NORTH AMERICAN DESERT RODENTS: A TEST OF THE MID …mccainc/PDFs/McCainJMAMM2003.pdf · American deserts based on climate and plant distributions, and the other was based on a com-bination

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Journal of Mammalogy, 84(3):967–980, 2003

NORTH AMERICAN DESERT RODENTS: A TEST OF THEMID-DOMAIN EFFECT IN SPECIES RICHNESS

CHRISTY M. MCCAIN*

Natural History Museum & Biodiversity Center and Department of Ecology & EvolutionaryBiology, Dyche Hall, 1345 Jayhawk Boulevard, University of Kansas,

Lawrence, KS 66045-7561, USA

Many biological theories have been proposed to explain latitudinal and elevational gradientsof species richness, but only recently have theories been proposed that suggest that thesepatterns may be due solely to geographic constraints. These null models predict mid-domainpeaks in species richness as a consequence of geometric patterns resulting from overlappingspecies ranges between 2 geographic boundaries. Desert rodents exhibit a marked mid-domain peak in species richness for boundaries defined by the latitudinal extent of NorthAmerican deserts (198N–458N). Empirical patterns are compared with predictions of 2 nullmodels: an analytical–stochastic model and the binomial model. Empirical species richnessoccurs almost entirely within 95% prediction curves of the analytical–stochastic model.Observed species richness is highly correlated with predictions of the binomial model (r2

5 93%) but does not generally occur within 95% confidence intervals, in part becauseempirical range-size distributions differ from predicted distributions. Other diversity theo-ries, species–area relationships, productivity gradients, latitudinal gradients, and Rapoport’srule are evaluated; none is consistent with empirical patterns. These results demonstratethat the mid-domain effect is a consequence of overlap of variably sized ranges within abounded region for both ecologically defined hard boundaries and boundaries determinedby the shape of the earth. The significant deviations from null-model predictions becomethe biological points of interest: skewed or localized (or both) pulses or depressions ofspecies richness. Deviations in the present analysis demonstrated a localized pulse in rich-ness caused by a local hard boundary, the Baja peninsula.

Key words: binomial null model, bounded ranges, desert rodents, mid-domain effect, RangeModel,species richness

MacArthur (1972:1) stated, ‘‘To do sci-ence is to search for repeated patterns, notsimply to accumulate facts.’’ MacArthur isone of many ecologists who have investi-gated patterns of species diversity, specifi-cally latitudinal and elevational gradients ofspecies richness (MacArthur 1965; Rosen-zweig 1995 and references therein). The lat-itudinal gradient, a negative relationship be-tween latitude and richness, with a peak inrichness at the equator, is a pattern that isevinced by many taxa throughout the

* Correspondent: [email protected]

world. Numerous theories have been pro-posed to account for the gradient (Colwelland Hurtt 1994; Kaufman 1995; Lees et al.1999; MacArthur 1965; Osman and Whit-latch 1978; Pagel et al. 1991; Pianka 1966;Rosenzweig 1992, 1995; Stevens 1989;Terborgh 1971; Willig and Lyons 1998;Wilson 1973). The less well-documentedelevational gradient of species richness canhave a mid-elevation peak in species rich-ness, and several biological theories exist toexplain this pattern (Colwell and Hurtt1994; Graham 1983; Heaney 2001; Patter-son et al. 1996; Rosenzweig 1992, 1995;

968 Vol. 84, No. 3JOURNAL OF MAMMALOGY

Sanchez-Cordero 2001; Stevens 1992). Themajority propose that the patterns resultfrom an underlying biological process, al-though no single theory has widespread ac-ceptance (Colwell and Hurtt 1994; Kauf-man 1995; Rosenzweig 1992).

Recently, several independently derivedmodels have emerged to explain these gra-dients based solely on geometric constraintson species ranges, without the incorporationof underlying biological mechanisms (Col-well and Hurtt 1994; Lees et al. 1999; Wil-lig and Lyons 1998). These null models arederived from the geometric pattern that re-sults from random range sizes and place-ments between the endpoints of 2 hardboundaries, a pattern termed the mid-do-main effect (Colwell and Lees 2000). Col-well and Lees (2000:72) defined the mid-domain effect as ‘‘the increasing overlap ofspecies ranges toward the centre of a sharedgeographic domain due to geometricboundary constraints in relation to the dis-tribution of species’ range sizes and mid-points.’’ Bounded range models assumethat all species considered in the analysisshare the same hard boundaries; therefore,all species’ ranges must be entirely withinthe bounded domain, and large ranges mustbe centered near the center of the domain.This results in increasing species richnesstoward the midpoint of the domain. An ex-ample of geographic boundaries limitingspecies ranges is that of terrestrial specieson an island where distinct limits to theranges are the edges of the island. Suchrange constraints can exist due to geograph-ic features, such as continental boundaries,elevational boundaries, or the perimeter ordepth of a body of water. Ecological rangeboundaries exist where species endemic toa specific ecological biome are constrainedby the biotic and abiotic distribution of thatecosystem. All proposed null models—thefully stochastic and analytical–stochasticmodels (Colwell and Hurtt 1994), the bi-nomial model (Willig and Lyons 1998), andthe probabilistic model (Lees et al. 1999)—predict a mid-domain effect in species rich-

ness due solely to geometric constraints, al-though each employs distinct mathematicalframeworks (Colwell and Lees 2000).

Null models suggest that underlying pat-terns in latitudinal and elevational gradientsof species richness are the result of geo-graphic boundaries such as coastlines andmountains (Colwell and Hurtt 1994). A di-versity peak at the equator and at middleelevations was documented before the nullmodels of mid-domain effect were pro-posed; therefore, additional empirical ex-amples of unknown species-richness pat-terns within bounded range limits need tobe examined to test the predictions of thesenull models. Two studies have confirmedthe mid-domain effect outside the contextof latitude or elevation. Pineda and Caswell(1998) examined bathymetric gradients, andLees et al. (1999) examined gradientsacross the island of Madagascar.

The North American desert biome hasrelatively distinct northern and southernecological boundaries (as well as east–westboundaries) that limit the ranges of desertendemics—198N–458N (Fig. 1; MacMahon1985). This ecological domain allows avaluable empirical test for null models ofspecies richness because the latitudinal pat-terns of species richness within the boundedregion have not been documented previous-ly and because the North American desertbiome includes taxonomic groups with nu-merous endemic desert taxa (e.g., Hetero-myidae). Herein, these desert endemicswere used in an empirical examination ofthe mid-domain effect. Null models predicta peak in species richness near the midpointof the geographic limits of North Americandeserts, although several other patterns ofspecies richness could be encountered. Forexample, if taxa were responding to envi-ronmental correlates of latitude, then spe-cies richness should increase toward lowerlatitudes, a pattern that has been shown forrodents in the New World (Kaufman 1995).Similarly, a uniform pattern could be en-countered where species richness was uni-

August 2003 MCCAIN—SPECIES RICHNESS OF DESERT RODENTS 969

FIG. 1.—The North American desert biomeincluding the Great Basin, Mojave, Sonoran, andChihuahuan deserts. The biome extends from458N to 198N (modified from MacMahon 1985).

FIG. 2.—A graphical representation of rangesize of each desert rodent compared with rangemidpoint and latitudinal range in the NorthAmerican desert biome. Solid circles representcontinental species and open circles, Baja pen-insular endemics. Horizontal lines are extent oflatitudinal range for each species, and trianglerepresents limits of possible range midpoint foreach range size.

formly distributed across the desert latitu-dinal gradient.

MATERIALS AND METHODS

An a priori delineation of North American de-serts between 198N and 458N was based on acombination of 2 maps by MacMahon (1985).One map depicts the classical ranges of NorthAmerican deserts based on climate and plantdistributions, and the other was based on a com-bination of climate and on distributions of floraand fauna. The most expansive delineationbased on these 2 maps was used in the presentanalysis (Fig. 1).

Thirty-seven rodent species endemic to NorthAmerican deserts (Appendix I) were used in anempirical examination of the latitudinal trends ofspecies richness. Desert endemism was definedas those species with the majority (.90%) oftheir range occurring within the a priori desertdelineation. The list of species and their rangeswas compiled by Anderson (1972), Baker(1956), Davis and Schmidly (1994), Durrant(1952), Findley et al. (1975), Hall (1981), Hoff-meister (1986), Ingles (1965), and Jameson andPeeters (1988). Taxonomy of Wilson and Reeder

(1993) was used to recognize species status. Thelatitudinal extent of the range of each specieswas calculated, producing 2 characteristics—thelatitudinal midpoint and latitudinal range (Fig.2). Species-richness curves were then calculatedby importing the empirical range sizes and mid-points into the computer program RangeModel(RangeModel: a Monte Carlo simulation tool forassessing geometric constraints on species rich-ness; http:/viceroy.eeb.uconn.edu/RangeModel).

Two groupings of the desert rodent endemicswere evaluated: all endemics within the conti-nental area of the North American deserts (n 537) and continental endemics excluding Baja en-demics (n 5 31). The 6 Baja endemics were ex-cluded from the 2nd grouping to remove possi-ble peninsular effects, which produce decreasingspecies richness toward the terminus of the pen-insula (Brown and Lomolino 1998). Taylor andRegal (1978) detected a peninsular effect in Bajafor various vertebrate groups including mam-mals and heteromyid rodents. Lawlor (1983) re-futed these patterns for mammals in general andbats in particular but found some evidence that


heteromyid rodents may show a peninsular ef-fect.

Empirical patterns of species richness werecompared with predictions of 2 null models—Colwell and Hurtt’s (1994) analytical–stochasticmodel and Willig and Lyons’ (1998) binomialmodel. Colwell and Hurtt (1994) created a groupof null models with different parameters; someare fully stochastic, whereas others are capableof simulations using empirical data sets (http:/viceroy.eeb.uconn.edu/RangeModel). The 2 ful-ly stochastic models, Models 2 and 3 of Colwelland Hurtt (1994), which correspond to the bi-variate uniform range model and the uniformrandom range midpoint and range-size modelsof the RangeModel program, are incapable ofusing empirical data. These models assume dif-ferent underlying distributions of range sizes andplacements of range midpoints; thus, all vari-ables except species number are predetermined.Model 2, the bivariate uniform model, is equiv-alent mathematically to the binomial model andMacArthur’s two-hit broken stick model (Col-well and Lees 2000). Therefore, the ensuing dis-cussion on the bivariate uniform model will beaddressed in accordance with the binomial mod-el. The uniform random models, 2 variations onModel 3, place 1st variable (either range size orrange midpoint) within the domain boundariesaccording to a uniform probability distributionand then randomly draw values for the 2nd var-iable from geometrically feasible values withinthe bounded domain. These Model 3 variationsare not used in the current analysis because em-pirical values cannot be incorporated.

Unlike Models 2 and 3, the 2 forms of Col-well’s analytical–stochastic model use empiricaldata from a system of interest, thus making theresults ‘‘conditional’’ on the imported variables.The analytical–stochastic models sample withreplacement from imported empirical (or hypo-thetical) data for 1 variable and then randomizethe placement of the other according to a mod-ified uniform distribution for feasible valueswithin 2 boundary endpoints to produce species-richness curves. The 1st analytical–stochasticmodel uses empirical range sizes and createsrandomized placements of midpoints betweenthe boundaries, whereas the 2nd form of themodel uses the empirical midpoint locations andcreates randomized range sizes constrained bythe domain limits. These were the simulationmodels used in the current analysis because ran-

domization using empirical data is better able toassess whether under random conditions, giveneither known range sizes or known range mid-points, a mid-domain effect occurs.

Empirical range sizes and midpoints of desertrodents were imported into RangeModel andwere used to generate 600 simulations for eachspecies group using random placement of em-pirical range sizes and again of empirical mid-points. Simulation results were then used to cre-ate 95% simulation prediction curves. The em-pirical species-richness data were then comparedwith the 95% simulation prediction curves to as-sess the accuracy of the null-model predictions.Random simulations were limited to 600 be-cause each successive set of 200 simulationsleads to minor changes in the 95% predictioncurves.

The binomial null model is based on the jointprobabilities of choosing 2 random points on anumber line between 0 and 1, such that the rangespans a sampling point, p, on the unit domain(Willig and Lyons 1998). The probability of arandomly chosen range spanning the samplingpoint is 2pq, where q 5 1 2 p. The resultingspecies-richness curve has a mid-domain effectwith the highest species richness at p 5 0.5, withthe predicted species richness being half the to-tal number of species in the analysis. This modelallows the calculation of standard deviations and95% confidence intervals using a corrected ver-sion of the formula presented by Willig and Ly-ons (1998, pers. comm.) as follows: var(2pqS)5 {2(S 2 1)/S3}{(3 2 2S)(1 2 2pq)2 1 2(S 22)(p3 1 q3) 1 (1 2 2pq)} from Nei (1975) andNei and Roychoudhury (1974), where S is thenumber of range termini or twice the number ofspecies in the analysis. Two standard deviationsmultiplied by species richness then give valuesto add and subtract from the predicted values todelineate approximate 95% confidence intervalsof the binomial model predictions. FollowingWillig and Lyons (1998), I also tested for a lin-ear association between richness and 2pq. Theempirical values of species richness at each lat-itudinal degree of the desert domain were re-gressed against 2pq, and r2 and 95% predictioncurves were calculated to show how well theempirical data conform to the null model.

The binomial null model predicts not only amid-domain effect but also an implicit distribu-tion of range sizes based on the joint probabilitydensity function of pairs of uniformly distributed


FIG. 3.—Empirical species-richness curves forNorth American desert rodent endemics plottedwith 95% simulation prediction curves fromRangeModel (http:/viceroy.eeb.uconn.edu/Range-Model) based on empirical range sizes. Curves forA) all species (n 5 37) and B) excluding Bajapeninsular endemics (n 5 31).

variables that delimit species’ latitudinal ranges.This implicit frequency distribution of range siz-es is a decreasing function from small to largeranges, thus implying that empirical species-richness patterns that fit the binomial null modelshould consist of many small-ranged species,few mid-ranged species, and very few large-ranged species. This was tested by comparingthe cumulative number of range sizes producedby the null model with the cumulative distribu-tion of range sizes in the empirical data using aKolmogorov–Smirnov goodness-of-fit test(MINITAB 1996). This requirement of a partic-ular distribution of range sizes is shared by Mac-Arthur’s two-hit broken stick model and the bi-variate uniform random model (Colwell andLees 2000) but not with the analytical–stochasticmodels. When the empirical distribution ofrange sizes differs from the underlying binomialmodel distribution (i.e., more larger-ranged spe-cies), the empirical species-richness curve willdiverge from the predicted curve.

Species richness frequently is correlated pos-itively with area (Rosenzweig 1995). The NorthAmerican desert biome does not have equal areathroughout its latitudinal extent. An estimate ofarea per latitudinal degree was calculated bydigitizing the desert boundaries into a geograph-ic information system using the latest version ofArcInfo 8.1 (ESRI 2001). The area estimateswere based on the Albers equal-area conic pro-jections using 248N and 418N as the standardparallels that support a north–south extent of upto 30–358 (258 extent for present analysis). Theeffect of area on the species-richness pattern wasassessed using regression analyses (MINITAB1996). Species richness was regressed against2pq alone, 2pq with area, and area alone. Ex-perimental lack-of-fit tests (MINITAB 1996)produced no evidence for curvilinearity (P .0.10) in regressions including 2pq with or with-out area.

RESULTS

Both species-richness curves showed astrong mid-domain effect (Fig. 3). The con-centration of small-ranged species endemicto the Baja Peninsula (n 5 6) created aslight skew in the peak of species richnessat 288N but otherwise was indistinguishablefrom the purely continental pattern. Thecontinental species-richness gradient also

had a marked mid-domain peak, with thehighest richness close to the center of thelatitudinal domain at about 328.

Six hundred RangeModel simulations us-ing the empirical range sizes for each spe-cies grouping and randomized placement ofmidpoints resulted in a mid-domain peak inspecies richness. A comparison of the em-pirical data with the 95% simulation pre-diction curves showed that the majority ofempirical points (116/120) occurred withinthe predicted range of the analytical–sto-chastic null model (Fig. 3). The 600RangeModel simulations with empiricalrange midpoints for each species groupingand randomized placement of range sizesalso resulted in a mid-domain peaks in spe-cies richness. Again, the majority of empir-ical points (119/120) occurred within the95% simulation prediction curves of the an-alytical–stochastic null model (Fig. 4).

Regressions of species richness per lati-


FIG. 4.—Empirical species-richness curves forNorth American desert rodent endemics plottedwith 95% simulation prediction curves fromRangeModel (http:/viceroy.eeb.uconn.edu/Range-Model) based on empirical range midpoints.Curves for A) all species (n 5 37) and B) exclud-ing Baja peninsular endemics (n 5 31).

FIG. 5.—Empirical species-richness curves forNorth American desert rodent endemics plottedwith 95% confidence interval from the binomialnull model (Willig and Lyons 1998). Curves forA) all species (n 5 37) and B) excluding Bajapeninsular endemics (n 5 31).

tudinal degree predicted by the binomialnull model (2pq) against empirical valuesresulted in high r2 values for both speciesgroupings: all desert rodent endemics, r2 50.88; species excluding Baja peninsular en-demics, r2 5 0.93. Even when all rodentspecies inhabiting the North American de-serts were included in the analyses (n 5 53,including 22 non-endemics), a strong mid-domain effect still was observed (r2 50.90). Regression analysis demonstratedhigh correlation between the observed andthe predicted species-richness values be-cause all empirical data occurred within the95% regression prediction curves (curvesbased solely on regression analysis). Theempirical distributions did not coincide,however, with the specific predicted valuesof species richness because 60% of the em-pirical data occurred outside the 95% con-fidence intervals based on the calculations

of variance, which include the restrictionsof underlying range distribution (Fig. 5).Observed species richness was higher thanpredicted by the binomial null model. Thiswas partially a result of the deviation of theempirical range-size distribution from thatpredicted by the binomial model. Althoughnot significantly different in cumulative de-viations (all species: P . 0.2; without Bajapeninsular endemics: P . 0.2), the desertspecies had fewer small ranges and moreintermediate and large range sizes than pre-dicted (Fig. 6). The small increase in num-bers of species with larger-range sizes leadsto the peak in species richness deviatingfrom the predicted value of n/2.

The area estimates for each degree of lat-itude were not equal for all the latitudinalbands within North American deserts (Fig.7A) or for the distribution excluding Baja(Fig. 7B). The greatest area occurred wherethe Sonoran and Chihuahuan deserts over-lapped between 298N and 338N, with a low-


FIG. 6.—Probability density functions forrange sizes of the binomial model comparedwith empirical distribution of range size forNorth American desert rodents. Probability den-sity function (gray) and empirical range sizes(black) for (upper) all rodent endemics and(lower) excluding Baja peninsular endemics.

FIG. 7.—Comparison between species-rich-ness curves of desert rodents and area associatedwith each degree of latitude for geographicaldistribution of North American deserts. Area andrichness of species for A) all deserts and B) de-serts excluding Baja peninsula.

er peak in area within the Great Basin De-sert (398N–428N). Plots of latitude versusarea had 2 peaks, whereas curves of speciesrichness showed a single peak (Fig. 7). Theregressions using 2pq alone to predict spe-cies richness had r2 values identical to val-ues of regressions including both 2pq andarea (all species, 0.88 and 0.88; and speciesexcluding Baja endemics, 0.93 and 0.93).The regression using area alone to predictspecies richness resulted in much lower r2

values (all species, 0.47; and species ex-cluding Baja endemics, 0.37).

DISCUSSION

Evaluation of null models supported theconclusion that the pattern of species rich-ness for North American desert rodent en-demics was a consequence of geometric

constraints within a bounded environmentaldomain. A comparison of the predictionsand deviations based on the 2 null modelstested illustrated the differences betweenand strengths of the 2 models.

RangeModel null model.—Empirical pat-terns of species richness agree closely withpredictions of analytical–stochastic modelsconstrained by empirical range sizes or em-pirical range midpoints, with only 5 out of240 data points occurring outside the 95%prediction limits (Figs. 3 and 4). All 5 out-liers were associated with the curve that in-cluded the Baja peninsular endemics. Therange midpoint simulations producedslightly lower richness than predicted to-ward the extreme limits of the desert lati-tudinal extent, and the range-size simula-tions showed slightly higher than expectedrichness at 288N. The peninsular effectcould bias data sets that included peninsularspecies by creating an exaggerated decrease


in species richness along the extent of thepeninsula. Therefore, species-richnesscurves including peninsular endemics maydeviate from null-model predictions at thesouthern extent of the peninsula. This wasnot the case in empirical analysis. The de-viations of lower richness were outside theextent of the peninsula.

The influence of peninsular endemicswas to shift the peak in richness toward thesouth because the Baja endemics were allclustered within a small extent of the desertdistribution. This is the likely reason for aslight deviation of higher than expectedrichness at 288N and slightly lower than ex-pected toward the extremes of the distri-bution. In a comparison of the 2 simulationsets, this reasoning becomes apparent be-cause the simulations using observed rangesizes with random midpoint placement didnot predict a cluster of species but a moreeven dispersion within the desert domain,whereas the simulations using empiricalmidpoint distributions, with the cluster ofpeninsular midpoints, predicted higher rich-ness slightly south of the center. The lackof a peninsular effect for the desert endem-ics confirms the suspicions of Lawlor(1983) that the suggestion there is a pen-insular effect in rodents is unfounded andthat only weak patterns exist for heteromyidrodents. A more accurate description ofBaja peninsula is that of a local hard bound-ary at the southern end of the peninsula. Insuch cases, a smaller, localized mid-domainpeak would be expected toward the centerof the local domain, which may create puls-es of higher richness in a broader diversitypattern. The local hard boundary at thesouthern end of Baja leads to more Bajaendemics overlapping toward the center ofBaja, thus creating a localized pulse in rich-ness, which led to the deviations from pre-dictions across the entire desert domain.

In this analysis, a priori knowledge of thepeninsular effect allowed explicit evalua-tion of the factor. Analyses of patterns ofspecies richness in less intensely investi-gated regions might identify such unusual

patterns as significant deviations from pre-dictions of the null model. Recognition oflocal hard boundaries within broader do-mains may clarify localized pulses in rich-ness that appear in the analysis as devia-tions. A comparison of the simulations sep-arately constrained by observed range sizesand observed range midpoints enables amore comprehensive evaluation of possiblecauses of divergent patterns than would useof models not constrained in such a manner(i.e., binomial model).

Binomial null model.—The binomialmodel serves as a null model for the mid-domain effect, as does the analytical–sto-chastic model of Colwell and Hurtt (1994),but the binomial has more specific predic-tions about the range-size distribution. Thegeneralized mid-domain effect predicts theshape of the richness gradient between 2distinct domain boundaries. It predicts peakrichness at the center of the domain, withspecies richness decreasing toward the lim-its of the domain, but it does not assumeany specific distribution of range sizes orany specific species-richness values. Alldistributions of variable range sizes canproduce mid-domain effects but of differentmagnitude of curvature. A distribution ofvariable small range sizes placed randomly,but in a uniform distribution across the do-main, will create a mid-domain peak witha flat and low curvature. A distribution ofvariable large and intermediate range sizeswill produce a steep curve in species rich-ness, with a distinct peak. Colwell’s modelsallow the testing for these different distri-butions of range sizes through simple dum-my data sets imported into his RangeModelprogram.

Using confidence intervals from the var-iance calculation of 2pq (Willig and Lyons1998) tests not only for a mid-domain ef-fect but also for a specific number of spe-cies at that peak and elsewhere (Rpredicted 52pqRtotal; R 5 species richness; i.e., peakspecies richness 5 Rtotal/2). The strict formof the model assumes a triangular distri-bution of range sizes (Fig. 6), such that the


majority of range sizes are small, few areintermediate, and very few are large. Sucha distribution of range sizes between the 2range constraints creates a mid-domain spe-cies-richness curve of a standardized lowcurvature, constraining the peak to be halfthe total species richness. The more largeand intermediate range sizes in the distri-bution, the greater the overlap of ranges to-ward the center of the domain, leading to ahigher peak and a more pronounced cur-vature to the species-richness pattern. Thisrelationship between range sizes and curveshape is demonstrated clearly by both Col-well and Hurtt (1994) and Colwell and Lees(2000).

Therefore, empirical species-richnesspatterns may be completely congruent withthe null-model predictions based on thegeometric effects of bounded ranges butmay not fall within the confidence intervalsof the binomial model if the empirical dis-tribution of range sizes includes more in-termediate or large-sized ranges than theunderlying distribution of the binomialmodel. This was the case with the desertrodent species-richness pattern (as well asthe species-richness patterns for bats ofWillig and Lyons 1998) because all indi-cations supported the mid-domain effect,whereas the 95% confidence intervals wereconsistently lower than the empiricalcurves. The distribution of range sizes fordesert rodent endemics included more (butnot significantly more) intermediate to largerange sizes than predicted by the binomialdistribution, resulting in more than half thespecies being present at mid-domain. Byoverlaying the 95% simulation predictioncurves of the RangeModel and the predict-ed curve and associated 95% confidencecurves of the binomial model, it is apparentthat the binomial species-richness predic-tions are low because the binomial predic-tion curve corresponds closely with thelower 95% simulation prediction curve ofRangeModel. Additionally, half the pointsof the lower-binomial 95% confidence

curve were outside RangeModel predic-tions.

According to range-size theory, manydistributions of range sizes are stronglyright-skewed and generally follow a log-normal distribution, although few empiricalcases have been tested for fit to a log-nor-mal distribution. Of those that have, manydeviate significantly from this distribution(Gaston 1996). The binomial model as-sumes a triangular distribution of range siz-es—a linearly decreasing function of siz-es—although this is not a frequently citeddistribution (Gaston 1996). Because therange-size distribution has received rela-tively little investigation and because theuniversality of a single range-size distribu-tion among variously sized groups of taxahas yet to be shown, the assumption of thetriangular range-size distribution of the bi-nomial model cannot yet be verified.

Biological theories.—Several biologicaltheories have been proposed that also couldproduce peaks in species richness within arange domain, namely the species–area re-lationship, latitudinal gradients, productivi-ty gradients, Rapoport’s rule, habitat com-plexity, and inadequate sampling. As statedearlier, the species–area relationship is apattern of increasing species richness withincreasing area (Lees et al. 1999; Rosen-zweig 1992, 1995; Willig and Lyons 1998).This pattern could produce a mid-domainpeak in species richness if the greatest areawere found toward the center of the distri-bution and tapers to the extremes. In NorthAmerican deserts, the area effect was smalland insignificant. Therefore, the species–area relationship or longitude (Bokma andMonkkonen 2000; Bokma et al. 2001) can-not be the primary underlying cause of thedesert rodent species-richness pattern.

With respect to the latitudinal species-richness gradient, the desert species-rich-ness pattern clearly does not follow a trendtoward increasing richness with decreasinglatitude because the lowest species richnesswas at the southernmost latitudes. Kaufman(1995) examined the latitudinal gradients of


FIG. 8.—Range of estimates of primary pro-ductivity (g m22 year21) for each desert withinthe North American desert ecosystem comparedwith species richness of desert rodent endemics(data from Waide et al. 1999 and referencestherein). Extent of each desert shown with hor-izontal bars. Range of productivity estimatesshown with vertical bars (with only a single es-timate for the Great Basin).

mammals by taxonomic orders, and thetrend for all mammals was a strong peak inspecies richness at the equator. The patternfor rodents was an irregular hump-shapedcurve with a general trend toward higherspecies richness near the equator but withseveral peaks and valleys between 458N and458S (Fig. 5; Kaufman 1995). Between198N and 458N, her curve for rodents isconcave, with the lowest local diversity atabout 308. This is opposite of the patterndemonstrated in this study for the desert ro-dents at these latitudes, further indicatingthat the desert pattern is divergent from theoverall rodent diversity gradient.

Productivity gradients frequently showhump-shaped relationships with speciesrichness, with peaks in richness at inter-mediate productivity levels along a gradientfrom low to high productivity (Mittelbachet al. 2001; Rosenzweig 1992, 1995; Waideet al. 1999), although other studies showtrends of increasing or decreasing speciesdiversity with increasing productivity(Brown 1975; Mittelbach et al. 2001; Ro-senzweig 1992, 1995; Waide et al. 1999).For deserts, productivity is relatively low,ranging from 0 to 600 g m22 year21 but hasbeen shown to be highly variable spatiallyand temporally (Brown 1975; Waide et al.1999). According to Waide et al. (1999), therelationship in arid ecosystems has not beeninvestigated specifically, but they did note2 general trends of particular value. Theyfound that, for large-scale patterns amongdeserts across the world, those deserts withlow to zero productivity have low speciesrichness for various groups of taxa, whereasthose with relatively high productivity havehigh species richness. However, at smallerscales, i.e., deserts within the same region,they did not find increased species richnesswith productivity (Fig. 8; Waide et al.1999). In North America for instance, theMojave Desert has the lowest productivitybut high species richness, whereas the Chi-huahuan Desert has the highest productivityestimates but lower richness. If productivitywere the primary underlying cause of the

mid-domain peak in species richness in theNorth American deserts, then the predictionwould be that either there is highest rich-ness at intermediate productivity levels orthere is highest richness at high productiv-ity levels. Neither of these cases is sup-ported with the present productivity esti-mates available on the regional scale. Pro-ductivity–diversity trends appear to bestrongly scale dependent (Mittelbach et al.2001; Scheiner et al. 2000; Waide et al.1999), and therefore productivity–diversitypatterns at local scales may show divergentpatterns from the regional scale studiedhere.

Rapoport’s rule, the tendency for meansizes of species ranges to decrease towardthe equator and toward mid-elevations, pre-dicts that as species richness increasesrange sizes decrease (Stevens 1989, 1992).Recently, Rapoport’s rule has caused a flur-ry of investigative effort applied to under-standing species-richness gradients, includ-ing a test of the universality of the pattern(Lyons and Willig 1997) and theoretical


modeling (Colwell and Hurtt 1994; Taylorand Gaines 1999). These studies suggestthat the universality and robustness of Ra-poport’s rule are questionable. Similarly,Rapoport’s rule was not corroborated in thepresent analysis because small range sizeswere not clustered toward the area of high-est species richness (Fig. 2).

Inadequate sampling has been shown toaffect richness trends (Colwell and Hurtt1994; Lees et al. 1999), although this mostoften is the case for tropical regions wherespecies are not well documented and rangesmay be far from accurate. In this case, themajority of species used in the study havebeen known since the beginning of the1900s, and most have well-known ranges(Hall 1981). Thus, none of inadequate sam-pling, area, latitudinal species gradient, pro-ductivity, and Rapoport’s rule appears toexplain the unimodal pattern of speciesrichness observed for desert rodents.

Some authors assert that latitudinal, ele-vational, and even desert mid-domain peaksin species richness are the result of in-creased habitat complexity (MacArthur1964; Pianka 1966). If habitat complexityis the result of higher diversity of plants andplant forms, and plant diversity is also high-est at mid-domain, that pattern may just bea coincident mid-domain species-richnesspeak for plant endemics bounded by thesame geographic or ecological boundariesas the animal kingdom. Thus, an interestingprediction of the mid-domain effect is thatpatterns of habitat complexity or plant spe-cies richness also would reflect geometricconstraints. Of course, habitat complexityalso may involve relationships with climaticvariables and be intertwined with produc-tivity hypotheses. To understand the ex-planatory power of these hypotheses, de-tailed empirical analyses are needed.

It has been suggested that the mid-do-main null model limits analyses to endem-ics within the boundaries of specified limitsand has biased the results by not includingnon-endemics, generalists of the same taxaalso present within the same region (R.

Holt, and J. Brown, pers. comm.). Somecritics argue that the mid-domain effectmay be a result of this culling of the dataset and predict divergent patterns of speciesrichness in analyses that include all speciesinhabiting the region. But when all rodentspecies inhabiting the North American de-serts were included in the analyses (n 5 53,including 22 non-endemics), a strong mid-domain effect still was observed (r2 50.90). Because non-endemic species tend tobe generalists, they have larger ranges thatencompass more of the extent of the do-main, which leads to a similarly shaped, butelevated, species richness curve with in-creased richness throughout the curve butparticularly pronounced toward the centerof the domain. Thus, adding non-endemicsto the analysis does not lead to divergentpatterns from the predictions of the nullmodels.

The mid-domain effect.—The mid-do-main effect is an unavoidable consequenceof bounded ranges of variable sizes. This istrue for bounded latitudinal ranges as wellas for longitudinal or 3-dimensional ranges.As in any null model, it is the basis withwhich novel species-richness patternsshould be compared. Significant deviationsfrom the null model could then be biolog-ically interesting patterns and indicate theneed for analysis of such factors as distri-bution of abiotic resources, competition,evolutionary history, ecological history,and biome shifts.

Empirical diversity patterns that conformto predictions of the mid-domain effectbased on randomizations of the empiricalrange sizes and midpoints do not signifythat the diversity pattern is random. Theempirical pattern consists of a distributionof species with different-sized overlappingranges within limited boundaries that resultin the mid-domain peak in species richness.Any random grouping of species with var-iably sized ranges within boundaries willshow a mid-domain peak. The biologicalrequirements and evolutionary history ofeach species have determined its range size


and location within the bounded range ofthe North American deserts. The partition-ing of the desert domain by each speciesand reasons for individual range distribu-tions are biologically interesting on a finercommunity scale. Osman and Whitlatch(1978:52) addressed this general issue, thatdiversity patterns ‘‘can exist regardless ofany assumptions concerning the importanceof competition, predation, species packing,niche characteristics, species ability toadapt, etc. Certainly, processes such ascompetition and predation may be impor-tant in determining the co-occurrence ofparticular suites of species. . . , but a diver-sity pattern could have resulted independentof these.’’ Therefore, in the scope of themid-domain effect, the diversity patternmay be a result of geometric boundaries,but species diversity in patches of the do-main (alpha diversity) may be controlled byvery different phenomena that are predom-inately biological.

RESUMEN

Se han propuesto numerosas teorıas paraexplicar el gradiente latitudinal y altitudinalde la riqueza de especies. Teorıas recientessugieren que estos patrones pueden deberseunicamente a limitaciones geograficas. Es-tos modelos nulos predicen picos de dom-inio medio en la riqueza de especies, comoconsecuencia de los patrones geometricosresultantes del solapamiento en el rango delas especies entre dos lımites geograficas.Los roedores de los desiertos exhiben unpico de dominio medio en riqueza de es-pecies en los lımites definidos por la exten-cion latitudinal de los desiertos norteamer-icanos (198N a 458N). Los patrones empır-icos se comparan con las predicciones de 2modelos nulos: un modelo analıtico-esto-castico y el modelo binomial. La mayorıade la riqueza de especies empırica se ob-serva dentro del 95% de las curvas de pred-iccion del modelo analıtico-estocastico. Lariqueza de especies observada esta alta-mente correlacionada con las prediccionesdel modelo binomial (r2 5 93%) pero ge-

neralmente no esta incluida en los interva-los de confianza de 95%; esto se debe, enparte, a que el tomano del rango de distri-bucion empırica es diferente al de las dis-tribuciones predichas. Otras teorıas de di-versidad, relaciones especies–area, gradien-tes de productividad, gradientes latitudina-les y Regla de Rapoport, son evaluadas;ninguna de estas es consistente con los pa-trones empıricos. Estos resultados demues-tran que el efecto de dominio medio es unaconsecuencia del solapamiento de rangos detomano variable en un region restringidapor fuertes lımites definidos ecologica-mente ası como lımites definidos por la to-pografıa de la tierra. Las desviaciones sig-nificativas de las predicciones del modelonulo son los puntos de interes biologico:pulsos sesgados y/o localizados o dismi-nucion de la riqueza de especies. Las des-viaciones en el presente analisis demostra-ron un pulso localizado en riqueza causadopor un fuerte lımite local, la Peninsula deBaja California.

ACKNOWLEDGMENTS

I am indebted to D. McClearn and the Orga-nization for Tropical Studies for giving me theopportunity to hear R. K. Colwell explain hisbounded range model and RangeModel soft-ware. T. E. Lawlor originally sparked my interestin biogeographic patterns in his mammalogycourse years ago, and C. Raxworthy urged meto further examine the trends found herein. I alsothank all who provided editorial suggestions onthe manuscript: R. P. Anderson, T. E. Lawlor, N.A. Slade, R. M. Timm, M. R. Willig, an anon-ymous reviewer, the mammal seminar group atthe University of Kansas, and the reviewers onthe Student Honoraria board of the AmericanSociety of Mammalogists for their valuable sug-gestions. I would especially like to thank N. A.Slade and J. Kelly for statistical assistance andR. Colwell for additional clarification ofRangeModel programs.

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Submitted 19 February 2002. Accepted 25 November2002.

Associate Editor was John G. Kie.

APPENDIX I

Rodent species endemic to North Americandeserts including desert affiliation (GB 5 GreatBasin Desert, M 5 Mojave Desert, S 5 SonoranDesert, C 5 Chihuahuan Desert) and latitudinalrange limits (degrees and minutes N). Species

endemic to the Baja Peninsula indicated by Bajain parentheses after latitudinal range.

Sciuridae.—Spermophilus atricapillus, S,258109–288009 (Baja); S. mohavensis, M,348209–368109; S. tereticaudus, M, S, 278009–378009; Ammospermophilus harrisii, S, 288009–368109; A. interpres, C, 258009–358009; A. leu-curus, GB, M, 248009–458009.

Geomyidae.—Geomys arenarius, C, 318509–348009; Pappogeomys castanops, C, 228309–388009.

Heteromyidae.—Dipodomys agilis, S, 258009–308009 (Baja); D. deserti, GB, M, S, 298009–408109; D. merriami, GB, M, S, C, 228009–418509; D. microps, GB, 348009–448209; D. nel-soni, C, 248009–298009; D. panamintinus, GB,M, S, 348409–398509; D. spectabilis, S, C,228009–378009; Microdipodops megacephalus;GB, 378009–458009; M. pallidus, GB, 378009–408009; Chaetodipus arenarius, S, 238309–328109(Baja); C. baileyi, S, 238309–348009; C. fallax,M, S, 278509–348109 (Baja); C. formosus, GB,M, S, 278009–408109; C. intermedius, S, C,278009–378009; C. lineatus, S, 218509–238309; C.nelsoni, C, 228009–328109; C. penicillatus, M, S,C, 238009–378009; C. spinatus, S, 238009–358009(Baja); Perognathus amplus, S, 308309–368409;P. longimembris, GB, M, S, 288309–438009.

Muridae.—Neotoma albigula, C, 198009–388009; N. goldmani, C, 238009–298009; N. lepi-da, GB, M, 238009–458009; Onychomys torridus,GB, M, S, C, 228009–408209; Peromyscus er-emicus, M, S, C, 228009–378109; P. eva, S,248109–258209 (Baja); P. merriami, S, 248009–338009; P. pectoralis, C, 208009–338509; P. po-lius, C, 288009–318009.

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NORTH AMERICAN DESERT RODENTS: A TEST OF THE MID …mccainc/PDFs/McCainJMAMM2003.pdf · American deserts based on climate and plant distributions, and the other was based on a com-bination