The allometry of patch selection in ruminantsJohn F Wilmshurst John M Fryxell and Carita M BergmanDepartment of Zoology University of Guelph Guelph Ontario Canada N1G 2WI

An axiomatic feature of food consumption by animals is that intake rate and prey abundance are positivelyrelatedWhile this has been demonstrated rigorously for large herbivores it is apparent from patch selectiontrials that grazers paradoxically tend to prefer short sparse swards to tall dense swards Indeed migratoryherbivores often shift from areas of high to low sward biomass during the growing season As nutritionalquality is an inverse function of grass abundance herbivores appear to sacricentce short-term intake for nutri-tional gains obtainable by eating sparse forage of higher quality Explicit models of this trade-oiexcl suggestthat individual ruminants maximize daily rates of energy gain by choosing immature swards of inter-mediate biomass As body mass is related positively to both ruminant cropping rates and digestibility thereshould be an allometric link between grass abundance and energy maximization providing a tool forpredicting patterns of herbivore habitat selection We used previously published studies to develop asynthetic model of trade-oiexcls between forage abundance and quality predicting that optimal sward biomassshould scale allometrically with body size The model predicts size-related variation in habitat selectionobserved in a guild of grazing ungulates in the Serengeti ecosystem

Keywords constraints foraging functional response herbivore resource partitioning Serengeti

1 INTRODUCTION

Due to the positive relationship between bite size andplant biomass cropping rates (grams of grass ingested perunit time) for herbivores of all sizes increase with swardbiomass (Black amp Kenney 1984 Short 1985 Lundberg1988 Gross et al 1993 Laca et al 1994) This occurs evenwhen the negative relationship between sward densityand grass quality resulting from phenological maturationof the sward is considered (Illius amp Gordon 1987)However centeld observations suggest that many grazingherbivores prefer low biomass grass patches when highbiomass patches are available (Vesey-Fitzgerald 1960Gwynne amp Bell 1968 Jarman 1974 Langvatn amp Hanley1993 Wilmshurst et al 1995) This suggests that thecurrent allometric theory of patch selection for grazers isat odds with observed behaviour

What is rarely incorporated into models is the inter-action of the poor nutritional quality of grass and the rateat which that grass can be processed in the gut (Illius ampGordon 1992) As grass swards mature they increase inbiomass and decrease in quality as they accumulatestructural carbohydrates (Waite 1963) Mature poorlydigestible grass requires longer retention in the rumenandor reticulum to reduce particle sizes sucurrenciently topass to the hind gut (Illius amp Gordon 1992) Faster passageof high-quality grass means that it can be consumed ingreater quantity by ruminants than can low-quality grass(Baile amp Forbes 1974) Poor digestibility and slow passageof mature grass are particularly problematic for smallruminants for which a gut centlled with slowly fermentinggrass both prevents further intake and provides little main-tenance energy (Wickstrom et al 1984) This constraint iseased for large ruminants with larger guts and relativelylower per unit mass metabolic demands (Illius amp Gordon1987) As body mass is related positively to ruminant

cropping rates voluntary intake and digestibility thereshould be an allometric link between grass abundance andenergy maximization providing a tool for predictingpatterns of herbivore habitat selection We modelled thistrade-oiexcl across a range of body sizes to detect possiblepatterns in habitat selection for a guild of grazing herbi-vores in Serengeti National ParkTanzania

2 METHODS

(a) The modelDaily intake of metabolizable energy (ME) for grazing rumi-

nants is regulated by opposing functions that we assume to beconstraining under average conditions (Owen-Smith 1993)These functions are a cropping constraint (I1 MJ of ME day71)that links forage digestibility to the grazerrsquos functional responseand a digestion constraint (I2 MJ of ME day71) that linksforage digestibility to the grazerrsquos daily voluntary intake (DVI)These lines cross for most parameter combinations and thepoint of intersection indicates maximum daily energy intake(centgure 1) In general the model predicts that ruminants shouldmaximize daily energy intake on low-to-intermediate biomassswards (Fryxell 1991)

Rates of dry matter intake increase with plant height leafsize and leaf bulk density in food-concentrated patches(Spalinger amp Hobbs 1992 Gross et al 1993) Using grass biomass(V g miexcl2) as a surrogate for these plant features we modelleddaily dry matter intake applying the Michaelis^Menten form ofthe instantaneous functional response multiplied by themaximum daily feeding time (tmax 13 h for all species) Wemultiplied daily dry matter intake by the maturational declinein forage quality (Q MJ giexcl1) (Rittenhouse et al 1971) to predictdaily digestible energy intake constrained by cropping

I1(M) ˆ Q (M) pound Rmax pound Vb Dagger V

pound tmax (1)

where M (kg) is body mass Rmax (g miniexcl1) is maximum instan-taneous cropping rate and b (g miexcl2) is grass biomass at whichintake is half maximum (centgure 1)

Proc R Soc Lond B (2000) 267 345^349 345 copy 2000 The Royal SocietyReceived 19 October 1999 Accepted 16 November 1999

Author and address for correspondence AAFC Research CentrePO Box 3000 Lethbridge Alberta CanadaT1J 4B1(wilmshurstjemagrca)

Model parameters for the cropping constraint were takenfrom 15 studies of functional responses of 12 ruminant speciesranging in size from 20 to 750 kg (table 1) We recorded para-meters that measured intake on two types of swards simpleswards composed solely of grass leaf or forbs and complexswards using whole grass tillers or intact grass communities

In studies where Michaelis^Menten parameters were notreported we calculated them using available information Grosset al (1993) report cropping rates relative to plant size using theSpalinger amp Hobbs (1992) form of the functional response Wecalculated b from their data by multiplying Rmax by h (averageminutes per plant) and plant density (plantmiexcl2) Murray ampBrown (1993) reported cropping rates as a multiple regression ofgreen-leaf biomass crude protein and stem density We calcu-lated cropping rates relative to green-leaf biomass alone bysubstituting mid-range values for crude protein and stem densitythey report and determined Michaelis^Menten parameters fromtheir data using nonlinear regression

We modelled daily intake on swards ranging from 0 to 300 g miexcl2

using a typical data set from the Serengeti ecosystem relating grassquality to grass biomass (Wilmshurst et al 1999) This data set isalso relevant to our subsequent empirical test of habitat use by theguild of Serengeti grazers Within this range of grass biomassdigestible energy (DE) content is a linear function of its in vitrodigestible organic matter (IVDOM) content (Rittenhouse et al1971) that is in turn a function of forage neutral detergentcentbre (NDF) content and animal body mass (IVDOMˆ 9017053 pound NDF() + 0013 poundM F2297 ˆ786 p50001r2 ˆ 035 H Meissner personal communication) NDFalso varieslinearly with biomass up to 300 g miexcl2 (F123 ˆ75 p ˆ 001r2 ˆ 025) although this relationship tends to be nonlinear acrossbroader ranges of grass biomass due to saturating NDFcontent on

dense swards (Breman amp de Wit 1983 Hobbs amp Swift 1985Gordon 1989) Hence across the range of sward biomass wemodelled DE() ˆ 6567027 pound biomass (g miexcl2) ME contentof the forage was calculated as 82 of DE (Van Soest 1982)Given a standard combustible energy content per gram of grassQ (M) is calculated as ME() pound 171 (MJ giexcl1) (Golley1961)

We calculated the digestion constraint as daily dry matterconsumption under ad libitum feeding conditions multiplied byforage quality Digestion constraints relative to body size werederived from a study of DVI for six ruminant species ranging insize between 30 and 550 kg (Meissner amp Paulsmeier 1995)While voluntary intake may not always represent maximumdaily intake due to variation in animal state or behaviour (Baileamp Forbes 1974) it is a useful estimate of ad libitum daily intakeMeissner amp Paulsmeier (1995) reported that DVI scaled isome-trically to forage quality but allometrically (M09) to body massWe modelled digestion constraints as a multiple regression equa-tion relating both per cent NDF of grass and animal body massto DVI (kg dry matter day71)

DVI ˆ 25 iexcl 0049 pound NDF Dagger 0061 pound M09 (2)

(r2 ˆ 095) (H Meissner personal communication) KilogramsDVI were converted as above to DVI of ME From this functionwe calculated I2

I2(M) ˆ DVI pound Q (M) (3)

To account for phylogenetic relationships we created dummyvariables to represent family and tribe classicentcations (Harvey ampPagel 1991) Model predictions of optimal grass biomass andmaximum energy intake for each species listed in table 1 weretested for dependency to body mass sward type and phylogenyusing stepwise multiple regression Relationships among signicent-cant eiexclects were determined using ANCOVA

(b) Field dataThe Serengeti ecosystem of East Africa provides an excellent

setting to test model predictions Due to a complex pattern oflocalized rainfall a substantial range of grass densities is avail-able to the diverse guild of Serengeti grazers in a small area Tomeasure local herbivore densities we drove twenty-centve 220-kmlong ground transects on the Serengeti plain (28321rsquoS 34857rsquo Eto 28561rsquoS 34821rsquoE) during the growing seasons of 1994 to1996 All large herbivores visible within an arc extending 200 mto the sides and front of the driver were counted at two randomlocations in each kilometre of transect At each location theheight and percentage cover of green vegetation was measuredusing visual estimation (Daubenmire1959) These measurementswere calibrated to grass biomass (g miexcl2) using clip-plots fromwhich quality relationships were also determined (Wilmshurst etal 1999) Five herbivore species were found in sucurrencient abun-dance for analyses Thomsonrsquos gazelles (Gazella thomsoni) Grantrsquosgazelles (Gazella granti) hartebeest (Alcelaphus buselaphus) wilde-beest (Connochaetes taurinus) and topi (Damaliscus lunatus) Grantrsquosgazelles have a 50 kg body mass (Estes 1991) body masses of theother species are listed in table 1

3 RESULTS

Predicted optimal sward biomass was dependent onbody mass and on the complexity of the sward on whichfunctional response parameters were measured but noton phylogeny On simple swards cropping constraints

346 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

40

30

10

20

01007550

grass biomass (g m - 2)

ME

inta

ke (

MJ

day- 1

)

0 25

cropping

digestion

Figure 1 Daily ME intake constraint curves for Thomsonrsquosgazelle grazing on complex swards (parameters given intable 1) The cropping constraint (I1) is the maximumamount of energy an individual can consume daily in theabsence of digestion constraints and the digestion constraint(I2) is the maximum amount of energy an individual canprocess daily in the absence of cropping constraints Realizeddaily ME intake as a function of sward biomass tracks theminimum of the two constraint lines The point of intersectionidenticentes the maximum daily ME intake on the ordinate andthe optimal grass biomass on the abscissa

increased steeply intersecting the digestion constraint atlow biomass (centgure 2) On complex swards functionalresponses increased more gradually causing theconstraints to intersect at an order of magnitude higherbiomass (centgure 2) This eiexclect of sward structure has beenshown using experimental manipulation of swardcomplexity in trials featuring grazing bison (Bergman etal 2000)

Predicted maximum energy intake rates were a positivelinear function of body mass and phylogenetic relatedness

but were not related to sward type (centgure 3) The energyfunction scaled to M086 indicating a stronger linkbetween energy maximization and digestion constraintswhich scaled to M090 (Meissner amp Paulsmeier 1995) thanto cropping constraints which scaled to M073 (Shipley etal 1994) The realized metabolic rate for mammals isapproximately two to three times the basal metabolic rate(Peters 1983) suggesting that our estimates of maximummetabolic energy gain (approximately 35 times the daily

Ruminant patch selection and allometry J FWilmshurst and others 347

Proc R Soc Lond B (2000)

Table 1 List of species parameters used to model constraint curves

species mass (kg) Rmax (g miniexcl1) b (g miexcl2) sources

Thomsonrsquos gazellea (Gazella thomsoni) 20 642 166 Wilmshurst et al (1999)sheepa (Ovis aries) 42 702 308 Black amp Kenney (1984)mule deera (Odocoileus hemionus) 42 222 197 Wickstrom et al (1984)white-tailed deerb (Odocoileus virginianus) 45 917 303 Gross et al (1993)axis deerb (Axis axis) 53 842 227 Gross et al (1993)reindeera (Rangifer tarandus) 70 637 317 Trudell amp White (1981)topib (Damaliscus lunatus) 75 170 106 Murray amp Brown (1993)hartebeestb (Alcelaphus buselaphus) 92 119 854 Murray amp Brown (1993)wildebeestb (Connochaetes taurinus) 97 202 994 Murray amp Brown (1993)cariboub (Rangifer tarandus) 104 163 782 Gross et al (1993)wapiti (yearling)a (Cervus elaphus) 170 312 1604 Wilmshurst et al (1995)bison (yearling)b (Bison bison) 180 548 992 Bergman et al (2000)elkb (Cervus elaphus) 266 474 712 Gross et al (1993)cowb (Bos taurus) 548 746 246 Gross et al (1993)cowa (Bos taurus) 750 1295 6886 Laca et al (1992 1994)

a Complex sward trialsb Simple sward trials

3

1

2

0302520

log10 body mass (kg)

log 1

0 op

tim

al g

rass

bio

mas

s (g

m- 2

)

10 15

Figure 2 Optimal grass biomass relative to body massfor modelled ruminants listed in table 1 The open pointsrepresent trials conducted on complex grass swardsdescribed by the function log10 y ˆ 70088+ 086 pound log10 x(dashed line) The centlled points represent trials conductedon simple leafy swards and are described by the functionlog10 y ˆ 7105 + 086 pound log10x (solid line) Slopes arehomogeneous (F111 ˆ 027 p ˆ 087 for heterogeneity) andmultiple regression including body mass and sward complexityconcentrmed the signicentcance of linear functions (F212 ˆ 328p50001 r2 ˆ 086)

25

15

20

05302520

log10 body mass (kg)

log 1

0 M

E in

take

(M

J da

y- 1)

10

10

15

Figure 3 Maximum daily ME intake relative to ruminantbody mass The open points represent cervids described bythe function log10 y ˆ 70302+ 091pound log10 x (dashed line)The centlled points represent bovids described by the functionlog10 y ˆ 7029 + 091pound log10 x (solid line) Slopes arehomogeneous (F111 ˆ 024 p ˆ 063 for heterogeneity) andmultiple regression including body mass and family concentrmedthe signicentcance of linear functions (F212 ˆ 95247 p50001r2 ˆ 099) The dotted line is the basal (ME) requirementsrelative to body mass (MJ dayiexcl1 ˆ 045poundkg073) (Konoplev etal 1978)

metabolic requirement for Artiodactyla (centgure 2)) realis-tically predict maximum daily values

Biomass of patches on which Serengeti grazers wereobserved was a function of their body mass Treating thedensity of each species in each year independently therewas a signicentcant positive relationship between body massand mean sward biomass of patches they occupied(log10 biomass (g miexcl2) ˆ 15 + 022 pound log10 body mass (kg)F113 ˆ54 p ˆ 004 r2 ˆ 03) The observed pattern bettermatched the predictions derived from complex swardsthan those from simple swards nevertheless the slope ofthe observed relationship among species was shallowerthan predicted by the model (022 compared with 086)

4 DISCUSSION

The sward biomass on which ruminants optimizeenergy gain is a positive decelerating function of bodymass This repoundects a gradual shift in the intersection ofthe digestion constraint and the cropping constraint fromlow biomass swards for small ruminants to swards ofhigher biomass for large ruminants with commensuratelylarger gut capacity Thus the positive relationshipbetween optimal sward biomass and ruminant body massis the result of both a relaxation of digestion constraints(Meissner amp Paulsmeier 1995) and increasing bite size(Gross et al 1993) in larger ruminants

Our assumption that energy gain by ruminants is ahump-shaped function of grass abundance (Fryxell 1991)makes our work fundamentally diiexclerent from previousallometric models We found that body mass-relatedhabitat selection can result purely from individual energymaximization independent of either plant species selec-tivity or interspecicentc competition and that in generalruminant herbivores should prefer short intermediatebiomass swards over tall high biomass swards In Illiusand Gordonrsquos (1987) allometric model of energy functionin ruminants daily energy gain is a positive function ofgrass abundance thus predicting that tall high biomasspatches should be preferred by grazing ruminants regard-less of body size They predict a positive relationshipbetween ruminant body mass and grass biomass as dowe but resulting from competition for tall high biomassswards Their model cannot explain the selection byruminants of low biomass swards when tall high biomassswards are available (McNaughton 1984 Langvatn ampHanley 1993 Wallis DeVries amp Schippers 1994 Wilm-shurst et al 1995 2000 Bradbury et al 1996)

It is interesting that we found no impact of phylogenyon predicted optimal sward biomass as this prediction isstrongly aiexclected by the form of the functional responsewhich is presumably under morphological control Never-theless we did centnd a slight diiexclerence between cervidsand bovids with respect to maximum daily energy gain(centgure 3) This suggests at least marginal phylogeneticlinkage between muzzle architecture and body masswhich has been postulated in other analyses of ruminantforaging strategies (Gordon amp Illius 1988)

The positive relationship we found between herbivorebody mass and sward biomass in the surveys of Serengetiherbivores lends qualitative support to the idea that allo-metric scaling in gut passage and cropping in ruminantsis linked to patch selection There is a tendency for small

ruminants to be found on lower biomass patches thanlarger ruminants during the growing season as predictedby our model Several processes could account for thedeviation of our model from the Serengeti observations Ifsward complexity is positively related to grass biomassthen predictions of optimal grass biomass for small rumi-nants would conform to the simple sward regressionmodel and predictions of optimal grass biomass for largeruminants would conform to the complex sward regres-sion model (centgure 2) Thus the eiexclects of swardcomplexity would predict a much shallower slope thanpredicted by either model In addition by choosing rela-tively simple representations of forage intake constraintswe ignore processes such as competition and predationthat inpounduence on herbivore distributions in the Serengeti(Sinclair 1985 Hofer amp East 1993 Durant 1998) Indeedwe found an inverse relationship between body mass andhow closely their observed patch choice matched thatpredicted perhaps the result of larger animals excludingsmaller animals from preferred patches

These results lend theoretical and empirical support tothe hypothesis that there is size-specicentc ecological separa-tion among grazing herbivores on the basis of diiexclerentialforaging ecurrenciency (Murray amp Brown 1993) The gradientbetween optimal patch and body mass suggests thatherbivores of similar body size and feeding style may becompeting Our work also suggests that large ruminantsshould perform better on more productive grasslandsthan do small ruminants with the converse true of low-productivity grasslands In highly productive grasslandsin which tillers grow and lose quality rapidly (Braun1973) large-bodied ruminants are favoured

This research was supported by an Ontario Graduate Scholar-ship to JFW a Natural Science and Engineering ResearchCouncil (NSERC) operating grant to JMF and an NSERCpostgraduate scholarship to CMB We are very grateful to HMeissner and the University of Pretoria for voluntary intakedata A Illius and M Murray for functional response para-meters and J M Gaillard and T D Nudds for valuablecomments on the manuscript We also thank A R E SinclairTanzania National Parks Serengeti Wildlife Research Instituteand the TanzaniaWildlife Corporation

REFERENCES

Baile C A amp Forbes J M 1974 Control of feed intake andregulation of energy balance in ruminants Physiol Rev 54160^214

Bergman C M Fryxell J M amp Gates C C 2000 The eiexclectof tissue complexity and sward height on the functionalresponse of wood bison Funct Ecol (In the press)

Black J L amp Kenney P A 1984 Factors aiexclecting diet selectionby sheep II Height and density of pasture Aust J Agric Res35 565^578

Bradbury J W Vehrencamp S L Clifton K E amp CliftonL M 1996 The relationship between bite rate and localforage abundance in wild Thomsonrsquos gazelles Ecology 772237^2255

Braun H M H 1973 Primary production in the Serengetipurpose methods and some results of research Ann UnivAbidjan E 6 171^188

Breman H amp de Wit C T 1983 Rangeland productivity andexploitation in the Sahel Science 221 1341^1347

Daubenmire R 1959 A canopy-coverage method of vegeta-tional analysis Northw Sci 33 43^64

348 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

Model parameters for the cropping constraint were takenfrom 15 studies of functional responses of 12 ruminant speciesranging in size from 20 to 750 kg (table 1) We recorded para-meters that measured intake on two types of swards simpleswards composed solely of grass leaf or forbs and complexswards using whole grass tillers or intact grass communities

In studies where Michaelis^Menten parameters were notreported we calculated them using available information Grosset al (1993) report cropping rates relative to plant size using theSpalinger amp Hobbs (1992) form of the functional response Wecalculated b from their data by multiplying Rmax by h (averageminutes per plant) and plant density (plantmiexcl2) Murray ampBrown (1993) reported cropping rates as a multiple regression ofgreen-leaf biomass crude protein and stem density We calcu-lated cropping rates relative to green-leaf biomass alone bysubstituting mid-range values for crude protein and stem densitythey report and determined Michaelis^Menten parameters fromtheir data using nonlinear regression

We modelled daily intake on swards ranging from 0 to 300 g miexcl2

using a typical data set from the Serengeti ecosystem relating grassquality to grass biomass (Wilmshurst et al 1999) This data set isalso relevant to our subsequent empirical test of habitat use by theguild of Serengeti grazers Within this range of grass biomassdigestible energy (DE) content is a linear function of its in vitrodigestible organic matter (IVDOM) content (Rittenhouse et al1971) that is in turn a function of forage neutral detergentcentbre (NDF) content and animal body mass (IVDOMˆ 9017053 pound NDF() + 0013 poundM F2297 ˆ786 p50001r2 ˆ 035 H Meissner personal communication) NDFalso varieslinearly with biomass up to 300 g miexcl2 (F123 ˆ75 p ˆ 001r2 ˆ 025) although this relationship tends to be nonlinear acrossbroader ranges of grass biomass due to saturating NDFcontent on

dense swards (Breman amp de Wit 1983 Hobbs amp Swift 1985Gordon 1989) Hence across the range of sward biomass wemodelled DE() ˆ 6567027 pound biomass (g miexcl2) ME contentof the forage was calculated as 82 of DE (Van Soest 1982)Given a standard combustible energy content per gram of grassQ (M) is calculated as ME() pound 171 (MJ giexcl1) (Golley1961)

We calculated the digestion constraint as daily dry matterconsumption under ad libitum feeding conditions multiplied byforage quality Digestion constraints relative to body size werederived from a study of DVI for six ruminant species ranging insize between 30 and 550 kg (Meissner amp Paulsmeier 1995)While voluntary intake may not always represent maximumdaily intake due to variation in animal state or behaviour (Baileamp Forbes 1974) it is a useful estimate of ad libitum daily intakeMeissner amp Paulsmeier (1995) reported that DVI scaled isome-trically to forage quality but allometrically (M09) to body massWe modelled digestion constraints as a multiple regression equa-tion relating both per cent NDF of grass and animal body massto DVI (kg dry matter day71)

DVI ˆ 25 iexcl 0049 pound NDF Dagger 0061 pound M09 (2)

(r2 ˆ 095) (H Meissner personal communication) KilogramsDVI were converted as above to DVI of ME From this functionwe calculated I2

I2(M) ˆ DVI pound Q (M) (3)

To account for phylogenetic relationships we created dummyvariables to represent family and tribe classicentcations (Harvey ampPagel 1991) Model predictions of optimal grass biomass andmaximum energy intake for each species listed in table 1 weretested for dependency to body mass sward type and phylogenyusing stepwise multiple regression Relationships among signicent-cant eiexclects were determined using ANCOVA

(b) Field dataThe Serengeti ecosystem of East Africa provides an excellent

setting to test model predictions Due to a complex pattern oflocalized rainfall a substantial range of grass densities is avail-able to the diverse guild of Serengeti grazers in a small area Tomeasure local herbivore densities we drove twenty-centve 220-kmlong ground transects on the Serengeti plain (28321rsquoS 34857rsquo Eto 28561rsquoS 34821rsquoE) during the growing seasons of 1994 to1996 All large herbivores visible within an arc extending 200 mto the sides and front of the driver were counted at two randomlocations in each kilometre of transect At each location theheight and percentage cover of green vegetation was measuredusing visual estimation (Daubenmire1959) These measurementswere calibrated to grass biomass (g miexcl2) using clip-plots fromwhich quality relationships were also determined (Wilmshurst etal 1999) Five herbivore species were found in sucurrencient abun-dance for analyses Thomsonrsquos gazelles (Gazella thomsoni) Grantrsquosgazelles (Gazella granti) hartebeest (Alcelaphus buselaphus) wilde-beest (Connochaetes taurinus) and topi (Damaliscus lunatus) Grantrsquosgazelles have a 50 kg body mass (Estes 1991) body masses of theother species are listed in table 1

3 RESULTS

Predicted optimal sward biomass was dependent onbody mass and on the complexity of the sward on whichfunctional response parameters were measured but noton phylogeny On simple swards cropping constraints

346 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

40

30

10

20

01007550

grass biomass (g m - 2)

ME

inta

ke (

MJ

day- 1

)

0 25

cropping

digestion

Figure 1 Daily ME intake constraint curves for Thomsonrsquosgazelle grazing on complex swards (parameters given intable 1) The cropping constraint (I1) is the maximumamount of energy an individual can consume daily in theabsence of digestion constraints and the digestion constraint(I2) is the maximum amount of energy an individual canprocess daily in the absence of cropping constraints Realizeddaily ME intake as a function of sward biomass tracks theminimum of the two constraint lines The point of intersectionidenticentes the maximum daily ME intake on the ordinate andthe optimal grass biomass on the abscissa

increased steeply intersecting the digestion constraint atlow biomass (centgure 2) On complex swards functionalresponses increased more gradually causing theconstraints to intersect at an order of magnitude higherbiomass (centgure 2) This eiexclect of sward structure has beenshown using experimental manipulation of swardcomplexity in trials featuring grazing bison (Bergman etal 2000)

Predicted maximum energy intake rates were a positivelinear function of body mass and phylogenetic relatedness

but were not related to sward type (centgure 3) The energyfunction scaled to M086 indicating a stronger linkbetween energy maximization and digestion constraintswhich scaled to M090 (Meissner amp Paulsmeier 1995) thanto cropping constraints which scaled to M073 (Shipley etal 1994) The realized metabolic rate for mammals isapproximately two to three times the basal metabolic rate(Peters 1983) suggesting that our estimates of maximummetabolic energy gain (approximately 35 times the daily

Ruminant patch selection and allometry J FWilmshurst and others 347

Proc R Soc Lond B (2000)

Table 1 List of species parameters used to model constraint curves

species mass (kg) Rmax (g miniexcl1) b (g miexcl2) sources

Thomsonrsquos gazellea (Gazella thomsoni) 20 642 166 Wilmshurst et al (1999)sheepa (Ovis aries) 42 702 308 Black amp Kenney (1984)mule deera (Odocoileus hemionus) 42 222 197 Wickstrom et al (1984)white-tailed deerb (Odocoileus virginianus) 45 917 303 Gross et al (1993)axis deerb (Axis axis) 53 842 227 Gross et al (1993)reindeera (Rangifer tarandus) 70 637 317 Trudell amp White (1981)topib (Damaliscus lunatus) 75 170 106 Murray amp Brown (1993)hartebeestb (Alcelaphus buselaphus) 92 119 854 Murray amp Brown (1993)wildebeestb (Connochaetes taurinus) 97 202 994 Murray amp Brown (1993)cariboub (Rangifer tarandus) 104 163 782 Gross et al (1993)wapiti (yearling)a (Cervus elaphus) 170 312 1604 Wilmshurst et al (1995)bison (yearling)b (Bison bison) 180 548 992 Bergman et al (2000)elkb (Cervus elaphus) 266 474 712 Gross et al (1993)cowb (Bos taurus) 548 746 246 Gross et al (1993)cowa (Bos taurus) 750 1295 6886 Laca et al (1992 1994)

a Complex sward trialsb Simple sward trials

3

1

2

0302520

log10 body mass (kg)

log 1

0 op

tim

al g

rass

bio

mas

s (g

m- 2

)

10 15

Figure 2 Optimal grass biomass relative to body massfor modelled ruminants listed in table 1 The open pointsrepresent trials conducted on complex grass swardsdescribed by the function log10 y ˆ 70088+ 086 pound log10 x(dashed line) The centlled points represent trials conductedon simple leafy swards and are described by the functionlog10 y ˆ 7105 + 086 pound log10x (solid line) Slopes arehomogeneous (F111 ˆ 027 p ˆ 087 for heterogeneity) andmultiple regression including body mass and sward complexityconcentrmed the signicentcance of linear functions (F212 ˆ 328p50001 r2 ˆ 086)

25

15

20

05302520

log10 body mass (kg)

log 1

0 M

E in

take

(M

J da

y- 1)

10

10

15

Figure 3 Maximum daily ME intake relative to ruminantbody mass The open points represent cervids described bythe function log10 y ˆ 70302+ 091pound log10 x (dashed line)The centlled points represent bovids described by the functionlog10 y ˆ 7029 + 091pound log10 x (solid line) Slopes arehomogeneous (F111 ˆ 024 p ˆ 063 for heterogeneity) andmultiple regression including body mass and family concentrmedthe signicentcance of linear functions (F212 ˆ 95247 p50001r2 ˆ 099) The dotted line is the basal (ME) requirementsrelative to body mass (MJ dayiexcl1 ˆ 045poundkg073) (Konoplev etal 1978)

metabolic requirement for Artiodactyla (centgure 2)) realis-tically predict maximum daily values

Biomass of patches on which Serengeti grazers wereobserved was a function of their body mass Treating thedensity of each species in each year independently therewas a signicentcant positive relationship between body massand mean sward biomass of patches they occupied(log10 biomass (g miexcl2) ˆ 15 + 022 pound log10 body mass (kg)F113 ˆ54 p ˆ 004 r2 ˆ 03) The observed pattern bettermatched the predictions derived from complex swardsthan those from simple swards nevertheless the slope ofthe observed relationship among species was shallowerthan predicted by the model (022 compared with 086)

4 DISCUSSION

The sward biomass on which ruminants optimizeenergy gain is a positive decelerating function of bodymass This repoundects a gradual shift in the intersection ofthe digestion constraint and the cropping constraint fromlow biomass swards for small ruminants to swards ofhigher biomass for large ruminants with commensuratelylarger gut capacity Thus the positive relationshipbetween optimal sward biomass and ruminant body massis the result of both a relaxation of digestion constraints(Meissner amp Paulsmeier 1995) and increasing bite size(Gross et al 1993) in larger ruminants

Our assumption that energy gain by ruminants is ahump-shaped function of grass abundance (Fryxell 1991)makes our work fundamentally diiexclerent from previousallometric models We found that body mass-relatedhabitat selection can result purely from individual energymaximization independent of either plant species selec-tivity or interspecicentc competition and that in generalruminant herbivores should prefer short intermediatebiomass swards over tall high biomass swards In Illiusand Gordonrsquos (1987) allometric model of energy functionin ruminants daily energy gain is a positive function ofgrass abundance thus predicting that tall high biomasspatches should be preferred by grazing ruminants regard-less of body size They predict a positive relationshipbetween ruminant body mass and grass biomass as dowe but resulting from competition for tall high biomassswards Their model cannot explain the selection byruminants of low biomass swards when tall high biomassswards are available (McNaughton 1984 Langvatn ampHanley 1993 Wallis DeVries amp Schippers 1994 Wilm-shurst et al 1995 2000 Bradbury et al 1996)

It is interesting that we found no impact of phylogenyon predicted optimal sward biomass as this prediction isstrongly aiexclected by the form of the functional responsewhich is presumably under morphological control Never-theless we did centnd a slight diiexclerence between cervidsand bovids with respect to maximum daily energy gain(centgure 3) This suggests at least marginal phylogeneticlinkage between muzzle architecture and body masswhich has been postulated in other analyses of ruminantforaging strategies (Gordon amp Illius 1988)

The positive relationship we found between herbivorebody mass and sward biomass in the surveys of Serengetiherbivores lends qualitative support to the idea that allo-metric scaling in gut passage and cropping in ruminantsis linked to patch selection There is a tendency for small

ruminants to be found on lower biomass patches thanlarger ruminants during the growing season as predictedby our model Several processes could account for thedeviation of our model from the Serengeti observations Ifsward complexity is positively related to grass biomassthen predictions of optimal grass biomass for small rumi-nants would conform to the simple sward regressionmodel and predictions of optimal grass biomass for largeruminants would conform to the complex sward regres-sion model (centgure 2) Thus the eiexclects of swardcomplexity would predict a much shallower slope thanpredicted by either model In addition by choosing rela-tively simple representations of forage intake constraintswe ignore processes such as competition and predationthat inpounduence on herbivore distributions in the Serengeti(Sinclair 1985 Hofer amp East 1993 Durant 1998) Indeedwe found an inverse relationship between body mass andhow closely their observed patch choice matched thatpredicted perhaps the result of larger animals excludingsmaller animals from preferred patches

These results lend theoretical and empirical support tothe hypothesis that there is size-specicentc ecological separa-tion among grazing herbivores on the basis of diiexclerentialforaging ecurrenciency (Murray amp Brown 1993) The gradientbetween optimal patch and body mass suggests thatherbivores of similar body size and feeding style may becompeting Our work also suggests that large ruminantsshould perform better on more productive grasslandsthan do small ruminants with the converse true of low-productivity grasslands In highly productive grasslandsin which tillers grow and lose quality rapidly (Braun1973) large-bodied ruminants are favoured

This research was supported by an Ontario Graduate Scholar-ship to JFW a Natural Science and Engineering ResearchCouncil (NSERC) operating grant to JMF and an NSERCpostgraduate scholarship to CMB We are very grateful to HMeissner and the University of Pretoria for voluntary intakedata A Illius and M Murray for functional response para-meters and J M Gaillard and T D Nudds for valuablecomments on the manuscript We also thank A R E SinclairTanzania National Parks Serengeti Wildlife Research Instituteand the TanzaniaWildlife Corporation

REFERENCES

Baile C A amp Forbes J M 1974 Control of feed intake andregulation of energy balance in ruminants Physiol Rev 54160^214

Bergman C M Fryxell J M amp Gates C C 2000 The eiexclectof tissue complexity and sward height on the functionalresponse of wood bison Funct Ecol (In the press)

Black J L amp Kenney P A 1984 Factors aiexclecting diet selectionby sheep II Height and density of pasture Aust J Agric Res35 565^578

Bradbury J W Vehrencamp S L Clifton K E amp CliftonL M 1996 The relationship between bite rate and localforage abundance in wild Thomsonrsquos gazelles Ecology 772237^2255

Braun H M H 1973 Primary production in the Serengetipurpose methods and some results of research Ann UnivAbidjan E 6 171^188

Breman H amp de Wit C T 1983 Rangeland productivity andexploitation in the Sahel Science 221 1341^1347

Daubenmire R 1959 A canopy-coverage method of vegeta-tional analysis Northw Sci 33 43^64

348 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

increased steeply intersecting the digestion constraint atlow biomass (centgure 2) On complex swards functionalresponses increased more gradually causing theconstraints to intersect at an order of magnitude higherbiomass (centgure 2) This eiexclect of sward structure has beenshown using experimental manipulation of swardcomplexity in trials featuring grazing bison (Bergman etal 2000)

Predicted maximum energy intake rates were a positivelinear function of body mass and phylogenetic relatedness

but were not related to sward type (centgure 3) The energyfunction scaled to M086 indicating a stronger linkbetween energy maximization and digestion constraintswhich scaled to M090 (Meissner amp Paulsmeier 1995) thanto cropping constraints which scaled to M073 (Shipley etal 1994) The realized metabolic rate for mammals isapproximately two to three times the basal metabolic rate(Peters 1983) suggesting that our estimates of maximummetabolic energy gain (approximately 35 times the daily

Ruminant patch selection and allometry J FWilmshurst and others 347

Proc R Soc Lond B (2000)

Table 1 List of species parameters used to model constraint curves

species mass (kg) Rmax (g miniexcl1) b (g miexcl2) sources

Thomsonrsquos gazellea (Gazella thomsoni) 20 642 166 Wilmshurst et al (1999)sheepa (Ovis aries) 42 702 308 Black amp Kenney (1984)mule deera (Odocoileus hemionus) 42 222 197 Wickstrom et al (1984)white-tailed deerb (Odocoileus virginianus) 45 917 303 Gross et al (1993)axis deerb (Axis axis) 53 842 227 Gross et al (1993)reindeera (Rangifer tarandus) 70 637 317 Trudell amp White (1981)topib (Damaliscus lunatus) 75 170 106 Murray amp Brown (1993)hartebeestb (Alcelaphus buselaphus) 92 119 854 Murray amp Brown (1993)wildebeestb (Connochaetes taurinus) 97 202 994 Murray amp Brown (1993)cariboub (Rangifer tarandus) 104 163 782 Gross et al (1993)wapiti (yearling)a (Cervus elaphus) 170 312 1604 Wilmshurst et al (1995)bison (yearling)b (Bison bison) 180 548 992 Bergman et al (2000)elkb (Cervus elaphus) 266 474 712 Gross et al (1993)cowb (Bos taurus) 548 746 246 Gross et al (1993)cowa (Bos taurus) 750 1295 6886 Laca et al (1992 1994)

a Complex sward trialsb Simple sward trials

3

1

2

0302520

log10 body mass (kg)

log 1

0 op

tim

al g

rass

bio

mas

s (g

m- 2

)

10 15

Figure 2 Optimal grass biomass relative to body massfor modelled ruminants listed in table 1 The open pointsrepresent trials conducted on complex grass swardsdescribed by the function log10 y ˆ 70088+ 086 pound log10 x(dashed line) The centlled points represent trials conductedon simple leafy swards and are described by the functionlog10 y ˆ 7105 + 086 pound log10x (solid line) Slopes arehomogeneous (F111 ˆ 027 p ˆ 087 for heterogeneity) andmultiple regression including body mass and sward complexityconcentrmed the signicentcance of linear functions (F212 ˆ 328p50001 r2 ˆ 086)

25

15

20

05302520

log10 body mass (kg)

log 1

0 M

E in

take

(M

J da

y- 1)

10

10

15

Figure 3 Maximum daily ME intake relative to ruminantbody mass The open points represent cervids described bythe function log10 y ˆ 70302+ 091pound log10 x (dashed line)The centlled points represent bovids described by the functionlog10 y ˆ 7029 + 091pound log10 x (solid line) Slopes arehomogeneous (F111 ˆ 024 p ˆ 063 for heterogeneity) andmultiple regression including body mass and family concentrmedthe signicentcance of linear functions (F212 ˆ 95247 p50001r2 ˆ 099) The dotted line is the basal (ME) requirementsrelative to body mass (MJ dayiexcl1 ˆ 045poundkg073) (Konoplev etal 1978)

metabolic requirement for Artiodactyla (centgure 2)) realis-tically predict maximum daily values

Biomass of patches on which Serengeti grazers wereobserved was a function of their body mass Treating thedensity of each species in each year independently therewas a signicentcant positive relationship between body massand mean sward biomass of patches they occupied(log10 biomass (g miexcl2) ˆ 15 + 022 pound log10 body mass (kg)F113 ˆ54 p ˆ 004 r2 ˆ 03) The observed pattern bettermatched the predictions derived from complex swardsthan those from simple swards nevertheless the slope ofthe observed relationship among species was shallowerthan predicted by the model (022 compared with 086)

4 DISCUSSION

The sward biomass on which ruminants optimizeenergy gain is a positive decelerating function of bodymass This repoundects a gradual shift in the intersection ofthe digestion constraint and the cropping constraint fromlow biomass swards for small ruminants to swards ofhigher biomass for large ruminants with commensuratelylarger gut capacity Thus the positive relationshipbetween optimal sward biomass and ruminant body massis the result of both a relaxation of digestion constraints(Meissner amp Paulsmeier 1995) and increasing bite size(Gross et al 1993) in larger ruminants

Our assumption that energy gain by ruminants is ahump-shaped function of grass abundance (Fryxell 1991)makes our work fundamentally diiexclerent from previousallometric models We found that body mass-relatedhabitat selection can result purely from individual energymaximization independent of either plant species selec-tivity or interspecicentc competition and that in generalruminant herbivores should prefer short intermediatebiomass swards over tall high biomass swards In Illiusand Gordonrsquos (1987) allometric model of energy functionin ruminants daily energy gain is a positive function ofgrass abundance thus predicting that tall high biomasspatches should be preferred by grazing ruminants regard-less of body size They predict a positive relationshipbetween ruminant body mass and grass biomass as dowe but resulting from competition for tall high biomassswards Their model cannot explain the selection byruminants of low biomass swards when tall high biomassswards are available (McNaughton 1984 Langvatn ampHanley 1993 Wallis DeVries amp Schippers 1994 Wilm-shurst et al 1995 2000 Bradbury et al 1996)

It is interesting that we found no impact of phylogenyon predicted optimal sward biomass as this prediction isstrongly aiexclected by the form of the functional responsewhich is presumably under morphological control Never-theless we did centnd a slight diiexclerence between cervidsand bovids with respect to maximum daily energy gain(centgure 3) This suggests at least marginal phylogeneticlinkage between muzzle architecture and body masswhich has been postulated in other analyses of ruminantforaging strategies (Gordon amp Illius 1988)

The positive relationship we found between herbivorebody mass and sward biomass in the surveys of Serengetiherbivores lends qualitative support to the idea that allo-metric scaling in gut passage and cropping in ruminantsis linked to patch selection There is a tendency for small

ruminants to be found on lower biomass patches thanlarger ruminants during the growing season as predictedby our model Several processes could account for thedeviation of our model from the Serengeti observations Ifsward complexity is positively related to grass biomassthen predictions of optimal grass biomass for small rumi-nants would conform to the simple sward regressionmodel and predictions of optimal grass biomass for largeruminants would conform to the complex sward regres-sion model (centgure 2) Thus the eiexclects of swardcomplexity would predict a much shallower slope thanpredicted by either model In addition by choosing rela-tively simple representations of forage intake constraintswe ignore processes such as competition and predationthat inpounduence on herbivore distributions in the Serengeti(Sinclair 1985 Hofer amp East 1993 Durant 1998) Indeedwe found an inverse relationship between body mass andhow closely their observed patch choice matched thatpredicted perhaps the result of larger animals excludingsmaller animals from preferred patches

These results lend theoretical and empirical support tothe hypothesis that there is size-specicentc ecological separa-tion among grazing herbivores on the basis of diiexclerentialforaging ecurrenciency (Murray amp Brown 1993) The gradientbetween optimal patch and body mass suggests thatherbivores of similar body size and feeding style may becompeting Our work also suggests that large ruminantsshould perform better on more productive grasslandsthan do small ruminants with the converse true of low-productivity grasslands In highly productive grasslandsin which tillers grow and lose quality rapidly (Braun1973) large-bodied ruminants are favoured

This research was supported by an Ontario Graduate Scholar-ship to JFW a Natural Science and Engineering ResearchCouncil (NSERC) operating grant to JMF and an NSERCpostgraduate scholarship to CMB We are very grateful to HMeissner and the University of Pretoria for voluntary intakedata A Illius and M Murray for functional response para-meters and J M Gaillard and T D Nudds for valuablecomments on the manuscript We also thank A R E SinclairTanzania National Parks Serengeti Wildlife Research Instituteand the TanzaniaWildlife Corporation

REFERENCES

Baile C A amp Forbes J M 1974 Control of feed intake andregulation of energy balance in ruminants Physiol Rev 54160^214

Bergman C M Fryxell J M amp Gates C C 2000 The eiexclectof tissue complexity and sward height on the functionalresponse of wood bison Funct Ecol (In the press)

Black J L amp Kenney P A 1984 Factors aiexclecting diet selectionby sheep II Height and density of pasture Aust J Agric Res35 565^578

Bradbury J W Vehrencamp S L Clifton K E amp CliftonL M 1996 The relationship between bite rate and localforage abundance in wild Thomsonrsquos gazelles Ecology 772237^2255

Braun H M H 1973 Primary production in the Serengetipurpose methods and some results of research Ann UnivAbidjan E 6 171^188

Breman H amp de Wit C T 1983 Rangeland productivity andexploitation in the Sahel Science 221 1341^1347

Daubenmire R 1959 A canopy-coverage method of vegeta-tional analysis Northw Sci 33 43^64

348 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

metabolic requirement for Artiodactyla (centgure 2)) realis-tically predict maximum daily values

Biomass of patches on which Serengeti grazers wereobserved was a function of their body mass Treating thedensity of each species in each year independently therewas a signicentcant positive relationship between body massand mean sward biomass of patches they occupied(log10 biomass (g miexcl2) ˆ 15 + 022 pound log10 body mass (kg)F113 ˆ54 p ˆ 004 r2 ˆ 03) The observed pattern bettermatched the predictions derived from complex swardsthan those from simple swards nevertheless the slope ofthe observed relationship among species was shallowerthan predicted by the model (022 compared with 086)

4 DISCUSSION

The sward biomass on which ruminants optimizeenergy gain is a positive decelerating function of bodymass This repoundects a gradual shift in the intersection ofthe digestion constraint and the cropping constraint fromlow biomass swards for small ruminants to swards ofhigher biomass for large ruminants with commensuratelylarger gut capacity Thus the positive relationshipbetween optimal sward biomass and ruminant body massis the result of both a relaxation of digestion constraints(Meissner amp Paulsmeier 1995) and increasing bite size(Gross et al 1993) in larger ruminants

Our assumption that energy gain by ruminants is ahump-shaped function of grass abundance (Fryxell 1991)makes our work fundamentally diiexclerent from previousallometric models We found that body mass-relatedhabitat selection can result purely from individual energymaximization independent of either plant species selec-tivity or interspecicentc competition and that in generalruminant herbivores should prefer short intermediatebiomass swards over tall high biomass swards In Illiusand Gordonrsquos (1987) allometric model of energy functionin ruminants daily energy gain is a positive function ofgrass abundance thus predicting that tall high biomasspatches should be preferred by grazing ruminants regard-less of body size They predict a positive relationshipbetween ruminant body mass and grass biomass as dowe but resulting from competition for tall high biomassswards Their model cannot explain the selection byruminants of low biomass swards when tall high biomassswards are available (McNaughton 1984 Langvatn ampHanley 1993 Wallis DeVries amp Schippers 1994 Wilm-shurst et al 1995 2000 Bradbury et al 1996)

It is interesting that we found no impact of phylogenyon predicted optimal sward biomass as this prediction isstrongly aiexclected by the form of the functional responsewhich is presumably under morphological control Never-theless we did centnd a slight diiexclerence between cervidsand bovids with respect to maximum daily energy gain(centgure 3) This suggests at least marginal phylogeneticlinkage between muzzle architecture and body masswhich has been postulated in other analyses of ruminantforaging strategies (Gordon amp Illius 1988)

The positive relationship we found between herbivorebody mass and sward biomass in the surveys of Serengetiherbivores lends qualitative support to the idea that allo-metric scaling in gut passage and cropping in ruminantsis linked to patch selection There is a tendency for small

ruminants to be found on lower biomass patches thanlarger ruminants during the growing season as predictedby our model Several processes could account for thedeviation of our model from the Serengeti observations Ifsward complexity is positively related to grass biomassthen predictions of optimal grass biomass for small rumi-nants would conform to the simple sward regressionmodel and predictions of optimal grass biomass for largeruminants would conform to the complex sward regres-sion model (centgure 2) Thus the eiexclects of swardcomplexity would predict a much shallower slope thanpredicted by either model In addition by choosing rela-tively simple representations of forage intake constraintswe ignore processes such as competition and predationthat inpounduence on herbivore distributions in the Serengeti(Sinclair 1985 Hofer amp East 1993 Durant 1998) Indeedwe found an inverse relationship between body mass andhow closely their observed patch choice matched thatpredicted perhaps the result of larger animals excludingsmaller animals from preferred patches

These results lend theoretical and empirical support tothe hypothesis that there is size-specicentc ecological separa-tion among grazing herbivores on the basis of diiexclerentialforaging ecurrenciency (Murray amp Brown 1993) The gradientbetween optimal patch and body mass suggests thatherbivores of similar body size and feeding style may becompeting Our work also suggests that large ruminantsshould perform better on more productive grasslandsthan do small ruminants with the converse true of low-productivity grasslands In highly productive grasslandsin which tillers grow and lose quality rapidly (Braun1973) large-bodied ruminants are favoured

This research was supported by an Ontario Graduate Scholar-ship to JFW a Natural Science and Engineering ResearchCouncil (NSERC) operating grant to JMF and an NSERCpostgraduate scholarship to CMB We are very grateful to HMeissner and the University of Pretoria for voluntary intakedata A Illius and M Murray for functional response para-meters and J M Gaillard and T D Nudds for valuablecomments on the manuscript We also thank A R E SinclairTanzania National Parks Serengeti Wildlife Research Instituteand the TanzaniaWildlife Corporation

REFERENCES

Baile C A amp Forbes J M 1974 Control of feed intake andregulation of energy balance in ruminants Physiol Rev 54160^214

Bergman C M Fryxell J M amp Gates C C 2000 The eiexclectof tissue complexity and sward height on the functionalresponse of wood bison Funct Ecol (In the press)

Black J L amp Kenney P A 1984 Factors aiexclecting diet selectionby sheep II Height and density of pasture Aust J Agric Res35 565^578

Bradbury J W Vehrencamp S L Clifton K E amp CliftonL M 1996 The relationship between bite rate and localforage abundance in wild Thomsonrsquos gazelles Ecology 772237^2255

Braun H M H 1973 Primary production in the Serengetipurpose methods and some results of research Ann UnivAbidjan E 6 171^188

Breman H amp de Wit C T 1983 Rangeland productivity andexploitation in the Sahel Science 221 1341^1347

Daubenmire R 1959 A canopy-coverage method of vegeta-tional analysis Northw Sci 33 43^64

348 J FWilmshurst and others Ruminant patch selection and allometry

Proc R Soc Lond B (2000)

Durant S M 1998 Competition refuges and coexistence anexample from Serengeti carnivores J Anim Ecol 67 370^386

Estes R D 1991 The behavior guide to African mammals LondonUniversity of California Press

Fryxell J M 1991 Forage quality and aggregation by largeherbivores Am Nat 138 478^498

Golley F B 1961 Energy values of ecological materials Ecology42 581^584

Gordon I J 1989 Vegetation community selection by ungulateson the isle of Rhum I Food supply J Appl Ecol 26 35^51

Gordon I J amp Illius A W 1988 Incisor arcade structure anddiet selection in ruminants J Anim Ecol 2 15^22

Gross J E Shipley L A Hobbs N T Spalinger D E ampWunder B A 1993 Functional response of herbivores in food-concentrated patches tests of a mechanistic model Ecology 74778^791

Gwynne M D amp Bell R H V 1968 Selection of vegetationcomponents by grazing ungulates in the Serengeti NationalPark Nature 220 390^393

Harvey P H amp Pagel M D 1991 The comparative method in evolu-tionary biology Oxford University Press

Hobbs N T amp Swift D M 1985 Estimates of habitat carryingcapacity incorporating explicit nutritional constraints JWildl Mgmt 49 814^822

Hofer H amp East M L 1993 The commuting system ofSerengeti spotted hyaenas how a predator copes with migra-tory prey II Intrusion pressure and commutersrsquo space useAnim Behav 46 559^574

Illius A W amp Gordon I J 1987 The allometry of food intakein grazing ruminants J Anim Ecol 56 989^999

Illius A W amp Gordon I J 1992 Modelling the nutritionalecology of ungulate herbivores evolution of body size andcompetitive interactions Oecologia 89 428^434

Jarman P J 1974 The social organisation of antelope in relationto their ecology Behaviour 48 215^266

Konoplev V A Sokolov V E amp Zotin A L 1978 Criterion oforderliness and some problems of taxonomy InThermodynamics of biological processes (ed I Lamprecht amp A LLotin) pp 349^359 Berlin deGruyter

Laca E A Ungar E D Seligman N amp Demment M W1992 Eiexclects of sward height and bulk density on bite dimen-sions of cattle grazing homogeneous swards Grass Forage Sci47 91^102

Laca E A Ungar E D amp Demment M W 1994Mechanisms of handling time and intake rate of a largemammalian grazer Appl Anim Behav Sci 39 3^19

Langvatn R amp Hanley T A 1993 Feeding-patch choice by reddeer in relation to foraging ecurrenciency Oecologia 95 164^170

Lundberg P 1988 Functional response of a small mammalianherbivore the disc equation revisited J Anim Ecol 57999^1006

McNaughton S J 1984 Grazing lawns animals in herds plantform and coevolution Am Nat 124 863^886

Meissner H H amp Paulsmeier D V 1995 Plant compositionalconstituents aiexclecting between-plant and animal speciesprediction of forage intake J Anim Sci 73 2447^2457

Murray M G amp Brown D 1993 Niche separation of grazingungulates in the Serengeti an experimental test J Anim Ecol62 380^389

Owen-Smith N 1993 Evaluating optimal diet models for anAfrican browsing ruminant the kudu how constraining arethe assumed constraints Evol Ecol 7 499^524

Peters R H 1983 The ecological implications of body sizeCambridge University Press

Rittenhouse L R Streeter C L amp Clanton D C 1971Estimating digestible energy from digestible dry and organicmatter in diets of grazing cattle J Range Mgmt 24 73^75

Shipley L A Gross J A Spalinger D E Hobbs N T ampWunder B A 1994 The scaling of intake rate in mammalianherbivores Am Nat 143 1055^1082

Short J 1985 The functional response of kangaroos sheep andrabbits in an arid grazing system J Appl Ecol 22 435^447

Sinclair A R E 1985 Does interspecicentc competition or preda-tion shape the African ungulate community J Anim Ecol54 899^918

Spalinger D E amp Hobbs N T 1992 Mechanisms of foraging inmammalian herbivores new models of functional responseAm Nat 140 325^348

Trudell J amp White R G 1981 The eiexclect of forage structureand availability on food intake biting rate bite size and dailyeating time of reindeer J Appl Ecol 18 63^81

Van Soest P J 1982 Nutritional ecology of the ruminant CorvallisOR O amp B Books

Vesey-Fitzgerald D F 1960 Grazing succession among eastAfrican game mammals J Mamm 41 161^172

Waite R 1963 Botanical and chemical changes in maturinggrass and their eiexclect on its digestibility Agr Prog 38 50^56

Wallis DeVries M amp Schippers P 1994 Foraging in a landscapemosaic selection for energy and minerals in free-rangingcattle Oecologia 100 107^117

Wickstrom M L Robbins C T HanleyT A Spalinger D Eamp Parish S M 1984 Food intake and foraging energetics ofelk and mule deer JWildl Mgmt 48 1285^1301

Wilmshurst J F Fryxell J M amp Hudson R J 1995 Foragequality and patch choice by wapiti (Cervus elaphus) Behav Ecol6 209^217

Wilmshurst J F Fryxell J M amp Colucci P E 1999 Whatconstrains daily intake in Thomsonrsquos gazelles Ecology 802338^2347

Wilmshurst J F Fryxell J M Farm B P Sinclair A R Eamp Henschel C P 2000 Spatial distribution of Serengeti wild-ebeest in relation to resources Can J Zool (In the press)

Ruminant patch selection and allometry J FWilmshurst and others 349

Proc R Soc Lond B (2000)