

One of the implications of the model is that if ‘island’ area were somehow reduced, there would be too many species for the predicted equilibrium; species should go locally extinct.

Here is one neat ‘experiment’ that demonstrates this phenomenon, called relaxation…

Barro Colorado Island was isolated by forming Lake Gatun in building the Panama Canal. It had been a hilltop. The ‘island’ was isolated in 1914. It is only about 100m from the shore of Lake Gatun, but the tropical birds will not cross this barrier. Between 1914 and 1974, Barro Colorado lost 15 species resident at isolation. Slowly, but inexorably, it will lose more.

Other aspects of history also play a role in where we find species. This is a sneaky way to begin in Chapter 24…

First, an example of strange island populations. During the cycles of glaciation, huge amounts of water were tied up in the glaciers, and as a result, sea level dropped. In southeast Asia, both among the Philippines and among islands around Java, land bridges developed until sea level again rose. Some islands became linked to the Asian mainland. That explains how a large mammal like the rhinoceros (not noted as a swimmer) is found on Java and Sumatra. Island biogeography (relaxation) partially explains why their number is declining, and these subspecies are considered endangered.

Rhinoceros sondaicusdistributed among islandsof Malaysia.

50 left in Java15 left in S. Vietnam

There is one last idea coming from island biogeography that was initially hard to accept – that the equilibrium is dynamic. The model and theory both indicate that there should be turnover – replacement of species on an island without a change in the total size of the list.

This was documented by Diamond, when he reviewed old data from the 9 Channel Islands off the southern California coast and compared them to new species lists he and Power collected.

The first species lists came from Howell (1917). Diamond’s survey came in 1968. Here’s a map showing you most of the islands…

The 9 islands range from 3 –>200 km2. They range from 5 –40 km from the nearest source of bird colonists.

We can detect extinctions if a bird there in 1917 was not there in 1968.

We can detect immigrations if a bird found in 1968 was not there in 1917.

How do the numbers compare?

Island 1917 1968 Extinctions ImmigrationsLos Coronados 11 11 4 4San Nicholas 11 11 6 6

San Clemente 28 24 9 5

Santa Catalina 30 34 6 10

Santa Barbara 10 6 7 3

San Miguel 11 15 4 8

Santa Rosa 14 25 1 12

Santa Cruz 36 37 6 7

Anacapa 15 14 5 4

There were many immigrations and many extinctions, but the diversity on most islands remained relatively constant, since rates of immigration and extinction were very similar.

The theory of island biogeography (and more recently ideas drawn from metapopulation biology) have been applied to conservation of species.

There are obvious reasons: human activities fragment formerly continuous habitats, creating islands within which the species must now live; we introduce exotic species that interact with natives and increase their extinction rates since there are fewer, if any, refuges; and we, as a species, poach and hunt species, reducing their population sizes.

We, therefore, need to design areas within which species are protected. They will be islands. How should we design systems of such islands to maximize the chances of persistence of species being conserved?

Design of Nature Reserves

Better Worse

Design of Nature Reserves

Better Worse

The suggestion that corridors are valuable to permit movement of island populations among reserves has proven more controversial than you might expect.

To preserve a sufficient corridor width to ‘protect’ a migrating species is problematic. If wolves move 30-40 km a day, does that mean a corridor to permit their movement from one protected area to another needs to be 40km wide?

Wolves may not be the best example. Smaller species need far narrower corridors, but their predators may not have easy access in the preserve. Is access equally difficult when they move along a narrow corridor? No!

Loss and fragmentation of tropical forest habitat has been particularly severe. Here are some careful estimates of percentage of tropical forest lost in a few countries of Africa and southeast Asia:

Country % lostKenya 48Madagascar 75Malaysia 41Thailand 74Bangladesh 94

The development of pasture land in the tropical forest area of Brazil has had parallel impact. But Brazil has at least attempted to protect areas…

To develop new pasture area, Brazil now requires that a significant percent of total area owned be preserved as undamaged tropical forest. In addition, there are separate reserves for indigenous peoples and as national parks.

Costa Rica has also legislated protection of large portions of remaining tropical forest as reserves. In Costa Rica, exploitation of those protected areas now takes the form of ecotourism.

Finally, what is now a classic example of the impact of exotic species. In moving military cargo among Pacific islands after WWII, the brown tree snake, Boiga irregularis, was introduced onto Guam. It is arboreal and has caused numerous extinctions of endemic birds on Guam (as well as numerous power outages when it suicidally shorts power lines).

What follows is a map of Guam. The arrows indicate known expansion of the range of the snake over Guam. For a number of sites, the number of forest birds in different years.

There were once (1940s) 10 species of forest birds on Guam. At each location, once the brown tree snake had reached the area the number of forest birds declined. There are now only 3 species left: 50 starlings at one site, 200-300 swiftlets at one site, and 20 crows at a third site.

Boiga won’t starve like a predator that has driven its prey extinct. Humankind also carried rats to Guam; Boiga likes rats, too.

The current concern is that the brown tree snake may invade the Hawaiian Islands, moved there by human traffic. It can survive for longer than the flight time from Guam to Hawaii. Dead brown tree snakes have already been found in cargo at Hawaii.