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Effect of scale on a pattern of mammalian geographical distribution: a comparison between Texas and North America.

Abstract. -- Frequency distributions of the sizes of the geographical ranges of mammalian species in Texas are bimodal; aggregations of species occur in both small and large areas, with relatively fewer numbers in areas of intermediate size. Similar data, at the scale of North America, are unimodal and strongly skewed to the right. This contrast is a qualitative effect of scaling between two areas that differ greatly in size. This empirical pattern may characterize many floral and faunal studies, at state or regional levels. Inferences, based on the assumption of geographical pattern invariance, across scalar transformations, should be done with caution.


The scale at which observations are made influences the patterns that are perceived (Erickson 1945; Levin 1992; Lyons & Willig 1999). This suggests that scale should be taken into consideration when inferences are made about processes responsible for observed patterns. Phenomena that are important at one scale may become unimportant, or even nonexistent, at a different scale. Since biogeographers frequently use mensurative scales in their methodology, and since nature is strongly scale dependent (Allen & Starr 1982), it is prudent to investigate the effects of transitions from one scale to another.

In this paper the effects of a scalar transition from the area of the state of Texas to the area of the continent of North America is investigated. The data are the mammalian species native to the state of Texas, USA and the area over which they are distributed within the state. The taxa considered are the class Mammalia and the orders Chiroptera, Rodentia and Carnivora. It is shown that a bimodal pattern for these taxa, at a state level, changes to a unimodal pattern when the scale is increased to include the entire continent. The pattern observed for Texas could not be extrapolated to North America because the two are qualitatively different. This change in pattern is interpreted as a direct consequence of scale.


The state of Texas occupies about 69.2 by [10.sup.4] [km.sup.2] in the south-central region of the USA. Since the states' size, shape and orientation were determined by political considerations, it may be considered to be an arbitrary (but not random) sample for the study of mammalian distributions. Outline maps were prepared of the geographical distributions, within Texas, of 141 species of mammals native to the state. All known records of marginal specimens were used as a guide to map preparation. A system of quadrats, each representing 63.9 km on a side, was fitted to the outline maps and species were recorded as either present or absent, within each quadrat. Such maps have been used as a basis for making inferences about the distributional biology of mammals (Simpson 1964; Pagel et al. 1991). The data are functionally equivalent to a full census.


Figure 1 has graphs of the number of species in Texas that occupy areas of different sizes within the state. Since a species and its range have a one-to-one correspondence, this figure is also a frequency distribution of geographical range sizes. Each of the four taxa, represented for Texas, has aggregations of species in small areas (Fig. 1). The value for carnivores is somewhat lower than the values for the other taxa, with respect to the range in the data.

In addition to aggregations in small areas, the class Mammalia and the orders Chiroptera and Carnivora also have aggregations of species in large areas of Texas. Values in large areas are relatively low for Chiroptera but high for Carnivora. There is only a slightly higher value in large areas for Rodentia. These taxa have bimodal frequency distributions, when species number is plotted as a function of the geographical area over which said species are distributed. Their graphs exhibit both a higher number of widely ranging species and a higher number of narrowly ranging species. Relatively fewer species have ranges in any one intermediate size class.

The graphs in Figure 1, at the scale of North America, were adapted from Pagel et al. (1991). These graphs were based on data tabulated from the presence or absence of species geographical ranges, in a square quadrat system, that was analogous to the one used to obtain the Texas data. The North American data are unimodal and very right skewed for Mammalia, Chiroptera and Rodentia. Aggregations in small areas are by far the most frequent. Carnivora is different. This order has a truncated mode on the left and a symmetrical mode on the right; in this sense Carnivora is bimodal at the continental level.



If one does not consider species aggregations in large areas of Texas for Mammalia, Chiroptera and Carnivora, than the data exhibit basic similarities at both the continental and state scales. Mammalia, Chiroptera and Rodentia in Texas are skewed to the right and concave upward. The corresponding graphs for North America also exhibit this basic pattern, except that they are even more strongly skewed to the right. The pattern of Carnivora in Texas is suggestive of its corresponding pattern for North America. Both have substantial aggregations in small areas but few species in large areas. The higher middle-right part of the graph for Texas Carnivora is suggestive of the higher middle-right part of the graph for North American Carnivora.

The most noteworthy difference, between the data for Texas and the continental data, is that the Texas-pattern has aggregations of substantial size in large areas for Mammalia, Chiroptera, Carnivora and possibly Rodentia. In contrast, North America does not exhibit this pattern. The data for North America lack aggregations of species in large areas and so are unimodal.

Aggregations in large areas, of the Texas data, may be caused by the considerable difference between the size of the state and the size, orientation and location of the full continental ranges of Texas mammals (Brown 1984; 1995). The continental spatial scatter of the centroids of distribution of Texas mammals, plus their different sizes and shapes, are sufficient conditions for this to be the case. For example, the mean range size for North American mammals is only 7.8% of the continent. The species with the largest range, the white-tailed deer, Odocoileus virginianus (Boddaert), occupies about 84% of the continent (Pagel et al. 1991). In contrast, Texas has about 14 species of mammals that occur throughout all or most of the state (Fig. 1, aggregations in large areas for Mammalia). Most of these same 14 species occur across only a fraction of the North American continent, as defined and treated by Hall (1981); none occurs throughout all of North America. In a continent wide study these same 14 species would shift position, from their place in the widespread mode relative to Texas, to a new place at an intermediate or even restricted mode, relative to the continent. The losses of the widespread mode would become the gains of the restricted mode. In principle such attrition could lead to the loss of almost the entire widespread mode, along with a concomitant buildup of the intermediate and restricted modes. A simple expansion of scale transforms bimodal data into unimodal data. In Texas the widespread mode cannot disappear completely because species, which are widespread with respect to the continent, will also probably be widespread with respect to Texas. Furthermore a suite of species of statewide occurrence is a known fact.

This general effect is reinforced by considerations of the average range sizes among orders. The average ranges of bats, rodents and carnivores share the same ordinal relationship for both Texas and North America, but are proportionally much smaller for North America (bats 4.4%, rodents 6.5% and carnivores 35.2%, of the continent respectively) than they are for Texas (29.6%, 30.8% and 55.1% of the state respectively). In both Texas and North America the ranges of bats and rodents are relatively small and differ from each other by only about 2%, whereas the ranges of carnivores are about 25 to 30% larger than those of either bats or rodents. This areal relationship biases the Texas data toward the right-hand, widespread mode of Figure 1, relative to patterns obtained by the same procedure at a continental scale.

One should not suppose that one scale is intrinsically right and the other wrong (Allen & Starr 1982; Levin 1992), both are correct and relevant with respect to their own frame of reference. The phenomenon of bimodality at one scale and unimodality at another should not be peculiar to Texas. If the matter were looked into, it should be found to characterize many works on the fauna and flora of spatially delimited areas that do not have natural boundaries. To whit, the frequency distributions emergent from a study of chiropteran or marsupial geographical ranges in North America, north of Mexico, would be strongly affected by the exclusion of the many chiropteran and marsupial species in Mexico and Central and South America.


I thank James H. Brown for substantive comments.


Allen, T. F. H. & T. B. Starr. 1982. Hierarchy: Perspectives for ecological complexity. Univ. Chicago Press, xvi+310 pp.

Brown, J. H. 1984. On the relationship between abundance and distribution of species. Am. Nat., 124(2):255-279.

Brown, J. H. 1995. Macroecology. Univ. Chicago Press, xiii+269 pp.

Erickson, R. O. 1945. The Clematis fremontii var. riehlii population in the Ozarks. Ann. Missouri Bot. Gardens, 32(3):413-460.

Hall, E. R. 1981. The Mammals of North America. Second ed. John Wiley and Sons, New York, 1:xv+1-600+90, 2:vi+601-1191+90.

Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology, 739(6):1943-1967.

Lyons, S. K. & M. R. Willig. 1999. A hemispheric assessment of scale dependence in latitudinal gradients of species richness. Ecology, 80(8):2483-2491.

Pagel, M. D., R. M. May & A. R. Collie. 1991. Ecological aspects of the geographical distribution and diversity of mammalian species. Am. Nat., 137(6):791-815.

Simpson, G. G. 1964. Species density of North American Recent mammals. Syst. Zool., 13(2):57-73.

James G. Owen

Universidad Salvadorena "Alberto Masferrer"

Apartado Postal 2053, San Salvador, El Salvador

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Author:Owen, James G.
Publication:The Texas Journal of Science
Geographic Code:1U7TX
Date:Aug 1, 2001
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