Evolution of Generalists and Specialist in Spatially Heterogeneous Environments
Author(s): Peter H. Van Tienderen
Source: Evolution, Vol. 45, No. 6 (Sep., 1991), pp. 1317-1331
Published by: Society for the Study of Evolution
Stable URL: http://www.jstor.org/stable/2409882
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Evolution,45(6), 1991, pp. 1317-1331
EVOLUTION
OF GENERALISTS AND SPECIALISTS IN SPATIALLY
HETEROGENEOUS ENVIRONMENTS
PETER
H. VAN TIENDEREN'
Departmentof Botany,Duke University,
Durham NC 27706 USA and
Institutefor Ecological Research,Heteren,THE NETHERLANDS
Abstract.-Quantitative genetic models are used to investigatethe evolution of generalistsand
specialistsin a coarse-grainedenvironmentwith two habitat typeswhen thereare costs attached
to being a generalist.The outcomes forsoftand hard selectionmodels are qualitativelydifferent.
Under softselection(e.g., forjuvenile or male-reproductivetraits)the population evolves towards
the single peak in the adaptive landscape. At equilibrium,the population mean phenotypeis a
compromise between the reaction that would be optimal in both habitats and the reactionwith
the lowest cost. Furthermore,the equilibrium is closer to the optimal phenotypein the most
frequenthabitat,or thehabitatin whichselectionon thefocaltraitis stronger.A specialistgenotype
always has a lower fitnessthan a generalist,even when the costs are high.
In contrast,under hard selection (e.g., for adult or female-reproductivetraits)the adaptive
landscape can have one, two, or threepeaks; a peak representsa population specialized to one
habitat,equally adapted to both habitats,or an intermediate.One peak is always foundwhen the
reactionwiththe lowest cost is not much different
fromthe optimal reaction,and this situationis
similar to the soft selection case. However, multiple peaks are presentwhen the costs become
higher,and the course of evolution is then determinedby initial conditions,and the region of
attractionof each peak. This implies thatthe evolution of specializationand phenotypicplasticity
may not onlydepend on selectionregimeswithinhabitats,but also on contingent,historicalevents
(migration,mutation).Furthermore,the evolutionarydynamicsin changingenvironmentscan be
widely different
for populations under hard and soft selection. Approaches to measure costs in
naturaland experimentalpopulations are discussed.
Key words.-Cost of adaptation, genotype-environment
interaction,phenotypicplasticity,quantitativegenetics.
Received October 18, 1990. Accepted February 15, 1991.
The adage "a jack-of-all-tradesis a masterofnone" regularlyappears in discussions
on the evolution of specialization in heterogeneousenvironments(e.g., MacArthur
and Connell, 1966). Yet, an organismdoes
not necessarilyhave to be a master of all
trades:afterall, a generalistcan exploitmultiple habitat typesor food sources,while a
specialist is limited to only one or a few.
The question to be addressed thenbecomes
under what conditionsspecialization is expected to evolve (Levins, 1968; Futuyma
and Moreno, 1988), forwhichthereappear
to be two main categories(Van Tienderen,
1990). In the firstplace, individual adaptations may not be feasible;then we are in
the realm of constraintson evolution,in all
its possible manifestations(Maynard Smith
et al., 1985; Gould, 1989). For instance,the
bill length of birds may determine their
feedingefficiencyon differentprey types.
' Correspondence:InstituteforEcological Research,
P.O. Box 40, 6666 ZG Heteren,The Netherlands.
Generalist birds with intermediate bill
lengths may evolve when prey types are
alike,specializationwhenmorediverseprey
typesrequirehighlydissimilarbeaks (MacArthurand Connell, 1966). Furthermore,
genetic polymorphism may occur under
certain conditions (Hedrick, 1986; Hoekstraet al., 1985). Anothermanifestationof
constraintsis a perfectgenetic correlation
betweenthe expressionof a traitin two environmentsthat precludes an adaptive selectiveresponse(Via and Lande, 1985; Via,
1987).
The secondreasonwhyspecializationmay
evolve is thatthe costs involved in being a
generalistare veryhigh.It probablycannot
be assumed that,in general,adaptive phenotypic plasticityin response to environmental factorsis withoutsome cost (Bradshaw, 1965). Althoughgeneralismis often
equated with plasticityin particulartraits,
generalismand its costs may also be associated with the abilityto maintain homeostasisacross environments.This paper considers the evolution of a quantitativetrait
1317
1318
PETER H. VAN TIENDEREN
optima
different
A
50
optima
fitness
equal
B
1.0
CD3
/
20
10 10
0
1
C
12
-
08-generalist
-
specialist
.. .specialist
1
2
0.4
~~~~~~~~~~~~02
0.0
habitat
habitat
habitat
in twohabitats.Optimaindicatedbysoliddots.Three
Selectionfora plasticand a staticphenotype
In (A), theoptimain thetwohabitatsaredifferent
arepictured,
twospecialists
and a generalist.
genotypes
(10
In (B), optimalphenotypes
arethesamein bothhabitats(25),
and 40 respectively),
i.e.,selectionforplasticity.
i.e., selectionforstasis.In (C), fitness
differences
are associatedwithboth(A) and (B) forthethreegenotypes.
The assumption
of a costto simultaneous
adaptationimpliesthatwithineach habitatthegeneralists
have a
lowerfitness
thanthespecialists,
despitetheirsimilarphenotypes
in thefocalhabitat.The genotypes
pictured
arethreeexamplesoutofa potential
arrayofgenotypes,
ranging
fromspecialists
to thegeneralist.
The outcome
ofselectiondependsbothon thefitness
withinthehabitats(C) and thewayin whichfitness
within
differences
habitatscombinesto makefitness
at thepopulationlevel.
FIG. 1.
in a coarse-grainedenvironmentwith two opmentcapable of producingdifferent
phehabitat types,assuming that genotypesde- notypes,and mechanismsforgatheringand
viating from a specific cost-freeresponse processingenvironmentalinformationmay
experiencea reductionin fitness.Both se- be costly(Futuymaand Moreno, 1988). The
lectionfora plastic (Fig. 1A) and a homeo- resourceinvestmentsneeded forthese two
staticresponse(Fig. 1B) may lead to a sim- processes need not be the same and, moreilarpatternoffitnessdifferences
betweenthe over, the two need not always be coupled.
generalistand specialiststrategies(Fig. 1C). If costs are mainly due to accurate assessSelection for a homeostatic reaction (Fig. mentof the environment,a random choice
1B) may occur for example in the case of between alternativephenotypeswith fixed
regulationof body temperaturein animals probabilities might be the best strategy
in temperature. (Cooper and Kaplan, 1982; Lloyd, 1984).
thatlive in habitatsdiffering
A constant internal temperaturemay be Althoughmakingmistakescan be seen as a
beneficialbecause it allows enzymesto react cost factorfora generalist,this possibility
at theiroptimal temperature.However, the is not furtherconsidered;in our models aspotential to keep body temperaturecon- sessmentof theenvironmentmay be costly,
stant can be achieved only by numerous but it is nonerratic.
plastic anatomical, physiologicalor behavVan Alstyne(1988) studiedgrazingofthe
ioral mechanisms,requiringresources,and brown alga Fucus distichus
by the herbivsuch a generaliststrategymay pay offonly orous marinesnail Littorina
sitkana.In the
if organismsdo indeed encounterhabitats field,the phenolic concentrationsin the alin ambient temperature.
differing
gae varied with herbivore density,and a
Fitness costs of adaptation to a hetero- herbivore-induceddefensemediatedby tisgeneous environmentmay have different sue damage was shown to exist. There is a
origins.The developmentalmechanismbe- two-week time-lag in production of phehind a conditionalreactionhas two aspects: nolics after tissue damage, during which
first,
developmentalpathwaysmustbe pres- damaged plants are even more attractiveto
ent that can resultin different
phenotypes, the snails than undamaged plants (Van Aland second, the particular path followed styne, 1988). Thus, in habitats with high
must depend on the environmentin which herbivoredensitiesalgae withthisinducible
the genotypeoccurs. Both a flexibledeyel- systemmay be outcompetedby specialized
EVOLUTION
OF GENERALISTS AND SPECIALISTS
1319
algae with high phenolic concentrations, next generationis independentof the focal
while in the absence of grazing they may trait (e.g., each subpopulation has a fixed
have a lower fitnessthan the specialistthat "carryingcapacity"). Holsingerand Pacala
cannot be induced (e.g., due to the costs of (1990) argue that this may pertain to jumale fitness,
detectinggrazingand maintainingprecur- venile traitsand traitsaffecting
sors,allowinga triggered
response).Similar because thesetraitsmay have littleeffecton
costs may occur in otherplantswithinduc- the total production of offspringin each
ible defenses against pathogens or herbi- habitat. In contrast,under hard selection
vores (Futuyma, 1983; Harvell, 1986; Ha- the contributionof a subpopulation to the
vel, 1987; Levin, 1976).
next generationdoes depend on the genoIn Figure 1 the reactions of only three typespresent,forinstanceon theirefficiency
genotypesare plotted:a generalistand two in utilizingavailable resources. This may
specialists.From Figure 1C it cannot be in- pertain to adult and female-reproductive
ferredwhichgenotypewill win; thiswill de- traits(Holsinger and Pacala, 1990). Also,
pend on the global fitnessof a genotype, under hard selection total population size
averaged over the two habitats. Further- may change duringevolution, while under
more,intermediategenotypesmay prove to softselectionitmayremainconstant(Chrishave an even higherfitnessthan a pure spe- tiansen, 1975; Via and Lande, 1985; Ancialist or generalist.In our approach the tonovics and Via, 1988), even thoughthe
quantitativetraitis assumed to have a nor- population may be poorly adapted to one
mal distributionof breedingvalues, but no or both habitats.
a prioriconstraintsare imposed by limiting
Dynamic equations for evolutionary
the number of different
genotypes,or pos- change will be derived, using standard
sible phenotypes. Consequently, the pre- quantitative genetic techniques (Falconer,
dicted outcome of selection is expected to 1981; Lande, 1979), withtheirassumptions
depend primarilyon the selection regimes (see Via and Lande, 1985, 1987). One trait
withinhabitats,and how theyare relatedto expressedin two habitatscan be viewed as
selection at the population level. The pur- two characterstatesthatare geneticallycorpose of this study was to see under what related(Falconer, 1.952).The genotypicvalconditions selection leads to specialists or ues of the two characterstates(i1, Z2) have
generalists,how thisrelatesto costs of phe- an additive and a nonadditive component.
notypic adaptation, the frequenciesof the The expressed characterstate, z1 or z2, is
different
habitats,and the mode of regula- the sum of the genotypicvalue and an ention of population density(softor hard se- vironmentaldeviation. W1 and W2 are the
lection).Evolutionarydynamicsare further fitnessesin habitat one and two, respecstudied in a case where environmentalfre- tively.When one assumes coststo plasticity,
quencies graduallychangein time;thismay the fitnessof a genotype(il, Z2) in habitat
lead to gradual or to punctuatedchangesin one, Wl(2l, Z2), dependsnot onlyon the
the population, dependingon the mode of expressedphenotypezl, but also on the two
regulationof populationdensity.In the dis- genotypicvalues (il, Z2), whichtogetherdecussion the importance of the results for terminethepotentialreactionofa genotype,
empiricalworkare examined,and methods and thereforeprovide the link to the interforstudyingpatternsof adaptation are sug- nal costs of the reaction.Genotypeswith a
gested.
low-cost reaction will be favored by selection withineach habitat (Fig. 1C); whether
THE MODEL
such specialistsare also selectedat the level
The model is a generalizationofthemod- of the global population requires further
el that Via and Lande (1985) used to in- analysis.
vestigateevolutionof a quantitativetraitin
Soft Selection
a coarse-grainedenvironment,in the absence of costs. Two modes of regulationof
Lande (1979) showed, that Ai\ = gijo
= gijVjln(14) gives the expected
populationsize are also considered,i.e., soft ln(RW)/o9j
and hard selection.Under softselection,the changein the mean value of traiti (Ai2) due
contributionof each subpopulation to the to selection on traitj, where the gradient
1320
PETER H. VAN TIENDEREN
operator(V1)standsfortakingthederivative
withrespectto traitj, and gijis the additive
geneticcovariancebetweentraiti and]. Under soft selection in two habitats, the expected selection response forthe character
stateof thetraitin thefirsthabitatbecomes:
AZ
=
qgl IVI(ln W1) + qg92V2(ln W1)
+ (1 - q)gIVI(ln W2)
+ (1 - q)g12V2(ln W2)
is the same as the one obtained by Via and
Lande (1 98 5). However, in theirderivation
theyassumed thattherewas no selectionon
traitsnot expressedin an environment[i.e.,
= 0]; the
a ln(Wl)/022= 0, a ln(W2)/021
presentresultshows thatthisassumptionis
easily relaxed.
Hard Selection
Under hard selection the frequenciesq
withA21Ithe changein population mean for and (1 - q) referto the relativepopulation
thecharacterstatein habitatone, and q and size in the two habitatsat colonization and
(1 - q) the frequenciesof habitat one and before selection,and the weightingfactors
two, respectively.No explicit assumptions qWllV/Wand(1 - q)JW2/Whave to be apare made regarding
thegeneticvariancesand plied to,link selectionwithinhabitatsto secovariances, so that when the genetic co- lection in the entirepopulation, with W=
variance between the characterstates (g12) qJWI+ (1 - q)W2. This leads to:
is nonzero, directselectionon the traitexpressed in habitat two can resultin a corq(w /W)V1(ln W1)
relatedresponsein thetraitexpressedin the
firsthabitat.The fourcomponentsof selec- /=
+ (1 - q)(W22/W)V1(ln W2)
G
tion can easily be identified,with the first
W1)
q(WV
/J'J)V2(ln
term the result of direct selection on the
+ (1
q)(J'V2/
W)V2(ln W2)
expressedtraitin habitatone, the second a
correlatedresponse due to selectionon the
G 'n1 [qqW+ (1 - q)]
(2)
unexpressedcharacterstate in thathabitat,
term three direct selection on the unexpressed characterstate in habitat two, and
The joint mean fitnessunder hard selecfinally,term four the correlated response tionequals thearithmeticmean ofthemean
due to selection on the expressed trait in fitnessesper habitat, the same functionas
habitat two. Under softselection,the first fora multiallelicautosomal locus. Again it
two termsare weightedby the frequencyof does not depend on the assumption that
the firsthabitat,the last two termsby the selection only acts on the expressed trait
frequencyof the second habitat.
(Via and Lande, 1985).
For both traitsand usingmatrixnotation
The dynamicequations forboth softand
this becomes:
hard selectioncan thusbe writtenin a form
thatinvolves a singlefunctionforthe mean
with reiv
G qVI(ln W1) + (1 - q)VI(ln W2)\ population fitness,differentiated
qqV2(ln W1) + (1 - q)V2(ln W2)J spect to both traits. This guarantees that
when selectionis weak thepopulationmean
fitness,given by these functions,increases
=
(1) monotonicallyduringselectionuntila local
ln[W1qW21-]
maximumis reached(Lande, 1979; Via and
with A2 the vector of changes in the mean Lande, 1985).
forboth characterstates,and G theadditive
Costs ofAdaptation
geneticcovariancematrixofcharacterstates.
Thus the joint mean fitnessunder soft
It will be assumed that the fitnessof a
selectionequals the geometricmean of the genotype, W(Zl, Z2) has two components.
mean fitnessesper habitat; this is identical The firstcomponentdescribes selectionon
to the formuladerived fora singlemultial- theexpressedcharacterstate,and itdepends
lelic autosomal locus (Cannings,1971). This on the differencebetween the expressed
functiondescribesan adaptive landscape for phenotypeof an individual and an optimal
softselection in a coarse-grainedenviron- phenotypicvalue forthecurrenthabitat.Asmentwithtwo habitattypes.This equation suming a gaussian fitness function, this
EVOLUTION
component becomes exp[- /2(zi -Z*)2/S,2]
forthe traitexpressedin habitati, wherezi*
and z2* are the optimal phenotypeswithin
habitat one and two, respectively,and s1
and s2 (thewidthsof thegaussian functions)
are inverselyrelated to the strengthof stabilizing selection on the expressed phenotypesin these habitats. The cost of a reaction to the environmentis assumed to be
betweenhabassociated withthe difference
itatsin average response. Consequentlythe
second fitnesscomponent is a functionof
the differencein the mean genotypicreaction between habitats and a reaction with
the lowest (internal)costs. For a gaussian
fitnessfunctionthis becomes exp[- '/2(Z2 Z2- *)2/ri2],withz2- * the cost-freerelaction and riinverselyrelatedto thestrength
of selectionagainstdeviatingfromthecostfreereactionin habitati. Both a moreplastic
and a less plastic reaction,relativeto Z2-1*,
resultin extracosts. The cost parametersr,
and r2are not necessarilyequal, forinstance
in a harsh environmentthe fitnessconsequences of a specificreactionmay be more
dramatic than under relatively favorable
conditions.
The mean fitness within habitats is
given by
Wi = v'[gi I I(1)i+ Pi)-I I]
*
exp[- /2( _- 0i)T(1i + Pi)1
*( - 0)]
(3)
with T denotingmatrixtransposition,01 =
(Z1*, Z1I +
02 =
Z2-1*),
(Z2*
-
Z2-1*,
Z2)T,
P1, P2 the phenotypiccovariance matrices
and 1)1, 1Q2 the selectionmatricesin habitat
one and two, respectively(see Appendix).
The selective forces on the two character
statescan be evaluated fromthe inverseof
the selectionmatrices
=
g
(rl2
Vllrl2
+ 1/s12 -l/r12)
-1 _ l1r22
122-1
-\
-1
r2 2
llrl2J
-1/r22
121/
r22 2
1321
OF GENERALISTS AND SPECIALISTS
those associated with selection on the expressedcharacterstatedisappear. It can also
be seen thatthereis correlatedselectionon
z withinhabitats,since the off-diagonalelementsof the selectionmatrixare nonzero.
Now thatwe have themean fitnesseswithin
each habitat(Eq. 3) the next step to get dynamical results is to combine selection
withinhabitats to selection at the population level, and performthe gradientoperation on the logarithmof the joint mean
fitnesses(Eqs. 1 and 2), separatelyfor the
softand hard selectioncase.
RESULTS
AdaptiveLandscape underSoft Selection
Under softselection,the dynamic equations (1) are linear fora bivariate gaussian
fitnessfunctionper habitat and a normal
frequencydistributionof phenotypes.Consequently,the adaptive landscape has only
a single peak that can be found by setting
oln[WIqW2l-q])/o9i equal to zero fori = 1,
2. Figure2 gives an example oftheresulting
adaptive landscape. Withoutcosts, it is the
familiar bell-shaped function (Via and
Lande, 1985); in this case the fitnesscontours are concentriccircles (Fig. 2A), because the frequenciesof the habitats and
selectionregimeswithinhabitats are equal
(q = 1 - q = 0.5, s, = S2). The second
component, the cost attached to the phenotypicreaction,resultsin a ridgewiththe
diagonal beingthetop oftheridge(Fig. 2B).
Both fitnesscomponents togetherresultin
an adaptive landscape with a single peak
(Fig. 2C).
The location of the peak depends on the
selection parameters and the phenotypic
(co)variance matrices.The solutionis quite
lengthyand cannot be interpretedeasily.
However, a very simple resultis obtained
when the cost functionis the same in both
habitats, r, = r2 = r, and the phenotypic
variance in the population is relative low,
i.e., P1 + 1ll -
l, P2 +
2 -12:
I I S22
Comparing the diagonal elements reveals
thatselectionon the expressedtrait(1/r2 +
1/S,2) is moreseverethanselectionon the
nonexpressedtrait(1/r2). If the cost componentis absent,ri- o?, all elementsexcept
z2*Z2
-Ii zl*
Z
z*1 -_2 Z2-
*
1
(1 -q)sI2
q(l -q)r2
+ (I
- q)s
12 +
qS22
(4a)
PETER H. VAN TIENDEREN
1322
~~~~~~~~~70
70
60
60
50
50
50
40
40
400
30
30
30
20
20
20
10
10
10
-g,
c
70
60
0
0
106
20
30
40
5'0
60
7a
0~~~~~~~~~~
0
10
20
30
40
50
60
70
0i
0
10
20
30
40
50
60
70
trait in habitat 1
FIG. 2. Exampleof a topography
of theadaptivelandscapeundersoftselection.Fitnesscontoursat 0.1
intervals,the
outercontourbeing0.1. Threeadaptivelandscapesare plotted:(A) in theabsenceofcosts(with
zj* = 20, z2*= 50, s1 = S2 = 10, r, = r2
?c, q = 0.5, P1 = P2 with elementsPII = P22= 1, P12 = 0.6); (B) in
theabsenceof selectionon theexpressedphenotype,
of fitness
i.e., involving
onlythecostcomponent
(as in
ofbothselectionwithinhabitatsas in A and
(A) exceptz2-I*= 0, s, = S2 ??, r, = r2 = 16); (C) combinatiQn
costsas in B. In (C), theadaptivepeakconstitutes
a compromise,
locatedin betweenoptimalresponse(20, 50)
and theclosestcost-free
reaction(35, 35).
freereaction,givenvalues forr, and r2,and
the equilibriumpopulation will be close to
Z2
Zi
Z 2-1
optimal withinboth habitats.
q22
When the elementsof the phenotypiccovariance matrixPi are largerrelativeto Q
+
+
(4b)
q(l -q)r2
(1
qS22
q)s12
thereis a wider distributionof phenotypes
withii theequilibriummeanvalue forthe and the adaptive surfacebecomes smoothtraitexpressedin habitati. The lefthand er,because the population mean fitnessfolsidesof theseequationsgivethedeviation lows fromthe integrationof fitnessvalues
over a widerrangeof phenotypespresentin
fromtheoptimumforeachhabitat,ii -Z;
betweenthereac- the population. The location of the joint
relativeto thedifference
tionthatcouldlead to thehighestfitnesses optimum only changes slightly,however,
z2* - z1*, andthecost- and varyingthe parametervalues resultsin
withinbothhabitats,
freereaction,Z2-1*. The righthand side is similar changes in location (Table 1). Difa value betweenzero and one (Eq. 4a) or ferentialcostsbetweenhabitats(r, =#r2)also
on affectthelocation ofthejoint optimum(Taminusone and zero(Eq. 4b), depending
andthefrequenciesble 1), with the optimum closer to the optheselection
parameters
ofthetwohabitats.Itcaneasilybe seenthat timumforthehabitatin whichthecosts are
thepopulationmeanis locatedcloseto the relativelylow (i.e., r relativelyhigh).
The trajectoriesforthe change in popuoptimumin bothhabitats,(z,*, z2*), if the
righthandsidesareclosetozero,i.e.,rvery lation mean duringselectiondepend on the
ofthecost adaptive landscape as well as on thegenetic
function
largeso thatthefitness
componentis veryflatand costsare low. (co)variances. However,thepopulationwill
of,say,habitatone is evolve towards the optimum, unless there
Also,ifthefrequency
veryhigh,(1 - q) close to zero,or if the is no geneticvariance or the geneticcorreselectionin habitatone is moresevere,s1 lation between characterstates is equal to
smallrelativeto s2, thepopulationmeanis one or minus-one(all leading to singularity
close to the optimumin thathabitat,and of the G matrix).
z*-
zi
-
z2l
farfromtheoptimumintheother
relatively
AdaptiveLandscapeunderHard
habitat(seealso Table 1).WhenthedenomSelection
inatorpartsofthelefthandsideoftheequaboth
equations under hard sewithin
The
dynamic
tionsare small,the optimum
habitatscan be realizedwitha smallerand lection are nonlinear.Unfortunately,solvtherefore
lesscostlydeviationfromthecost- ing forthe equilibriummean populationby
EVOLUTION
70
70
Ci 60
50
C:
70
60 -60
10
20
30
40
50
60
70
0
10
304050650
40
40
0 -
20
40
1
30
30
30
20
20
20
10
10
10
0
1323
OF GENERALISTS AND SPECIALISTS
1-0
20
30
40
50
60
70
0(
~10
20
30
40
50
60
70
0
10
20
30
40
510
60
70
trait in habitat 1
FIG. 3. Exampleof a topography
of theadaptivelandscapeunderhardselection.Fitnesscontoursat 0.1
intervals,
theoutercontourbeing0.1. Threeadaptivelandscapesareplotted:(A) in theabsenceofcosts(with
zj* = 20, z2* = 50, s, = s2 = 10, r, = r2
?c, q = 0.5, P1
= P2
wi.thelementsPI IP22
= 1, P12 = 0.6); (B) in
theabsenceof selectionon theexpressedphenotype,
of fitness
i.e., involving
onlythecostcomponent
[as in
ofbothselectionwithinhabitatsas in A and
(A) exceptz2-I* = 0, sI = S2 oo, ri = r2= 16];(C) combination
costsas in B. In (C) threeadaptivepeaksare present,
in betweentheoptimalresponse
thefirst
a "generalist"
(20, 50) and theclosestcost-free
reaction(35, 35),and two"specialists,"
eachcloseto beingoptimalforone of
thehabitatsbutveryfarfromtheoptimumin theotherhabitat.
takingthe derivativesof the mean popu- elementof P at row i, columnj, see Aplationfitness(Eqs. 2 and 3) does not lead pendix).Figure4A showsthelocationand
to explicitsolutionsforpossible optima. numberofpeaksin theadaptivelandscape,
Changesin theadaptivelandscapewiththe plottedagainston theabscissathestrength
of themodelwerestudiednu- ofselection
parameters
againstdeviations
fromthecostresults
merically.Qualitativelydifferent
werefoundcomparedto thesoftselection
withan TABLE 1. The effectoftheamountofphenotypicvaricase, whichfirstwillbe illustrated
example(Fig. 3). Withoutcosts,theadap- ance (P) in characterstateson thelocation oftheadaptivelandscapehas a peak at thejoint op- tive peak undersoftselection.All variables are scaled
outin fourdi- in the standarddeviation unitsof the selectionwithin
timum,witharmsstretching
one (si). Deviationsare givenasD1 I(i1 -Z
rections(Fig. 3A; Via and Lande, 1985). habitat
-z
[Z2* - zI*
fromtheoptimum
1*11: thedeviation
The costattachedto thereactionagainre- withinhabitats relative to the differencebetween the
sultsin a ridge(Fig.3B). Lookingat Figures optimumand the reactionwiththe lowestcost (cf. Eq.
3A and 3B it becomesapparentthatwhen 4). D-values rangefrom0 and 1, fromoptimal forthe
botharecombinedtheresultis an adaptive focal to optimal forthe alternativehabitat,respectivelandscapewiththreepeaks(Fig. 3C). With ly. No phenotypiccorrelation(P12 = 0)multiplepeaks in the adaptivelandscape,
P- 0
P=1
thecourseofevolutiondependson theiniS2
D2
D2
SI
ri r2
DI
DI
in thepopuof genotypes
tial distribution
1 1 1 1 0.40 0.40 0.43 0.43
lation.Each peak has a certaindomainof q= 0.5
1 1 1 2 0.36 0.36 0.33 0.42
on theadaptivelandattraction,
depending
1 1 2 1 0.36 0.36
0.42 0.33
scape, but also on the geneticcovariance
1 1 2 2 0.25 0.25 0.30 0.30
matrix.
1 2 1 1 0.18 0.73 0.23 0.69
of
For further
investigation
oftheeffects
1 2 1 2 0.17 0.69
0.19 0.67
1 2 2 1 0.17 0.69
0.24 0.62
thedifferent
on thenumberand
parameters
1 2 2 2 0.14 0.57 0.19 0.56
locationofpeaksin theadaptivelandscape
1 1 1 1 0.21 0.63 0.21 0.69
0.75
q=
a reference
statewas takenwithbothhab1 1 1 2 0.20 0.61 0.16 0.68
itatsequallyfrequent
(q = 0.5), stabilizing
1 1 2 1 0.18 0.53 0.20 0.57
selectionequal in bothhabitats(s, = S2 =
1 1 2 2 0.14 0.43 0.14 0.54
s), equal phenotypic
variancematrices(P1
1 2 1 1 0.07 0.87 0.09 0.86
= P2 = P) and littlephenotypic
1 2 1 2 0.07 0.86 0.07 0.85
variation
1 2 2 1 0.07 0.82
0.09 0.80
relativeto the curvatureof the adaptive
1 2 2 2 0.06 0.75
0.07 0.76
landscape(PII= P22 = S2/8,P12 = 0, pij the
a
1324
PETER H. VAN TIENDEREN
freereaction(l/r),on theordinatethedif- population may evolve towards this ridge
ferencebetweenthe optima withineach in the adaptive landscape, but its position
on top oftheridgemay be affectedpredomhabitatand thecost-freereaction( I Z2 -z1
- Z2 1 1)- Onlyonepeakis present
inregion inantlyby drift;thus experimentalistsmay
betweentheoptima observe populations thatrangefromeither
[G],whenthedifference
reaction specialistto thegeneralistwithoutbeingable
inthetwohabitatsandthecost-free
in seis small.For Iz2* - z*-z2*I <2s this to explain the patternby differences
of lection regimes.When costs are high,howofthestrength
appearsto be irrespective
adaptiveland- ever, the two specialistpeaks are separated
selectionl/r.The resulting
scape is similarto the softselectioncase, by deep valleys of maladaptation.
Now theeffects
ofvaryingtheparameters
to
and againtheadaptivepeakcorresponds
populationthatis a compro- in this referencemodel will be dealt with.
a "generalist"
mise betweenthe optimawithinhabitats Figure 4B shows the adaptive peaks when
and thecost-free
reaction;forthesymmet- habitat one is more common (q = 0.75).
state(q = 0.5, s1 = S2) and Three adaptive peaks are found under a
ricalreference
weakselection(P1 + Q1 ,- Q1 P2 + Q2 1- smaller range of parameter values when
referencestate
Q2), thepeakis locatedat thesameposition compared to the symmetric
as undersoftselection.Therearetwopeaks (region[G + S1 + S2], Fig. 4B). Again only
in theadaptivelandscapewhencostsofsi- one peak is found when the cost-freereacarehighandthecost- tion is close to the optimal reaction(I Z2adaptation
multaneous
fromthe Z1 - Z2 1* small).However,thispeaknow
considerably
freereactiondiffers
betweentheoptimawithinhab- graduallyshiftswithincreasingIZ2 - Z1difference
itats(Fig. 4A, region[S1 + S2]). At these Z2- 1 I and 1/rfroma generalist(region[G])
peaks the population is predominantly to a specialistforthe most common habitat
adaptedto eitherone habitat,and can be ([S1]). There are two separate regions in
referred
to as "specialist"populations,in which two adaptive peaks are found,either
populationof withtwo specialistpeaks (region[S 1 + S2]),
contrastwiththe generalist
region[G]. Finally,threepeaks are found or a combination of the generalistand the
in a thirdregion[G + S1 + S2], thetwo specialistto the most common habitat (reThis occurs gion [G + S 1]).
specialistsand the generalist.
Figure4C shows thattherangeof paramwhenthe cost of deviationfromthecostfreereactionis low relativeto selection eter values in which three adaptive peaks
withinhabitats(at least 1/r< 1/s),but at occur (region [G + Si + S2]) is again relthe same timea relatively
largedifferenceativelysmall when selectionwithinhabitat
betweentheoptimainbothhabitatsandthe one is more severe than in habitat two (1/
reaction(approx. IZ2*-z, - z2cost-free
sI > 1/s2). In the regionwithtwo peaks, the
> 3s).
firstpeak is always the specialistto thehab-
In somecaseswithtwoor threepeaksin itat in which selectionis less severe (in this
theadaptivelandscapethesepeaksare sep- case habitat two), whereas the location of
aratedbysaddlepointsthatareonlyslightly thesecondpeak is variable:a generalistwhen
in fact,at the costs are low (leftpart of the region,[G +
lowerin joint mean fitness;
bordersoftheregions[G] and [S1 + S2] as S2], Figure4C), it graduallybecomes more
wellas [G + Si + S2] and [Si + S2], the and morea specialist,thuslosingadaptation
generalist
peak changesfroman optimum to habitattwo, when costs are higher(right
to a saddlepoint,and thenthereis a range part of the region[S1 + S2]). Again, in the
of populationmeans withapproximatelyregionwithonlyone adaptive peak, a gradfrom ual shiftin location is foundfromgeneralist
jointmeanfitnesses,
equal population
theone specialistto theother(cf.Fig. 3C). ([G]) to the specialistforhabitatone ([S1]).
This is probablymoreimportant
biologi- Figure 4D shows that a similar situationis
observation
that foundwhen deviatingfromthecost-freerecallythanthemathematical
thereareexactlytwoorthreepeaks,because action is more costlyin habitatone (1l/r1>
evolutionwillproceedveryslowlyin a di- l/r2).Whenever two peaks are found,one
rectioninwhichtheincreaseinmeanfitness peak is the specialist to the environment
is verysmall.Undersuchcircumstances
a withthelowestcosts(in thiscase two),while
1325
EVOLUTION OF GENERALISTS AND SPECIALISTS
A
6
5 S
*
N\
N
1
1+2
5
1+S2
X
B
6
s1+
S1+S2
5~~~~~~~~~~2
44
GS
33
N
*
X
2
6
2
\
|
2
Si
G+
G
*N
cost
0
1/8
ofdevitingfomfre
1/2
114
1
G reacton,1
2
1/8
6
'-
1/4
1/2
1
2
6
0
0 5
Si1+S2
1+S2
5
14
G
Si+S2
Si1+S2
4
G+S2
E
~~~~~~~~~3
3
I~~~~~~~~~~G4-S21
4_j
0
G
1/8
1/4
cost
~ ~
1/2
~
1
~
2
~
1
1/8
G
1/4
1/2
1
2
of deviating from free reaction, 1I/r
FIG.4. The numberofpeaksin theadaptivelandscapeunderhardselection,
plottedagainston theabscissa
thestrength
of selectionagainstdeviatingfromthecost-free
reaction,l/r,and on theordinatethedifference
betweentheoptimaperhabitatand thecost-free
z *. Bothaxesexpressed
z2 *- zreaction,
relativeto the
meanselectionwithinhabitats,
s = (s, + s2)/2.Capitalletters
refer
to locallystableoptimain theseregions:G
forthegeneralist,
S forthe specialistto habitatone, S2 forthespecialistto habitattwo.(A) Symmetrical
referencestate: q = 1 - q = 0.5, s1 = S2 = s, r, = r2 = r, P1 = P2. with elementsPI1 = P22 = s/8, P12 = 0. (B)
Habitatone morecommon:as (A), exceptq = 0.75. (C) Stabilizing
in habitatonemoresevere:as (A),
selection
exceptl/s1= 2 x 1/s2.(D) Costofdeviating
fromthecost-free
slopehigherin habitatone: as (A), exceptllr
= 2 x I/r2,with r = (r1 + r2)/2.For meaningof parameterssee text.
the otheris variable. In the leftpart of this + S2]). In the regionwitha singleadaptive
region,the otherpeak is a generalist([G + peak, its location again varies froma genS2]); however, the location of this peak eralistto the specialist to the environment
graduallychanges to a specialist with in- withthe highestcosts.
creasingcosts (rightpart of the region,[SI
In conclusion, generalistand specialist
1326
PETER H. VAN TIENDEREN
strategiesmay occur as a single adaptive
peak, in any combination of two peaks, or
all threepeaks together,dependingon actual
parametervalues. In general,one generalist
peak is found when being adapted to both
habitatsis relativelyeasy,and two specialist
In betweenthese
peaks whenthisis difficult.
extremes,intermediatestates and combinations of state are found.
diminishedpeak, does the population rapidlyevolve towardsthe new peak (Fig. 5C).
Eventuallythepopulationbecomes adapted
to the by then predominanthabitat. Phenotypicvariation between characterstates
in the two habitats is presentonly during
therelativelyshortperiod of change.Under
these conditions evolution may thus be
characterizedbyprolongedperiodsofstasis,
interspersedwithperiods of a rapid change,
Changeunder high phenotypicvariation, and low popuTrackingofEnvironmental
Hard and SoftSelection
lation size.
This patternof evolutionarychange reSuppose thatthe frequencyof one of the
two habitats changes slowly from one to sembles the episodic nature of evolution
a successionalprocess,or proposed in the theoryof punctuatedequizero, representing
a climatic change, and that these habitats libria (Eldredge and Gould, 1972; Gould,
optimal phenotypes.Under 1980; cf. Charlesworthet al., 1982). In the
have different
softselection,this resultsin a gradual shift presentmodels theprocessis drivenentirely
of the peak in the adaptive landscape and by selective forcesin a changingenvironthe population mean will follow this shift ment, and developmental/genetic con(Fig. 5A), provided thatgeneticvariationis straintsare notinvolved.Changestakeplace
not constrainingthe evolutionaryresponse graduallywhena populationtracksa "movgenetic ing" adaptivelandscape.However,whenthe
(i.e., G not singularand sufficient
variationto keep up withthe change in lo- adaptive landscape is characterizedby mulcation of the adaptive peak). A difference tiple adaptive peaks that rise and fall, are
betweencharacterstatesin the two habitats born or cease to be, the population may
(reflectinga generalist,plastic population) remainunchangedforlong periods of time,
becomes apparentat a low frequencyof the and then leap from one peak to another,
second habitat, and persistsuntil the first e.g., initiatedby crossinga thresholdin the
habitathas almost completelydisappeared. frequencyof habitats.
The mean fitnessin the population firstdeDISCUSSION
creases, remains relativelyconstant for a
These models describe evolution of an
longperiodoftime,and thenincreasesagain
(Fig. 5B). However, rememberthat under arbitraryquantitativetrait,assuming ransoftselectionthe total population size need dom dispersal of individuals betweenhabitats,while stillindividuals spend theirlife
not be affected(Christiansen,1975).
Under hard selection,thepopulationalso in one habitattype.This situationmay apstartsas specialiststo theinitiallyprevailing ply to animals that live in an environment
habitat (Fig. 5C), similar to softselection. with differentkinds of patches (carrion,
The correspondingadaptive peak decreases dung), or to plants and othersessile organin heightas the frequencyof this habitat isms, although limited dispersal between
graduallyfalls. However, neitherlocation habitats may violate the assumptions
nor local stabilityof the peak is affected, (Bradshaw, 1972). The resultsshow thatuntherefore
thepopulationmean remainscon- der softselection a population is expected
stant and does not reflectthe ongoing en- to evolve towards a compromise between
vironmentalchange.Only mean fitness(Fig. the reaction that would be optimal within
5D) and thus population size may show a each ofthehabitatsand a cost-freereaction.
decline. Meanwhile, a second peak in the For instance, inducible defense reactions
adaptive landscape startsto rise.Depending may reflectsuch a compromise, in which
on the actual selection parameters(cf. Fig. the phenotype,e.g., levels of phenolic com4), this second peak may eitherbe the gen- pounds, is suboptimalboth in the presence
eralistor the specialistpeak forthe habitat and absence of herbivores.Optimal levels
increasingin frequency.But only afterthis withineach habitatare not reachedbecause
second peak has absorbed the first,by then the benefitsare outweighedby highercosts,
hard selection
soft selection
-Z
z
1l
Z2
Z
A
40
C
4
0/
30
30
20 L
20
~~~~~~~~~~~~~~10
10
B
1.0
CO
2
50
50
>'
1327
OF GENERALISTS AND SPECIALISTS
EVOLUTION
0.8
1.0
-
0.8
0.6
0.4
-
0.4
E
0.2
-
0.2
0
1
2
3
4
5
/
0.6
-
C
0.0
o..
6
generation
7
8
9
Thusands)
10
0.0
J
0
1
2
3
4
5
6
generation
7
8
9
10
(Thousands)
in whichthefrequency
of habitatone declines
of changeduring10,000generations
FIG. 5. Trajectories
meanfitness
undersoftselection.
and (B) in (geometric)
from1 to 0. (A) Changein meanphenotype
linearly
underhardselection.
Undersoftselection
and (D) in (arithmetic)
meanfitness
(C) Changein meanphenotype
in time,underhardselectionpopulationsize followsthemeanfitness
curve.
populationsize remainsconstant
Parameters
forbothcasesare z, = 10,z2*= 40, z21l = 0, s12= S22 = 80, r12= r22= 400,p11= P22 = 10, P2 =
4,gll = 922 = 4, g12= 0.
e.g., of making more precursorsor having underutilizedhabitat (Futuyma and Morehighersyntheticcapacity. The continuous, no, 1988). Under hard selection a similar
gaussian cost functionimplies that fitness outcome is obtained under conditionsthat
decreases withthe deviation fromthe cost- make it relativelyeasy to have a phenotype
freereaction,and thereforethe outcome is that is close to the optimum forboth haba compromise. Other cost functionscould itats (low costs, and/or optimal and costbe analyzed in a similar fashion. For in- freereactionrelativelysimilar). When this
multiplelocallystastance,some inducibledefensemechanisms becomes moredifficult,
may perhaps cause a certain,fixed fitness ble equilibria exist. The change fromgenreduction,irrespectiveof the exact strength eralistto eitherspecialistunder hard selecoftheresponse;a (static)specialistmay then tionagreeswithresultsfromsimilarmodels
evolve when costs are high,or a generalist of adaptation in a heterogeneousenvironwitha fullyoptimal phenotypein each hab- ment (e.g., MacArthurand Connell, 1966;
itat when costs are low, but a compromise Lloyd, 1984). However,a possible existence
generalistseems unlikelywith such a cost of threelocally stable solutions,the generalist and two specialists,was not foundprefunction.
Optimization of the geometricmean fit- viously; furthermore,under some condiness under softselectionimplies frequency tions two locally stable equilibria can be
dependent selection, so that a specialized present,in which one adaptive peak corpopulation always can be invaded by ge- respondsto a specialistpopulation and the
notypesthatare betteradapted to theother, otherto a generalistpopulation. In between
1328
PETER H. VAN TIENDEREN
the stable peaks are locally unstable equi- whatis optimal withinhabitats;it mightbe
libria, eithervalleys or saddle points. The a compromisedue to costs.Historicalevents
population is expected to evolve towards such as foundereffectsmay have driventhe
one of the locally stable peaks (Felsenstein, population towards a local equilibrium.
1979; Kirkpatrick,1982), but the rate of Perturbationsmay cause a switchto a difevolution near valleys or saddle points can ferent equilibrium. Reciprocal-transplant
be low. Valleys are sometimesonly slightly experiments,
introduction
ofspecialistsfrom
lower than the adjacent adaptive peaks, es- neighboringpopulations, (temporary)perpeciallywhen thereare threepeaks, so that turbationsof frequenciesof habitats,or redriftmay cause a population to fluctuate productiveisolationofthedifferent
habitats
between the generalistand any of the spe- (to see whether specialization starts to
cialists. Moreover, such peaks may easily evolve) could all give informationon the
coalesce due to a temporaryincreasein phe- state of the population. The measurement
notypicvariation(Kirkpatrick,1982). Evo- of contemporaryselection regimes in the
lutionarydynamicsunderhard and softse- fieldmay also help to reveal therole ofcosts
lection can differ substantially when in adaptations to a heterogeneousenvironfrequenciesof the habitats or selection re- ment. A firstapproach is to examine the
gimeswithinhabitatschangein time.Under selection differentials
in a natural populasoftselectionthe population may be able to tion (Falconer, 1981; Lande and Arnold,
trackthe adaptive peak. Under hard selec- 1983; Arnold and Wade, 1984). A presence
tion, however,the adaptive peak mightbe ofa compromiseequilibrium,i.e., a balance
thepeak mightmove, or itmight between the optimallyadaptive phenotype
unaffected,
completelydisappear so thatthepopulation withinhabitatsand costs of the phenotypic
will startto evolve towardsan entirelydif- reactionsinvolved, could be detectedin the
ferentstate.
followingway. Regressionsof fitnesswithin
These resultshave some consequencesfor each of the habitats on the traitof interest
the interpretationof fielddata: one cannot in that site may show that (i) thereis phealways assume that selective forcesdeter- notypicselection on the expressed traitin
mine whethera generalistor specialiststrat- both habitatsifphenotypesare suboptimal,
egy evolves. Instead, the outcome of selec- and (ii) the apparent selection differentials
tion now may depend on initialconditions, (covariance between relative fitness and
for instance, the mean traitvalue and ge- trait)in the subpopulations have opposite
netic variation of migrantsthat startedthe signs (cf. Eq. 4). However, there are three
population. Suppose that migrants were possible explanationsforsuch results.First,
specialists and predominantlyadapted to the population is in a transientstate (i.e.,
habitatone. Under hardselectionthismight phenotypicselection present,selection rebe a locallystableequilibrium,and thepop- sponse present).Second, observed selection
ulation would not change, despite the fact differentials
do not resultin a change in the
thatperhapsa generaliststrategy
would lead population because thereis no appropriate
to a much higherfitness.Under softselec- geneticvariation (i.e., phenotypicselection
tion this could never happen, as the single present,no selectionresponse). Finally,the
adaptive peak can be reachedfromall initial apparent selective forces are counterbalconditions,provided, of course, that there anced by selection for lower costs of the
is sufficientgenetic variation (i.e., in the genotypicreaction (i.e., no phenotypicsepresentmodels nonsingularity
ofthegenetic lection presentat the population level and
covariance matrix).
consequentlyno selection response); selection forhighervalues forthe characterstate
Measuring Selection in the Field to
in a certainhabitat are then accompanied
Evaluate Costs
by selectionforlower values in otherhabEvolution in a coarse-grainedenviron- itats.
mentis complex. A populationcan be comThe regressionmethod formeasuringseposed of specialists, generalists,or inter- lection using fielddata on a natural popumediates, or it can be in a transientstate. lation,however,does not allow a directasThe equilibrium mightbe determinedby sessmentof selectionon costs and therefore
EVOLUTION
OF GENERALISTS AND SPECIALISTS
cannot discriminateamong these possibilities. Data on clonallyreplicatedgenotypes
or genotypeswithknown familialrelations
such as sib-familiesare needed forthispurpose; this usually necessitates an experimental setup. Regressionof the overall fitness in the population (measured directly,
or estimatedfromthe fitnesseswithinhabitats, the frequencies of habitats and the
mode of population regulation)can thenbe
used to test whetheror not the selective
forceswithinhabitatscancel out at thepopulation level, suggestingequilibrium. Ideally, the data consist of measurementsof
the expressedphenotypeand fitnessof each
individual replicatein both habitats,as well
as measuresof the mean phenotypeand the
mean fitnessesofreplicatedgenotypes.This
allows regressionof the fitnesswithin,say,
habitat one (W1), on both the expressed
phenotypes(zl) and the average reactionof
1329
ic variation is present.However, detecting
selective forces mightbe more likely in a
study of a population in a heterogeneous
habitat than in a homogeneous habitat. In
a compromise equilibrium state, selective
forces are operatingevery generationand
the equilibriumis maintainedby opposing
selective forcesbetween habitats,while in
a population in a homogeneous environment selection close to an adaptive peak
may be weak and hard to detect. Comparison of observed patternswith predictions
from models such as presented here also
requiresinformationon the underlyinggenetic basis of traits. Fortunately,when
experimentswith replicated genotypes or
sib-families are employed, as sketched
above, both selective forces and genetic
(co)variances can be inferredat the same
time, which will make such an effortmore
promising.It seems thatsuch experiments,
genotypes
(2 - Z1). If thereis a generalist, togetherwith experimentalmanipulations
compromiseequilibrium,theregressionsof such as perturbationsor introductionof
fitnesswithinhabitatsare expectedto show othergenotypes,may be veryusefulto undirectionalselection on the expressedphe- ravel the complex patternsof adaptation,
notypetowards the optimum forthe focal and the mechanismsinvolved.
environment,and directional selection on
thegenotypicreactiontowardsthecost-free
ACKNOWLEDGMENTS
reaction.The neteffectof both components
I would like to thank J. Antonovics, B.
of selection within each habitat would be
directionalselectionforthe expressedchar- Bradshaw,G. de Jong,R. Lande, and S. Via
acter state towards its optimal value (zl*), forstimulatingdiscussions and/orvaluable
and directional selection of the character comments on a previous version of the
stateexpressedin theotherhabitat(z2*)away manuscript.This work was fundedby the
fromits optimum,the latterbecause thisis NetherlandsOrganizationforScientificReassociated withdecreasingcosts in thefocal search (NWO).
habitat. The effectsare expected to cancel
out in the regressionsof the overall fitness
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APPENDIX
HARVELL, C. D. 1986. The ecologyand evolution of
inducibledefensesin a marinebryozoan:Cues, costs,
The expressedcharacter
statein habitati, z,,ofan
and consequences. Am. Nat. 128:810-823.
individualis thesumofa genotypic
value 2,,and an
HAVEL, J. E. 1987. Predator-induceddefenses:a re- environmental
deviation(z, - 2,) witha univariate
view. In W. C. Kerfootand A. Sih (eds.), Predation: normaldistribution
t(z,- 2,)withzeromeanandvariDirect and indirectimpacts on aquatic communi- ance e,,.The meanfitness
in habitati can be derived
ties. UniversityPress of New England, Hanover, bytaking
theaverageoverphenotypes,
values
breeding
NH.
In ourcasethelatteris mostconvenient,
orgenotypes.
inhetHEDRICK, P. W. 1986. Genetic
polymorphism
erogeneous environments:A decade later. Annu.
=
y(1, 2)W,(I, Z2) d2i d22 (Al)
Rev. Ecol. Syst. 17:535-566.
withy(i1,Z2) thedistribution
ofgenotypic
valuesbefore
AND A. J. DOLMAN.
HOEKSTRA, R. F., R. BuiLSMA,
(underrandomdispersalbeingequalin both
1985. Polymorphismfromenvironmentalhetero- selection
and W,(i1,Z2) thefitness
ofgenotype
geneity:Models are onlyrobustifthe heterozygote habitats)
(i1, Z2)
ofgenotypic
valuesofthe
is close in fitnessto the favoured homozygotein in habitati. Thedistribution
character
statesin thetwohabitatsis assumedto be
each environment.Genet. Res. 45:299-314.
1990. Multi- bivariate normal, y(z-)= exp[- ?2( - 2)T(G + D)-1(i
HOLSINGER, K. E., AND S. W. PACALA.
matrices
of
ple-nichepolymorphismin plantpopulations.Am. - 2)], withG and D the2 x 2 covariance
additiveand nonadditive
forcharacter
geneticeffects
Nat. 135:301-309.
and 2 and z thevectorsofpopuKIRKPATRICK, M. 1982. Quantumevolutionand states,respectively,
values,respectively.
punctuatedequilibria in continuous geneticchar- lationmeansand genotypic
The averagecomponent
offitness
due to stabilizing
acters.Am. Nat. 119:833-848.
on theexpressed
in habitati has
phenotype
LANDE, R. 1979. Quantitative genetic analysis of selection
overall possibleenvironmental
values
multivariateevolution,applied to brain: body size tobe integrated
thatthegenotype
can attain,
allometry.Evolution 33:402-416.
LANDE, R., AND S. J. ARNOLD. 1983. The measurement of selectionon correlatedcharacters.Evolut(z,- 2,)exp[-1/2 (z, - z*)2/S2] dz,
tion 37:1210-1226.
+ e)-']
_\[S,2(s,2
LEVIN, D. A. 1976. The chemical defensesof plants
*exp[(A2)
/2(2, - Z *)2/(S,2 + e)]
to pathogensand herbivores.Annu. Rev. Ecol. Syst.
7: 121-159.
The secondcomponent
due to stabilizing
on
selection
LEVINS,R. 1968. Evolution in changing environ- the reactionwiththe lowestinternalcost becomes
ments.PrincetonUniv. Press, Princeton,NJ.
and is assumedto be
exp[- 1/2(22- -z2 *)2/r12],
LLoYD, D. G. 1984. Variation strategiesof plants in genotype
specific.
heterogeneousenvironments.Biol. J.Linn. Soc. 21:
Combining
bothcomponents
givestheaveragefit357-385.
nessesofa genotype
(i1, Z2) as
w
f
ff
EVOLUTION
WI'(l, i2)
f
-
exp[-Y/2(92 -
=
OF GENERALISTS AND SPECIALISTS
*)21r,2]
- z *)2/S2]
t(z - z,) exp[- V12(z,
dz
(A3)
Rewriting
(A3)ina bivariate
gaussianform,
using(A2),
yields
W(Z)
=
+
\[S,2(s,2
e')-l]
- 0,)Tqf,-1(2 - 6)]
*exp[-1/2(
withT denoting
matrixtransposition,
=
62 =
*
I
T,
(21, X2)
(Z2*
5
-
12+
ell
12 + ell
22+
S'2
Z2-
22+
1 =
(Zl*,
*,Z2*)T,
S12
Z*
+
Z2-
and
+ ell
SI + r,2 + el,J
2
r22 + e22
S22 + e22
e22
s 2
+ e2
)
1*),T
(A4)
1331
thematrices
describing
selection
at thegenotypic
level
in habitatoneand two,respectively.
The meanfitness
overall genotypes
(Al) thusbecomes
w, V[IQI (0Q+ P,)-II] exp[-V/2(f (0, + Pj)-1(2 - ,)],
O,)T
(A5)
equation3 in thetext,withP, = G + D + E,, E, a 2
x 2 matrixofenvironmental
deviationswithell elementsequal to e,,,and Q, = ', - E,. The off-diagonal
elements
ofthephenotypic
covariancematrices
P, are
not undefined
(cf.Via and Lande, 1985) despitethe
factthatthephenotypic
correlation
betweencharacter
statescannotbe measuredon thesameindividual.