CORRELATIONS OF SOME CLIMATIC VARIABLES WITH MAMMALIAN SPECIES RICHNESS IN TEXAS.

Abstract.--The statistical correlation between mammalian species richness and a suite of twelve climatic variables is examined for the state of Texas. The taxa include the total number of native land mammals studied (141 sp.) as well as the number of species of the orders Chiroptera (31 sp.), Rodentia (62 sp.) and Carnivora (29 sp.). At the taxonomic and geographical scales of this analysis, climate is a weak predictor of mammalian species richness. Many of the climatic variables are not orthogonal to each other. The presence of variables that are not mutually orthogonal, introduces multicollinearity into regression models, when these parameters are used as independent variables. It is suggested that these may be scaling effects.

Owen & Schmidly (1986) compiled a suite of twelve climatic variables for Texas and reported their matrix of simple correlation. These climatic variables represent aspects of temperature and precipitation. Long-term climatic averages are known to closely match the distributions of a few species. An excellent example for mammals is the contemporary distribution of the common vampire bat Desmodus rotundus. Laboratory experiments have demonstrated that this species is a poor thermoregulator at an ambient temperature below 10[degrees]C (McNab 1969). Its northern limits of distribution closely match the 10[degrees]C minimal isotherm for January in northern Mexico; its southern limits, in southern South America, match the 10[degrees]C minimal isotherm for July (McNab 1973). This coincidence of geographical and climatic patterns, in combination with mechanistic laboratory studies that relate climate to organismal physiology, make a strong argument for the influence of climate in setting the distributional limits of vampires.

Other studies have correlated mammalian species richness in North America with actual evapotransporation, which is a measure of available environmental energy (Wilson 1974; Currie 1991). Mechanistic interpretations of the functional relationship between ambient energy and richness may depend on scale. At a continental scale energy is positively correlated with richness in Mammalia. On regional and local scales it has a hump-shaped relationship with richness in Rodentia (Abramsky & Rosenzweig 1984; Rosenzweig 1995).

The purpose of this paper is to explore the relationships between climate and mammalian species richness through an analysis of their simple correlation coefficients. These correlation coefficients also are compared and contrasted with their corresponding regression coefficients in Owen (1990). This paper differs from Owen (1990) because correlation coefficients and regression coefficients do not provide the same information (Montgomery & Peck 1982), unless the variables constitute an orthogonal set (not the case here). This is because the absolute values and signs of the coefficients in a multiple regression model are influenced by the presence of the other regressor variables. One cannot predict the value that a particular variable, in a multiple regression model, would have had if the variable had been taken alone. In contrast, the simple correlation coefficient, by definition, is a symmetrical relationship that is only dependent upon the two variables under consideration.

The climatic and taxonomic variables, their pairwise correlations and their significance levels, as well as the definitions of the variables will follow. The mammalian taxa considered include the total number of native land mammals (141 sp.) as well as the individual species of the orders Chiroptera (31 sp.), Rodentia (62 sp.) and Carnivora (29 sp.) (Owen 1985). Davis & Schmidly (1994) list a total of 142 species of native land mammals for Texas, including 32 species of Chiroptera, 64 Rodentia and 28 Carnivora. These slight changes are not considered significant for the purposes of this study. The study area is the state of Texas and the scale is regional. The word regional is used in reference to an area that it is large enough to include several of the Life Areas of North American (Kendeigh 1974) but smaller than the entire continent. Such is the case for Texas. This definition concords with usage of the term in the literature (Ricklefs 1987).

It is worthwhile to bear in mind the difference between species distributions and distribution of species richness. Richness is the total number of species that coexist (at the scale of measurement under consideration) at a given place and time. Distribution is essentially a concept of occupied area, its location and its perimeter. Ultimately richness dependents upon a coincidence of distributions, but because of the individualistic nature of distributions (Brown et al. 1996), there is no exact inferential relationship between the two.

The level of aeriographic resolution of this report was a system of square quadrats 63.9 km on a side. The system, consisting of 189 squares, was randomly superimposed on a Lambert's conical projection map of Texas. Within each quadrat, the presence or absence of 141 species of native mammals, whose geographical ranges include Texas or some closely adjacent areas in Mexico and New Mexico, were recorded (Owen 1988). The species richness of a given quadrat is represented by the number of species present or potentially present in it, as depicted by the range maps.

Personnel of the federal government at 183 independent weather stations, spanning the entire state, collected the original climatic data. Most of the climatic information was obtained from summary sheets published by the U.S. Department of Commerce. The time periods for which climatic data were available varied among quadrats, according to the date at which weather stations had been established at different places. Almost all of the variables (Table 1) were based on a minimum of 10 years worth of data, many on considerably more years.

A normality test (Kolmogorov-Smirnov) indicated that the data varied significantly from the pattern expected if it were drawn from a population with a normal distribution. Therefore, a test for independence using the nonparametric Spearman's [r.sub.s] was conducted. This is the same as the classical sample correlation coefficient applied to the rankings of the x and y observations within their respective samples (Hollander & Wolfe 1973).

RESULTS

At an alpha level of 0.05 or less, about 69% of the entries in Table 2 were significant. Each variable was significant for one or more taxa. Two variables, mean annual precipitation and mean intermonthly variability of precipitation, were significant for each of the four taxa. The strongest correlations were with mean annual precipitation. Mean annual precipitation is strongly associated with estimates of primary productivity in Texas, [r.sub.s] = 0.99 (Owen & Schmidly 1986), thus these two variables may be used as statistical surrogates for each other. The signs of mean annual precipitation and mean intermonthly variability of precipitation were negative for Mammalia, Chiroptera and Rodentia.

These negative signs reflect the high richness of these groups in western Texas, where productivity is low. Carnivora has higher richness in the more central parts of the state (Owen 1988; 1990), where some carnivore species may be responding to Balcones Fault riprarian habitat. A regression of carnivore richness on precipitation, or its statistical surrogate productivity, has a significant quadratic term and is curvilinear. The mode of this curve occurs over precipitation values characteristic of quadrats in central Texas (Owen 1988). This explains, statistically, why carnivore richness is not highest in eastern Texas, as the correlation coefficient might suggest.

The signs of the partial regression coefficients in Owen (1990) matched the signs of the correlation coefficients in this paper, with the exception of the variable mean January temperature, for Chiroptera. Five of the variables in Owen (1990) that had significant partial regression coefficients had simple correlation coefficients that were not significant. Inconsistencies between the values of the regressors presented in Owen (1990), and their corresponding correlation coefficients in this paper, may be explained by the effects of mutual correlations between the independent variables themselves (Steel & Torrie 1980). When the regressors in a model are correlated, i.e., not orthogonal, the functional response of any given variable dependents on the values of the other variables that are present. Regression coefficients are subject to change in magnitude, sign and variance according to model specification (Chatterjee & Price 1977; Montgomery & Peck 1982). This appears to have been the case with the equations in Owen (1990), in spite of having relatively low variance inflation factors. It is noted, parenthetically, that multicollinearity does not effect the predictive value of the models used by Owen (1990). This same problem probably obtains for many suites of environmental variables used in ecological studies.

DISCUSSION

Long-term climatic conditions may be useful in explaining the geographic distributions of some species. Nevertheless, knowledge of the effects of climate on the distributions of a few climate sensitive species may be of little help in explaining patterns of geographical richness at a regional scale. This is because richness depends by definition, not on distribution, but on distributional overlap, and the effects of climate on distributions, and hence their overlap, are highly individualistic (Brown et al. 1996).

It is unlikely that any two randomly chosen species, even if they turned out to be limited by the same climatic variable, e.g., temperature extremes, would be limited by that variable to the same degree. One species would probably tolerate higher extremes better than the other would. The more temperature tolerant species would extend its range out farther along a temperature gradient, thus reducing species richness in the zone where the two species do not overlap. At the same time the more temperature tolerant species could come into contact with a third species that is not sympatric with the first two. There are many combinational possibilities. See McNab (1982:Figure 28) for examples of temperature limited distributions of neotropical bats. Add to this variation other idiosyncratic aspects of species autecology and the degree of range overlap may become intractable for the purposes of prediction.

The data for Texas do not reveal a consistent or strong coincidence between climate and mammalian species richness. These taxa exhibit only a modest number of statistically significant but generally low correlations with the states overall climate. Here the appelative "low" means that these correlations do not have sufficient magnitude to be useful as predictors (Mendenhall 1979); it is recognized that usefulness is a matter of degree and so the meaning of "low" becomes somewhat arbitrary. This lack of association characterizes both the number of significant values within a given variable across taxa and the number of significant values within a taxon across variables. The mean absolute value of the correlation coefficients is 0.31. In a simple regression the value 0.31 would explain less than 10% of the variation in the data. These data do not support the conjecture that regional mammalian richness is strongly influenced by the regional climate.

Usually the climate changes only slowly in Texas, with horizontal distance, between two places that remain at about the same elevation. Except for the Trans-Pecos, Texas does not have substantial topographical relief. Distances in the state could be too small for climatic differentials to be effective as determinants of richness patterns inmammals. Perhaps one would have to correlate climate with richness by using a geopolitical boundary on the scale of the United States, or by using all of North America, to resolve large differences. Clearly bat richness and temperature are correlated on a continental scale from Canada to Costa Rica (Simpson 1964; Wilson 1974).

Many species of mammals can maintain homeostasis through appropriate physiological and behavioral responses over a substantial range of climatic conditions (Schmidt-Nielsen 1997). This control may allow them to have wider geographic distributions, with respect to climate, vis-a-vis other groups of vertebrates such as amphibians or reptiles. Under this scenario the same set of mammalian species could inhabit a relatively larger segment of a climatic gradient and thus exhibit a flat response to it. The major effects of climate on species richness in Texas may be associated with the susceptibility of members of particular clades or historical biogeography. They are probably local and directly related to the ecological and physiological tolerances of suites of related species, for example members of the same genus such as Dipodomys (kangaroo rats), Chaetodipus and Perognathus (pocket mice).

Several studies have interpreted climatic variation as an abiotic disturbance factor (Boyce 1979; Strong 1983; Sousa 1984), which increases species richness by preventing competitive displacement (Huston 1979). The theorized mechanism that connects ambient disturbance to richness occurs at the scales of local and metapopulations. It is highly dependent on the frequency and intensity of disturbances and on the intrensic rate of increase of the suite of species involved (Huston 1979). The feasibility of making extrapolations from local to region scales needs further research (Ricklefs 1987).

It was suggested that the taxomonic categories analyzed in this study are so large that it is impossible to find discrete groups, amongst all the variation, whose geographical richness is related to a specific climatic regime. It is probably true that the members of certain taxa are not random assemblages with respect to climate, e.g., heteromyid rodents are limited by, or at least correlated with low rainfall. The taxonomic affinities of a suite of species inhabiting one set of climatic conditions may differ substantially from the affinities of a suite of species inhabiting another set of climatic conditions. If this study treated taxonomic groupings of mammals, as operational units at the familial or generic levels, then one could probably find certain sets which correlate strongly with climate. By treating wide-ranging taxa (such as the white-footed mouse Peromyscus leucopus, the deer mouse P. maniculatus and the Hispid cotton rat Sigmodon hispidus, etc.) together with more geographically restricted taxa this study probably obscured some differences within the matrix of overall variance. Still, the Class Mammalia is a realistic division and it is worthy of attention, in and of itself.

Much of the lack of concordance between mammalian richness and climate, that is emergent in this study, may be attributable to the effects of scale; taxonomic, temporal and spatial (Allen & Starr 1982; Sousa 1984). The use of class and ordinal levels may obscure real correlations at the familial or generic levels (taxonomic scale). The use of species presence or absence, in range maps of fixed size, represents a kind of temporal stasis or equilibrium (temporal scale). It does not take into account the enormous dynamic variation that characterizes species true distributions, especially near their range borders. The state of Texas may represent a scale too large to detect local climate-richness patterns in the Temperate Zone, yet too small to detect continental patterns (spatial scale). A different interpretation is that here the important factor is not size, per se, but rather size plus geographical location. Species ranges of North American mammals are often smaller in the tropics (Pagle et al. 1991). Theref ore, an area the same size as Texas, but located in Central America, say from Panama northwards, might show significant climate-richness patterns.

If this characterization is the general case, then a simple increase or decrease in scale could lead one to conclude that climate is important for richness, a conclusion diametrically opposite to the principal finding of this paper. It would be a mistake though, to think that one scale represents ontological truth better than another does. All scales provide information but relevant scales provide relevant information. Scale needs to be matched, a priori, to the question being asked and that may not be an easy task. (Allen & Starr 1982; Ricklefs 1987). Students of mammalian geography at regional scales will find the information in Table I useful, both with respect to Texas and as a reference for comparative studies at other geographical locations.

ACKNOWLEDGMENTS

I thank two anonymous reviewers for comments.

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Table 1. Definitions of climatic variables.

(1) Number of hot days. -- Mean number of days per year with an average temperature [greater than or equal to] 32[degrees]C.

(2) Maximum temperature. -- Maximum temperature recorded in period of record.

(3) Mean July temperature. -- Hottest month.

(4) Standard deviation of mean July temperatures. -- Standard deviation of mean temperatures of hottest month.

(5) Number of cold days. -- Mean number of days per year with average temperature [less than or equal to] COG.

(6) Minimum temperature. -- Minimum temperature recorded in period of record.

(7) Mean January temperature. -- Coldest month.

(8) Standard deviation of mean January temperatures. -- Standard deviation of mean temperatures of coldest month.

(9) Mean annual temperature. -- Mean of average monthly temperatures.

(10) Mean annual temperature range. -- Mean of July temperatures minus mean of January temperatures.

(11) Mean annual precipitation.-- Sum of mean of monthly precipitation totals.

(12) Mean intermonthly variability of precipitation. -- Mean value of absolute differences between average precipitation totals of consecutive months.

Table 2. Spearman rank correlation
coefficients [r.sub.s] (left) and their
corresponding values ot alpha, (right)
between 12 environmental variables
and mammalian species richness in
Texas, n = 189 (number of quadrats).
Environmental variables        Mammalia          Chiroptera
 (1) Number hot days            0.29 (0.000)     0.12 (0.10)
 (2) Maximum temperature        0.13 (0.07)     -0.12 (0.10)
 (3) Mean July temperature      0.006 (0.93)    -0.21 (0.005)
 (4) Standard deviation mean
     July temperature           0.15 (0.04)      0.10 (0.18)
 (5) Number cold days           0.14 (0.05)      0.12 (0.11)
 (6) Minimum temperature        0.01 (0.84)      0.18 (0.01)
 (7) Mean January tempera
     ture                      -0.0003 (0.997)   0.02 (0.81)
 (8) Standard deviation mean
     January temperature       -0.38 (0.000)    -0.24 (0.000)
 (9) Mean annual temperature   -0.02 (0.76)     -0.06 (0.38)
(10) Mean annual
     temperature range         -0.04 (0.60)     -0.16 (0.03)
(11) Mean annual precipi-
     tation                    -0.46 (0.000)    -0.43 (0.000)
(12) Mean intermonthly varia-
     bility of precipitation   -0.24 (0.001)    -0.29 (0.000)
Environmental variables          Rodentia       Carnivora
 (1) Number hot days           -0.07 (0.31)    0.33 (0.000)
 (2) Maximum temperature        0.17 (0.02)    0.07 (0.37)
 (3) Mean July temperature     -0.37 (0.000)   0.57 (0.000)
 (4) Standard deviation mean
     July temperature           0.41 (0.000)  -0.40 (0.000)
 (5) Number cold days           0.66 (0.000)  -0.68 (0.000)
 (6) Minimum temperature       -0.44 (0.000)  -0.40 (0.000)
 (7) Mean January tempera
     ture                      -0.54 (0.000)   0.64 (0.000)
 (8) Standard deviation mean
     January temperature       -0.38 (0.000)   0.07 (0.31)
 (9) Mean annual temperature   -0.56 (0.000)   0.66 (0.000)
(10) Mean annual
     temperature range          0.46 (0.000)  -0.51 (0.000)
(11) Mean annual precipi-
     tation                    -0.73 (0.000)   0.57 (0.000)
(12) Mean intermonthly varia-
     bility of precipitation   -0.62 (0.000)   0.52 (0.000)