Species ranges

An exhaustive database of distributions of 625 mammal species, encompassing 13 orders, 55 families and 235 genera, was originally complied following IUCN et al. (2004), Sheng et al. (2005), Pan et al. (2007) and the Vertebrate Species Information Database of our research group [39]–[42]. We excluded primarily marine and aquatic species, whose geographical ranges are unique from terrestrial mammals. We digitized the range maps and updated them according to comprehensive literature, faunistic atlases, nature reserve biodiversity survey reports, documents of museum collections and field survey records from our laboratory. Numerous zoologists were also consulted to modify the database. One-hundred and ten species that were subject either to taxonomic disputes or lacking comprehensive distributional information were removed from the overall data set, leaving 515 terrestrial mammal species in our analyses.

For each species, we recorded the maximum and minimum latitudes of its distribution. Further, the mid-point and latitudinal range of each species was calculated as the average and difference between the maximum and minimum latitudes respectively. To evaluate the relationship between mean species range and latitude, the total latitudinal gradient was divided into eight bands of 5° latitudinal intervals. In addition, we rasterized the range maps into equal-area grids of 100 km×100 km [37].

Environmental predictors

To evaluate the effects of environmental factors, we used nine predictive variables that were collapsed into the four grouped environmental variables reported below, all of which were processed into 100 km×100 km equal-area grids. Coastal cells were excluded if they contained <50% of the land masses.

Analyses

We examined the relationship between mean latitudinal range size and latitudes among 5° bins using Steven's method [4], the mid-point method [27], Pagel's method [28] and the cross-species method [8]. Linear and 2nd order polynomial fits were calculated, and the fit with the highest R² was selected to represent the relationship. Rapoport's rule is supported where the relationship between those variables is positive [15]. Moreover, we assigned each species range raster with its latitudinal range, and calculated the arithmetic mean in each 100 km×100 km grid cell [20], to reveal any spatial pattern in range size and ultimately, analyze the relationship between range size and environmental factors.

We tested the impacts of two factors: (1) the MDE and (2) environmental effects. First, we detected the MDE by comparing the observed latitudinal range pattern with the null model built by reshuffling species ranges based on an empirical distribution range model [30], [31] parsed in 5° latitudinal bands system. The simulation was performed using a Monte Carlo algorithm and implemented in the modules Mid-Domain Null [48] and Range Model 5 [49]. We ran 10000 Monte Carlo simulations of empirical range sizes sampled without replacement to ensure that all species were reshuffled [15]. The mean latitudinal range size from those 10000 simulations was considered to be the prediction of the null model [50], and a linear regression of the empirical mean range sizes and the null model was carried out to interpret the impact of the MDE [51], [52]. For the linear regressions, we checked normality (K–S test) and homoscedasticity (Levene's test) of the data, all of which detected no significant departure from either normality or homoscedasticity (all P >0.05). Second, we processed generalized linear models (GLMs) between mean latitudinal range sizes and four groups of environmental variables separately over the 100 km×100 km quadrat system to explain the environmental impacts on range size gradient [15]. To ameliorate the problems of high correlations between explanatory variables (Pearson's correlation coefficient >0.7), we used stepwise procedures in the GLMs. The relationships among variables, latitudes and mean latitudinal range sizes were also determined using Pearson's correlation coefficients [15].

Our statistical analyses were carried out in SAS Version 9.1 and SPSS Version 13.0. The spatial analyses were conducted in ESRI ArcGIS 9.2.

Species latitudinal range size distributions

The mean latitudinal range size of terrestrial mammals in China was 11.01±8.13° (mean±SD; applies to all subsequent values) (n = 515), with the median of 9.58°. The distribution of range size was formally right-skewed (Fig. 1(a)), and the log₁₀ transformed range sizes were not normal but assumed a modestly left-skewed distributed (Fig. 1(b)). Only 17 (3.3%, the percentage of the total species number; applies to all subsequent values) and 34 (6.6%) species had ranges of >30° and <2°, respectively (Fig. 1(a)). More than three quarters of the species (79.8%, 411 species) occupied ranges of 2°–20°, and 90.1% species (464 species) occupied 2°–30° of latitudes (Fig. 1(a)).

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Figure 1. Species latitudinal range size distribution for terrestrial mammals in China

. (a) untransformed latitudinal range size; (b) log₁₀-transformed latitudinal range size.

https://doi.org/10.1371/journal.pone.0027975.g001

Spatial pattern of latitudinal range size

The latitudinal range size patterns predicted by Steven's, Pagel's and the cross-species methods were related positively to latitudes, which conforms to Rapoport's rule (Fig. 2). Steven's method showed that the range size was between 13° to nearly 25°, and attained its minimum between 15° N and 25° N, increasing northward (β = 0.296, p = 0.002, R² = 0.948; Fig. 2(a)). Pagel's method revealed a similar pattern, but with a steeper slope than Steven's method (β = 0.541, p <0.0001, R² = 0.960; Fig. 2(c)). Application of Pagel's method resulted in a mean range size of <3° in the southernmost band (Fig. 2(c)). The scatter diagram representing results obtained via the application of the cross-species method revealed a mean range size between Steven's and Pagel's methods, with a positive latitudinal gradient explained by limited variation in range size pattern (β = 0.285, p <0.0001, R² = 0.286; Fig. 2(d)). Application of the mid-point method, however, revealed a hump-shaped relationship, peaking in the vicinity of 30° N−35° N with significant declines both to the north and south (p = 0.028, R² = 0.821; Fig. 2(b)). These latter findings do not support Rapoport's rule, and suggested that the maximum and minimum of mean range size were 20° and 5° respectively (Fig. 2(b)).

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Figure 2. Mean latitudinal range size of terrestrial mammals among latitudes in China.

Solid lines represent the fitted correlations between mean latitudinal range sizes and latitudes: (a) Steven's method (sample size within each 5° band (left to right): 206, 233, 201, 161, 161, 124, 56); (b) mid-point method (sample size within each 5° band (left to right): 114, 138, 83, 64, 74, 37, 5); (c) Pagel's method (sample size within each 5° band (left to right): 37, 119, 94, 65, 45, 86, 69); (d) cross-species method (total sample size was 515).

https://doi.org/10.1371/journal.pone.0027975.g002

The latitudinal range size map revealed no pattern consistent with Rapoport's rule (Fig. 3). It showed larger mean range sizes between 25°N and 40°N. The eastern and southeastern coastal areas were characterized by the biggest species ranges in China, followed by the northeastern, central and southern part of the country. By contrast, the smallest ranges were found along the northern border. The mean range size in the vast western inland remained relatively small, and indicated a slight increase toward the west (Fig. 3).

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Figure 3. Geographical pattern of mean latitudinal range size of terrestrial mammals in China, resolved to 100 km×100 km.

The color gradient represents the mean latitudinal range extent in each grid cell.

https://doi.org/10.1371/journal.pone.0027975.g003

Impact of the MDE on mean range size pattern

Our results indicated an obvious and important impact of MDE in shaping the latitudinal gradient of range size. The Monte Carlo simulations (null model) indicated a hump-shaped range distribution of size variation (R² = 0.971, p <0.0001; Fig. 4). The highest mean range size (nearly 15°) emerged among the mid-latitudes (25° N–35° N), whereas the smallest range was located near the northern (smaller than 5°) and southern (nearly 8°) borders of China (Fig. 4). The MDE revealed a similar gradient to the mid-point method, but with a gentler slope (Fig. 4). The linear regression (β = 0.623, p = 0.005, R² = 0.802) revealed that the null model explained 80.2% of the range size variation.

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Figure 4. Simulated mean latitudinal range size in each 5° band from 10000 Monte Carlo simulation runs (black points, using mid-point method).

The black (y = −24.566+2.409x–0.037x², R² = 0.971, p <0.0001) and dotted lines show the 2nd order polynomial fits of the predicted and empirical mean latitudinal range sizes respectively.

https://doi.org/10.1371/journal.pone.0027975.g004

Impacts of environmental factors on mean range size pattern

The relationships of environmental variables and latitude indicated that mean climate condition, ambient energy and topography decreased with increasing latitude, but climate variability was positively correlated with latitude (Table 1). AMT (r_l = −0.831) and AP (r_l = −0.666) were strongly negatively related to latitude, whereas, TAR (r_l = 0.964) and TS (r_l = 0.957) were strongly positively related to latitude (Table 1). The residual variables had correlation coefficients of <0.6 (Table 1). Mean climate conditions and ambient energy were positively correlated with range size variation, while climate variability and topography were negatively correlated with range size variation (Table 1). The relationships between AP (r_m = 0.522) and NDVI (r_m = 0.453) with range size were strongly positive, whereas, the residual coefficients of those relationships were <0.4 (Table 1).

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Table 1. Pearson's correlations of environmental factors with mean range size (r_m) and latitude (r_l).

https://doi.org/10.1371/journal.pone.0027975.t001

The environmental factors were not deterministic of range size, but contributed moderately to the observed range size gradient, in that the GLMs explained only limited variation (R² <0.30, Table 2). The explanatory power of the mean climate conditions to range size was 27.7%, and AP accounted for 27.1% of the variation in range size. Climate variability and ambient energy explained 28.7% and 21.7% of that variation, while, TS and NDVI explained 18.6% and 20.5% respectively. Topography had the lowest contribution, with ALT accounting for only 9.2% of the variation in range size (Table 2).

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Table 2. Stepwise generalized linear models (GLMs) between the four groups of environmental variables and mean species range sizes.

https://doi.org/10.1371/journal.pone.0027975.t002

Species latitudinal range size distributions

The distribution of latitudinal range size of terrestrial mammals in China was right skewed, with small ranges for the majority of species (Fig. 1(a)). Most species occupied medium sizes of ranges, and very few species enjoyed very broad or very limited ranges. This result is consistent with those identified among most animal assemblages [17], [53], [54]. The departure from a normal distribution (left skewed pattern, Fig. 1(b)) of logarithmic ranges also parallels that documented in previous studies of birds and mammals [17], [53]–[55]. Such a pattern may be caused by either an absence or excess of rare species in the database [23], [56], [57], along with range size limitations imposed by the limited dispersal abilities of species, precluding their migration to all major land masses >[17].

The effect of methodology on testing Rapoport's rule

The method used to test Rapoport's rule had a pronounced impact on the results obtained [18], [19], [58], [59]. The averaging of range sizes, in particular, moderates the difference in the magnitude of range size pattern [18]. Most studies have used one-dimensional statistical approaches based on scatter plots and correlation analyses between range sizes and latitudes across individual species, or directly map the mean range size over continents [17], [18], [20], [23].

In this study, the results obtained with Steven's method, Pagel's method and the cross-species method revealed significant overall positive trends, which support Rapoport's rule (Fig. 2). The mid-point method, however, suggested that the range size-latitude relationship was non-linear with a peak in range size at intermediate latitudes (Fig. 2). Similar gradients were reported in previous research on vascular plants of Taiwan and Mt. Shennongjia, China, which, like our study, contrasted the results of the same four methods [58], [59]. Gaston et al. (1998), Bhattarai & Vetaas (2006), Feng et al. (2006) and Hausdorf (2006) all reported that different methods could lead to variation in the results obtained [14], [19], [60], [61]. Such findings not only reveal complementary information on species range patterns, but reflect the sensitivity of such techniques to the different methods of reducing the original information to basic data for analyses [18], [25]. Steven's method is susceptible to problems of autocorrelation [27]. The mid-point and Pagel's methods are strongly influenced by the geometrical boundary, and can produce abnormal results when limited data are available in some latitudinal bins [8], [62]. The cross-species method is sensitive to the underlying species richness pattern [8], [58]. Where statistics are being used as an indicator of the relationship between latitude and species range size, it is important to take the impact of the methodology underlying that generation of that statistic into account [18].

The mid-point method provided results that corresponded most directly with those apparent from visual examination of the mean range size map, but did not support Rapoport's rule (Fig. 3). The map showed larger ranges in the mid-latitudes (25°N–40°N), especially in the eastern and southeastern parts of China. Range sizes in the tropics (sub-tropics) and boreal zones (north to 40°N) were much smaller.

Impact of the MDE on mean range size pattern

Colwell et al. (2004) argued that the mid-domain peaked pattern may occur in the absence of any contributing heterogeneity in underlying environmental factors [31] particularly where geometric constraints themselves act as barriers against species dispersal [63]. It has been suggested, however, that the MDE alone may not adequately account for this pattern, and thus, the integration of non-random factors would be required to explain variation in range size with changing latitude [3]. Geographic boundary effects and environmental, topographical and biological variations typically interact strongly, and the apparent explanatory power of the MDE may be an indirect product of the effects of climate, ambient energy or geographical complexity on species' distributions [3]. Considering the deviation of the empirical range size gradient from the null model proves valuable in disentangling the impacts of these factors [30]. Furthermore, as the MDE could change species' immigration/emigration mode in an area, it could also modify the range size pattern through the “Rapoport-rescue effect” [32].

The results of our study revealed a hump-shaped latitudinal range size gradient, and detected marked impacts of the MED (Fig. 4). Our results also supported the expectations of the null model, implying significant contributions of geometric constraints or geographic boundary effects. Our findings are in accord with those from previous research on flowering plants [64], the New World mammals [48], [65], [66], birds [67], [68], African vertebrates and insects [69] and marine species [70], [71]. By contrast, Bokma et al. (2001), Diniz-Filho et al. (2002), Hawkins & Diniz-Filho (2002), Sanders (2002) and Moreno et al. (2008) reported findings that were inconsistent with the MDE [15], [32], [72]–[74].

Impacts of environmental factors

Mean range size may be correlated with environmental variables. Climate and the variation therein have been reported to be deterministic of species range sizes [4], [21], [75], in that environmental variation sets the minimum tolerance range for a species, and the interaction between mean climatic conditions and variation generate the commonly observed pattern of increasing range size with increasing latitude [19], [21]. If mean climate condition and climate variability hypotheses operated, species occupying areas at higher latitudes would be subject to selection expanding their tolerances and range sizes, so as to allow survival in the face of greater environmental variation and at lower mean climatic condition [19], [33]. The results of research on both the continental and global scale involving plants, fish, birds and mammals support that contention [4], [8], [28], [54]. Ambient energy determines the baseline environmental capacity for species diversity, and greater heterogeneity in spatial and topographical habitat structure could permit finer subdivision of limiting resources and, hence, promote greater specialization of species [1], [76]. Thus, the ambient energy hypothesis could account for the co-existence of a greater number of species in equatorial regions, with presumably more frequent interaction among species, and thereby result in increasing range size with increasing latitude [77]–[79]. Topographical heterogeneity hypothesis predicts a negative relationship between topographical variation and range size. Studies on plants, invertebrates, fish, reptiles and birds provide data that conform to these species richness and distribution patterns [80]–[83].

In this study, climate, ambient energy and topography contributed minimally to the observed variation in range size, while AP, TS and NDVI accounted for substantial proportions of the observed variation (Table 1, Table 2). Our results did not support the mean climate condition, climate variability, ambient energy or the topographical heterogeneity hypotheses, in that all of these mechanistic hypotheses predict narrower range sizes at higher latitudes (Table 1, Table 2). That said, our findings may well be accounted for, at least in part, by the “Rapoport-rescue effect” [4], [55], [84]. If species at different latitudes have similar underlying dispersal abilities, species at lower latitudes may disperse outside what could be considered optimum habitat than species residing in areas at higher latitudes [4], [84]. This difference in range size expansion, which occurred as a result of dispersal, might account for latitudinal range size gradient we detected.