Macroecological Analyses Research Articles

Grids versus regional species lists: are broad-scale patterns of species richness robust to the violation of constant grain size?

Where distribution maps do not exist ecologists often use regional species lists to examine geographic patterns of species richness, despite the fact that inconsistent grain sizes across areas may complicate interpretation of the results. We compare patterns of species richness of European butterflies and dragonflies using regional species lists (varying grain size) and regular grids (constant grain size). We asked if species lists give results comparable to the gridded data when used in simple macroecological analysis of environmental correlates of species richness. We generated two equal-area grids (220 × 220 km and 440 × 440 km) to map the richness gradients and model species richness as a function of actual evapotranspiration (AET) and range in elevation. Then we used species checklists of 33 administrative regions of unequal sizes to construct the same environmental models while accounting for differences in area. Analysis of butterfly checklist data produced comparable results to the analysis of gridded data. In contrast, dragonfly checklist data had a distorted spatial pattern and much weaker associations with environmental variables than the gridded data. The robustness of checklist data appears to be variable, even within a single geographical region, and may not generate patterns congruent with those found using equal-area grids.

Model selection and information theory in geographical ecology

ABSTRACTAim Although parameter estimates are not as affected by spatial autocorrelation as Type I errors, the change from classical null hypothesis significance testing to model selection under an information theoretic approach does not completely avoid problems caused by spatial autocorrelation. Here we briefly review the model selection approach based on the Akaike information criterion (AIC) and present a new routine for Spatial Analysis in Macroecology (SAM) software that helps establishing minimum adequate models in the presence of spatial autocorrelation.Innovation We illustrate how a model selection approach based on the AIC can be used in geographical data by modelling patterns of mammal species in South America represented in a grid system (n = 383) with 2° of resolution, as a function of five environmental explanatory variables, performing an exhaustive search of minimum adequate models considering three regression methods: non‐spatial ordinary least squares (OLS), spatial eigenvector mapping and the autoregressive (lagged‐response) model. The models selected by spatial methods included a smaller number of explanatory variables than the one selected by OLS, and minimum adequate models contain different explanatory variables, although model averaging revealed a similar rank of explanatory variables.Main conclusions We stress that the AIC is sensitive to the presence of spatial autocorrelation, generating unstable and overfitted minimum adequate models to describe macroecological data based on non‐spatial OLS regression. Alternative regression techniques provided different minimum adequate models and have different uncertainty levels. Despite this, the averaged model based on Akaike weights generates consistent and robust results across different methods and may be the best approach for understanding of macroecological patterns.

Towards an integrated computational tool for spatial analysis in macroecology and biogeography

ABSTRACTBecause most macroecological and biodiversity data are spatially autocorrelated, special tools for describing spatial structures and dealing with hypothesis testing are usually required. Unfortunately, most of these methods have not been available in a single statistical package. Consequently, using these tools is still a challenge for most ecologists and biogeographers. In this paper, we present sam (Spatial Analysis in Macroecology), a new, easy‐to‐use, freeware package for spatial analysis in macroecology and biogeography. Through an intuitive, fully graphical interface, this package allows the user to describe spatial patterns in variables and provides an explicit spatial framework for standard techniques of regression and correlation. Moran's I autocorrelation coefficient can be calculated based on a range of matrices describing spatial relationships, for original variables as well as for residuals of regression models, which can also include filtering components (obtained by standard trend surface analysis or by principal coordinates of neighbour matrices). sam also offers tools for correcting the number of degrees of freedom when calculating the significance of correlation coefficients. Explicit spatial modelling using several forms of autoregression and generalized least‐squares models are also available. We believe this new tool will provide researchers with the basic statistical tools to resolve autocorrelation problems and, simultaneously, to explore spatial components in macroecological and biogeographical data. Although the program was designed primarily for the applications in macroecology and biogeography, most of sam's statistical tools will be useful for all kinds of surface pattern spatial analysis. The program is freely available at http://www.ecoevol.ufg.br/sam (permanent URL at http://purl.oclc.org/sam/).

Assessing the fidelity of the fossil record by using marine bivalves

Taxa that fail to become incorporated into the fossil record can reveal much about the biases of this record and provide the information needed to correct such biases in empirical analyses of the history of life. Yet little is known about the characteristics of taxa missing from the fossil record. For the marine Bivalvia, which have become a model system for macroevolutionary and macroecological analysis in the fossil record, 308 of the 1,292 living genera and subgenera (herein termed "taxa") are not recorded as fossils. These missing taxa are not a random sample of the clade, but instead tend to have small body size, reactive shell structures, commensal or parasitic habit, deep-sea distribution, narrow geographic range, restriction to regions exposing few Neogene marine sediments, or recent date of formal taxonomic description in the neontological literature. Most missing taxa show two or more of these features and tend to be concentrated in particular families. When we exclude the smallest taxa (<1 cm) and deep-sea endemics, date of published description and geographic range become the strongest predictors of the missing taxa; other factors are statistically insignificant or have relatively small effects. These biases might influence a variety of analyses including the use of fossil data in support of phylogenetic analyses, molecular clock calibrations, and analyses of spatial and temporal dynamics of clades and biotas. Clade inventories such as these can be used to develop protocols that minimize the biases imposed by sampling and preservation.

Determinants of local abundance in a major radiation of Australian passerines (Aves: Meliphagoidea)

AbstractAim To identify the factors that contribute to variation in abundance (population density), and to investigate whether habitat breadth and diet breadth predict macroecological patterns in a suborder of passerine birds (Meliphagoidea).Location Australia (including Tasmania).Methods Mean abundance data were collated from site surveys of bird abundance (the Australian Bird Count); range size and latitudinal position data from published distribution maps; and body mass and diet breadth information from published accounts. A diversity index of habitats used (habitat breadth) was calculated from the bird census data. We used bivariate correlation and multiple regression techniques, employing two phylogenetic comparative methods: phylogenetic generalized least squares and independent contrasts.Results Body mass and latitude were the only strong predictors of abundance, with larger‐bodied and lower‐latitude species existing at lower densities. Together, however, body mass and latitude explained only 11.1% of the variation in mean abundance. Range size and habitat breadth were positively correlated, as were diet breadth and body mass. However, neither range size, nor habitat breadth and diet breadth, explained patterns in abundance either directly or indirectly.Main conclusions Levels of abundance (population density) in meliphagoid birds are most closely linked to body mass and latitudinal position, but not range size. As with many other macroecological analyses, we find little evidence for aspects of niche breadth having an effect on patterns of abundance. We hypothesize that evolutionary age may also have a determining effect on why species tend to be rarer (less abundant) in the tropics.

The significance of geographic range size for spatial diversity patterns in Neotropical palms

We examined the effect of range size in commonly applied macroecological analyses using continental distribution data for all 550 Neotropical palm species (Arecaceae) at varying grain sizes from 0.5° to 5°. First, we evaluated the relative contribution of range‐restricted and widespread species on the patterns of species richness and endemism. Second, we analysed the impact of range size on the predictive value of commonly used predictor variables. Species sequences were produced arranging species according to their range size in ascending, descending, and random order. Correlations between the cumulative species richness patterns of these sequences and environmental predictors were performed in order to analyse the effect of range size. Despite the high proportion of rare species, patterns of species richness were found to be dominated by a minority of widespread species (∼20%) which contained 80% of the spatial information. Climatic factors related to energy and water availability and productivity accounted for much of the spatial variation of species richness of widespread species. In contrast, species richness of range‐restricted species was to a larger extent determined by topographical complexity. However, this effect was much more difficult to detect due to a dominant influence of widespread species. Although the strength of different environmental predictors changed with spatial scale, the general patterns and trends proved to be relatively stabile at the examined grain sizes. Our results highlight the difficulties to approximate causal explanations for the occurrence of a majority of species and to distinguish between contemporary climatic factors and history.

The distribution–abundance (density) relationship: its form and causes in a tropical mammal order, Primates

AbstractAim Across a wide variety of organisms, taxa with high local densities (abundance) have large geographical ranges (distributions). We use primatology's detailed knowledge of its taxon to investigate the form and causes of the relationship in, unusually for macroecological analysis, a tropical taxon.Location Africa, Central and South America, Asia, Madagascar.Methods To investigate the form of the density–range relationship, we regressed local density on geographical range size, and also on female body mass, because in the Primates, density correlates strongly with mass. To investigate the biological causes of the relationship, we related (1) abundance (density × range size) and (2) residuals from the density–range regression lines to various measures of (i) resource use, (ii) reproductive rate and (iii) potential specialization. All data are from the literature. Analyses were done at the level of species (n = 140), genera (n = 60) and families/subfamilies (n = 17). We present various levels of results, including for all data, after omission of outlier data, after correction for phylogenetic dependence, and after Bonferroni correction of probabilities for multiple comparisons.Results Regarding the form of the relationship, Madagascar primates are clear outliers (high densities in small ranges). Among the remaining three realms, the relation of density to range is weak or non‐existent at the level of species and genera. However, it is strong, tight and linear at the level of families/subfamilies (r2 = 0.6, F1,10 = 19, P &lt; 0.01). Although among primates, density is very significantly related to mass, at no taxonomic level is range size related to body mass. Consequently, removing the effects of mass makes little to no difference to density–range results. Regarding the biology of the relationship, only traits indicative of specialization are associated with abundance (meaning numbers): rare taxa are more specialized than are abundant taxa. The association is largely via range size, not density. Across families, no traits correlate significantly with the density–range relationship, nor with deviations from it, despite the strength of the relationship at this taxonomic level.Main conclusions We suggest that in macroecology, analysis at taxonomic levels deeper than that of the relatively ephemeral species can be appropriate. We argue that the several purely methodological explanations for the positive density–range size relationship in primates can be rejected. Of the various biological hypotheses, those having to do with specialization–generalization seem the only applicable ones. The fact that the relationship is entirely via range size, not via density, means that while we might have a biology of range size, we do not yet have one of the density–geographical range relationship. It is probably time to search for multivariate explanations, rather than univariate ones. However, we can for the first time, for at least primates, suggest that any association of abundance or range size with specialization is via the number of different subtaxa, not the average degree of specialization of each subtaxon. The implication for conservation is obvious.

Sensitivity of macroecological patterns of South American parrots to differences in data sources

ABSTRACTA criticism of macroecological studies has been their extensive use of secondary data sources. In this note we evaluate how different data sources affect macroecological patterns for the parrots of South America. We mapped extents of parrot occurrence based on four sources of range maps. We compared basic statistics for geographical range size distribution (mean, variance and skew) and calculated correlations between geographical range size estimates and grid cell species richness estimates. Finally, results from multiple regression analyses of species richness against six environmental variables were also compared. We found that patterns were very robust to the data source, with only relatively slight quantitative differences. Our results reinforce the notion that patterns emerging from macroecological analyses are robust to variations in data sources and cannot be merely artefacts resulting from low data quality, notably poorly defined mapping and conflicting taxonomy.

The influence of spatial resolution on macroecological patterns of range size variation: a case study using parrots (Aves: Psittaciformes) of the world

AbstractAim To assess the extent to which the resolution at which geographical range sizes are measured influences macroecological patterns in this variable.Location Global.Methods Data on the geographical ranges of parrot species were digitized, and a Geographic Information System used to produce nine range size estimates for each species using different degrees of spatial resolution. The inter‐correlation of these estimates was then compared, together with their patterns of covariation with population size, body mass and migratory behaviour (across species and controlling for phylogeny), their pattern of phylogenetic correlation, and the frequency distributions of the different measures.Results Strong correlations exist among all nine range size measures across species, albeit that measures of similar spatial resolution are more strongly correlated. All measures show similar patterns of covariation with population size, body mass and migratory behaviour, and similar patterns of phylogenetic correlation. The skewness of frequency distributions increases towards zero as the resolution of the range size measure declines.Main conclusions The results of macroecological analyses are little affected by the resolution with which geographical range sizes are calculated, at least for the parrots of the world. Previously published studies based on crude measures of range size would be unlikely to have produced markedly different conclusions had they used more refined range size metrics.

Body size and area‐incidence relationships: is there a general pattern?

ABSTRACTAim This paper tests firstly for the existence of a general relationship between body size of terrestrial animals and their incidence across habitat patches of increasing size, and secondly for differences in this relationship between insects and vertebrates.Location The analysis was based on the occupancy pattern of 50 species from 15 different landscapes in a variety of ecosystems ranging from Central European grassland to Asian tropical forest.Methods The area‐occupancy relationship was described by incidence functions that were calculated using logistic regression. A correlation analysis between body size of the species and the patch area referring to the two given points of the incidence function was performed. In order to test for an effect of taxon (insects vs. vertebrates), an analysis of covariance was conducted.Results In all species, the incidence was found to increase with increasing patch area. The macroecological analysis showed a significant relationship between the incidence in habitat patches and the body size of terrestrial animals. The area requirement was found to increase linearly with increasing body size on a log‐log scale. This relationship did not differ significantly between insects and vertebrates.Conclusions The approach highlighted in this paper is to associate incidence functions with body size. The results suggest that body size is a general but rather rough predictor for the area requirements of animals. The relationship seems valid for a wide range of body sizes of terrestrial animals. However, further studies including isolation of habitats as well as additional species traits into the macroecological analysis of incidence functions are needed.

Detection of macro-ecological patterns in South American hummingbirds is affected by spatial scale.

Scale is widely recognized as a fundamental conceptual problem in biology, but the question of whether species-richness patterns vary with scale is often ignored in macro-ecological analyses, despite the increasing application of such data in international conservation programmes. We tested for scaling effects in species-richness gradients with spatially scaled data for 241 species of South American hummingbirds (Trochilidae). Analyses revealed that scale matters above and beyond the effect of quadrat area. Species richness was positively correlated with latitude and topographical relief at ten different spatial scales spanning two orders of magnitude (ca. 12,300 to ca. 1,225,000 km2). Surprisingly, when the influence of topography was removed, the conditional variation in species richness explained by latitude fell precipitously to insignificance at coarser spatial scales. The perception of macro-ecological pattern thus depends directly upon the scale of analysis. Although our results suggest there is no single correct scale for macro-ecological analyses, the averaging effect of quadrat sampling at coarser geographical scales obscures the fine structure of species-richness gradients and localized richness peaks, decreasing the power of statistical tests to discriminate the causal agents of regional richness gradients. Ideally, the scale of analysis should be varied systematically to provide the optimal resolution of macro-ecological pattern.

Reply from K.J. Gaston, T.M. Blackburn and J.I. Spicer

We are delighted that Cowlishaw and Hacker find our review of Rapoport's rule[1xGaston, K.J., Blackburn, T.M., and Spicer, J.I. Trends Ecol. Evol. 1998; 13: 70–74Abstract | Full Text | Full Text PDF | PubMed | Scopus (200)See all References][1]worthy of extension. In response, we would make two points.First, we agree that if one excludes analyses that do not account for problems of spatial and phylogenetic non-independence and analyses based on geographic range area, rather than latitudinal extent, then those that remain support Rapoport's rule. We also wholeheartedly support the argument, implicit in Cowlishaw and Hacker's observations, that it is desirable to perform statistically rigorous analyses. However, the fact that the most rigorous analyses conducted support Rapoport's rule should not be interpreted either as evidence that the rule may be a general one or as a basis for dismissing conclusions based on other less rigorous analyses. The effect of using geographic range area is, to some extent, ameliorated by the general high correlation between latitudinal and longitudinal extents[2xLutz, F.E. Am. Mus. Novitates. 1922; 5: 335–366See all References, 3xBrown, J.H. and Maurer, B.A. Science. 1989; 243: 1145–1150CrossRef | PubMedSee all References, 4xSee all References].Moreover, failing to account for spatial and phylogenetic non-independence actually biases analyses towards finding evidence for Rapoport's rule when it does not exist; both artificially inflate degrees of freedom, leading to a likelihood of spurious statistical significance. Thus, the observation that a high proportion of studies performed in this way do not support the rule is a conservative basis for rejecting the notion that it is a general one and, therefore, worthy of being termed a `rule' (with the significant caveat that studies of Rapoport's rule are highly biased with respect to taxon and biogeographic region). This seems to us a more compelling argument for rejecting the generality of Rapoport's rule than for accepting it on the basis of the three studies that Cowlishaw and Hacker find suitable.Second, and on a more general note (notwithstanding our comments above), we urge circumspection in the pursuit of ever more statistical rigour in analyses. The history of the study of Rapoport's rule has been one of increasing analytical complexity. Indeed, we note that none of the three studies that Cowlishaw and Hacker regard as acceptable, including their own[5xCowlishaw, G. and Hacker, J.E. Am. Nat. 1997; 150: 505–512CrossRef | PubMedSee all References][5](published after completion of our review), has accounted for the recently highlighted problems of boundedness[6xColwell, R.K. and Hurtt, G.C. Am. Nat. 1994; 144: 570–595CrossRef | Scopus (356)See all References][6], which may be subtle and need not necessitate that ranges abut continental limits[7xLyons, S.K. and Willig, M.R. Oikos. 1997; 79: 568–580CrossRefSee all References][7]. Although we applaud increased rigour, particularly because it can reveal the existence of artefactual patterns[8xBlackburn, T.M. and Gaston, K.J. Am. Nat. 1998; 151: 68–83CrossRef | PubMed | Scopus (124)See all References][8], we do worry that the continual pursuit of the `perfect' analysis may have two undesirable side effects.First, this pursuit may be given greater emphasis than is warranted by the general body of evidence for or against the existence of a particular macroecological pattern. To take one example, no empirical analysis of latitudinal gradients in species richness, of which we are aware, has ever accounted for the non-independence of data points. Technically, all published analyses are, therefore, statistically flawed and, as such, invalidated. However, no one would seriously doubt that the species richness of the vast majority of major taxonomic groups is higher towards lower latitudes.Second, this pursuit might result in enormous variation in how macroecological patterns are tested and reported, seriously constraining, and sometimes precluding, any possibilities for comparison and contrast of the results of different studies. In this vein, we would propose that, alongside more-rigorous analyses, some standard plots and statistics for macroecological analyses should be established and routinely reported.