Rarity in the tropics: latitudinal gradients in distribution and abundance in Australian mammals

Authors

  • C. N. Johnson

    1. Department of Zoology and Tropical Ecology and Cooperative Research Centre for Tropical Rainforest Ecology and Management, James Cook University of North Queensland, Townsville, Queensland 4811, Australia
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Abstract

1. In many groups of species, range size and population density are positively correlated (the ‘distribution−abundance relationship’) and range size is positively correlated with latitude (‘Rapoport's Rule’). This study investigated these two relationships among Australian forest mammals, and also tested for the existence of a relationship between population density and latitude in the same fauna.

2. All three relationships were significant, with the distribution–abundance relationship the strongest pattern of the three, and Rapoport's Rule the weakest. Partial correlation analysis showed that: (i) range size and population density remained positively correlated when latitude was held constant; and (ii) population density and latitude remained positively correlated when range size was held constant; but (iii) latitude and range size were not significantly correlated when population density was held constant. For (i) and (ii), partial correlation did not reveal stronger relationships than were revealed by simple correlation. These results suggest that the distribution–abundance relationship is conditioned by latitude to produce small ranges and low population densities in the tropics, and that tropical species tend to have low population densities relative to range size.

3. Body mass accounted for little variation in population density, and for no variation in range size and latitudinal position. The small ranges and low population densities of tropical species were not related to a latitudinal gradient in species richness, which did not occur in this fauna.

4. The latitudinal gradient in population density held within widespread species as well as among species. The effect of Bergmann's Rule (the tendency for organisms in cool environments to be larger bodied than organisms in warm environments) meant that in some species, population energy use rose more steeply with latitude than did population density.

5. I argue that all three relationships might be due to a tendency for the foraging efficiency of animals to be lower in tropical than in temperate ecosystems, as a result of a lower concentration of nutrients in tropical ecosystems. For resource-limited species, foraging efficiency should influence both range size and population density. Differences in foraging efficiency may therefore produce the distribution−abundance relationship as well as latitudinal gradients in range size and population density.

Introduction

Geographic range and local abundance tend to be positively correlated among species. This effect (the ‘distribution–abundance relationship’) has been found in many different groups of species from a broad taxonomic and ecological range (Gaston 1996). It has attracted a great deal of theoretical interest because it suggests that some common process regulates both the geographical distribution and local abundance of species; despite much discussion, however, it is not yet clear what that process might be. Several hypotheses on the cause of the distribution–abundance relationship have been proposed, but as yet none of these has clear empirical support (Hanski, Kouki & Halkaa 1993; Lawton et al. 1994; Gaston et al. 1997). A second statistical generalization describes variation in range size of species: this is Rapoport's Rule, the tendency for range size to increase with latitude. Like the distribution–abundance relationship, Rapoport's Rule has been found in many different groups of species (for examples see Rapoport 1982; Stevens 1989; France 1992; Letcher & Harvey 1994; Taylor & Gotelli 1994; Ruggiero 1994; Blackburn & Gaston 1996a; Lyons & Willig 1997; Mourellle & Ezcurra 1997; but note counter-examples in Rohde, Heap & Heap 1993 and Roy, Jablonski & Valentine 1994). It too has attracted significant theoretical interest. Stevens (1989) argued that the Rapoport effect may cause the latitudinal gradient in species richness, but this has been disputed (Rohde et al. 1993). More generally, the existence of Rapoport's Rule implies systematic variation in the ecology of species with latitude but, again, although there are several hypotheses on the cause of the relationship (see Discussion), none has clear empirical support.

The general occurrence of the distribution–abundance relationship and Rapoport's Rule implies the existence of a third pattern: if species with small ranges have low population densities and if tropical species have small ranges, we might expect tropical species in general to have low population densities. This is a reasonable expectation, but whether it is true depends on how the variation in range size that is described by the distribution–abundance relationship overlaps with the variation described by Rapoport's Rule. If these two components of variation in range size are independent of one another, the existence of the first two correlations implies nothing about the correlation of local abundance with latitude. This question is relevant to the problem of identifying causes of the distribution–abundance relationship and Rapoport's Rule, because if the two relationships are statistically independent of one another this would imply that they have different causes. On the other hand, if the variation in range size described by Rapoport's Rule is also described by the distribution–abundance relationship, this would suggest that both relationships might have a common cause, such that the mechanism producing the correlation between distribution and abundance is conditioned by latitude to produce small ranges and low population densities at low latitudes.

At present, it is not clear whether the distribution–abundance relationship and Rapoport's Rule are independent of one another because, although both patterns have been widely examined, no study has yet investigated their joint effects in a single group of species, and theories on the cause of each one of the two relationships have been developed without reference to their potential in causing the other. Further, no study has yet tested for the existence of latitudinal gradients in abundance among species that are ecologically and phylogenetically comparable. This is in spite of the fact that there are grounds for expecting population densities to vary with latitude but no clear prediction on the direction the trend should take. One proposition is that the generally higher primary productivity of the tropics might allow tropical species to maintain higher population densities (Currie & Fritz 1993). On the other hand, the fact that species richness generally increases from the poles to the tropics might result in tropical species having lower population densities because available resources are divided among more species in the tropics (Rapoport 1982). Alternatively, the effects on population density of productivity and species richness might compensate exactly, so that population density remains constant with latitude.

In this study, I analysed the interrelationships among population density, range size and latitude in Australian non-volant forest mammals. This group is suitable for this analysis because it occurs over a wide span of latitudes, the ranges of all species are well documented, and ecological studies have produced reliable estimates of population density for many species. The fauna is ecologically and taxonomically diverse, resulting in wide variation between species in typical densities and range sizes, but phylogenetic relationships are well known so that the effects of phylogeny can be removed from ecological and geographical patterns. The study had three specific objectives. These were: first, to test for the occurrence of the distribution–abundance relationship and Rapoport's Rule in this fauna, while also showing whether population density varied with latitude; second, to show whether these patterns were independent of one another, using partial correlation analysis to test (for example) whether range size and latitude remained positively correlated when the distribution–abundance relationship was removed by holding population density constant; and third, to show how patterns in range size and population density related to latitudinal variation in species richness.

Methods

Study region and collection of data

The study region was defined as all wooded habitats (vegetation types 1, 5–9, 21, 23, 24, 26 and 28 in Bridgewater 1987) on mainland Australia east of 140° E. This comprises a continuous band of wooded habitat extending over a latitudinal range of 28° and having an average and near-constant width of about 5° of longitude. The study was restricted to this region to minimize longitudinal variation in habitat extent, and also to exclude major habitat barriers such as deserts. Also, data on population density are unavailable for most species in shrubland and grassland/ desert habitats, and for some of these species data on range size are probably incomplete.

Range sizes were measured from published distribution maps (Strahan 1995) as the number of degrees of latitude between the northern and southern limits for each species, except that where species had range disjunctions of more than 5° of latitude, the parts of the range were treated as separate units for analysis (in most cases where this was true the distinct populations have subspecific status). Latitudinal position was expressed as the mid-point of the northern and southern limits for each species (or subspecies/ population). For species with ranges that extend beyond wooded habitats, range size and position were measured only for the portion of the total range that overlapped wooded habitats. This adjustment affected only nine species. Because the objective of the analysis was to analyse interactions among range size, latitudinal position and population density, only species for which there were data on abundance as well as distribution were included in the data set. There were 69 such species (including four pairs of values representing northern and southern populations of the same species), out of a total of 100 that occurred in the study region. The list of references consulted in compiling this data base is too extensive to include here, but the entire data set and reference list is available on request.

Measures of local population density (N km−2) were compiled from published and unpublished ecological studies that used formal census techniques to estimate population density. I excluded studies that surveyed large areas without reference to the habitat preferences of the species being censused; such studies are likely to estimate crude rather than ecological densities. Studies of small mammals were excluded if they used trapping grids of less than 2 ha, to minimize the chance that trapping returns would be inflated by animals attracted from outside the grids. Also excluded were studies of populations on islands or enclosed in small reserves, as their densities are often extraordinarily high. Where several estimates of density were available for the same species I used the arithmetic mean value.

Individual energy expenditure was estimated for each species using separate published equations relating body mass to field metabolic rate in macropodoid marsupials, non-herbivorous marsupials and rodents (Nagy 1987; Green 1997); these relationships typically have r2 values of greater than 0·9. Population energy use was calculated as individual energy expenditure multiplied by population density, and expressed in units of kJ km−2 day−1. Data on body weights (average of male and female weights in grams) were compiled from Strahan (1995). Blackburn & Gaston (1996b), Smallwood & Schonewald (1996) and Smallwood, Jones & Schonewald (1996) have pointed out that in comparisons of population density among mammal species, size of study area is negatively related to measured population density and accounts for more variation in density than does body size. These authors argue that observed relationships between body size and population density are to a large extent artefactual, reflecting the tendency for populations of large mammals to be studied over areas much larger than those used to study small mammals. An effect of this kind could confound latitudinal comparisons of density if there is a tendency for scale of study to vary with latitude. For example, if the studies that produce estimates of population density in tropical regions tend to be broad-scale surveys, and if these are compared with studies in temperate regions that are more often focused on selected species in small areas of their preferred habitat, this may produce an artefactual correlation between population density and latitude. I tested for such an effect in a preliminary analysis that demonstrated a weak positive association of latitude with (log10)size of study area (F1,115 = 6·16, P < 0·05), when the association of body mass with scale of study was removed by multiple regression. This effect cannot account for the result that population density increased with latitude (see below).

Species richness was measured by counting the number of species present in grid squares measuring 1° latitude × 1·5° longitude, and taking the mean of these counts at each interval of latitude. This provides a measure of the mean density of species per grid cell at each latitude.

Data analysis

Relationships between variables were assessed using Pagel's version of Felsenstein's method of independent contrasts (Harvey & Pagel 1991; Pagel 1992) as implemented in the CAIC package (Purvis & Rambaut 1995). This method is designed to remove from ecological relationships the non-independence due to phylogenetic association. The phylogeny of Australian marsupials and rodents used for this analysis was compiled from the following partial phylogenies: relationships of marsupial families –Aplin & Archer (1987), Baverstock, Krieg & Birrell (1990); genera and subgenera of Dasyuridae –Archer (1982); species of SminthopsisArcher (1981), Baverstock, Adams & Archer (1984); genera of Perameloideae –Groves & Flannery (1990); species of IsoodonClose, Murray & Briscoe (1990); genera and species of Phalangeroideae –Flannery (1995); genera and species of Macropodoideae –Baverstock et al. (1989), Flannery (1989), Eldridge, Johnson & Close (1991); genera and subgenera of Muridae –Watts et al. (1992); species of Melomys –Baverstock et al. (1980), and species of Rattus –Baverstock, Adams & Watts (1986). In cases where more than one phylogeny for the same group was available there was usually clear agreement, so no major difficulties arose in reconciling phylogenies from different sources. The phylogeny is not reproduced here, but is available on request. A consistent set of measures of branch lengths was not available. CAIC allows for two assumptions on branch lengths when true branch lengths are unknown: all branch lengths may be set equal, or the ages of taxa may be assumed to be proportional to the number of species they contain. This analysis made the equal-branch-lengths assumption, as simulations suggest that it causes the least distortion (Purvis & Rambaut 1995).

All original variables (except latitudinal position) were log10-transformed for analysis.

Results

Relationships among latitudinal range, latitudinal position and population density

Population density and latitudinal range were positively correlated with one another, and both variables were positively correlated with latitudinal position (Fig. 1, respectively, r = 0·52, P < 0·0001; r = 0·44, P < 0·001; and r = 0·37, P < 0·01; 56 d_f. in each case). That is, the distribution–abundance relationship, the latitudinal gradient in abundance, and Rapoport's Rule were all significant in this sample of species, with the distribution–abundance relationship the strongest pattern of the three and Rapoport's Rule the weakest.

Figure 1.

Relationships among Australian forest mammals between: (a) range and population density (the distribution–abundance relationship), (b) range and latitudinal position (Rapoport's Rule), and (c) population density and latitudinal position. The axes show the values of phylogenetically independent contrasts in each variable. Each point represents the magnitude and direction of change in one variable associated with a change in the other variable, when two taxa are being compared. Range size is measured as log10 of the number of degrees of latitude between the northern and southern limits of each species; latitudinal position is taken as the midpoint of this range.

The independence of these three relationships was tested by using partial correlation to remove the influence on each relationship of the third variable (Table 1). When this was carried out the correlations between latitudinal range and population density (the distribution–abundance relationship) and between latitudinal position and population density remained significant though reduced in strength, but the correlation between latitudinal position and latitudinal range (Rapoport's Rule) lost significance.

Table 1.  Relationships between variables, when the effect of the third variable on each relationship has been removed by partial correlation. The data used to calculate these correlations were independent contrasts in the original variables named in the table
RelationshipPartial r (56 s_f.)
Latitudinal range vs. latitudinal
position (Rapoport's Rule)0·17, NS
Population density vs. latitudinal
range (distribution–abundance
relationship)0·43, P < 0·01
Latitudinal position vs. population
density0·32, P < 0·01

Population density and energy use within species

The latitudinal gradient in population density occurred within as well as among species. Thirteen species in the sample had ranges that extended over more than half of the latitudinal span examined in this study, and had been studied in both the northern and southern halves of the region. In these species, population densities tended to be higher in the south than in the north. In some of these species body size declines from south to north according to Bergmann's Rule (Yom-Tov 1986; Quinn et al. 1996), so that latitudinal differences in the rate of energy use by populations (population density multiplied by individual energy use, which is a function of body mass) were even greater than for density (Fig. 2). On average, tropical populations used about one order of magnitude less energy than did temperate populations of the same species.

Figure 2.

Ratios of mean population density (N km−2, stippled bars) and mean population energy use (kJ km−2 day−1, open bars) in the southern half of eastern Australia to the northern half for 13 widespread mammal species. The distribution of log10-transformed ratios differs significantly from zero, the null hypothesis of no difference, in each case (for density, mean = 0·70, t = 4·231, P < 0·01; for population energy use mean = 0·77, t = 4·81, P < 0·001). Species included are Macropus giganteus (Shaw 1790), M. robustus (Gould 1841), M. parryi (Bennett 1835), Petauroides volans (Kerr 1792), Petaurus australis (Shaw 1791), P. breviceps (Waterhouse 1839), Trichosurus vulpecula (Kerr 1792), Phascolarctos cinereus (Goldfuss 1817), Isoodon macrourus (Gould 1842), Antechinus stuartii (Macleay 1841), A. flavipes (Waterhouse 1838), Melomys cervinipes (Gould 1852) and Rattus fuscipes (Waterhouse 1839).

Other variables: body mass and species density

There were no significant correlations between independent contrasts in body mass and latitudinal range (r = 0·06, ns) or latitudinal position (r = 0·001, ns), and there was a negative correlation between body mass and population density (r = −0·26, P = 0·05). Partial correlation analyses of body mass with the three variables latitudinal position, latitudinal range and population density (that is, the correlation of body mass with each one of these three variables while the other two were held constant) produced similar results: body mass was not correlated with latitudinal range (r = 0·22, ns) or latitudinal position (r = 0·09, ns) but was significantly correlated with population density (r = −0·35, P < 0·01). Regression (by ordinary least squares) of population density on body mass produced an estimate of the slope of the relationship of −0·46 and a coefficient of determination of 0·07. Inclusion of body mass in a multiple regression model with latitudinal range and latitudinal position explained 48% of the variation in population density.

The relationship between body mass and population density among the original variables is shown in Fig. 3. The correlation between the two variables was highly significant (r = −0·57, P < 0·0001, 67 d_f.). There was no significant correlation between the original variables of body mass and latitudinal range (r = 0·13, P = 0·26, ns, 67 d_f.).

Figure 3.

Relationship among original variables between population density and body mass (r = −0·57, P < 0·0001; n = 69 species). By ordinary least squares regression: log10 density = 3·11–0·44 [log10 mass], F1,68 = 32·98, P < 0·0001, R2 = 0·33.

There was no clear trend for species density to decline with latitude in either marsupials or rodents or in marsupials and rodents combined (Fig. 4).

Figure 4.

Relationship between latitude and species density for rodents (dashed line), marsupials (full line) and rodents and marsupials combined (heavy line) in wooded habitats in eastern Australia. Each point shows the mean number of species in grid squares measuring 1° latitude × 1·5° longitude at each latitude.

Discussion

This study demonstrated the existence in Australian forest mammals of both the distribution–abundance relationship and Rapoport's Rule as well as their corollary, the latitudinal gradient in population density. The distribution–abundance relationship was the strongest of the three patterns, and Rapoport's Rule was the weakest. When latitude was held constant by partial correlation, the distribution–abundance relationship remained significant, but when population density was held constant Rapoport's Rule did not. This result shows that there was no latitudinal variation in range size additional to that described by the distribution–abundance relationship, and that the distribution–abundance relationship described a greater proportion of the total variation in range size than Rapoport's Rule. However, when range size was held constant there was still a weak correlation between latitude and density, suggesting that at low latitudes density tended to be low for any given range size. The first major conclusion of the study therefore was that tropical species were rare on two counts. They had small geographical ranges and low population densities; moreover, there population densities were low relative to their range sizes.

Smith, May & Harvey (1994) also looked for Rapoport's Rule among Australian mammals, but did not find it. There could be two reasons for this difference in conclusions. First, Smith et al. analysed patterns of range size over the whole of the Australian continent. This approach introduces potentially very large effects of habitat as well as latitude on range size. Most of inland Australia consists of arid and semi-arid habitats, with wooded and mesic habitats concentrated in the north and around the east coast. Therefore an analysis of geographical ranges over the whole continent will be influenced by the transition from deserts at high and mid-latitudes to tropical woodlands and rainforests at lower latitudes. To the extent that these major differences in habitat constrain mammal distributions they will obscure any clear expression of Rapoport's Rule. The area of deserts in central and southern Australia is large and it might be thought that this would produce an effect on range size in the same direction as Rapoport's Rule, but Australian deserts are very heterogeneous habitats and many species within them appear to have small ranges. Restricting the analysis to wooded habitats along the eastern coast of Australia avoided this problem because it defined a continuous band of habitat from the southern to the northern limits of the continent.

Secondly, Smith et al. (1994) analysed their data by plotting the latitudinal ranges of species against their mid-latitudinal positions. This approach may reveal a Rapoport effect when a large latitudinal range is analysed and when even the more widespread species occupy small proportions of this total range, but the Australian continent covers a latitudinal range of only 28° and a number of species extend over the whole of this range. Such widespread species inevitably fall into the middle of a latitudinal range/latitudinal position plot, and they obscure any tendency for range size to increase with latitude among less widespread species (Lyons & Willig 1997). Analysing the data using the method of independent contrasts reduces this effect because it asks, for all phylogenetically independent comparisons, whether more northerly taxa are also more or less widespread than more southerly taxa, and thus largely removes the influence on the relationship of absolute range position.

There are many other published examples of the distribution–abundance relationship and Rapoport's Rule, but I know of only one other study that has examined latitudinal differences in population density (Currie & Fritz 1993). That study differed from this one in that it included a very heterogeneous set of species and encompassed a very large latitudinal range, but it too found that tropical species tended to have relatively low abundance and energy use. It remains to be seen how general this result will be, but the generality of both the distribution–abundance relationship and Rapoport's Rule suggests that positive correlations between latitude and population density will also be found in many faunas.

Previous analyses of large-scale variation in abundance, and to a lesser extent range size, have been dominated by consideration of the effects of body size: population density usually declines with body size and range size usually increases (Peters 1983; Damuth 1987; Gaston & Blackburn 1996; Brown, Stevens & Kaufman 1996). In the present study, even though body mass varied by four orders of magnitude, there was no significant correlation between body mass and range size and the correlation between body mass and population density was weak.

The simplest interpretation of the correlation analysis presented in this paper is that the mechanism causing the distribution–abundance relationship was conditioned by latitude to produce small ranges and low densities at low latitudes. Had there been independent causes, for example, of the distribution–abundance relationship and Rapoport's Rule, we might have expected each to confound the other in a simple correlation analysis and partial correlation analysis would then have revealed stronger relationships, but this was not the case. This result suggests that it might be possible to understand all three patterns in terms of a common causal mechanism. Variation in niche breadth is a candidate for this common cause. Brown (1984) suggested that the distribution–abundance relationship arises because species with broad niches are both more abundant and widespread than species with narrow niches. Stevens (1989) argued that because species that live year-round at high latitudes experience extreme seasonal fluctuations in their environments they are selected to have broad niches, and their broad niches allow them to have large ranges; tropical species experience less seasonal variation and consequently have narrow niches and small ranges. Stevens’ hypothesis is a partial statement of Brown’s, and if both are correct the statistical redundancy of Rapoport's Rule is neatly explained: Rapoport's Rule is caused only by the variation in niche breadth due to latitudinal position, whereas the distribution–abundance relationship is caused by this variation as well as by a component due to differences in niche breadth among species at the same latitude. If niche breadth does increase with latitude, as proposed by Stevens, then Brown's hypothesis could also explain the correlation of population density with latitude. However, at present, empirical support for the niche breadth hypothesis is equivocal. Niche breadth is often not correlated with either local abundance or geographical range, even in groups where there are positive correlations between local abundance and range size (Hanski, Kouki & Halkaa 1993; Lawton et al. 1994; Gaston et al. 1997). The niche-breadth hypothesis may be difficult to test fully and there has probably been too little work carried out on it so far to justify its rejection as an explanation of either the distribution–abundance relationship or Rapport's Rule, but for the purposes of this discussion other models must be sought.

Hypotheses on the cause of the distribution–abundance relationship have recently been reviewed by Gaston et al. (1997) who identify several alternatives to Brown's niche-breadth hypothesis. Briefly, these are: (i) that observed correlations are artefacts of sampling bias, causing species that typically have low population densities to be inaccurately recorded as having small ranges (McArdle 1990; Wright 1991); (ii) that the relationship reflects an underlying pattern in the distribution of resources, with resources that are widespread also being locally abundant (Gaston 1994); (iii) that it is due to density-dependent habitat selection, such that species that achieve higher densities in favourable habitats are also found in a greater range of less-favourable habitats (O’Connor 1987); (iv) that it arises as a consequence of metapopulation dynamics, with high population density in occupied patches promoting both local persistence and the probability of colonization of empty patches (Hanski 1982; Hanski et al. 1993); and (v) that it arises as a result of the demographic parameters of different species varying roughly in parallel along common environmental gradients (Holt et al. 1997). An additional hypothesis discussed by Gaston et al. (1997), the ‘range position hypothesis’, is not relevant here as it addresses the patterning of distribution and abundance within the range, rather than variation in range size. Also, the suggestion that the significance of some published relationships may have been exaggerated owing to phylogenetic non-independence of species used in analysis does not apply here, as all correlations were based on phylogenetically independent contrasts.

Similarly, there are several hypotheses on the cause of Rapoport's Rule which do not invoke differences between species in niche breadth. These include that (i) the effect is due to the different climatic histories of tropical and temperate regions, which in particular may have triggered postglacial range extensions, and caused extinctions of narrowly distributed species during glaciations, in temperate but not tropical faunas (Rohde & Heap 1996; Lyons & Willig 1997); (ii) it is due to a more rapid pace of evolution in the tropics (Rohde 1992), resulting in more frequent bisecting of the ranges of tropical species by speciation events (Lyons & Willig 1997); (iii) it is caused by the latitudinal gradient in species richness, which produces compression of the ranges of tropical species as a result of a higher pressure of interspecific competition (Rapoport 1982); (iv) it reflects a tendency for the areas of habitats to increase away from the tropics (Pagel, May & Collie 1991; Lawton et al. 1994) and (v) it is an artefact due to sampling bias such that the ranges of species in highly species-rich (tropical) regions tend to be underestimated (Colwell & Hurtt 1994).

Only one hypothesis – systematic bias in the measurement of range size – appears on both of the lists given above. The ranges of forest mammals in eastern Australia are very well known, so it is probably safe to assume that systematic biases have not contributed to the patterns documented in this study. This leaves no model that can account for both the distribution–abundance relationship and Rapoport's Rule in the Australian mammal fauna. Moreover, none of the non-niche based proposals on the cause of Rapoport's Rule can readily be extended to predict a latitudinal gradient in population density. Thus, a higher rate of speciation in the tropics could result in smaller mean range sizes to the extent that daughter taxa do not invade one another's ranges, but this kind of process should not alter population densities within daughter taxa. Similarly, it is not clear how historical events that have allowed some species to expand their ranges at high latitudes would also have allowed those species to permanently increase their population densities; in any case, this hypothesis is unhelpful in the present context because glaciations at high latitudes have had much less influence on the distributions of faunas in Australia than in the northern hemisphere. There are more species of mammals in the northern half of Australia than in the southern half – this can be seen from the fact that northern species have smaller ranges but the extent of range overlap (species density) is roughly constant with latitude – and while it might be argued that competition at species borders maintains the smaller size of ranges at low latitudes, this cannot explain why population densities are also lower. Finally, the habitat area hypothesis addresses the distribution of habitat at very broad scales, and is probably irrelevant to population processes that determine population densities within habitats.

Similarly, it is not clear how the factors proposed as causes of the distribution–abundance relationship could be conditioned by latitude to produce smaller ranges and lower densities in the tropics. The direction of these latitudinal gradients is, in fact, counter-intuitive. Primary productivity generally increases towards the tropics (Begon et al. 1996) and a simple prediction would be that population densities and geographical ranges should increase with productivity when, as in this case, there is no countervailing increase in species density. I offer as an explanation for the direction of these gradients the following argument. The higher biomass production of the tropics may result in low concentrations of nutrients in soil and plant tissues, and this might reduce the availability of essential nutrients to consumers in tropical ecosystems. A lower concentration of nutrients would be expected if tropical ecosystems are not in general supplied with nutrients at a higher rate than temperate ecosystems: on average a similar input of nutrients must be distributed through a much higher primary biomass in the tropics, resulting in a lower density of nutrients per unit of primary biomass. In support of this, there is evidence that nitrogen concentrations in plant tissue tend to be lower in tropical than in temperate grasslands (Coupland 1979) and soil nutrient availability in the majority of tropical rainforest ecosystems is low (Sanchez 1989); additionally, the availability of nutrients in tropical savannas is reduced by losses due to frequent fires and low rates of decomposition during dry seasons, even though annual primary biomass production may be quite high (Archibold 1995).

If nutrient concentrations in primary biomass are generally lower in tropical than in temperate ecosystems, it follows that for animals exploiting any given foraging niche, food resources are effectively more sparsely distributed in the tropics. A detritivore or herbivore in a tropical ecosystem, for example, would need to process more material at a lower efficiency to gain the same intake of nutrients as an equivalent consumer in a temperate ecosystem. Such a reduction in the efficiency of foraging by tropical organisms would have two effects: population density would be lower, and the range of habitats (where habitats are differentiated by levels of available resources) that can be used would be less. A reduction in the range of habitats that can be used by a species would result in a reduction in the size of its geographical range. These effects would also apply to species at higher trophic levels, unless higher-level consumers in the tropics compensate for low densities of their prey species by consuming broader ranges of prey. Two studies provide examples of positive correlations between latitude and foraging efficiency within particular foraging niches: Minson & Wilson (1980) showed that tropical grasses have lower digestibilities to mammalian herbivores than temperate grasses, and Thiollay (1988) showed that small insectivorous birds have lower foraging success in tropical than in temperate ecosystems. A similar argument to the one presented here was used by Huston (1979) to suggest that population growth and the pace of succession should be lower in tropical than in temperate ecosystems.

The model presented above assumes no latitudinal variation in niche breadths of species, and it simultaneously explains not only the correlated gradients with latitude of range size and population density among species, but also the latitudinal gradient in population density within widespread species. This within-species gradient can be seen as a simple reflection of changes in the availability of nutrients with latitude, but it is not consistent with a niche-breadth model as that model does not explain why a wide-ranging species that has high population densities and (supposedly) occupies a broad niche at high latitudes should not also achieve high densities in the tropical parts of its range. This model also explains the greater strength of the distribution–abundance relationship compared with the other two relationships. If differences between species in foraging efficiency affect both population density and range size, then the distribution–abundance relationship will describe variation due to differences in the foraging adaptations of species independent of latitude as well as being conditioned by latitudinal gradients in nutrient availability. This line of argument is, however, not able to explain why population densities tend to be low relative to range sizes in the tropics. An effect like this could be due to some latitudinal variation in the steepness of the environmental gradients that limit distribution. If such gradients tend to be less steep in the tropics then tropical species would tend to have larger ranges for a given mean density and, conversely, lower densities for any given range size.

The results of this study can throw some light on two other issues – the cause of latitudinal gradients in species richness, and the extinction-proneness of tropical species. Stevens (1989) suggested that Rapoport's Rule provides part of the cause of latitudinal gradients in species richness. He argued that because the habitat requirements of tropical species are apparently more narrowly defined than those of temperate species, tropical species should be more likely to disperse into habitats that are unfavourable to them (assuming that the dispersal abilities of species do not vary with latitude). This would tend to elevate within-habitat species richness in the tropics. This process is clearly not at work in Australian mammals, as, although there is a Rapoport effect, there is no latitudinal gradient in species density. This observation, together with the converse demonstration by Rohde et al. (1993) that the latitudinal gradient in species richness occurs in faunas that do not display a Rapoport effect, casts doubt on the generality of the mechanism proposed by Stevens (1989).

Finally, theory suggests that local abundance and range size contribute independently to extinction risk. Species with low population densities should be more likely to suffer local extinctions due to demographic, environmental and genetic stochasticity, and species with small ranges should be especially vulnerable to extinctions due to changes in the distribution of habitat. An obvious effect of this independence would be to compound the vulnerability to extinction of tropical organisms. This is consistent with some evidence from the fossil record for a heightened extinction rate in tropical faunas (McKinney 1997).

Acknowledgements

I thank James Brown, Julian Caley, Andrew Cockburn, Bill Foley, David Green, Elsie Krebs, Sarah Legge, Rob Magrath and Penny Olsen for comments on previous versions of this paper. Much of the paper was written during a visit to the Division of Botany and Zoology at the Australian National University, and I thank Andrew Cockburn for providing facilities. I am grateful to Alison Payne for her help in compiling information on range sizes. For unpublished data on mammal densities I thank Scott Burnett, Andrew Dennis, Murray Evans, Alan Horsup, Stephen Jackson, Peter Jarman, Luke Leong, Roger Martin, Alistair Melzer, Graeme Newell, Karl Vernes, Paula Winkel and Andrew Woolnough. This work was partly supported by a grant from the Australian Research Council.

Received 11 June 1997; revisionaccepted 13 November 1997

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