Vol. 149,No. 3
The American
Naturalist
March1997
SEXUAL TRANSMISSION OF DISEASE AND HOST MATING SYSTEMS:
WITHIN-SEASON REPRODUCTIVE SUCCESS
PETER H. THRALL,*JANisANTONOVICS,tAND JAMESD. BEVERt
Department
ofBotany,Duke University,
Durham,NorthCarolina27708
SubmittedNovember27, 1995; Revised June24, 1996; Accepted June27, 1996
Abstract.-While
thereis an extensive
literature
on theevolution
ofmating
inanimals,
systems
littleconsideration
has beengivento thepossibleevolutionary
interactions
betweensexually
transmitted
pathogens
and thematingsystemsoftheirhosts.We use individual-based
models
thatincorporate
measurable
per-contact
probabilities
ofinfection
andfertilization
to showthat
notonlycan thepresenceof sexuallytransmitted
(and sterilizing)
pathogenhave significant
effects
on optimalwithin-season
forbothmalesandfemales.We showthat,
matingstrategies
to expectations,
is notalwayspredicted
contrary
monogamy
to be theoptimalstrategy.
The
willnot
optimalstrategy
mayalso oftendiffer
betweenthetwosexes,andtheoptimalstrategy
diseasetransmission.
we showthattheoptimal
alwaysbe theone thatminimizes
Similarly,
levelofvirulence
fora sexuallytransmitted
ofthedegreeofpromiscuity
is a function
pathogen
of its host.Overall,theseresultssuggestthatsexuallytransmitted
diseasescan impacthost
mating
behavior,oftenin nonintuitive
directions.
The enormousvariationin animalmatingbehavior,bothwithinand among
ofevolutionary
theinterest
species,has longattracted
biologists(Darwin1871).
Discussionsoftheevolution
behaviorhavepositeda variety
ofmating
ofecological factorsto explainthisdiversity
ofmatingsystemsin adaptiveterms(WittenandTilson1980;Flinnand Low 1986).Morerecently,
berger1979;Wittenberger
interest
betweensexuallytransmitted
has grownin theevolutionary
interaction
diseases and hostmatingbehavior.This increasedinterest
is primarily
fortwo
realization
thatfarfrombeinga small
reasons.First,therehas been increasing
and curioussubsetof diseases (Rosebury1971;Hunteret al. 1993),sexually
transmitted
diseases (STDs) are commonin naturalpopulationsof bothplants
(Mink1993;Thrallet al. 1993,1995)andanimals(OrielandHayward1974;Smith
and Dobson 1992;Lockhartet al. 1996). Second, it has been speculatedthat
evolveas a consequenceofdiseasepresence,either
itselfmight
matingstructure
in a quitegeneralsense (Hamiltonand Zuk 1982)or withregardto STDs in
particular(Freeland1976;Hamilton1990; Sheldon1993;Loehle 1995). It has
even been suggestedthathumanmonogamy
is an outcomeof venerealdisease
transmission
(Immerman
1986).
* E-mail:[email protected].
t E-mail:[email protected].
t E-mail:[email protected].
Am.Nat. 1997.Vol. 149,pp. 485-506.
? 1997byThe University
Allrights
reserved.
ofChicago.0003-0147/97/4903-0004$02.00.
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486
THE AMERICANNATURALIST
In a recentreview,Loehle (1995)presentedevidenceof the ways in which
varioustypesof socialbehaviorsmightprovidemechanisms
forpreventing
disease spreadinnaturalpopulations
ofanimals.In particular,
Loehleraiseda numberof interesting
questionswithrespectto STDs and howtheymightinfluence
theevolutionof matingbehaviorsthatwouldreducediseasetransmission
(e.g.,
through
matechoiceor monogamy).
He hyopothesized
thatone of theprimary
reasonsfortheoccurrenceof lifetime
in long-lived
monogamy
species of birds
mightbe to avoid infection
by sexuallytransmitted
pathogens.Indeed,disease
transmission
duringmatingis beingsuggestedmoreand morefrequently
as a
factorthatcould influence
matingbehavior(Birkheadand M0ller1993;Hunter
et al. 1993;Hardy1994;Able 1996).
In spiteoftheseemingly
obviousand intimate
connections
amonghostsexual
activity,
studies
reproductive
success,and disease risk,no rigoroustheoretical
oftheroleof STDs in shapinghostmatingbehaviorhave been done. Likewise,
therateoftransmission
ofa sexuallytransmitted
evolupathogen(andtherefore
tionof SDT virulence)willbe critically
dependent
on thenumberof sexualcontactsbetweeninfected
anduninfected
hosts,whichinturnwillbe determined
by
thematingstructure
ofthehostpopulation.For example,it has been suggested
thatthe evolutionof virulenceof HIV maybe guidedby changesin human
fortransmission
behaviorand opportunities
(Ewald 1994).In thepresentarticle,
schemebased on the idea thatassociatedwitheach
we focuson a theoretical
of disease transmission
and a probability
of
copulationeventare a probability
We incorporate
fertilization.
different
aspectsofdiseaseexpression(e.g., effects
on hostfertility
vs. mortality)
andhostmating
vs. promiscusystems(monogamy
framework
to examinehowmatingsystemand
ity).We thenuse thistheoretical
disease severity
interact
to determine
thereproductive
successof a hostand its
sexuallytransmitted
pathogen.
THE MODELS
in a sexuallytransmitted
To examinethe relationship
betweentransmission
pathogenand hostreproductive
success, we assumethatsexual contactscan
orboth.We describetheseprocesseson thebasis
resultinfertilization,
infection,
fromthatused in
of singlecontactor copulationevents.This approachdiffers
manydiseasetransmission
modelsinwhicha contactis definedas a sexualpartnerrather
andinwhichthetransmission
thana singlesexualencounter
parameter
willinfecta susceptible
individual
thatan infected
P is definedas theprobability
partneroverthecourseof thepartnership
(e.g., May and Anderson1987;May
theimportance
et al. 1988;Andersonet al. 1989;Anderson1991).Although
of
transmission
rateshas been recognizedin thetheoretical
literature
per-contact
(e.g., Heesterbeekand Metz 1993),theuse of theper-partnership
transmission
ofhumanSTDs (Hethratehas beenlargelya pragmatic
decisioninthemodeling
cote and Yorke1984;Garnett
et al. 1992;Swintonet al. 1992),because informais limited.For example,it has
tionon per-sexact probabilities
of transmission
out
been pointed that,withrespectto the spreadof HIV-1 in Africa,data on
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
487
forunderper-sex act probabilities
of transmission
are likelyto be important
standing
theepidemiology
ofthedisease(Andersonet al. 1991).
seasonpathogenandhost
Initially,
we developexpressions
forwithin-breeding
assumptions.
First,we asreproductive
success. We makeseveralsimplifying
thecourseofa matingseason
sumethatdiseasefrequency
does notchangeduring
becauseoftherequirement
(i.e., within-season
diseasespreadis slow).Typically,
forpartnerexchange(whichis usuallylimited),sexuallytransmitted
pathogens
wouldbe expectedto havelowerratesofspreadthanmanyothertypesofpathogens(e.g., respiratory
tractinfections).
Lockhartet al. (1996)showedthatSTDs
were distinguishable
fromotherinfectiousdiseases by havingcharacteristics
moretypicalofendemicdiseases(e.g., less populationcycling).Second,we asis notlimiting
to reproductive
successofeithermales
sumethatmateavailability
or females.Moreover,becausesexuallytransmitted
diseasesare oftensterilizing
and have relativelylow effectson host mortality(Lockhart et al. 1996), we as-
in termsof effectson
sumethatthenegativeeffectsof thedisease are entirely
fertilityand that there is no within-seasonmortality.Finally, we assume that
thereis no latentperiodforthedisease; thatis, individuals
are infectious
with
event,inrespectto all matesacquiredsubsequentto thedisease transmission
fectedmales have reducedprobability
of fertilizing
any subsequentmates,inhavereducedprobability
of successfulreproduction
fectedfemales(iffertilized)
(as is generallythe
(in thatbreedingseason),and all contactsare heterosexual
successare
case in mostanimals).We ask howhostand pathogenreproductive
permate,disease
influenced
by thenumberofmates,thenumberofcopulations
For reference,
a completelist
prevalence,and theeffectof disease on fertility.
and definitions
of modelparameters
is givenin theappendix.
Disease Transmissionand Female ReproductiveSuccess
We beginbyconsidering
thesituation
inwhichfemalescan materepeatedly
but
can haveonlyone successful
season.Withina
reproductive
episodeperbreeding
thathaverepeatedsexualcontact),the
singlepartnership
(i.e., pairofindividuals
of a healthyunfertilized
femaleendingup as eitherhealthyand
probabilities
unfertilized
(Phu=hu), healthyand fertilized
(Phu=>hd, infectedand unfertilized
areas follows(see bifurcation
andfertilized
diagram,
(Phu=iu),or infected
(Phu=>if)
fig.1):
Phu hu =
Phu hf =
(1
-
(1
-
y)[l
Y)
-
-
(1
y(l
Phu>iu
-
p)C
p)C]
-
+ y[(l
+ y(l
pI)C 1 -(1
-
-
)(
6)C[1
_- )C],
(1)
- pI)]C'
-
(1
-
PI)C]
,
(2)
(3)
and
(4)
(1 - P)] [1 - (1 - )C],
the
wherewe assumethatthereare c copulationswithina singlepartnership,
is 8, and y is thepopulationdisease freof infection
per-copulation
probability
thata femalewill be
quency.The parameterp is the per-contact
probability
fertilized
of fertilization
by a healthymale,and p' is thediscountedprobability
Phu>if =
y[l
-
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THE AMERICANNATURALIST
488
P
PI
(-p)
p
(lp)
-6)
successshowingthepossibleoutforfemalereproductive
FIG. 1 -Bifurcationdiagram
femaleand eithera healthy(open
healthy
c contactsbetweenan initially
comesfollowing
of a constantpopulation
(filledtriangle)maleundertheassumption
triangle)or infected
and femalesby
by triangles
(y). In thediagram,malesare represented
diseasefrequency
by filledsymbols.
are represented
individuals
circlesand squares;forbothsexes,infected
respecindividuals,
and fertilized
unfertilized
For females,squaresand circlesrepresent
p is theper-contact
of infection,
probability
8 is theper-copulation
tively.The parameter
by a healthymale(p), and p' is thediscounted
thata femalewillbe fertilized
probability
of
explanation
male(see theappendixfora further
offertilizaton
byan infected
probability
symbols).
by an infectedmale,wherep' = (1 - -y,,)pand y,,1is the degreeof sterility
in males.
causedby theinfection
arealso possiblebecausefemalescan
Withsubsequentmates,othertransitions
mate.Thus,theotherpossibletransibe in anyoftheabove statesafterthefirst
tionsforfemalesare givenby
Phf=>hf=
1 - y[1
Phf=>if= y[1
Piuiu =
Piu>if= I
-
- (1-
(1
(1 - y)( - p)
- (1 - p)C(1 -
and
Pif if=
H)] ],
(5)
,
(6)
8
+
y)
y(l - y(1
p)C)
- p)C
(7)
(8)
(9)
(i.e.,
assumesthatthereis no recoveryfrominfection
Note thatthisformulation
= 1).
the transitionprobabilityforPif?,if
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
489
intomatrix
The expressionforfemalereproductive
successcan be translated
algebranotation
usingequations(1)-(9). The completematrix
fortheamong-state
transition
probabilities
(C) is givenby
C -(1 - y)Hc + yDc,
wherethematricesC, H, and D are as shownin figure
2.
We can extendthisis to considertheentirebreeding
seasonas follows.Let m
ofpartnerships).
Ifwe multiply
ofmatesencountered
be thenumber
(i.e., number
theinitialdistribution
thematrixC by a vectorvorepresenting
offemalesamong
thefourpossiblestates(healthyand unfertilized;
infected
healthyandfertilized;
and unfertilized;
and fertilized),
we obtain
infected
Vm=
Cin Vo '
ofbeingin one ofthefourstatesat the
wherevmis a vectoroftheprobabilities
end ofthebreedingseasonafterm sexualpartners.
Assumingtheprobability
of
femaleis 0'
successfulreproduction
of a healthyfemaleis 0 and of an infected
(= [I
-
caused by the disease in females),
yf]0 where yfis the degreeof sterility
the seasonal fertility
thatshe successfully
of a female(i.e., probability
bears
is then
offspring)
Ff =
V
VW,
wherevWis thevectorof weightsused to calculatefemalefitness(fig.2). Note
infigure
2 thatthereproductive
fromvW
successofinfected
femalesis discounted
at theendofthebreedingseasonratherthanforeach sexualcontact,as it is for
males(see nextsection).
Disease Transmissionand Male ReproductiveSuccess
We can calculatethereproductive
successof maleswithina breedingseason
by an analogousprocedure.For malereproductive
success,thereare onlytwo
initialstates(healthy
or infected).
We assumeunlimited
spermsuppliessuchthat
the previousfemaleis irrelevant
to the
whethera male successfully
fertilized
of spermfrom
outcomeof thecurrent
matingand thatthereis no displacement
in naturefemalesare likelyto bethefemale'slast sexualencounter.
Although
comelimitedas thebreedingseasonprogressesand thenumberof successfully
matedfemalesincreases,herewe assumethatno suchlimitexists(i.e., regardless
ofchoosinga healthyandunfertilofhowmanymatesa malehas,theprobability
ized femaledoes notchange).
of a male remaining
We beginby calculatingtheoverallprobability
healthy
a
female.
This
c
contacts
with
is
h)
following
probability
straightforwardly
(Ph=,
calculatedfromthebifurcation
diagramshownin figure
3, where
Ph=>h = I - Y + Y (1 _ 8)c ,(10)
and theprobability
ofbecominginfected
(Ph.>i) is simply1 - Ph.>h.We assume
in thesensethatmalesthatbecomeinfected
is notinstantaneous
thatinfection
of fertilization
have the same probability
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A. MultipleContactswitha SinglePartner
0
0
P
Ol
0
0 i-p
0
0
p
1J
0
0
0
p/(1-)
(i-p')8
1-8
0
0
i-p'
0
p'8
8
p'
1
i-p
H
0
L0
(1-p')
D
=
-
(1-8)
O
B. MateStates
Phu-hu
0
Phu-hf Phf-hf
=
Phuiu
Phu-if
0
0
0
?
?
Piu-iu
?
Phf-if
Piu-if
Pif-if.
C. TotalFitnesswithina BreedingSeason
~0.
P-HUVm =
p
P-HF
vo
=
~0
0
VW = t
6
FIG. 2.-Description of matricesand vectors used to derive within-seasonfemale fitness
functions.A, Contacts witha singlepartner:H and D are per-contacttransitionmatricesfor
contacts witha healthyor infectedmale, respectively.B, Mate states: the matrixC gives
among-statetransitionprobabilities,followingc contacts witha singlepartner(hu, healthy,
if,infected,fertilized);forexamunfertilized;
hf,healthy,fertilized;iu, infected,unfertilized;
is the probabilityof a healthybut unfertilized
femalebecomingboth infectedand
ple, Phu=>if
fertilized.
season fitness:the vectorsvM,vW,and vo represent,
C, Total within-breeding
respectively,the total probabilitiesof being in one of the fourpossible states (hu, hf,iu, if)
at the end of the breedingseason, weightsused to calculate female fitness,and the initial
distributionof females(see the appendix forall parameterdefinitions).
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SEXUALLY
p
TRANSMITTED DISEASE AND MATING BEHAVIOR
(-p)
491
(
FIG.3.-Bifurcation
diagram
formalereproductive
successshowing
thepossibleoutcomes
a healthy
following
c contactsbetweenan initially
maleandeither
orinfected
female.
healthy
All symbolsandparameters
are thesameas thosedefined
forfigure1.
quentcontactswiththatfemale.Onceinfected,
however,contactswithall subsewithprobability
quentfemalesresultinfertilization
p' ratherthanp.
Usingthe bifurcation
diagramshownin figure3 and equation(10), we can
also calculatethejointprobabilities
associatedwithfertilization
of femalesand
infectionof males. These joint probabilitiescan then be divided by the total
probability of a male remaining healthy (Ph.,h) or becoming infected (Ph.>i) to
derivetheconditionalprobabilitiesassociated witheach mate (note thattheprobabilityof remaininginfectedif already in thatconditionis one since thereis no
recoveryfrominfection):
h) = (1 - y)[1
P(hf/h
P(if/h=> h) = (1
= y[1
P(if/h1i)
P(hf/i1i)
=(1
-
8)cI1
-
(1 - P)C]/Ph=h,
y(l
-
P)C]/Ph?hv
(1 - p)C][1 - (1 - 8)C]/Ph i,
-
y)(I - 8)C[1 - (1
-
( 1)
(12)
p)c]
and
P(if/i 4i)
=
I - (1 - p')C][1 - (1 - y)(I - 8)C]
(13)
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492
THE AMERICANNATURALIST
For example,P(hf/hC h) is theprobability
thata male thatremainedhealthy
fertilized
a healthy
female;P(if/ha i) is theprobability
thata malethatbecame
an infected
infected
fertilized
female.
Because femalesthathavebeenfertilized
havethepossibility
of subsequently
successof malesmustbe discounted
matingwithothermales,thereproductive
thata fertilized
by the probability
(buthealthy)femalewill go on to become
infectedby one of her subsequentmates.At the upperlimit,we assume that
a totalof m mates,and in thiscase thediscounting
femalesencounter
function
(DH) is givenby
DH
=
Ophmf1hf
+
0(1-
-
Ph
f),
(14)
wherePhf?hfis theprobability
thata healthyfertilized
femalestayshealthyafter
c contactswitha mate(eq. [5]). Notethatthediscounting
termgivenin equation
(14) equals 0 ifeither
Phf?,hf= 1 (e.g., iffemalesdo notcontinueto mateonce
theyhave been successfully
fertilized)
or thediseasedoes notcause sterility
(0'
= 0). However,ingeneral,thereproductive
successofmalesmustalso takeinto
of fertilized
in
accountthediscountedfertility
butinfected
females.Therefore,
thesummary
expression
formalereproductive
success(see below),theprobabilitiesgivenby equations(II), (12), and (13) mustbe multiplied
by 0'.
We developthesummary
recursion
formalereproductive
successby firstdetheconditional
fining
expectations
forthefitnessof initially
healthymalesthat
remainhealthyafterc contactswitha female,initially
healthymalesthatbecome
and malesthatare infected
at thestartofthebreedingseason,where
infected,
E(rs/h= h) = P(hf/h h)DH + P(if/h
a h)0',
E(rs/ha? i)
=
P(if/h4>i)0',
and
E(rs/i
a i) = P(hf/i
a i) DH + P(if/ia i)0').
As an example,E(rs/hz i) is theexpectedfitness
ofa malethatbecomesinfected
sexual contactwithan infectedfemale;the probability
following
thatshe will
producehis offspring
is theproductoftheprobability
thathe successfully
fertilized her (P[if/h= i]) and herown discountedprobability
of bearingoffspring
success (RS) of a malethatis initially
(0'). The overallreproductive
healthyat
thebeginning
of thebreedingseason is thencalculatedas follows:giventhata
maleis healthyat thebeginning
ofthebreedingseason,afterc encounters
with
a singlefemale,malereproductive
successis givenby
RS = Ph?,hE(rs/h4ah)+ Ph?,iE(rs/h
a i);
(15)
aftertwomates,reproductive
successis
RS = 2P2 hE(rs/hB
hh) + Phi hPhi [E(rs/ha h) + E(rs/ha i)]
(16)
+ Ph i[E(rs/hi i) + E(rs/ia i)];
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
493
and afterthreemates,reproductive
successis
RS = 3P3hE(rs/h4a h) + P 2thPh=i[2E(rs/h P h) + E(rs/h4a i)]
+ Ph hPh>i[E(rs/h> h) + [E(rs/h> i) + E(rs/ia i)]
(17)
+ Ph [E(rs/hi i) + 2E(rs/ia i)].
As the numberof matesincreases,so does the numberof possiblepathways
alongwhichmalereproductive
successcan be calculated.Simpleinspectionof
thepatterndevelopedin equations(15)-(17) allowsderivation
ofthesummation
givingtotalwithin-season
reproductive
successformalesthatare healthyat the
beginningof the breedingseason (Fhm),and withm mates:
m
Fhm= mPin hE(rsh
h) + PhiZ E
I
-h[(j
j=1
+ E(rs/h>i)
1)E(rs/hA h)
(18)
+ (m -j)E(rs/i>i)].
Calculationofreproductive
successformalesthatareinfected
at thebeginning
ofthebreeding
season(Fim)is relatively
simplebecausethereare onlytwopaths
malesmayfertilize
females:
by whichinfected
Fim= mE(rs/iaiI) .
In general,thederivations
are morecomplicated
formalesthanforfemalesbecause oftheassumption
thatmalescanfertilize
femalesduring
a breeding
multiple
season. Thismeansthatcalculationofreproductive
successrequiresknowledge
of intermediate
statesand the finalstateof a male at the end of the breeding
is noteasilytranslated
season; thissituation
intomatrixnotation.
RESULTS
Female Mating Behavior
Within-seasonreproductivesuccess.-If
there are no costs associated with
havingadditional
contactsor mates,then,as expected,in theabsenceofdisease
on infected
effects
(or ifthediseasehas negligible
sterilizing
hosts,i.e., 'y 0),
reproductive
success increaseswithbothnumberof copulationsper mateand
numberof matesto an asymptote
givenby 0. However,whenthediseasehas a
on hostfertility,
therearelikelytobe multiple
largeeffect
optimaforreproductive
success. Figure4 showswithin-season
fitnesssurfaces,wheretheleft-hand
rear
in whichfemaleshave a singlecontact
faceofeach surfacerepresents
situations
withmanymates(= promiscuity),
whilethe right-hand
frontface represents
in whichfemaleshave manycontactswitha singlemate(= monogsituations
at each ofthesefacesare approximated
amy).For smallvaluesof y,asymptotes
The asymptote
formonogamy
is greater
by 0(1 - y) and 0(1 - yy)respectively.
thantheasymptote
forpromiscuity
wheneverthediseaseis presentand thereis
a negativeeffectofthediseaseon fertility
(O < y < 1 and y > 0). However,for
largervalues of y thereare intermediate
optima,such thatneitherasymptote
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494
THE AMERICAN NATURALIST
A
W
E 5
1
B
0
1
C
5
2?
+~~~~~~~~~~~~~~~~~~~~~AA11
D
15~~~~
PtafO4
20
FIG. 4.-Within-season
fitness
surfaces
forfemalereproductive
successfordifferent
values
oftheper-contact
probability
ofinfection
(8) andpopulation
diseaseprevalence
(y). A, 8 =
0.02,y = 0.3;B, 8 = 0.2,y = 0.3;C, 8 = 0.02,y = 0.7;D, 8 = 0.2,y = 0.7. Inallof
thesefigures,
we assumethatthereis no costto additional
contactsor matesbutthatthere
are largenegativeeffects
ofinfection
(y = 0.9 forall surfaces).We further
assumethatthe
per-contact
offertilization
by males(p = 0.5) and theprobability
thata female
probability
willsuccessfully
producean offspring
(0 = 0.95) are heldconstant.
success(fig.4B,
necessarily
represents
themaximum
within-season
reproductive
of infection
D). As theprobability
increases,havingeithermultiplecontactsor
multiple
matesbecomesless advantageous;
thiseffect
is morepronounced
as the
degreeof sterility
caused by infection
increases(not shown).Whenboththe
of infection
populationdecreaseprevalenceand theper-contact
are
probability
success is maximizedby havingmultiplecontacts
high(fig.4D), reproductive
witha singlemate.
innaturethateitherthenumberof sexualcontactsper
It is extremely
unlikely
mateor thenumberofmatesis unlimited.
For example,in manycases, thereare
ofcontacts(e.g.,decreased
likelytobe costsassociatedwithan increasednumber
foraging
time,limitedspermsupplies,energyexpendedon thematingact itself,
riskof predation;Daly 1978;Rowe et al. 1994)or withswitching
mates(e.g.,
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
495
newmates,riskofdisease;Daly 1978;Hunteret al.
costsassociatedwithfinding
1993).Alternatively,
positiveeffectsmaybe associatedwithhavingadditional
new matesthrough
learnedbehavior,enmates(e.g., increasedskillat finding
hancedabilityto detectinfection
inpotential
mates,previoussuccessincreasing
successwithsubsequentmates).We can easilyencapsulatethesepossibilities
by
assumingthatthetotalnumberofcontactsperseason,k, is givenby
k= mc - mo,
(19)
where (x is the cost (or benefit,for(x < 0) associated withacquiringa new mate.
This assumesthe simplestcase in whichmate acquisitioncosts are constant
throughout
theseason.
If (xis unityor greater(fig.5A) and theper-contact
ofinfection
probability
(8)
is small,thenfemalereproductive
successis maximizedat an intermediate
numberofmates.When8 is larger,therearetwolocalmaximaforfemalereproductive
ofindividuals
success,whichsuggests
thepossibility
becoming"stuck"'at subopIf (xis less thanunityor negative(fig.5B), thenforsmallvalues
timalstrategies.
number
ofmates,butforlargervalues
of8, thereis stillan intermediate
optimum
if8 is fixedandthedegreeofsterility
is alwaysfavored.Similarly,
of8 monogamy
caused by infection
(y) is allowedto vary,femaleshave highestreproductive
is optimalwheny is
successwithmultiple
matingsif y is small,butmonogamy
large.
ofthe
The preceding
resultsassumethatfemalesare healthyat thebeginning
to ask whetherthe optimalreproductive
breedingseason. It is also of interest
ofan initially
femalewouldbe different.
Giventhatthereis no
infected
strategy
and thatthereare no costs to additionalcontactsor
recoveryfrominfection
at thebeginning
ofthe
successoffemalesinfected
mates,thenthereproductive
season will clearlybe maximizedwhen both c and m are large, regardlessof the
or thedegreeof sterility
ofinfection
caused by infection
per-contact
probability
betweencontactsand
to lose). If we assumea trade-off
(i.e., theyhave nothing
mates of theformgivenby equation(19) witha = 1 (thereforea cost to additional
buta broadrangefortheoptimalnumber
mates),thenthereis no clearoptimum
of mates(withm > 1).
Probability
of infection.-In general,underthe assumptionthatper-contact
are the same frommalesto femalesas forfemalesto
of infection
probabilities
forfemales(following
c copulationswitha
of infection
males,the probability
of becoming
singlemate)is thesame as thatformales.The overallprobability
fora femalewhohas m matesduringa breedingseasonis simply
infected
1 - (1
- ph , in i
(20)
ofinfection
wherePhzi is theper-mate
probability
givenearlier(see eq. [10]).
Male Mating Behavior
Within-seasonreproductivesuccess.-For
males, reproductivesuccess is a
functionof the totalnumberof femaleswithwhomtheymateand who then
Similarto theresultsforfemales,undertheassuccessfully
produceoffspring.
ofno coststo multiple
diseaseeffects,
contactsor matesand negligible
sumption
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THE AMERICAN NATURALIST
496
A
0.8
0.6
0.4
0.2
Mn
5
10
15
20
5
10
15
20
B
0.8
0.6
0.4
0.2
Numberof Mates
of
successas a function
of per-contact
FIG. 5.-Within-season
reproductive
probability
between
infection
and numberof matesforinitially
healthy
females,assuminga trade-off
ofmates(i.e., c = k/m- of).A, (x = (i.e., there
number
ofcontactspermateandnumber
is a cost to acquiring
additionalmates);B, (x = - 1 (i.e., thereis a benefit
to acquiring
fixedvaluesof 8 (fromtop to bottom,
linesrepresent
additionalmates).In bothfigures,
and all otherparameters
are fixed
8= 0.01,0.05,0.1, 0.2, 0.3, 0.4, and0.5, respectively),
(y 0.3, y = 0.9, p = 0.5, and0 = 0.95).
success whenboththenumberof contacts
maleshave maximum
reproductive
has severeeffects
per mateand thenumberof matesare high.Wheninfection
on fertility
(largevaluesof y) but8 is small(fig.6A, C), thenmalereproductive
withfewcontactspermateand manymatesregardlessof
successis maximized
diseaseprevalence.For largervaluesof 8 butwithlow disease prevalence(fig.
a maleshouldhave manymatesbut
6B), thereis morethanone local optimum;
successby eitherhavingfewor many
can achieverelatively
highreproductive
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DISEASE AND MATINGBEHAVIOR
SEXUALLYTRANSMIUTED
A
497
B
i.5~~~~~~~~~~~~~~~~~~~~~~.
10~~~~~~~~~~~~1
20
C
20
D
20~~~~~~.
FIG. 6.-Within-season
successforinitially
notradereproductive
healthy
males,assuming
offbetweennumber
ofmatesbutlargenegativeeffects
ofinfection.
ofcontactsandnumber
For all surfacesshown,y = 0.9, p = 0.5, and 9 = 0.95.A, 8 = 0.02,y = 0.3; B, 8 = 0.2,
y = 0.3; C, 8 = 0.02, y = 0.7; D, 8 = 0.2, y = 0.7.
infection
rateand disease prevalence
contactsper mate.If boththeper-contact
are high(fig.6D), theninitially
malesare likelyto becomediseasedearly,
healthy
and (as withinitially
infected
males)theyshouldmateas muchas possible.
ifwe assumea costto havingadditional
matesanduse thetrade-off
In contrast,
function
combinations
of fyand 8
givenby equation(19), thenforall parameter
thatwe examined,the reproductive
success of initiallyhealthymales is maxthe expectationthat
imizedforintermediate
values of m (fig.7A). Therefore,
malesshouldalwaysmaximizethenumberofmatesis notborneoutin themore
When
realisticsituation(i.e., numbersof contactsor matesare notunlimited).
thereare benefits
to havingadditionalmates,thenformostvalues of 8, males
shouldmatewithas manyfemalesas possible;at veryhighvalues of 8, male
forvaluesclose to unity(fig.7B).
reproductive
successwillbe optimized
In the resultspresentedearlier,forpurposesof calculatingthe discounting
expressionDH in equation(14), we assumethatfemalesare promiscuous(i.e.,
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THE AMERICAN NATURALIST
498
3.53
2.5
2
1.5
0.5
VI)
5
10
5
10
15
20
8
6
4
2
15
20
Numberof Mates
successas a function
of per-contact
FIG. 7.-Within-season
of
reproductive
probability
and number
ofmatesforinitially
thatc = k/m- ci. A,
infection
healthy
males,assuming
additional
( = 1 (i.e., thereis a costto acquiring
mates);B, (x = - 1 (i.e., thereis a benefit
linesrepresent
fixedvaluesof8 (fromtopto
to acquiring
additional
mates).In bothfigures,
and all otherparameters
bottom,8 = 0.01,0.05,0.1, 0.2, 0.3, 0.4, and 0.5, respectively),
valuesare thesameas
are fixed(y = 0.3, y = 0.9, p = 0.5, and0 = 0.95). All parameter
thoseforfigure
5.
the numberof mates(forfemales)
alwayshave m mates).Whileincorporating
intothe modelas a variablewouldcomplicatethe formulations
considerably,
in whichfemalesare completely
we can easilyexplorethecontrasting
situation
In thiscase, thediscounting
monogamous.
term(DH) reducesto 0. Whenthere
are no costs to additionalmates,so thatbothc and m can potentially
be quite
successofinitially
malesincreaseswithincreasing
large,thereproductive
healthy
m and c; whencostsare assumed,malereproductive
successis maximizedin a
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
499
mannerqualitatively
similarto thatinthesituation
inwhichfemalesare assumed
to be promiscuous
(see fig.7A). It is interesting
thatinthecase in whichfemales
forveryhighvalues of 8, male reproductive
are assumedto be promiscuous,
success is maximizedforvaluesof m close to unity;thisdoes notoccurwhen
femalesare assumedto be monogamous
(and,instead,intermediate
numbersof
matesare alwaysoptimalformales).
Probability
of infection.-If theprobability
of infection
following
sexualcontactwitha singlemateis thesameformalesas forfemales(see above),thenthe
overall probabilityof infectionwithina breedingseason is the same as that for
females(see eq. [20]).
DISCUSSION
The issueofhowsexuallytransmitted
diseasesshouldinteract
withthemating
systemsof theirhosts has been, untilrecently(Sheldon 1993; Loehle 1995),
on matingsystemevolution.This studyprovides
largelyignoredin theliterature
an initialsteptowarddeveloping
a quantitative
framework
forexamining
mating
thatcan takeintoaccounta rangeofbehaviorsbetween
system-STDinteractions
We do thisusingbiologically
theextremesofpromiscuity
andmonogamy.
meaningful(and measurable)per-contact
probabilities
offertilization
and infection
as
a basis forexploringthe problem.The presentstudyconfirms
thatSTDs can
have majorimpactson hostmatingsystemevolutionand that,conpotentially
the evolutionof pathogen
versely,host matingsystemsmaygreatlyinfluence
characteristics.
However,we also show thatthe outcomesare oftennot intuwe confirm
thatitis reasonableto expect
itivelyobvious.For example,although
willlead to higherratesoftransmission
thatpromiscuity
and diseaseprevalence
thecorresponding
thatmonogamy
willalways
thanwillmonogamy,
expectation
evolve in the presenceof STDs (Freeland1976;Immerman
1986)is not borne
out. We have shownthatthe situationis morecomplex,witha possibility
of
multiple
optimasuchthatsimilarhighlevelsof reproductive
success can result
fromdifferent
behaviors.Forexample,infemales,whenper-contact
infecmating
tionratesarehigh,havingmultiple
matesresultsina highprobability
ofinfection.
herprobability
Therefore,
a femalecan eitherminimize
ofbecomingdiseasedby
beingmonogamousor be promiscuousand maximizeher probability
of being
ofthehighprobability
fertilized
thatshewillbecomediseased(see fig.
regardless
5A). In otherwords,ifthefirstmateis likelyto be infected
(becausepopulation
diseaselevelsare high),thenthefemalemaybe betteroffmaximizing
herreproductivesuccessby havingmanymates.Thisleads to theexpectation
thatthere
indegreeoffemalepromiscuity
at highlevelsofdisease.
maybe morevariability
The simpleassumptions
of ourmodelslead to theprediction
thatbothmales
in theabsenceofdisease. Therefore,
and femalesshouldbe highly
promiscuous
our resultthattheoptimalmatingsystemin thepresenceof disease maydiffer
betweenmalesand femalesindicatesthatdisease alone (ratherthan,say, costs
ofrearing
can influence
theevolutionofdifferences
betweenthesexes
offspring)
in matingbehavior.For example,if we assumefemaleshave at mosta single
successfulreproductive
episodeperbreeding
season,inthepresenceofa sterilizThis content downloaded from 129.237.046.008 on October 25, 2016 11:29:03 AM
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500
THE AMERICAN NATURALIST
ingSTD, femalesshouldgenerally
be monogamous,
and males shouldbe completelypromiscuous.
However,becausetheseoptimahavebeencalculatedindependently
formalesand females,theactualevolutionary
outcomeis difficult
to
predict;thisprediction
wouldrequireotherapproachesthatincorporate
thejoint
optimization
ofmaleand femalereproductive
success.
An interesting
betweentheinfection/fertilization
biologicaldifference
process
inmalesandfemalesis thatthereproductive
successofa femaledoes notdepend
on whether
themalewithwhomshematesbecomessubsequently
infected
(either
by herselfifshe is diseasedor by anotherdiseasedfemale).On theotherhand,
male reproductive
success does dependon whetherthe femalewithwhomhe
copulatedbecomesinfected
duringthatmatingor duringsubsequentmatingsin
thatbreeding
season.Thisasymmetry
occursbecausethefemaleusuallyharbors
thezygotefora periodafterfertilization
(inourcase, untiltheendofthebreeding
behaviorsinmalesandfemalesmaythereseason).Selectionfordifferent
mating
forebe at leastin partdiseasedrivenand notsimplya consequenceofdifferent
demandsor ecologicalrisksassociatedwithrearingoffspring.
physiological
One area of evolutionary
biologyin whichmatingsystemand disease have
been explicitly
consideredis theevolutionof secondarysexualcharacteristics.
Hamilton(1990) and Hamiltonand Zuk (1982) suggestthatsecondarysexual
characteristics
mayhaveevolvedas a signalofgoodhealth.However,giventhat
theevolutionary
thediseaseinquestionis sexuallytransmitted,
expectations
may
be quitedifferent.
For example,because attractive
malesare likelyto be doing
themajority
ofthemating,
theymaybe morelikelyto carryan STD. Therefore,
it is conceivablethatfemalesthatavoid matingwithsuch males mayactually
maleswithconspicuous
have a greaterreproductive
success. Correspondingly,
secondarysexual featuresmay be healthier(now) because they have been
one mightexpectsexuallytransavoided(in thepast)byfemales.Furthermore,
of theirhostssince
mittedpathogensthemselves
to increasetheattractiveness
thereare numerous
recthiswouldclearlyincreasetheirtransmission.
Certainly,
eitherhostbehaviorand/orappearanceto enhancetheir
ordsofparasitesaltering
own transmission
(Moore 1984;Dobson 1988),and some STDs are knownto
or sexualactivityof infectedhosts(Lockhartet al.
increasethe attractiveness
in horses,
1996). For example,dourine,a sexuallytransmitted
trypanosome
causes infectedstallionsto increasetheirlevel of sexual activityrelativeto
rehealthymales.A bacterialSTD in cattle,bovinegenitalcampylobacteriosis,
sultsin abnormally
longestrouscyclesin infected
cows,and,in herdsituations,
and forlongerperiodsthanwouldoccur in healthy
bullswill materepeatedly
because infectedfemalesdo not conceive.Maintenanceof
herds,presumably
in malesmaytherefore
be
geneticvariationin secondarysexualcharacteristics
ofsuchtraitswithsexuallyversusnonsexually
drivenin partbytheinteractions
transmitted
pathogens(Able 1996).
resultto emergefromour analysesis
Anotherobviousbutratherinteresting
thattheoptimalmating
systemmaynotbe theone thatreducesdiseasetransmisresultedin thelowest
sionthemost.In all cases thatwe examined,monogamy
was clearlynotalwaysthefavoredmating
disease transmission,
yetmonogamy
thatare optimalwith
hostsmayevolve matingstrategies
strategy.
Therefore,
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
501
strategies
maypermitsubstantial
yettheseself-same
regardto theirownfitness,
because meancontactnumberis
disease spreadand persistence.Furthermore,
transmisalwaysthesamebetweenthetwosexes (and assumingmale-to-female
diseaseincidencewillalso be indepentransmission),
sionequalsfemale-to-male
behaviors.
mating
thetwosexesmayhavequitedifferent
dentofsex eventhough
studieshavebeendoneofsex-specific
It shouldbe notedthatfew,ifany,rigorous
In humans,
ofinfection
forSTDs inanimalpopulations.
per-contact
probabilities
mayoftenbe
probabilities
ofinfection
thatsingle-exposure
ithas beensuggested
higherfrommalesto femalesthanfromfemalesto malesbecause of ejaculate
in the vagina(e.g., gonorrhea:Hook and Handsfield1990; HIV and
retention
HTLV: Ewald 1994).
success,
reproductive
Even thoughouranalysesonlyconcernedwithin-season
to lifetime
reproductive
success undercertain
the lattermay be proportional
and survivalof adultsremainconstant
conditions.If we assumethatfecundity
inmanyspecies
approximated
aftertheyreachreproductive
age (e.g., a situation
ofbirds,at leastduringmiddleage; Forslundand Part1995),thenwe can repreofhosts(X) as
sentthegrowthrateofa population
dX = SQFX--X
age, percapita
to reproductive
whereSO, F, and [ are thesurvivalofnewborns
In thissituation,
lifetime
reproductive
output,andadultdeathrate,respectively.
reproductive
success(LRS) is givenby
LRS
-
S.F
UsuallyF and pLare considered"normal"birthand deathrates,buttheycan
If we also
or mortality.
also be functions
thatincludedisease-induced
sterility
thehost'slifespan
remainsconstantthroughout
assumethatdiseasefrequency
or changing
is at equilibrium
veryslowlyrelativeto
(i.e., thediseasefrequency
ofthehost
thelifetime
ofthehost),thenthediseasewouldreducethefecundity
in a proportional
mannereverybreedingseason. Underthese circumstances,
to the within-season
the LRS of the hostis directly
reproductive
proportional
success.
in thatwe calcuare simplified
earlier,ourcurrent
formulations
As mentioned
ofeach other.Although
successindependently
latemaleandfemalereproductive
as to how mating
thisassumption
precludesus frommakinggeneralpredictions
in severalspecificcases. This
systemswillevolve,it maynotbe unreasonable
assumption
impliesthateitheraccess to matesis notlimited(e.g., matingoccurs
ofthealternative
mates)orthatmatesare sampledwith
withonlya smallfraction
disease frequency
does not change
replacement
(and, as assumedthroughout,
these assumptionsare
the season). In mostreal-worldsituations,
throughout
probablyonlyreasonableforfemales.However,itshouldbe notedthatthemean
thattheothersex is notlimiting)
RS ofthefocalsex (calculatedon theassumption
willbydefinition
equalthemeanRS oftheothersex,buttheformofthedistribubehaviorsandhowtheysumto givethatmeanRS in the
tionofindividalmating
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502
THE AMERICANNATURALIST
in whichmales
For example,considerthesituation
othersex willbe undefined.
success in females.If females
are not limiting
and we determine
reproductive
thenwe wouldexpectnumber
ofmatespermale
samplemaleswithreplacement,
withmostmaleshavingfewmatesbut a few
to followa Poissondistribution,
maleshavingmanymates.The consequencesofvarianceinthenumberofmates
therefore
fordisease transmission
also needsto be evaluated.However,in the
contextofthemodelsdevelopedhere(i.e., assumingthatdiseaselevelswithina
it can be seenfromequation(18) thatdisease transseason remainunchanged),
missionis independent
ofthedistribution
ofm.
within-season
diseasetransmission
However,ifthereis substantial
(or transandaseasonal,as inhumans),reproductive
continuous
missionis essentially
sucinfluenced
cess is likelyto be strongly
by variancein thenumberof contacts.
Those individualswitha largenumberof mates(or partners)may contribute
to diseasetransmission,
andtransmission
becomesa function
disproportionately
of boththe meanand varianceof the numberof partners(May and Anderson
wouldapplytolifetime
1987;Andersonetal. 1989).A similarargument
reproductivesuccess,iftherewereamong-season
in their
covarianceamongindividuals
in varianceare oftenused as a basis formating
numberof mates.Differences
For example,polygyny
systemclassification.
(one malematingwithseveralfemales)impliesthatthevariancein matingsuccessofmalesis muchgreaterthan
thatof females(givena 50:50 sex ratio);underthesesituations,
within-season
diseasetransmission
maybe underestimated
byonlytakingintoaccounttheaverage numberofmates.
Althoughwe do not presentformalanalyses,it can be readilyshownthat
success willalwaysincreasewiththe numberof mates
pathogenreproductive
benefit
andnumber
ofcontactspermate,buttherewillbe a decreasing
persexual
as c increases.If varioustrade-offs
are present(e.g.,
contactper partnership
betweenvirulence
andtheper-contact
oftransmission)
andifthetotal
probability
numberof copulationsper season is constant(see eq. [19]) then,as expected,
thereis some intermediate
level of virulencethatmaximizespathogenfitness.
The preciselevelofvirulencewilldependon boththeformofthecost function
and the matingsystem.It has been generallyarguedthatpathogenvirulence
(definedas a negativeeffectof thepathogenon hostfitness)willincreasewith
as long as the transmission
mode remainsthe same
transmission
opportunity
thatSTDs are no exception.
(Ewald 1988,1990,1994);ourstudiesconfirm
Althoughit is easy to speculateon the potentialrevolutionaryinteractions
betweenSTDs andanimalmating
almostno explicittestsoftherelationsystems,
It has been
shipbetweenSTDs and hostmatingsystemshave been performed.
shown(Thrallet al. 1993)thatpollinator-transmitted
anthersmutswere more
commoninplantspeciesthatwereoutcrossing
andhadlargerflowers.Smithand
Dobson (1992)have suggested
thatthevariation
hostspecies
amongmammalian
in matingbehaviormaycorrelatewiththedegreeof sexualtransmission
of the
bacterialpathogen
Brucellaspp. (Nielsenand Duncan1990).Moreover,Sheldon
behaviorsinbirds(e.g., cloacalinspection,
(1993)has postulatedthatmating
the
likelihoodof extrapaircopulations)mightbe relatedto the risk of infection
sexualtransmission.
One clearexamplefrom"culturalevolution"is the
through
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SEXUALLY TRANSMITTED DISEASE AND MATING BEHAVIOR
503
recentshiftin humanmatingbehaviordue to thewidespreadfearof AIDS (Ostrow1990;Schwartzand Gillmore1990).
Application
ofourmodelsto real-world
situations
minimally
requiresdetailed
knowledgeof notonlythematingsystembutalso theper-contact
transmission
andfertilization
rates.We knowofno system(otherthanhumans)inwhichthese
aspectshave been investigated,
let alone characterized
quantitatively.
Tests of
modelpredictions
theimpactofSTDs on matingsystemevolutionmay
regarding
requirethedevelopment
of experimental
systems.Recently,Hurstet al. (1995)
demonstrated
thatthemiteCoccipolipushippodamiae
is transmitted
amongadult
two-spotted
ladybugs(Adalia bipunctata)duringmatingin laboratorypopulations;moreover,behaviorsobservedin Adalia duringmatingmaywell be the
resultofevolutionto avoidmitetransmission
orto avoidcopulating
withalready
infectedmates.Whisler(1968) studiedsexualtransmission
and effectson host
longevity
ofa fungaldisease(Stigmatomyces
baeri,Laboulbeniales)foundon the
flyFannia canicularis.Such sexuallytransmitted
fungaldiseases appearto be
commonplacein insects(Thaxter1896;Strandberg
and Tucker1974;Whitney
1982)and mayprovidesomeofthebestexperimental
systemsin whichto study
thenumerical
and evolutionary
dynamicsof STDs.
beenarguedthatmatingand social structure
Whileithas frequently
are determinedby the distribution
of resourcesand avoidanceof predators,pathogens
mayhavean equallyimportant
influence
(Dobson 1988;Dobsonand Lyles 1989).
Ourstudyprovidesa theoretical
theinteractions
between
forstudying
framework
sexuallytransmitted
pathogensand theirhosts.Our resultsindicatethatSTDs
can, at leastin theory,impacton hostmatingbehavior;however,it remainsto
be seen howtheseresultsrelateto thediversity
of matingsystemsactuallyobservedin nature.
ACKNOWLEDGMENTS
forusefuldiscussions,suggestions,
We thankA. Dobson and D. Rubenstein
and commentson some of the ideas containedin the manuscript.
This article
was improvedby the commentsand suggestions
of K. Holsinger,P. Ewald,
J. Kingsolver,and an anonymousreviewer.The supportof NationalScience
FoundatongrantDEB-9408207is gratefully
acknowledged.
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THE AMERICAN NATURALIST
504
APPENDIX
TABLE Al
DEFINITIONS
OF MODEL
PARAMETERS AND SYMBOLS
Definition
Symbol
Within-season
reproductivesuccess:
c
m
y
k
(x
8
y
p
p
0
0'
Numberofsexualcontactspermate
Numberofmatesencountered
diseaseprevalence
Population-level
Totalnumber
of sexualcontactsavailable(assumedto be fixed)
betweenc and m is asCost/benefit
ofaddedmateswhena trade-off
sumed (see eq. [19]); (x > 0 = cost, (x < 0 = benefit
ofinfection
Per-contact
probability
offertilization
forinfected
intheprobability
males;
Fractional
reduction
ofsuccessfully
forinin theprobability
bearingoffspring
reduction
fectedfemales
forhealthy
males
offertilization
Per-contact
probability
forinfected
males(= p[1 - y])
offertilization
Per-contact
probability
femalesuccessfully
thata healthy
fertilized
produces
Probability
offspring
femaleproducesoffspring
(andfertilized)
Probability
thatan infected
(=
[1 - y])
Lifetime
reproductive
success:
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