Biogeography Jay M. Ver Hoef Volume 1, pp 183–186 in Encyclopedia of Environmetrics (ISBN 0471 899976) Edited by Abdel H. El-Shaarawi and Walter W. Piegorsch  John Wiley & Sons, Ltd, Chichester, 2002

Biogeography Biogeography, as defined by Brown and Lomolino [3], is ‘the science that attempts to document and understand spatial patterns of biodiversity. It is the study of distributions of organisms, both past and present, and of related patterns of variation over the earth in the numbers and kinds of living things.’ Biogeography can be split taxonomically, with phytogeographers studying plants, and zoogeographers studying animals. Biogeography can also be split by time, with paleoecology studying relationships between organisms and past environments, and ecological biogeography studying present distributions of organisms and how they relate to the physical and biotic environment. Biogeography is at the crossroads of multiple disciplines: systematics (see Systematics, numerical methods), ecology, evolution, geology, and climatology, to name a few. Biogeography often deals with scales of space and time that are very large, and consequently it is mostly observational rather than experimental. Critical is the observation of spatial patterns, and from these, inference on processes that produce the observed patterns. Four typical inferences in biogeography are: 1. Classifying geographic regions based on criteria of species assemblages. For example, there are many schemes for classifying regions of North America based on climatic changes of temperature and rainfall in latitudinal and elevational gradients; see [1]. 2. Reconstructing the historical development of species and/or species assemblages. For example, the theory of plate tectonics [9] was not widely accepted until the late 1960s, but it revolutionized historical biogeography and required new explanations for observed patterns of species distribution. 3. Explanation of patterns of biodiversity. 4. Explanation of geographic variation in behavior or morphology of species (see Morphometrics). For example, a classical observation on a morphological pattern is know as Bergmann’s rule [2], which states that for warm-blooded animals, taxa from cooler climates tend to have larger body sizes than those from warmer climates. The reason is clear: the larger bodies tend

to have smaller surface to volume ratios, which help conserve body heat in colder climates.

Distribution of Single Species The distribution of a single species can be envisioned in two ways. The more obvious way is the spatial distribution of a species; however, this is more complicated than it first appears. For example, consider a plant species. Its range is thought of as some area on a map, for example an area of a state. But upon closer inspection, it is seen that the range is composed of various populations (see Plant strategies). When a specific population is targeted, it is seen that it is composed of individual plants [5]. There is a hierarchy of individuals grouped into larger populations. If animals that move are considered, then it becomes more complicated. The description of the range of a species is thus difficult. Spatial statistics [4] can be used to estimate species or population ranges (see Spatial analysis in ecology). For example, if abundance data on species have been collected, geostatistical methods can be used to interpolate abundance values at unmeasured locations. If the predicted abundance is greater than some cutoff value, c, then it forms part of the range of the population. Another example of a type of data on distribution is the presence or absence of a species in a county in the US. Lattice models (Ising models for binary data; see Disease mapping) can be used to assess the probability that the 0 values are really zero. The Ising model estimates the underlying probability that produced the observed value of 0 or 1 for each cell. A range map can consist of all cells with a probability greater than some specified cutoff; e.g. 0.5. Another example of data on the range of a population consists of the locations of actual individuals. When mapping at a fine resolution, locations of all individuals are known, and methods from spatial point processes (see Point processes, spatial) can produce an intensity surface that can be used to make a range map. At a coarser scale, only a very small fraction of individuals is observed. Thus, biogeographers often draw range maps by eye using available information, often called ‘dot’ maps showing known locations (e.g. from herbarium or museum collections). Better statistical methods are needed for these ‘partial realizations’ of the point process. While these methods describe where a species exists physically, they lack explanation.

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Biogeography

The second main way of envisioning a species distribution is through its niche, which explores why a species exists where it does. The geographic range of a species is a spatial realization of its niche. Hutchinson [6] developed the concept of the multidimensional niche to describe how the environment and other factors limit species distribution. Some factors that might limit a species include climatic, geological, disturbance, or the presence of certain other species. The representation of species abundance as curves along many axes representing different factors was called the hypervolume. The niche of a species is the intersection of environments that are favorable for species growth and survival. A species has a distribution in this abstract space as well as in physical space. From a statistical viewpoint, the niche can be thought of as a multiple, nonlinear regression model, where the response (abundance) is modeled as a function that is typically unimodal and drops to zero at extremes for each independent variable, but the functional form may vary for each factor. Often, the niche is not fully occupied, as we witnessed, for example, when species are introduced to new areas and become exotic pests. This difference is often referred to as the potential and realized niche. An area needing further attention is relating the niche concept (abstract space) to the spatial methods (geostatistics, lattice models, point processes) used to model the range (physical space). For example, universal kriging incorporates explanatory variables into kriging models, lattice models also allow covariates, and inhomogeneous point processes incorporate explanatory variables into point processes.

The Distribution of Communities A community (see Community, ecological) consists of a group of individuals of various species living together in some particular place. An example of a well-defined community is a lake with its associated plants, fish, insects, etc. Ecosystems include not only the community, but all of the physical environment and the nutrient and energy flows among them. An example of an ecosystem is a forest stand, with the flow of carbon from the air to the soil, through plants and animals that feed on them, and back to the air (see Forest carbon cycling). Biomes (also known as life zones or ecoregions) are large areas with certain climates that cause distinctive types or organisms to

inhabit them. An example of a biome is the arctic tundra with its characteristic low growing plants and well-insulated mammals. There has often been acrimonious debate on the nature of communities in the landscape. Some scientists prefer to categorize communities into types producing a classification. Multivariate clustering algorithms are among the statistical methods that have been used. Other scientists view communities as a continuum of variation. Their statistical methods have been ordination methods that include principal components analysis, factor analysis, correspondence analysis, and multidimensional scaling, to name a few. Recently, a compromise view has emerged that both are useful ways to reduce the dimensionality of high-dimensional data that often have more variables than samples (see Multivariate data visualization). It is useful to produce a classification, which is arbitrary but adapted to the purposes at hand, and to map the classification for land use management. It is also useful to display communities in a continuum formed by a few axes to explore relationships between communities, species, and the environment.

Historical Biogeography The history of the earth is dynamic. In relatively recent times, glacial cycles have caused local climates to shift dramatically. Plate tectonics have moved continents. Large asteroids have impacted the earth. In order to survive local changes, species have had to undergo two basic processes: evolution and dispersal/migration. Those that failed became extinct. Owing to the processes of evolution and speciation and dispersal and migration, the current locations of individuals of species today are observed. These are by no means the only places on earth they could exist. Often times the historical paths of populations have left them trapped by barriers that may be as obvious as an ocean or as subtle as a parasite. The fact that thousands of plants and animals have been introduced and thrived in new habitats demonstrates that species often exist in only a part of their potential range. When that range is very restricted and localized, it has been termed endemic. Another pattern that is sometimes observed is disjunction, where a species occurs in two or more areas that are widely separated. A final example of a pattern is called cosmopolitan, which describes a species that varies widely across regions and

Biogeography continents. Biogeography attempts to classify patterns of distribution and explain their existence through historical, evolutionary, and ecological reasoning.

As stated earlier, biogeography is largely an observational science, rather than an experimental one. For this reason, ecologists since Darwin have been interested in islands, which offer ‘natural’ experiments that allow scientists to investigate phenomena such as niche shifts for different combinations of species as well as other ecological and evolutionary responses. Islands are also present on land, represented as isolated habitats. Lakes are islands to fish, cattle droppings are islands to certain collections of species, etc. MacArthur and Wilson [7, 8] presented the theory of island biogeography, which has had a large impact on ecology and biogeography. Larger islands generally support more species than smaller ones. Generally, this species–area relationship can be expressed as S D cAz , where S is the number of species, c is a constant that varies depending on the taxonomic group and location, A is the area of the island, and z is an exponent that varies for different island systems and taxonomic groups (but generally in the range from 0.24 to 0.33). On the log scale, logS D logc C z[logA], so regression analysis (see Linear models) can be used to estimate z. Another observation is that more isolated islands contain fewer species than islands close to a mainland or part of a large archipelago. One model for this species–isolation relationship is S D kfexpdIg, where k and d are constants for a particular area and taxonomic group, and I is the isolation of an island. Transforming to the log scale, logS D logk  dI. Providing that the isolation factor can be quantified, linear regression can be used to estimate k and d. A final observation is that although the number of species on islands may be relatively constant, there is turnover in the composition of the species. MacArthur and Wilson [7, 8] developed a dynamic theory to explain patterns seen in island biogeography given above: (a) the species–area relationship, (b) the species–isolation relationship, and (c) the species turnover. For simplicity, assume that rates of immigration can be modeled as S D ˛P  S for 0  S  P, where ˛ is the immigration rate with

Extinction Rate

Island Biogeography

3

Immigration

0

Se

P

Number of species

Figure 1 MacArthur and Wilson’s [7] equilibrium theory of island biogeography. Immigration and extinction rates change linearly, and in opposing ways, with numbers of species. An equilibrium is attained at Se when immigration equals extinction. Reproduced from [7] with permission from Evolution

no species present on the island and P is the number of species in the ‘pool’ that can disperse to the island. Similarly, let the extinction rate υ be modeled as υS D ˇS, where ˇ is a parameter for the extinction rate. MacArthur and Wilson reasoned that at equilibrium, immigration would equal extinction. The number of species at equilibrium, Se , is found by setting S D υS where we obtain ˛P  S D ˇS, and solving for S, Se D ˛P/˛ C ˇ. This solution is given in Figure 1. The equations can be made nonlinear by simple transformations of the ordinate, and they are often depicted in that way. Extinction rates are expected to be largely governed by the size of the island, with smaller islands having higher extinction rates. Immigration rates are expected to be largely governed by the proximity to the pool of available species. Thus, the set of curves given in Figure 2 is obtained. From Figure 2, the theory of island biogeography predicts that, based on principles of immigration and extinction, the number of species for larger islands near to the species pool, SLN , will be greater than the number of species for smaller islands that are farther from the species pool, SSF . It also predicts that species turnover for smaller islands near the species pool, TSN , will be greater than species turnover for larger islands far from the species pool, TLF . This has been a short introduction to a very broad topic. Biogeography touches many aspects of biology and uses many mathematical and statistical

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Biogeography References [1] Rate

ar ne

all Extinction sm ge lar

Immigration

far

[2]

[3]

T SN

[4]

T LF 0

S SF

S LN

P

[5]

Number of species

[6]

Figure 2 Some predictions from MacArthur and Wilson’s [7] equilibrium theory of island biogeography. Immigration is affected by distance from the species pool, and two curves are shown representing near and far distances. Extinction is affected by the size of the island, and two curves are shown representing small and large islands. The intersection of the immigration and extinction curves is the predicted number of species at equilibrium, with S denoting the number of species and T the species turnover, with the first subscript S for small island or L for large island, and the second subscript N for near island or F for far island. Reproduced from [7] with permission from Evolution

methods. A good modern text is provided by Brown and Lomolino [3], with many references from which much of this material was drawn.

[7]

[8]

[9]

Bailey, R.G. (1996). Ecosystem Geography, SpringerVerlag, New York. ¨ Bergmann, C. (1847). Uber die Verh¨altnisse der W¨armeo¨ konomie der Theire zu ihren Gr¨osse, G¨ottinger Studien 1, 595–708. Brown, J.H. & Lomolino, M.V. (1998). Biogeography, 2nd Edition, Sinauer, Sunderland. Cressie, N. (1993). Statistics for Spatial Data, Wiley, New York. Erikson, R.O. (1945). The Clematis fremontii var. riehlii population in the Ozarks, Annals of the Missouri Botanical Garden 32, 413–460. Hutchinson, G.E. (1957). A Treatise on Limnology, Vol. 1, Wiley, New York. MacArthur, R.H. & Wilson, E.O. (1963). An equilibrium theory of insular zoogeography, Evolution 17, 373–387. MacArthur, R.H. & Wilson, E.O. (1967). The Theory of Island Biogeography. Monographs in Population Biology, No. 1, Princeton University Press, Princeton. Taylor, F.B. (1910). Bearing of the tertiary mountain belt on the origin of the earth’s plan, Geological Society of America Bulletin 21, 179–226.

(See also Ecological statistics; Population dynamics; Population ecology; Species diversity) JAY M. VER HOEF