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The Science of Biogeography

Biogeography is the science studying the distribution of species and ecosystems in geographic space and through time. It is usually considered a subset of physical geography because it often is related to the study of the physical environment, and how it affects species and shapes their distribution across space. It is concerned not only with habitation patterns, but also with the factors responsible for variations in distribution. It aims to analyze where species live, and in what abundance. Biogeography has strong ties to biology, ecology, evolution, climatology and soil science.

Overview of the chapter

This chapter provides the basic notations and ideas that form the foundation of biogeography-based optimization (BBO). This chapter first gives an introduction to natural biogeography in section 1.1, and then focuses on island biogeography in section 1.2. Some interesting factors that influence biogeography and that inspire BBO algorithmic features are described in section 1.3.

1.1. Introduction

The science of biogeography can be traced to the work of 19th Century naturalists, most notably Alfred Wallace [WAL 06] and Charles Darwin [KEY 01] (see Figure 1.1). Wallace is usually considered the father of biogeography, although Darwin is much better known because of his preeminence in publishing the theory of evolution. Science views the distribution of species in the world as a result of continuous evolution. Some species evolve locally.

Figure 1.1. Photographs of Charles Darwin (left) and Alfred Wallace (right)

The science of biogeography answers many varied questions. As writer David Quammen put it [QUA 96], ".biogeography does more than ask Which species? and Where. It also asks Why? and, sometimes more crucially, Why not?" Biogeography developed in an attempt to answer some of these questions, such as why there are so many kinds of animals and plants in the world. It seeks to explain why some of these animals and plants are rare while others are common. It seeks to explain why some animals and plants are widely dispersed while others are confined to a limited area. It seeks to explain why some parts of this world are richer in species than others. The study of biogeography helps us to answer these types of questions.

Modern biogeography is the study of the geographical distribution of animals and plants while taking into account species counts, present and past, the habitats in which they are found, and ecological relationships. By observing the geographic distribution of species, we can see that the following factors are associated with biogeography: air pressure, physiography, ocean currents, latitude, temperature, amount of sun light, precipitation and wind. Biogeography combines information and ideas from many fields, ranging from the physiological and ecological constraints on species dispersal, to geological and climatological phenomena that operate at global spatial scales and evolutionary time frames. The short-term interactions within a habitat and between species comprise the ecological application of biogeography. Historical biogeography deals with the long-term, evolutionary periods of time, and broader classifications of species.

There are two important theories in biogeography that have been developed to address the distribution of biological species in the world: the distance-decay theory [NEK 99] and the island biogeography theory [MAC 67]. The distance-decay theory asserts that the correlation and similarity between species in any two geographical locations will continue decreasing as the distance between the two increases. Island biogeography asserts that those islands that are closely spaced will support more biological species than islands that are far apart. It is this second theory that explains that species on closely spaced islands are rarely threatened by extinction, compared to tiny isolated islands. Geographic information systems scientists say that the above two theories were developed in order to explain the distribution of species, but not the distribution or even the movement of humans. That is, the purpose of these theories is to understand the factors affecting species distribution, to predict future trends in species distribution, and to solve ecological problems that have a spatial aspect.

Because of the focus of this book, we do not emphasize one theory more than the other, and we do not further discuss the essence of the science of biogeography. We focus instead on using island biogeography to inspire an evolutionary algorithm to solve optimization problems: biogeography-based optimization (BBO).

1.2. Island biogeography

In the early 1960s, Robert MacArthur and Edward Wilson began working on mathematical models of island biogeography, culminating in their classic 1967 book The Theory of Island Biogeography [MAC 67]. They were mostly interested in the distribution of species between neighboring islands, and mathematical models of the extinction and migration of species. Since MacArthur and Wilson's work, biogeography has become a major subset of biology [HAN 97]. Figure 1.2 shows photographs of Robert MacArthur and Edward Wilson.

Figure 1.2. Photographs of Robert MacArthur (left) and Edward Wilson (right)

Biogeography is most keenly focused on islands. Islands are often manageable areas of study because they are more condensed than larger ecosystems on the mainland. Islands are also attractive locations for study because they allow scientists to look at habitats that new invasive species have only recently colonized, and to observe how they disperse throughout the island and change it. Scientists can then apply their understanding to similar but more complex mainland habitats. Islands are very diverse in their biomes, ranging from tropical to arctic climates. This diversity allows for a wide range of species studies in different parts of the world.

Mathematical models of island biogeography describe speciation (the evolution of new species), the migration of species between islands, and the extinction of species. The term island here is descriptive rather than literal. An island is considered any habitat that is geographically isolated from other habitats. In the classic sense of the term, an island is isolated from other habitats by water. But islands can also be habitats that are isolated by stretches of desert, rivers, mountain ranges, predators, man-made artifacts or other obstacles. For example, an island could consist of a riverbank that supports herbs, or a pond that supports insects [HAN 97].

Geographical areas that are friendly to life are said to have a high habitat suitability index (HSI) [WES 87]. Features that correlate with HSI include factors such as rainfall, vegetative diversity, topographic diversity, land area and air temperature. These features that characterize habitability are called suitability index variables (SIVs). In terms of habitability, SIVs are the independent variables of the habitat, and HSI is the dependent variable.

Islands with a high HSI tend to support many species, and islands with a low HSI can support only a few species. Islands with a high HSI have many species that emigrate to nearby habitats, simply by virtue of the large number of species that they host. Emigration from an island with a high HSI does not occur because species want to leave their home; after all, the home island is an attractive place to live. The reason that emigration occurs from these islands is due to the accumulation of random effects on a large number of species with large populations. Emigration occurs as animals ride flotsam, swim, fly or ride the wind to neighboring islands. When a species emigrates from an island, the species does not completely disappear from the island; only a few representatives emigrate, so an emigrating species remains present on its home island while at the same time migrating to a neighboring island.

Islands with a high HSI not only have a high emigration rate, but they have a low immigration rate because they already support many species. The species that arrive at such islands will tend not to survive, even though the HSI is high, because there is too much competition for resources.

Islands with a low HSI have a high immigration rate because of their low populations. Again, this is not because species want to immigrate to such islands; after all, these islands are undesirable places to live. The reason that immigration occurs on these islands is because there is a lot of geographical room for additional species. Whether or not the immigrating species can survive in its new home, and for how long, is another question. However, species diversity is correlated with HSI, so more species arriving at a low HSI island will result in a greater chance that the island's HSI will increase [WES 87].

Figure 1.3 depicts species migration between islands, and Figure 1.4 illustrates a model of species abundance on a single island [MAC 67]. The immigration and emigration rates are functions of the number of species on the island. We have depicted the migration curves as straight lines, but in general they might be more complicated curves, as we will discuss later.

Figure 1.3. Species migrate between islands via flotsam, wind, flying, swimming and other methods. For a color version of this figure, see www.iste.co.uk/ma-simon/evolutionary.zip

Figure 1.4. Species migration model of an island,...