Herd Size in Large Herbivores: Encoded in the Individual or Emergent?

8 Pages·2002·3.4 MB·

by  Jean-Francois Gerard

Reference: Biol. Bull 202: 275-282. (June 2002)
Herd Size in Large Herbivores:
Encoded in the Individual or Emergent?
JEAN-FRANCOIS GERARD1'*, ERIC BIDEAU1, MARIE-LINE MAUBLANC1.
PATRICE LOISEL2 AND CAROLE MARCHAL1
,
ll>istiti(t de Recherche stir les Grands Mammiferes. INRA, BP 27. 31326 Castanet Tolosan Cedex,
France: and 2Laboratoire d'Analyse des Systemes et Biometrie, INRA, 2 Place Vialu.
34060 Montpellier Cedex 1. France
Abstract. In large mammalian herbivores, the increase of (Spinage. 1969: Johnson. 1983: Wirtz and Lorscher. 1983:
group size with habitat openness was first assumed to be an Table 1 ). Second, herd size increases with habitat openness:
adaptive response, encoded in the individual. However, it whereas groups are small in forested habitats, they are much
could, alternatively, be an emergent property: if groups larger in grassland and other open landscapes. This second
were nonpermanent units, often fusing and splitting up. then trend was initially reported in African antelope taken as a
any increase of the distance at which animals perceive one whole, considering the typical habitat and herd size ofeach
another could increase the rate of group fusion and thus species (Estes. 1974; Jarman. 1974). It was then recorded
mean group size. Dynamical models and empirical data within species using habitats of varying openness (Leu-
support this second hypothesis. This is not to say that thold. 1970: Evans. 1979: LaGory, 1986: Hillman. 1987:
adaptive modifications of mean herd size cannot occur. Table 2: Fig. 1 ).
However, this changes the way in which we can envisage These two general trends were rapidly explained in two
the history ofgregariousness in large herbivores during the diverging ways. As early as 1964, Caughley hypothesized
Tertiary. that groups of large herbivores were nonpermanent units
that often fused and split up. On this basis, the author
Introduction suggested that any increase in population density should
Large mammalian herbivores, such as ruminants or kan- increase the rate of group meeting, and thus the average
garoos, make up groups that are easily recognizable in the group size. This purely mechanistic proposal is equivalent
field: they consist of individuals located a short distance to saying that group size is an emergent property, resulting
from one another and most often engaged in a common from multiple fusion and fragmentation events, andthat it is
activity, forexample, feeding, traveling, orresting. The size sensitive to variations of population density.
of these groups is very variable and has been a matter of In contrast to Caughley's proposal, the variation ofgroup
study for ethologists and ecologists for about 40 years. size with habitat openness was assumed to be a biological
Two general trends were early identified. First, within a adaptation, encoded in the individual. A central argument,
species, group sizetendsto increase with population density developed by Estes (1974) and Jarman ( 1974), was that in
closed habitat, a herbivore can easily reduce the probability
of being detected by predators by being discreet and, espe-
*To whom correspondence should be addressed. E-mail: jfgerard@ cially, by living in small groups. By contrast, in open
toulouse.inra.fr
This paper was originally presented at a workshop titled The Limil\ to habitat, it is more difficult to escape notice. Being sur-
Self-OrganizationinBiologicalSystems.Theworkshop,whichwasheldat rounded by many conspecifics should then ensure the best
the J. Erik Jonsson Center ofthe National Academy ofSciences, Woods protection against predators because, in the event of an
Hole, Massachusetts,from 11-13 May 2001.wassponsoredby theCenter attack, there is a high probability that the victim will be
fLoarboArdavtoarnyc,edanSdtufduinedsedinbtyhethSepaNcaetiLoinfaelSAceireonncaeustiatcsthaenMdaSrpianceeBAiodlmoigniicsa-l another group member ("selfish avoidance of predators by
tration underCooperative Agreement NCC 2-896. aggregation"; Hamilton, 1971). As a consequence, natural
275
276 J.-F. GERARD ET AL.
Table 1
Variation ofgroup size withpopulation density in differentspeciesoflarge herbivores (Macropus spp. are kangaroos, which are marsupials:
the otherspeciesare ruminants i.e., eutherians)
HERD SIZE IN LARGE HERBIVORES 277
POP.DENSITY:
7-8 DEER/ 100 HA
DECIDUOUS
FOREST
^
(Dourdan)
278 J.-F. GERARD ET AL
more, this shows that Sibly's model is incompatible with the groups arriving in view of each other merge with a proba-
hypothesis proposed by Caughley for the increase ofgroup bility that is independent of their sizes, but not necessarily
size with population density. equal to 1. Second, the groups are assumed to split into two
Sibly's model was further developed during the 1980s (and not only to lose single individuals) with a probability
and 1990s, by introducing altruism towards relatives and/or |3.v, where ft is a constant and .v, the group size. Here, /3 can
thepossibility forgroupmembers to limit the increaseofthe be interpreted as the probability with which any individual
size of their group by repelling joiners (see Giraldeau and adopts a trajectory differing from that of the other group
Caraco, 2000, for a review). Indeed, the initial model ig- members and is possibly followed by some of them. In
nored kin selection. Moreover, by joining a group whose practice, the size distribution ofsplitting groups is assumed
to be uniform.
size is larger than orequal to the optimal size, an individual
enhanced its fitness but lowered the fitness of the group The assumptions ofour model (Gerard and Loisel, 1995)
members, so that the latter could be assumed to repel the are more complicated than those considered by Bonabeau
joiner. Some of these modifications of the initial model and Dagorn. and Gueron and Levin. First, as is more or less
improve the first property described above in that they lead, implicit in the two latter models, each individual is assumed
at equilibrium, to a mean group size that tends to be closer to be able to detect any conspecific present inside an area a,
to the optimal size. However, they do not improve the other characterizing habitat openness. Second, each individual
properties of the model. So, they remain both inconsistent oscillates in a probabilistic way between a"social" state and
with the data recorded in large herbivores and incompatible an "individualistic" state. When in the social state, an ani-
with Caughley's hypothesis. maljoins every perceived conspecific, then behaves in such
a way as to stay with it. By contrast, when in the individ-
Fusion-Fission Models ualistic state, an animal moves without taking conspecifics
into account. As a consequence, groups fuse through attrac-
According to Caughley ( 1964), an increase in population tion and split up. When two individuals (or groups of
density should increase the mean size of groups that fre- individuals) in the social state perceive one another, the
quently fuse and split up, by enhancing the rate of group individuals merge and form a single group. When an indi-
encounter and thus fusion. Following the same rationale, it vidual (or a group of individuals) in the social state per-
could be hypothesized that any increase ofhabitat openness, ceives an animal in the individualistic state, itjoins it. In this
and thus of the distance at which groups can perceive one case, the resulting group actually includes a leader, which is
another, should increase the rate of group fusion, and thus the animal in the individualistic state. However, if, within a
mean group size (Gerard et ai. 1993). This should at least group of this kind, a second individual turns out to be
be the case, provided group fusion results from an attraction individualistic, then the group includes two leaders moving
between groups. Clearly, ifgroup fusion results from simple independently of each other; as a consequence, the other
"collisions," then the distanceat which animalscan perceive group members distribute themselves at random (with prob-
one another should be without influence. ability 1/2) near the two leaders, and the group splits up.
The plausibility of this hypothesis was confirmed in the The probability e of shifting from the social state to the
amnidd-1L9e9v0isn,(w19h9e5n),BaonndabtewaouoafndtheDaaguothronrs(1o9f95t)h,e Gpureesreonnt sihnidfitviindgualairsetifcixesdt,atseoatnhadt tthhee ipnrdoibvaibdiulailt'ysjbu,ehoafvitohre irsevienrdsee-
paper (Gerard and Loisel, 1995) developed new dynamical pendent of habitat openness, population density, and group
models of group formation. These models contrasted with
size.
Sibly's model in that groups were assumed to fuse and split Though they rely on different assumptions, the Bonabeau
up without any group size being preferred by the individu- and Dagorn model (1995), the Gueron and Levin model
balys.CTohheeyn (w1e9r7e1i),nifnawcthigcehne"rcaalsiuzaaltigornosuopfs"awperreeviaosussummeoddetlo ( 1995). and our model exhibit remarkably similar emergent
properties.
increase or decrease by a single individual (see also Okubo.
1986: pp. 45-49). 1. The first property that the three models have in com-
The model by Bonabeau and Dagorn (1995) is probably mon is that the group size distributions obtained at equilib-
the simplest. First, the groups (solitary individuals included) rium resemble those ordinarily recorded in large herbivore
that compose the population are assumed to move al ran- populations: the group frequency exhibits a single maxi-
dom. Second, two groups arriving within the same portion mum for isolated individuals or a small group size, then
ofspace systematically merge, then behave as a single group. monotonously decreases with group size; moreover, the
Third, at each time step, a fractionp ofthe individuals leave standard deviation ofgroup sizes tends to be large when the
the groups they are in by temporarily becoming solitary. mean is large.
In its basic version, the model by Gueron and Levin 2. Whatever the model, the group size distribution ob-
(1995) differs from the latter in two aspects. First, two tained at equilibrium for any given values ofthe parameters
HERD SIZE IN LARGE HERBIVORES 279
POP. DENSITY: POP. DENSITY:
10INDIV./100HA 20 INDIV./ 100 HA
i
PERCEIVED
AREA:
a=0.5 ha
PERCEIVED
AREA:
= 16.0ha
282 J.-F. GERARD ET AL.
Peek, J. M., R. E. LeResche, and D. R. Stevens. 1974. Dynamics of Spinage,C.A. 1969. TemtonalityandsocialorganizationoftheUganda
moose aggregations in Alaska. Minnesota, and Montana. J. Mammal defassa waterbuck Kohus ciefassa ugaiulae. J. Zool. Lt>nd. 159: 329
55: 126-137. 361.
Putman, R. J. 1988. The Natural History ofDeer. Christopher Helm. Taylor, R. J. 1982. Groupsize inthe Eastern grey kangaroo,Macropus
London. giganteus. and the wallaroo, Macropus rolnistus. Aust. Wildl. Res. 9:
Richard-Hansen, C., G. Gonzalez, and J.-F. Gerard. 1992. Structure 229-237.
sociale de 1'isard (Rupicapra pyrenaica) dans trois sites pyreneens. Taylor, R. J. 1983. Association ofsocial classes ofthe wallaroo, Mac-
GibierFaune Stiuvage 9: 137149. mpu\ ri>hitstn.\ (Marsupialia: Macropodidae). Aust. Wildl. Res. 10:
Schaal, A. 1982. Influence de I'environnement sur les composantes du 39-45.
groupe social chez le daim Ccn-us (Dama) Jama L. Rev. Ecol. Terre Toi'go,C.,J.-M.Gaillard,andJ.Michallet. 1996. Lafailledesgroupes:
Vie 36: 161-174. un hioindicateur de 1'effectifdes populations de bouquetin des Alpes
Sibly, R. M. 1983. Optimal group size is unstable. Aiiiin. Brluii: 31: (Capra ihcx //>f.v)?Mammalia 60: 463-472.
947-948.
Soutkhawneglalr,oo,C.MaJc.ro19p8u4sa.gigaVnatreiuasb.iliI.tyGrionupgrdoeunpsiintgy ainndtghreouEpasstiezre.nAgurset.y WaltBhreoro,keF~.1XR2.7)1i9n7t2h.eSeSroecnigaeltigrnoatuipoinnaglpianrkG.raZn.t'Tsiergpaszyeclhloel.(G3a1z:el3l4a8-gr4a0n3t.i
Wildl. Res. 11: 423-435. Wirtz, P., and J. Lorscher. 1983. Group sizes ofantelopes in an East
Southwell, C. J. 1984h. Variability in grouping in the Eastern grey African national park. Behaviour84: 135-156.
kangaroo.Macropusgignnteiis. II. Dynamicsofgroupformation.Aust.
Wild!. Res. 11: 437-449.
Appendix
Mean group size at equilibrium in the model by Bonabeau and Dagorn
We here correct an error made by Bonabeau and Dagorn
(1995) when deriving the mean group size from their fu-
sion-fission model. We furthershow that once thecorrection and the mean size of groups
is made, increasing the population density or the area per-
ceived by the individuals by a multiplicative factor k has
exactly the same effect on mean group size. \f2pN
Mean group size therefore varies with vn/N, and not
Analytical expression ofmean group size with V/i/A7 as found by Bonabeau and Dagorn. Further-
In the model by Bonabeau and Dagorn, space is divided more, once corrected, the analytical expressionsofthe num-
into N sites, the whole population included n individuals ber and mean size of groups at equilibrium become strictly
(n <S N), and the individuals simultaneously present within equivalent to those obtained by Gueron and Levin (1995)
any given site are considered as the members of a single with their own model.
group. At each discrete time step, a fraction p of the /;
individuals of the population leave the group they are in as Effect ofpopulation clensit\ and habitat openness
solitary animals, and are reinjected at random into the N In the model of Bonabeau and Dagorn, groups entering
sites. In addition, each group moves towards a randomly the same site aggregate into a single group. So, a site can be
selected site, and the groups (and solitary individuals) en- considered as an area in which any individual perceives its
tering the same site aggregate to form a single group. conspecifics. IfA designates the area available to the whole
As a consequence of these assumptions, the expectNed+ population, then the area ofeach site is a = AIN. It follows
number of groups (i.e., the number of sites occupied) that the mean size of groups at equilibrium is
varies between two successive time steps according to:
lad
N~(t + 1 ) = N^(t) + pn
[N+(t) + pn][N+(t) + pn - 1] 1 =
where </ nlA is the population density. It then appears that
2 N'
multiplying the area perceived by the individuals (n) or the
The denominator ofthe right part of the equation is N, and population density (J) by a factor k has exactly the same
not N2 as written by Bonabeau and Dagorn (1995). At effect on the mean size of groups at equilibrium. The same
equilibrium, N+ (t + 1 ) = N+ (t), so that the expected is true with the model by Gueron and Levin (1995) and ours
number of groups is approximately (Gerard and Loisel. 1995: appendix B).
Reference: Biol. Bull. 202: 283-288. (June 2002)
Self-Organization and Natural Selection in the
Evolution of Complex Despotic Societies
C. K. HEMELRIJK
Department ofInformation Technology and Anthropological Institute and Museum.
University ofZurich, Swit
Abstract. Differences between related species are usually side effect of the change of one single trait proper to an
explained as separate adaptations produced by individual se- egalitarian society, in the real world a despotic society may
lection. Idiscussin thispaperhowrelatedspecies, whichdiffer alsohave arisen asasideeffectofthe mutationofa single trait
in many respects, may evolve by a combination ofindividual ofan egalitarian species.
selection, self-organization, and group-selection, requiring an Ifgroups with different intensitiesofaggression evolve in
evolutionary adaptation ofonly a single trait. In line with the this way. they will also have different gradients of hierar-
supposed evolution ofdespotic species of macaques, we take chy. When foodisscarce, groups with the steepest hierarchy
as a stalling point an ancestral species that is egalitarian and may have thebestchance to survive, because at leastasmall
mildly aggressive. We suppose it to live in an environment number of individuals in such a group may succeed in
with abundant food and we put the case that, iffood becomes producing offspring, whereas in egalitarian societies every
scarce and more clumped, natural selection at the level ofthe individual is at risk ofbeing insufficiently fed to reproduce.
individual will favor individuals with a more intense aggres- Therefore, intrademic group selection (selection within an
sion (implying, for instance, biting and fierce fighting). interbreeding group) may have contributed to the evolution
Using an individual-centered model, called DomWorld, I of despotic societies.
showwhathappenswhen the intensity ofaggression increases.
InDomWorld,grouplifeisrepresentedbyartificial individuals Introduction
that live in a homogeneous world. Individuals are extremely
simple: all they do is flock together and, upon meeting one The assumption that evolution occurs through a single
another, they may perform dominance interactions in which evolutionary process is no longer tenable (e.g., see Plotkin
tinhteeenfsfietcytsofofawgignrensisnigonanidnltohseinmgoadreelselisf-irnecinrfeoarsceidn,g.aWchoemnpltehxe oarnidesOdhlaivneg-sSlomweley, b1e9c81o)m,eamndormeulatcicpelep-tleedve(le.gs.e.leHcotigoenwethge,-
feedback between the hierarchy and spatial structure results: 1994; Maynard Smith and Szathmary, 1995: Mitteldorfand
Wilson, 2000). Multiple-level selection processes may in-
via self-organization, this feedback causes the egalitarian so- clude some, or all, of the following factors: the multi-level
cbieettwyeeton cthheantgweo itnytpoesaodfeasrptoitfiiccialonseo.ciTethyeclmoasnelyy cdiofrfreersepnocneds cathianrgacotnertohfembi(oLleowgiocnatlins,ys1t9e7m0s; aHnodgenwaetugr,al19s9e4l;ectSioobneropaenrd-
to those between despotic and egalitarian macaques in the real Wilson, 1998), self-organization and its consequences for
world. Given that, in the model, the organization chanses as a evolution (Boerlijst and Hogeweg, 1991), and nonlinear
genotype-phenotype mappings (Kauffman, 1993; Huynen
E-mail: hemelrij<S'iri.unizh.ch and Hogeweg. 1994; Kauffman, 1995).
This paper was originally presented at a workshop titled The Limits to Within this framework of multiple-level selection theo-
Self-OrganizationinBiologicalSystems.Theworkshop,whichwasheldat ries. I present in this paperan example ofthe way in which
the J. Erik Jonsson Center ofthe National Academy ofSciences, Woods
Hole,Massachusetts, from 11-13 May 2001,wassponsoredbytheCenter a certain type of society may evolve. In studies of animal
forAdvanced Studies in the Space Life Sciencesat the Marine Biological behavior, a distinction is usually made between two types of
Laboratory, and funded by the National Aeronautics and Space Adminis- societies egalitarian and despotic. In her studies of birds,
tration underCooperative Agreement NCC 2-896. Vehrencamp (1983) distinguishes between these two on the
283
282 J.-F. GERARD 7 AL
Peek, J. M., R. E. LeResche, and D. R. Stevens. 1974. Dynamics of Spinage,C.A. 1969. TemtorialityandsocialorganizationoftheUganda
moose aggregations in Alaska, Minnesota, and Montana. J. Mammal. defassa waterbuck Kobus defassa ugandae. J. Zoo/. Land. 159: 329-
55: 126-137. 361.
I'mnun. R. J. 1988. The Natural History ofDeer. Christopher Helm. Taylor, R.J. 1982. Group size in the Eastern grey kangaroo.Macropus
London. giganteus. and the wallaroo. Macropus robustiis. Aust. Wildl. Res. 9:
Richard-Hansen. C., G. Gonzalez, and J.-F. Gerard. 1992. Structure 229-237.
sociale de 1'isard (Rupicapra pyrenaica'i dans trois sites pyreneens. Taylor, R. J. 1983. Association ofsocial classes ofthe wallaroo, Mac-
GiliierFaune Sauvage 9: 137-149. ropus riihiixnix (Marsupialia: Macropodidae). Aust. Wildl. Res. 10:
Schaal, A. 1982. Influence de 1'environnement sur les composantes du 39-45.
groupe social chez le daim Cen'iis (Damn) itumii L. Rev. Ecol. Tern- Toi'go,C.,J.-M.Gaillard.andJ.Michallet. 1996. Latailledesgroupes:
Vie 36: 161-174. un hioindicateur de 1'effectifdes populations de bouquetin des Alpes
Sibly, R. M. 1983. Optimal group size is unstable. Aniin. Behav. 31: (Capru ibex ibex}''Mammalia 60: 463 172.
947-948.
SoutkWhaiwlnedg!la.lr,oRoe.Cs..Ma1J1c.:ro149p28u34s-a4.g3i5g.aVnatreiuasb.ili1.tyGrionupgrdoeunpsiintgy ainndtghreouEpasstiezren.Agnrset.y WWiarlttBzhr,eoroP,k.,eKa.1n8R2d.7)J.1i9nL7t2oh.resScehSreoercni.gaelt1i9g8rn3oa.tuipoinnGaglropiuanrpkG.rsaiZnzte'Tssieo/gfpaszayenclthleoel/o.(pGe3a1sz:eil3nl4aa8n-gr4Ea0an3st.ti
Southwell, C. J. 1984b. Variability in grouping in the Eastern grey African national park. Behaviour84: 135-156.
kangaroo,Macropusgiganteus. II. Dynamicsofgroupformation.Aust.
Wildl. Res. 11: 437-449.
Appendix
Mean group size at equilibrium in the model by Bonabeau and Dagorn
We here correct an error made by Bonabeau and Dagorn ATU) = A/
(1995) when deriving the mean group size from their fu-
sion-fission model. We furthershow thatonce thecorrection and the mean size of groups
is made, increasing the population density or the area per-
ceived by the individuals by a multiplicative factor k has ~N^~WN'
exactly the same effect on mean group size.
Mean group size therefore varies with Vn/N, and not
Analytical expression ofmenu xroup size with X/H/A/" as found by Bonabeau and Dagorn. Further-
In the model by Bonabeau and Dagorn, space is divided more, once corrected, the analytical expressionsofthe num-
into N sites, the whole population included n individuals ber and mean size ofgroups at equilibrium become strictly
a(/niy<gAiOv,enansditethaereincdoinvisdiudaelrsedsiamsultthaenemoeumslbyerpsresoefntawsiitnhgilne ewqiutihvatlheeinrtotwonthmoosdeelo.btained by Gueron and Levin (1995)
group. At each discrete time step, a fraction p of the 71
individuals ofthe population leave the group they are in as Effect ofpopulation density and habitat openness
solitary animals, and are reinjected at random into the N In the model of Bonabeau and Dagorn, groups entering
sites. In addition, each group moves towards a randomly the same site aggregate into a single group. So, a site can be
selected site, and the groups (and solitary individuals) en- considered as an area in which any individual perceives its
tering the same site aggregate to form a single group. conspecih'cs. IfA designates the area available to the whole
As a consequence of these assumptions, the expectNe+d population, then the area ofeach site is a = AIN. It follows
number of groups (i.e., the number of sites occupied) that the mean size of groups at equilibrium is
varies between two successive time steps according to:
lad
N+(t + 1) = AT(r) + pn
~
P" 1] where d = nIA is the population density. It then appears that
2 N' multiplying the area perceived by the individuals () or the
The denominator ofthe right part of the equation is N, and population density (d) by a factor k has exactly the same
not N2 as written by Bonabeau and Dagorn (1995). At effect on the mean size ofgroups at equilibrium. The same
equilibrium, N+ (t + 1 ) = /V+ (/), so that the expected is true with the model by Gueron and Levin (1995) and ours
number of groups is approximately (Gerard and Loisel, 1995: appendix B).