-
Interspecific Contact and Competition May Affect the
Strength
and Direction of Disease-Diversity Relationships
for Directly Transmitted Microparasites
Suzanne M. O’Regan,1,2,* John E. Vinson,1 and Andrew W.
Park1,3
1. Odum School of Ecology, University of Georgia, Athens,
Georgia 30602; 2. National Institute for Mathematical and
Biological Synthesis,University of Tennessee, Knoxville, Tennessee
37996; 3. Department of Infectious Diseases, College of Veterinary
Medicine, University ofGeorgia, Athens, Georgia 30602
Submitted July 22, 2014; Accepted June 3, 2015; Electronically
published September 4, 2015
Online enhancements: appendix, scripts.
abstract: The frequency of opportunities for transmission is key
tothe severity of directly transmitted disease outbreaks in
multihostcommunities. Transmission opportunities for generalist
micropara-sites often arise from competitive and trophic
interactions. Addition-ally, contact heterogeneities within and
between species either hinderor promote transmission. General
theory incorporating competi-tion and contact heterogeneities for
disease-diversity relationshipsis underdeveloped. Here, we present
a formal framework to exploredisease-diversity relationships for
directly transmitted parasites that in-fect multiple host species,
including influenza viruses, rabies virus, dis-temper viruses, and
hantaviruses. We explicitly include host regulationvia intra- and
interspecific competition, where the latter can be depen-dent on or
independent of interspecific contact rates (covering
resourceutilization overlap, habitat selection preferences, and
temporal nichepartitioning). We examine how these factors interact
with frequency-and density-dependent transmission along with traits
of the hosts inthe assemblage, culminating in the derivation of a
relationship describ-ing the propensity for parasite fitness to
decrease in species assemblagesrelative to that in single-host
species. This relationship reveals that in-creases in biodiversity
do not necessarily suppress frequency-dependentparasite
transmission and that regulation of hosts via interspecific
com-petition does not always lead to a reduction in parasite
fitness. Our ap-proach explicitly shows that species identity and
ecological interactionsbetween hosts together determine
microparasite transmission outcomesin multispecies communities.
Keywords: biodiversity, dilution effect, disease ecology,
epidemiology,host-parasite interactions, transmission.
Introduction
Directly transmitted microparasites often infect multiplehost
species, and consequently the ecology of species in-teractions is
crucial for determining parasite establishment
and persistence in multihost communities. The frequencyand
magnitude of disease outbreaks is often determined bythe rate of
transmission opportunities in the assemblage.Cross-species
contact—achieved, for example, throughfeeding on or utilizing a
common resource—may facilitateparasite spillover from one host
species to another. Alter-natively, ecological interactions that
regulate susceptiblehost species, such as intra- and interspecific
competition,can control or possibly promote parasite transmission
inmulti-host-species communities. For example, reducedhost species
abundances resulting from interspecific com-petition may lead to a
decreased number of cross-speciestransmission events. Additionally,
community structuresthat result in contact heterogeneities within
and betweenspecies will affect disease outcomes (Dalziel et al.
2014).Given that interspecific competition and contact may beeither
correlated or independent of one another accordingto community
contexts (fig. 1), it is unclear under whatconditions competitive
interactions and contact betweenmultiple hosts combine to enhance
or, alternatively, re-duce the risk of outbreaks of microparasitic
infections inmultispecies communities.To quantify how community
structure and ecological
context, including competition and contact heterogeneities,may
affect outbreak tendency, it is possible to calculate thefitness of
a parasite in a community of host species. Parasitefitness is
typically measured by the basic reproductionnumber R0, the average
number of secondary infectionscaused by one infectious individual
(Anderson and May1991). Although this was originally defined to
describetransmission in a susceptible single-species host
popula-tion, the basic reproduction number of the parasite in
amultihost community can be readily derived through calcu-lation of
the dominant eigenvalue of the next-generationmatrix obtained from
linearizing the infected-host sub-system at the disease-free
equilibrium (Diekmann et al.
* Corresponding author; e-mail: [email protected].
Am. Nat. 2015. Vol. 186, pp. 480–494. q 2015 by The University
of Chicago.0003-0147/2015/18604-55653$15.00. All rights
reserved.DOI: 10.1086/682721
vol . 1 86 , no . 4 the amer ican natural i st october 20 1
5
-
2010). Theoretical studies have considered how parasite fit-ness
in a multihost community (hereafter, community R0)is impacted by
the composition and abundance of the hostcommunity (Norman et al.
1999; Roche et al. 2012; Mihal-jevic et al. 2014). Dobson (2004)
explored the conditionsunder which species richness, in combination
with trans-mission mode, increases or decreases the propensity
foroutbreaks, which he quantified by calculating the basic
re-production number acrossmultispecies communities. Rudolfand
Antonovics (2005) described how reduction in parasiteincidence
might arise from different assumptions abouttransmission in
combination with regulation mechanisms,but their study investigated
the effects of intraspecific com-petition and frequency-dependent
transmission only. Neitherof the latter models included
interspecific competition. Whilemodels for interspecific
competition and disease transmis-sion are well developed, they are
rarely examined jointly(but see Bowers and Turner 1997; Peixoto and
Abramson2006). Recently, community epidemiology has made prom-ising
advances in the study of parasite transmission in mul-tispecies
host communities by invoking phenomenologicalassumptions linking
species richness, abundance, and even-ness (Roche et al. 2012;
Joseph et al. 2013; Mihaljevic et al.2014), but these studies do
not include interspecific contactheterogeneities and host
competition. Our approach intro-
duces these scenarios and asks under what conditions is
par-asite fitness in a multi-host-species community reduced
rel-ative to parasite fitness in a community consisting of asingle
focal host species. This question represents a funda-mental
knowledge gap concerning how broad assumptionsabout transmission
mechanisms and strength of competi-tion contribute to the spread of
directly transmitted para-sites in multispecies communities. This
“missing piece” in-cludes the potential independence of contact
rates andstrength of competition mediated by variable overlap
inresource-utilization functions, habitat selection, temporalniche
partitioning, and behavioral avoidance.Accordingly, we consider
simple epidemiological mod-
els encompassing intra- and interspecific competition alongwith
intra- and interspecific contact. We compare parasitefitness across
communities of a single host species (the res-ident or focal host)
and communities composed of a focaland alternative host species.
Analytical results of the effectof host species richness on
parasite fitness are achieved via aone- and two-host species
comparison, and themain resultsare shown to hold in larger host
species assemblages bymeans of numerical simulations (appendix,
available on-line). The models are flexible in their assumptions
aboutthe correlation between contact rates and strength of
com-petition (fig. 1). Contrasting contact and regulatory
regimes
Figure 1: Ecological contexts encompassing competition and
interspecific contact structure that may affect microparasite
transmission inmultispecies communities. Four separate cases are
considered: (i) low interspecific contact and weak interspecific
competition, (ii) highinterspecific contact and weak interspecific
competition, (iii) low interspecific contact and strong
interspecific competition, and (iv) highinterspecific contact and
strong interspecific competition. The degree of susceptible host
regulation that arises from interspecific competitionstrengthens
along the interspecific competition axis. We use this framework to
explore how susceptible host regulation through competitionand
cross-species contact interact to drive parasite transmission.
Disease-Diversity Relationship Framework 481
-
include (i) low interspecific contact and weak
interspecificcompetition (e.g., when host species are spatially
separatedor select different habitats); (ii) high interspecific
contactand weak interspecific competition (e.g., host species
usedifferent resources, but the resources co-occur); (iii)
lowinterspecific contact and strong interspecific competition(e.g.,
host species compete for a limiting resource but havelimited
contact with each other, such as through temporalpartitioning or
behavioral avoidance); and (iv) high contactand strong
interspecific competition (e.g., when species arecompeting for a
common resource).
In addition to regulatory forces, the transmission modealso
influences parasite fitness in a community of host spe-cies. Per
capita contact rates may increase with host den-sity, for example,
if the parasite is transmitted primarilythrough random contact
between individuals (density-dependent transmission).
Alternatively, contact rates mayremain approximately constant
across a range of densities,for example, if parasite transmission
occurs through sex-ual contact or between members of populations
that arestrongly socially structured (frequency-dependent
trans-mission). We incorporate mechanistic host competitioninto
susceptible-infectious-susceptible (SIS) mathematicalmodels
spanning frequency- and density-dependent trans-mission. Using
these models, we derive analytical relation-ships that describe the
propensity for amplification and re-duction of disease transmission
as a function of host speciesrichness by calculating basic
reproduction numbers, whichmeasure parasite fitness (Dobson 2004;
Roche et al. 2012).These expressions for the disease-diversity
relationship canbe represented graphically in ecologically relevant
parame-ter space. Our results demonstrate that
disease-diversityrelationships are more complex than is often
recognized,including the potential for disease amplification in
host-parasite systems with frequency-dependent transmissionand
decreased outbreak potential in communities
exhibitingdensity-dependent transmission. Additionally, we
demon-strate that elements of community composition, such as
hostspecies traits and contact patterns between species, are
keycomponents of disease-diversity relationships that shouldnot be
neglected by predictive models. In “Discussion,” wesummarize
caveats linked to our modeling approach. Fi-nally, we place our
findings in the context of the dilution-effect hypothesis, which
broadly posits that the net effectof increasing biodiversity is
reduction in parasite trans-mission (quantified in this article as
the propensity for de-creases in parasite fitness as species
richness increases).
Quantifying Parasite Fitness across Communities
Here, we extend theoretical studies that have examined
theeffects of increasing biodiversity—for example, throughchanging
species richness or evenness—on parasite dy-
namics (Norman et al. 1999; Holt et al. 2003; Dobson2004; Rudolf
and Antonovics 2005). To quantify parasitefitness across host
communities, we use the basic repro-duction number of the parasite
in a community of hosts,R0, which has been used to identify
conditions for in-creased and decreased parasite transmission in
multihostdisease systems (Norman et al. 1999; Dobson 2004; Rocheet
al. 2012; Joseph et al. 2013; Mihaljevic et al. 2014). Tocalibrate
the effect of increasing host species richness,we additionally
calculate the basic reproduction numberof the parasite in a single
host species, Rj0. The advantageof using basic reproduction numbers
to quantify parasitefitness is that they are epidemiological
properties corre-lated with parasite incidence and prevalence and
may be ex-pressed analytically for single- and two-species
communi-ties. Moreover, the basic reproduction number describesthe
initial growth rate of the parasite population in an en-tirely
susceptible mono- or heterospecific host community,and consequently
it is a measure of the propensity for out-breaks across different
communities.
Model Formulation and Analysis
We consider a focal host species (species 1) that is a
per-manent community resident and the introduction of a sec-ond
alternative host species (species 2) to the communitysuch that
parasite transmission occurs between the resi-dent and additional
host species. We use the SIS frame-work as a general model for
parasite transmission. By set-ting parameters to 0, it is easy to
generalize this model bynoting that the form of the next-generation
matrix used tocalculate community R0 is the same for models that
makedifferent assumptions regarding immunity and reinfec-tion, such
as SI, SIR, and SIRS systems (see the appendix).The SIS model for a
two-species community can be writ-ten as
dS1dt
p ½b01 2 b11(N1 1a12N2)�N1 2X2jp1
b1j f (.)IjS1 2 m1S1 1 g1I1,
dI1dt
pX2jp1
b1j f (.)IjS1 2G1I1,
dS2dt
p ½b02 2 b12(N2 1a21N1)�N2 2X2jp1
b2j f (.)IjS2 2 m2S2 1 g2I2,
dI2dt
pX2jp1
b2j f (.)IjS2 2G2I2.
(1)
Parameters and variables of the model are listed in table 1.The
model encompasses single- and two-species commu-nities, with the
single-species model being achieved by
482 The American Naturalist
-
Table 1: Model parameters and formulas
Symbol/formula Meaning
Sj Number of susceptible individuals ofspecies j
Ij Number of infectious individuals ofspecies j
Nj p Sj 1 Ij Population size of species jm Number of species in
the communityb0j Per capita natural birth rate of species jb1j Per
capita density-dependent reduction in
birth rate of species jmj Per capita natural mortality rate
of
species jrj p b0j 2 mj Per capita natural growth rate of species
jKj p rj=b1j Carrying capacity of species jsj Susceptibility of
species jij Infectiousness of species jpjk p sjik Transmissibility
of the parasite from
species k to species jcjk Per capita contact rate between
members
of species j and kbjk p pjkcjk Per capita transmission rate from
a
member of species k to a member ofspecies j
gj Per capita recovery rate of species jdj Per capita
disease-induced mortality rate
of species jGj pgj 1 dj 1 mj Per capita removal rate from the Ij
classajk Competition coefficient (relative compet-
itive effect of species k on species j)ajk p 0 Interspecific
competition absent0
-
setting symbols with subscript 2 to 0. For analytical
trac-tability and to allow ease of comparison of this model
withother published models (e.g., Getz and Pickering 1983;Holt and
Pickering 1985; Dobson 2004; Rudolf and An-tonovics 2005; McCormack
and Allen 2007), we assume thatdensity dependence arises via
reduction in birth rates withincreasing host density. Density- and
frequency-dependenttransmission modes are characterized by the
function f(.).We assume that both intra- and interspecific
transmissionoccur in the two-species system. The per capita
transmissionrate bjk from species k to species j is the product of
transmis-sibility of the parasite pjk and the number of contacts
perunit of time per infected host k with susceptible host j, cjk.If
transmission is density dependent, the per capita contactrate
between hosts of species j and k scales linearly withcommunity
size,
cjk(Nj,Nk)p cjk(Nj 1Nk),
and we assume that the force of infection exerted by spe-cies k
hosts on species j hosts is bjkIk. If transmission is fre-quency
dependent, the per capita contact rate betweenhosts of species j
and k is constant,
cjk(Nj,Nk)p cjk,
and the force of infection is bjkIk=(Nj 1Nk). Thus, the forceof
infection is proportional to the frequency of infectiousindividuals
of species k relative to the total communityabundance. Intuitively,
the proportion of infectious indi-viduals of species j (probability
of contacting species jhosts) is reduced when an alternative host
species k isadded to the assemblage, which may reduce disease
trans-mission (encounter reduction, sensu Keesing et al. 2006).
Our framework can be adapted to flexibly account for dif-ferent
encounter probabilities (appendix).
Heterogeneities in Host Contact Ratesand Transmissibility
Contact patterns—for example, through foraging, sexual,or
antagonistic encounters—are key to the transmissionprocess. To
describe the interspecific mixing patterns infigure 1
mathematically, we use the who-acquires-infection-from-whom (WAIFW)
matrix (Anderson and May 1991),whose entries are composed of the
per capita transmissionrates bjk,
Wp
�b11 b12b21 b22
�p
�p11c11 p12c12p21c21 p22c22
�,
noting that the per capita contact rate cjk in each entry
isconstant for frequency-dependent transmission and equalto cjk(N1
1N2) for density-dependent transmission. In ad-dition to mixing
between species, the WAIFW matrix con-veniently describes elements
of host competence. Competenceis central to studies of parasite
transmission in multispecieshost communities and embodies the ways
in which differenthost species contribute unequally to parasite
fitness. Compo-nents of competence include behavioral exposure
(Hawleyet al. 2011), grooming of ectoparasites and vectors
(Keesinget al. 2009), and parasite replication, shedding, and
immuneactivation (Komar et al. 2003).We allow variation in
compe-tence to be manifested in susceptibility (sj),
infectiousness(ij), or both (fig. 2A). Here, we assume that
transmissibilitypjk is composed of the product of susceptibility of
host j
1 2
1 2
β21=ci1s2
β12=ci2s1 β22=c22i2s2β11=c11i1s1
2β21
β11
p11c11 p12c
p21c p22c22WS I=
1s1c11 i2s2c
2s1c i2s2c =
11 0
21 0W = =
1i1c11 0
s2i1c21 0
A
B
Figure 2: Schematics representing transmission networks for
species 1 and 2. Circles represent species 1 (resident host) and 2
(alternativehost species), and arrows represent transmission rates
within and between species. The corresponding
who-acquires-infection-from-whommatrix is shown for each network.
A, Transmission rates are composed of host susceptibility,
infectiousness, and per capita contact rates.B, Spillover from the
resident host (circle 1) to an alternative dead-end host for
transmission (circle 2). Arrows indicate transmission rateswithin
and between members of each population. Since species 2 is a
dead-end host, no transmission occurs between members of this
species.
484 The American Naturalist
-
and the infectiousness of host k. For example, if compe-tence is
driven by susceptibility and the infectiousness ofeach host species
in the assemblage is equal, then each en-try of the WAIFW matrix
is
Wjk p sjicjk.
On the other hand, if transmission is driven by infectious-ness
ik and the susceptibility of each host is equal to s, theneach
entry of the WAIFW matrix is
Wjk p sikcjk.
To summarize the contributions of inter- and
specifictransmission to parasite fitness, we introduce the ratio
ofinter- to intraspecific transmission coefficients,
bpb12b21
b11b22.
Interestingly, b depends only on the ratio of interspecific(c12
p c21 p c) to intraspecific (cjj) contact rates,
bps1i2c#s2i1c
s1i1c11#s2i2c22p
c2
c11c22.
Thus, under this framework, differences in host contact ratesare
the key determinant of the interspecific-intraspecifictransmission
ratio, not parasite transmissibility heteroge-neities.
Consequently, we assume that b is a function ofcontact only and
hereafter refer to it as a contact ratio.If interspecific contact
is weak (b< 1), then spillover ofthe parasite between species
may occur infrequently, whereasstrong interspecific contact (b >
1) will facilitate spillover.The ratio of inter- to intraspecific
transmission rates hasbeen shown to determine parasite
establishment and per-sistence in some contexts (e.g., Bowers and
Turner 1997;Holt et al. 2003; Begon et al. 2008). Since b
summarizesthe relative degree of mixing between species, we
considerthe following subcases for the contact ratio
representingdifferent contact networks: (1) bp 1 (e.g., high
degreeof mixing due to shared resource utilization; panel ii infig.
1); (2) b > 1 (e.g., species are highly territorial and
en-counter other species more frequently than members oftheir own
species); and (3) b< 1 (e.g., species with high so-ciality
within groups). We will show that b is a key contrib-utor to
predicted parasite fitness outcomes in multispeciescommunities.
Criterion for Comparing Parasite Fitness acrossMono- and
Heterospecific Communities
To compare parasite fitness across mono- and hetero-specific
communities, we compare the basic reproductionnumber of the
parasite in a resident host (R10) to community
R0. We use equation (1) to calculate single-host- and
two-species-community basic reproduction numbers (see theappendix
for details and table 1 for expressions). In a two-species
assemblage, community R0 is expressed analyticallyin terms of the
resident and alternative hosts’ basic repro-duction numbers (R10
and R20; see table 1). For example, as-suming that a second host
species is added to an assem-blage at the same abundance as the
resident host, with thetwo species having equal interspecific
competitive effectson one another, and additionally assuming that
transmis-sion is density dependent, the community R0 for the
two-species assemblage is expressed as
R0 p12
R10
11a1
R2011a
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�R10
11a1
R2011a
�22 4
R10R20(11a)2
(12 b)
s !,
where a is the symmetric interspecific competition coeffi-cient,
b is the ratio of inter- to intraspecific transmission, and
Rj0 pbjjKjGj
,
jp 1, 2, is single-species R0. This expression is derived in
thesection titled “Density-Dependent Transmission and Intra-and
Interspecific Competition” in the appendix, whereas theassumption
of symmetric competition is relaxed in the sec-tion titled
“Density-Dependent Transmission and Intraspe-cific and Asymmetric
Interspecific Competition” in the ap-pendix. If competition is
asymmetric, the community R0expression is different (table 1).We
posit that the net outcome of community interac-
tions and increase in biodiversity is reduction of fitnessof the
parasite in a heterospecific community relative toits fitness in a
monospecific resident host community (adilution effect) if the
following inequality is satisfied:
R0 R10 as anamplification effect.
Results
Table 2 summarizes the analytical conditions on the
modelparameters for which relation (2) will hold for a
two-speciescommunity and predicted outcomes for parasite fitness
(seethe appendix for mathematical details). A dilution effect isnot
a ubiquitous outcome (fig. 3). In all combinations oftransmission
mode and competition that we examined, in-creasing species richness
through adding a second host spe-cies to the assemblage may result
in enhanced parasite fit-ness (i.e., R0 > R10). Since the
addition of a second hostincreases overall population abundance,
the combinationof density-dependent transmission and regulation by
intra-
Disease-Diversity Relationship Framework 485
-
specific competition cannot lead to a reduction in parasite
fit-ness (e.g., as shown in Dobson 2004), but a dilution effect
maymanifest through all other transmission-competition
combi-nations. Importantly, neither frequency-dependent
transmis-sion nor susceptible host regulation via interspecific
competi-tion guarantees reduction of parasite transmission.
The analytical conditions in table 2 for reduction of par-asite
fitness in a two-host-species community relative toparasite fitness
in a community consisting of a single focalhost species are
characterized by the degree of contact be-tween species and host
traits. Specifically, conditions forR0 pR10 are represented by a
linear configuration of the ra-tio of the single-host basic
reproduction numbers (j) andthe ratio of inter- to intraspecific
contact coefficients (b).In addition to intraspecific contact
rates, the ratio of basicreproduction numbers j captures
species-level properties,such as carrying capacity, life span,
recovery, and disease-induced mortality rates, thereby quantifying
relative differ-ences in life-history traits (carrying capacity,
life span, trans-mission competence) as well as effects of
parasites on hostsurvival and morbidity (virulence, infectious
period). Onthe other hand, the interspecific-intraspecific contact
ratio bcharacterizes the relative contact rates between and
withinspecies only. For brevity, we refer to trait ratio and trait
effectsto emphasize that the ratio of the single-host basic
reproduc-tion numbers j includes intrinsic host-species properties
andeffects of parasites on hosts, whereas b simply refers to
ecolog-ical contact rates.
The linear configurations in table 2 divide
contact-traitparameter space into disjoint regions for which
dilutionand amplification of parasite fitness manifest (fig. 3),
withthe slope and intercept of each line determining the
orien-tation. Above and to the left of each line in figure 3 are
pa-rameter pairs for which a dilution effect occurs, whereasbelow
and to the right of each line are parameter pairsfor which
amplification in parasite fitness is the outcomein a two-species
community.
When transmission is density dependent and popula-tions of each
species are regulated by interspecific compe-
tition, resulting in fewer available susceptible hosts, the
ex-pression arising from the dilution-effect criterion is
j >(12a12)b
a12(12a12a21)1
12a2112a12a21
. (3)
The relative competitive effect of the alternative host
(spe-cies 2) on the resident host (species 1), a12, determines
theparameter space for which a dilution effect manifests be-cause
it is the dominating parameter in the slope term.As a12 increases,
the magnitude of the slope declines (asdoes, to a lesser extent,
the intercept), and the parametercombinations for which an
amplification effect may man-ifest declines in area (compare fig.
3C with 3D). This sug-gests that as competition strengthens, a
dilution effect maymanifest even if the additional host species
possesses prop-erties that make it a more competent host for the
parasite(R20 > R10). On the other hand, high interspecific
contact(b > 1) is predicted to overwhelm the diluting effect
ofadding a less competent host to the assemblage, and
weakcompetition facilitates this amplification effect. The
analyt-ical results generalize to multispecies communities
exhib-iting density-dependent transmission and interspecific
com-petition (appendix, figs. A2, A3; figs. A1–A3 are
availableonline). In conclusion, interspecific competition,
manifestedas an increase in the competitive effect of the
additional hostspecies on the resident, facilitates a reduction in
parasitetransmission for the resident host species.In contrast, if
transmission is frequency dependent and
species are regulated through intraspecific competition,the
relative abundances of each species at carrying capac-ity feature
in the relationship:
j >K1b
K1 1K21
K2K1 1K2
. (4)
The slope depends on the relative abundance of the resi-dent
host species, and the intercept is a function of the rel-ative
abundance of the additional host species. Since therelative
abundances of each host species sum to 1, there
Table 2: Predicted parasite transmission outcomes for directly
transmitted microparasites in a two-host species assemblage
Density-dependenttransmission Dilution-effect criterion
Frequency-dependenttransmission
Dilution-effectcriterion
Additive (regulation byintraspecific competi-tion)
Amplification/nochange
. . . Amplification/dilution j > K1bK1 1K2 1K2
K1 1K2
Substitutive (regulationby interspecificcompetition)
Amplification/dilution j > (12a12)ba12(12a12a21)
1 12a2112a12a21 Amplification/dilution j
>K1(12a12)b1K2(12a21)K1(12a12)1K2(12a21)
Note: Rows describe the means of regulation, and columns
represent transmission mode. A row-column combination represents
the predicted outcomes formodels with those combinations (eq. [1]).
Each relationship is linear in jpR10=R20, and bpb12b21=b11b22. The
analytical relationships arise from the criterionR0
-
is an inverse relationship between the slope and the inter-cept
(compare fig. 3A with fig. 3B). Notably, an amplifica-tion effect
is possible if a host species with a single-host re-production
number that is less than that of the resident(hereafter, a diluting
host species) and a lower carrying ca-pacity than the resident host
species is added to the assem-blage, provided cross-species contact
is sufficiently high(R10 > R20, K1 > K2; fig. 3A). On the
other hand, an ampli-fication effect is predicted if the additional
host species has
properties that enhance parasite transmission and its carry-ing
capacity is greater than that of the resident, even if
inter-specific contact is low (b< 1, R20 > R10, K2 > K1;
fig. 3B). Therelative disease-free equilibrium abundances
additionallyfeature in the relationship for frequency-dependent
transmis-sion and interspecific competition between host species
(ta-ble 2). Finally, we note that the predictions for
frequency-dependent transmission result from the assumption thatthe
force of infection depends on the frequency of infec-
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
trait
ratioσ
DE
AE K1 K2
AE
DE
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
1.5
2.0
trait
ratioσ
contact ratio b
DE
DE
DE
α = 0.95
A
B
C
D
Figure 3: Analytical relationships for combinations of
frequency-dependent transmission and intraspecific competition and
density-dependent trans-mission and interspecific competition. The
horizontal axis in eachfigure represents the ratio of inter- to
intraspecific transmission (contact ratio, b), andthe vertical axis
describes the ratio ofR10 to R20 (trait ratio, j). The black lines
represent parameter sets (b, j) for which community R0 equals the
basicreproduction number of the parasite in the resident host, R0
pR10. These relationships separate parameter pairs for which a
dilution effectmanifests (R0 R10; gray region below each
line).Symbols representing parameter pairs that result in dilution
(DE) and amplification (AE) are discussed in detail in the text. A,
The black lineseparating parameter sets that result in
amplification or dilution is a linear configuration resulting from
frequency-dependent transmission, in-traspecific competition, and
no interspecific competition (eq. [4]) when K1 K2. Here, K1 p 90
andK2 p 10. C, The black line delineating parameter pairs that lead
to amplification or dilution is a linear configuration arising from
density-dependenttransmission and symmetric interspecific
competition, jp ½1=(11a)�½(b=a)1 1�. Here, ap 0.5 (moderate
competition). D, A linear configura-tion arising from
density-dependent transmission and strong symmetric interspecific
competition. Here, ap 0.95.
Disease-Diversity Relationship Framework 487
-
tious hosts relative to the community abundance Ik=(Nj 1Nk). We
show in the section titled “Generalizing the Disease-Diversity
Relationship for Frequency-Dependent Transmis-sion” in the appendix
that reduction of parasite transmissionfor the focal host will not
arise unless the frequency of infec-tious hosts is reduced when a
second species is added.
Relating the Analytical Conditions Back to the EcologicalContext
(Fig. 1): Interspecific Contact, Host Traits,and Parasite Effects
as Drivers of Transmission
Outcomes in Communities
The derived relationships shown in table 2 indicate thatthe
ratio of single-species reproduction numbers, j (whichencompasses
host traits such as reservoir competence andlife span), and b
(which determines the degree of parasitespillover mediated by
interspecific contact) are both key tomanifestation of a dilution
effect for a focal host when aparasite is directly transmitted.
Parameter pairs with j > 1represent communities with a resident
species that is amore competent host for the parasite than the
speciesadded to the assemblage by providing a more optimal
en-vironment for the parasite to grow and spread in the ab-sence of
alternative host species (since R j0 represents para-site fitness
in a population consisting of a single hostspecies). Intrinsic host
traits that lead to enhanced R10 rel-ative to R20 include longer
life span or infectious periodof the resident than the additional
host species and greatercarrying capacity if transmission is
density dependent.Parasites with relatively low virulence and
resident hostswith high transmission competence also lead to larger
R10relative to R20. Alternatively, parameter sets with j< 1
indi-cate that the additional host species has properties thatmake
it a more competent host for the parasite than thefocal species. In
particular, we are interested in the effectof introducing a second
host species to the assemblage thatis either a diluting host (i.e.,
j > 1) or an amplifying host(j< 1) on parasite fitness in a
community.
Examining where the relationships shown in table 2 liein
parameter space enables us to distinguish between trait-based
(species-specific intrinsic properties that determineparasite
fitness in a single host) and contact-based (ecolog-ical)
mechanisms that determine parasite transmissionoutcomes in
different contexts. Figure 4 is a schematicrepresenting the
possible outcomes for community R0depending on combinations of b
and j. The slope and in-tercept of the line, which are determined
by transmissionmode and the influence of interspecific competition,
affectthe range of parameters for which each outcome can man-ifest.
Vertical movement away from the horizontal jp 1line represents host
species becoming less alike in terms ofcarrying capacity, life
span, competence, infectious period,and virulence. Using figure 4
as a guide, we will describe
what outcomes occur for low and high interspecific contactcases
separately (under ecological contexts depicted in panels iand iii
and in panels ii and iv, respectively, of fig. 1). We sum-marize
the suite of outcomes for frequency-dependent trans-mission in an
assemblage where each species is regulated byintraspecific
competition in table 3 and the outcomes fordensity-dependent
transmission where each species is reg-ulated by interspecific
competition in table 4.
Model Predictions Assuming Low Interspecific Contact(b ≤ 1;
Panels i and iii in Fig. 1)
A dilution effect is predicted if interspecific contact is
weak(b≪ 1), the transmission competence of the additional
hostspecies is weak relative to the resident (j > 1), and
trans-mission is frequency dependent (figs. 3, 4). We term this
di-lution effect a “trait- and contact-driven dilution effect”
be-cause host and parasite traits, along with low contact
betweenspecies, combine to reduce community R0 relative to
R10.Counterintuitively, if the additional host provides
higherparasite fitness than the resident (R10
-
resident (compare the cross symbol in fig. 3C with its
coun-terpart in fig. 3D).
Model Predictions Assuming High Interspecific Contact(b ≥ 1;
Panels ii and iv of Fig. 1)
In cases of high interspecific contact (e.g., panels ii and ivof
fig. 1) and assuming frequency-dependent transmis-
sion, the addition of a second host species will result
incontact- and trait-driven amplification effects if R10 R20,
although this does not guaranteethe effect.
Table 3: Summary of conditions and potential transmission
outcomes in different interspecific contact contexts (fig. 1) given
thattransmission is frequency dependent and species are regulated
by intraspecific competition
Contact ratioRegulationregime Analytical result Potential
outcomes
b > 1 ii R10 > R20 is not a sufficient condition for
dilution Trait-driven dilution effectContact-driven amplification
effect
bp 1 ii R10 > R20 is a necessary and sufficient conditionfor
dilution
Trait- and contact-driven amplificationeffect
0< b< 1 i R10 > R20 is a sufficient condition for
dilution Contact-driven dilution effectTrait-driven amplification
effectTrait- and contact-driven dilution effect
Figure 4: Schematic based on linear relationship for
frequency-dependent transmission and intraspecific competition
(bold line). Thedashed vertical line at bp 1 indicates the
parameter pairs for which per capita interspecific contact rates
equal per capita intraspecific contactrates. The dashed horizontal
line at jp 1 indicates the parameter pairs for which parasite
fitness as propagated by the resident species equalsthat propagated
by the additional host species (R10 pR20). The schematic is
relevant for frequency-dependent transmission (since jp 1 at bp
1;eq. [4]) but is also representative of transmission outcomes when
interspecific competition is a component of community interactions.
Thebold and dashed lines divide parameter space into regions for
which different kinds of amplification and dilution effects can
manifest. Blueregions indicate intuitive outcomes for the
disease-diversity relationship, and red regions suggest
counterintuitive outcomes. For example, in-troducing an alternative
host species with low transmission competence of the parasite
relative to that of the focal host, together with highsociality
within species and a low interspecific contact rate, leads to a
dilution effect, as expected (trait- and contact-driven dilution
effect,in blue), but this type of social regime, combined with an
additional species with transmission competence higher than that of
the resident,could also lead to dilution (contact-driven dilution
effect, in red), contrary to expectations.
Disease-Diversity Relationship Framework 489
-
Again, the relative abundance of the alternative host spe-cies
is important to transmission outcomes. Greater abun-dances of
diluting alternative hosts may counteract the am-plifying effect of
strong interspecific contact, thereby drivinga net dilution effect
mediated by traits of the host and para-site (triangle in fig. 3A).
Less obviously, if the abundance ofthese additional hosts is less
than the resident abundance, acontact-driven amplification effect
is predicted (triangle infig. 3B) because of the similarity of
parasite fitness in each hostspecies (R10 is only slightly greater
than R20 in this scenario).As the intercept of the line (eq. [4])
increases, the parameterspace for trait-driven dilution effects
increases in area (e.g.,triangle in fig. 3A; fig. 4).
Additionally, trait-driven dilution and
contact-drivenamplification are possible outcomes if transmission
is den-sity dependent and species are regulated by
interspecificcompetition. In this context, the competitive effect
of theadditional species on the resident, along with relatively
poorcompetency of the additional species, combine to overcomethe
potential for spillover via high contact between speciesand thereby
drive a dilution effect (compare the outcomesfor the systems
represented by the squares in fig. 3D [dilu-tion] with those in
fig. 3C [amplification]). In the appendix,we show that
contact-driven amplification effects generalizeto multispecies
communities exhibiting interspecific compe-tition (fig. A2).
Special Case: Spillover of the Parasite to Dead-End Hosts
Many species novel to a parasite are capable of becominginfected
but do not play a role in onward transmission(e.g., humans are
“dead-end” hosts for directly transmitteddiseases such as rabies
and hantavirus). Figure 2B shows atransmission regime between the
focal host and an addi-
tional dead-end host species. Assuming that the additionalhost
is not infectious (i.e., i2 p 0), the WAIFW matrix is
Wp
�b11 0b21 0
�p
�s1i1c11 0s2i1c21 0
�.
To investigate whether the dilution effect occurs, we com-pared
the expression for community R0 derived from thenext-generation
matrix to the basic reproduction number ofthe parasite in the
resident species R10 for all transmission-competition combinations
previously considered (table 5).A dilution effect occurs if
transmission is frequency de-pendent and if hosts are regulated by
interspecific competi-tion when transmission is density dependent.
Addition ofa dead-end species to the community does not lead to
am-plification effects in these contexts since the expressionsfor
community R0 are a fraction of R10 (table 5).
Discussion
We have presented a simple tractable model to link host-species
diversity, abundance, and parasite transmission tocompare the
propensity for infectious disease outbreaksacross mono- and
multihost communities. Adding more spe-cies can either increase or
decrease parasite fitness, dependingon ecological context and the
traits of the species in an assem-blage.We demonstrate that disease
transmission outcomes inmultihost communities are more complex than
expected, in-cluding the potential for disease amplification in
communi-ties exhibiting frequency-dependent transmission and
di-lution of outbreak risk in density-dependent
transmissionsystems. Our approach offers important insights to
otherstudies that have exploited robust empirical or phenomeno-
Table 4: Summary of conditions and potential transmission
outcomes in different interspecific contact contexts (fig. 1) given
thattransmission is density dependent and species are regulated by
interspecific competition
Contact ratio Regulation regime Analytical result Potential
outcomes
bp 1 iv R10=R20 > 1=a12 (necessary andsufficient)
Trait-driven dilution effectContact-driven amplification
effect
b > 1 iv: weak competitive effectof species 2 on species
1(a12 → 0)
R10=R20 →∞⇒R10≫R20 Contact-driven amplification effectTrait- and
contact-driven amplification effect
iv: strong competitive effectof species 2 on species 1(a12 →
1)
R10=R20 → 1⇒R10 > R20 Trait-driven dilution
effectContact-driven amplification effectTrait- and contact-driven
amplification effect
0< b< 1 iii: weak competitive effectof species 2 on
species 1(a12 → 0)
R10 > R20 is not a sufficientcondition for the dilution
effect
Trait-driven amplification effectContact-driven amplification
effectTrait- and contact-driven amplification effect
iii: strong competitive effectof species 2 on species 1(a12 →
1)
R10 > R20 is not a sufficientcondition for the dilution
effect
Contact-driven dilution effectTrait-driven amplification
effectTrait- and contact-driven dilution effect
490 The American Naturalist
-
logical patterns, including the predictability of host
commu-nity changes (Johnson et al. 2013) and relationships
betweenspecies richness and abundance (Roche et al. 2012;
Mi-haljevic et al. 2014). Our findings emphasize the importanceof
contact rates, competition, and relative interspecies dif-ferences
in parasite fitness in developing theory describ-ing the
relationship between diversity and microparasiticdisease outbreak
propensity, thus corroborating empiricalstudies that have shown
these elements to be importantfor disease-diversity relationships
(e.g., Clay et al. 2009; Hallet al. 2009; Johnson et al. 2013).
Incorporating competitionand contact heterogeneities into simple
models changes ourpredictions of how increasing species richness
alters com-munity R0 (e.g., Dobson 2004; Rudolf and Antonovics
2005).
Our findings may be interpreted in the context of
thedilution-effect hypothesis, which is broadly stated as the
re-duction of parasite transmission in increasingly diverse
hostcommunities, acknowledging that some researchers some-times
refer to the particular risk of infection in one species,for
example, Lyme disease in humans (Ostfeld and Keesing2000a, 2000b;
Schmidt and Ostfeld 2001). Many empiricalstudies have indicated
that there is an association betweenhigh biodiversity and reduced
infectious disease risk, for ex-ample, Lyme borreliosis in small
mammals and ticks (Lo-Giudice et al. 2003), West Nile virus in wild
birds (Ezenwaet al. 2006) and mosquito vectors (Allan et al. 2009),
hanta-virus in rodents (Suzán et al. 2009), trematodes in
amphibians(Johnson et al. 2013), fungal pathogens of rice crops
(Zhu et al.2000), and yellow barley virus in plants (Lacroix et al.
2014).However, reduction of infectious disease risk in diverse
com-munities may be idiosyncratic and more likely determined
byecological interactions between host species (Salkeld et
al.2013). Simple mathematical models have been used to de-scribe
hypothetical mechanisms for a dilution effect, such asencounter
reduction and susceptible host regulationmediatedby nonhost species
(Keesing et al. 2006), but not to study howdiluting mechanisms
might reduce parasite transmission in amultihost community under a
general framework with flexi-bility in transmission mode and
dominant competitive forces.Our tractable models bridge this gap in
theory, in particularby providing a theoretical basis for the
effects of communitycomposition on the propensity for disease
outbreaks inmulti-host assemblages. Our results suggest that
reduction of para-
site transmission in multispecies communities will occur
ifinterspecific contact rates are sufficiently low and species
inthe assemblage differ substantially in their parasite
trans-mission potential. Importantly, the propensity for disease
out-breaks may be enhanced on adding additional host specieswhen
transmission is either frequency or density dependent,and this
propensity is host, parasite, and ecological contextdependent.We
have shown that reduction of parasite transmission
in multihost communities may manifest for all contact
andcompetition regimes considered. However, the predictedoutcomes
for parasite transmission are due to different mech-anisms.
Dilution effects driven by life-history traits such astransmission
competence tend to manifest in high interspe-cific contact
scenarios, for example, if there is high overlap inspecies’
resource acquisition functions or if species interactwith each
other through antagonistic encounters. In general,hosts in an
assemblage that compete with each other for alimiting resource must
differ substantially in their parasitefitness for a dilution effect
to manifest. On the other hand,dilution effects driven by low
contact rates between speciestend to occur if species exploit
different niches or are com-petitors that avoid one another. These
are new theoreticallines of inquiry that could potentially be
tested empirically.Our work challenges some of the key assumptions
of the
dilution-effect hypothesis (Ostfeld and Keesing 2012); weshow
that adding a less competent host to the assemblagedoes not
inevitably lead to a dilution effect and that addinga more
competent host does not invariably lead to amplifi-cation of
disease risk. Our analysis suggests that it is possiblefor host
traits to negate the effect of contact on transmissionoutcomes and
for interspecific contact to neutralize the in-fluence of relative
parasite fitness afforded by different hostspecies. Our findings
lend theoretical support to empiricalstudies that have shown that
species identity is key to thedisease-diversity relationship
(LoGiudice et al. 2008; Salkeldand Lane 2010; Venesky et al. 2014).
For example, the pres-ence of a noncompetent host has been shown to
drive a di-lution effect in many systems (Johnson et al. 2008; Hall
et al.2009; Keesing et al. 2009). On the other hand, the presenceof
competent hosts may enhance parasite transmission insome cases
(Power and Mitchell 2004; Hamer et al. 2011).Our findings suggest
potential new avenues for empirical ex-
Table 5: Conditions that guarantee a dilution effect when a
dead-end host for the infection isadded to the assemblage, where
K1=(K1 1K2) is the abundance of susceptible resident hosts
rel-ative to community abundance
Transmission mode and regulation regime Community R0 Result
Density dependent, intraspecific competition R01 No change
Frequency dependent, intraspecific competition K1R10
K1 1K2Dilution effect
Density dependent, interspecific competition
(12a12)R1012a12a21
Dilution effect
Disease-Diversity Relationship Framework 491
-
ploration that may clarify mechanisms behind dilution
andamplification of parasite transmission and may help refinethe
predictions of the effect of species identity on disease riskin
communities.
The generality of the hypothesis that biodiversity is
pro-tective against disease has been questioned (Randolph andDobson
2012; Wood and Lafferty 2013). Our results eluci-date conditions
under which dilution and amplification ofdisease transmission with
increased species richness can beexpected in simple models. We
demonstrate that both dilu-tion and amplification effects are
possible if a diluting hostis added to the assemblage (i.e., the
single-host reproductionnumber of the additional species is less
than that of the resi-dent). Whether dilution or amplification is
observed dependson ecological context (degree of contact and
strength of com-petition). For example, a greater relative
abundance of lesscompetent additional hosts is not sufficient to
guarantee a di-lution effect in frequency-dependent transmission
systems ifthe degree of interspecific contact is high (e.g., in
marine orfreshwater assemblages). Ecological dynamics as well
astraits of the host species and parasite effects all combine
todetermine the fate of parasite transmission, even in simplemodels
of two-host-species assemblages.
Naturally, the simple analytical model developed here hassome
limitations. We compare parasite transmission acrossmultihost
communities that are monospecific and hetero-specific rather than
comparing how increasing diversity af-fects parasite transmission
in a focal host. Parasite fitness ina community is measured using
R0, a quantity capturing par-asite dynamics in single and
multispecies communities thatis correlated with parasite
prevalence. Infectious disease riskhas been measured by various
means in empirical studies, in-cluding, for example, prevalence in
the focal host, rate ofchange of infected hosts, prevalence in the
community, den-sity of infected vectors, and prevalence of infected
vectors(e.g., Mitchell et al. 2002; Johnson et al. 2008, 2013;
Lo-Giudice et al. 2008; Clay et al. 2009; Salkeld and Lane
2010;Searle et al. 2011). We use R0 as a measure of disease
riskacross communities, acknowledging that it may not
directlymeasure disease risk in the focal host when a second
speciesis added to the assemblage and that it measures
outbreakpotential in naive host populations only.
Community ecology is more complicated than the
simpleLotka-Volterra models that we use here to calculate
com-munity R0. We ignore trophic levels above and below thelevel of
the host species, which may control host speciesabundance via
top-down and/or bottom-up effects (Keesinget al. 2006).
Additionally, the structure of contact networks,host age structure,
and the effects of demographic stochas-ticity are elements that
affect the propensity for outbreaks(Newman 2002; Meyers et al.
2005; Dalziel et al. 2014) thatare not included in our simple
models. We do not examinethe impact of correlations between
life-history traits and
the effects of parasites on hosts (Keesing et al. 2010). Allof
these complexities will impact transmission outcomes,underscoring
the importance of initially studying simplemodels, which here lead
to more nuanced predictions fordilution and amplification
effects.In conclusion, predictions for the level of
microparasite
transmission in communities cannot be made simply fromknowledge
of parasite transmission mode or host regulatorymechanism. Metrics
of biodiversity such as species richnessand evenness may fail to
capture predictable outcomes ofcommunity assembly and disassembly
on parasite fitness.We demonstrate the importance of contact rates,
competi-tion, and relative interspecies differences in R0 on the
pro-pensity for disease outbreaks in multispecies
communities.Moreover, our analysis demonstrates that even simple
ca-nonical models predict that directly transmitted
parasitetransmission outcomes in community settings are likely
todepend on the context in which the ecological dynamicsplay out.
We recommend that these elements be includedas components of more
complicated predictive models ofdisease-diversity
relationships.
Acknowledgments
We thank T. Dallas, B. Dalziel, J. Haven, the associate edi-tor,
and three anonymous reviewers for valuable commentson the
manuscript. We also thank K. Carter for assistancein preparing
figure 1. This research was funded by grant220020193 from the James
S. McDonnell Foundation.S.M.O. completed this work while a
postdoctoral fellow atthe National Institute for Mathematical and
Biological Syn-thesis, an institute sponsored by the National
Science Foun-dation (NSF) through NSF award DBI-1300426, with
addi-tional support from the University of Tennessee,
Knoxville.
Literature Cited
Allan, B. F., R. B. Langerhans, W. A. Ryberg, W. J. Landesman,
N. W.Griffin, R. S. Katz, B. J. Oberle, et al. 2009. Ecological
correlates ofrisk and incidence of West Nile virus in the United
States. Oecologia158:699–708.
Anderson, R. M., and R. M. May. 1991. Infectious diseases
ofhumans: dynamics and control. Oxford University Press,
Oxford.
Begon, M., R. S. Ostfeld, F. Keesing, and V. T. Eviner. 2008.
Effectsof host diversity on disease dynamics. Pages 12–29 in R. S.
Ostfeld,F. Keesing, and V. T. Eviner, eds. Infectious disease
ecology: theeffects of ecosystems on disease and of disease on
ecosystems.11th Cary Conference, Millbrook, NY, May 2005. Princeton
Uni-versity Press, Princeton, NJ.
Bowers, R. G., and J. Turner. 1997. Community structure and the
in-terplay between interspecific infection and competition. Journal
ofTheoretical Biology 187:95–109.
Clay, C. A., E. M. Lehmer, S. S. Jeor, and M. D. Dearing. 2009.
Test-ing mechanisms of the dilution effect: deer mice encounter
rates,
492 The American Naturalist
-
Sin Nombre virus prevalence, and species diversity.
EcoHealth6:250–259.
Dalziel, B. D., K. Huang, J. L. Geoghegan, N. Arinaminpathy, E.
J.Dubovi, B. T. Grenfell, S. P. Ellner, et al. 2014. Contact
heteroge-neity, rather than transmission efficiency, limits the
emergence andspread of canine influenza virus. PLoS Pathogens
10:e1004455.
Diekmann, O., J. A. P. Heesterbeek, and M. G. Roberts. 2010.
Theconstruction of next-generation matrices for compartmental
epi-demic models. Journal of the Royal Society Interface
7:873–885.
Dobson, A. 2004. Population dynamics of pathogens with
multiplehost species. American Naturalist 164:S64–S78.
Ezenwa, V. O., M. S. Godsey, R. J. King, and S. C. Guptill.
2006. Aviandiversity and West Nile virus: testing associations
between biodi-versity and infectious disease risk. Proceedings of
the Royal SocietyB: Biological Sciences 273:109–117.
Getz, W. M., and J. Pickering. 1983. Epidemic models:
thresholdsand population regulation. American Naturalist
121:892–898.
Hall, S. R., C. R. Becker, J. L. Simonis, M. A. Duffy, A. J.
Tessier, andC. E. Cáceres. 2009. Friendly competition: evidence for
a dilutioneffect among competitors in a planktonic host-parasite
system.Ecology 90:791–801.
Hamer, G. L., L. F. Chaves, T. K. Anderson, U. D. Kitron, J.
D.Brawn, M. O. Ruiz, S. R. Loss, et al. 2011. Fine-scale
variationin vector host use and force of infection drive localized
patternsof West Nile virus transmission. PloS ONE 6:e23767.
Hawley, D. M., R. S. Etienne, V. O. Ezenwa, and A. E. Jolles.
2011.Does animal behavior underlie covariation between hosts’
expo-sure to infectious agents and susceptibility to infection?
implica-tions for disease dynamics. Integrative and Comparative
Biology51:528–539.
Holt, R. D., A. P. Dobson, M. Begon, R. G. Bowers, and E.
M.Schauber. 2003. Parasite establishment in host communities.
Ecol-ogy Letters 6:837–842.
Holt, R. D., and J. Pickering. 1985. Infectious disease and
species co-existence: a model of Lotka-Volterra form. American
Naturalist126:196–211.
Johnson, P. T. J., R. B. Hartson, D. J. Larson, and D. R.
Sutherland.2008. Diversity and disease: community structure drives
parasitetransmission and host fitness. Ecology Letters
11:1017–1026.
Johnson, P. T. J., D. L. Preston, J. T. Hoverman, and K. L.
D.Richgels. 2013. Biodiversity decreases disease through
predictablechanges in host community competence. Nature
494:230–233.
Joseph, M. B., J. R. Mihaljevic, S. A. Orlofske, and S. H.
Paull. 2013.Does life history mediate changing disease risk when
communitiesdisassemble? Ecology Letters 16:1405–1412.
Keesing, F., L. K. Belden, P. Daszak, A. Dobson, C. D. Harvell,
R. D.Holt, P. Hudson, et al. 2010. Impacts of biodiversity on the
emer-gence and transmission of infectious diseases. Nature
468:647–652.
Keesing, F., J. Brunner, S. Duerr, M. Killilea, K. Logiudice, K.
Schmidt,H. Vuong, et al. 2009. Hosts as ecological traps for the
vector ofLyme disease. Proceedings of the Royal Society B:
Biological Sciences276:3911–3919.
Keesing, F., R. D. Holt, and R. S. Ostfeld. 2006. Effects of
species di-versity on disease risk. Ecology Letters 9:485–498.
Komar, N., S. Langevin, S. Hinten, N. Nemeth, E. Edwards,
D.Hettler, B. Davis, et al. 2003. Experimental infection of
NorthAmerican birds with the New York 1999 strain of West Nile
virus.Emerging Infectious Diseases 9:311–322.
Lacroix, C., A. Jolles, E. W. Seabloom, A. G. Power, C. E.
Mitchell,and E. T. Borer. 2014. Non-random biodiversity loss
underlies
predictable increases in viral disease prevalence. Journal of
theRoyal Society Interface 11:20130947.
LoGiudice, K., S. T. K. Duerr, M. J. Newhouse, K. A. Schmidt, M.
E.Killilea, and R. S. Ostfeld. 2008. Impact of host community
com-position on Lyme disease risk. Ecology 89:2841–2849.
LoGiudice, K., R. S. Ostfeld, K. A. Schmidt, and F. Keesing.
2003. Theecology of infectious disease: effects of host diversity
and commu-nity composition on Lyme disease risk. Proceedings of the
NationalAcademy of Sciences of the USA 100:567–571.
McCormack, R. K., and L. J. S. Allen. 2007. Disease emergence
inmulti-host epidemic models. Mathematical Medicine and
Biology24:17–34.
Meyers, L. A., B. Pourbohloul, M. E. J. Newman, D. M.
Skowronski,and R. C. Brunham. 2005. Network theory and SARS:
predictingoutbreak diversity. Journal of Theoretical Biology
232:71–81.
Mihaljevic, J. R., M. B. Joseph, S. A. Orlofske, and S. H.
Paull. 2014.The scaling of host density with richness affects the
direction,shape, and detectability of diversity-disease
relationships. PLoSONE 9:e97812.
Mitchell, C. E., D. Tilman, and J. V. Groth. 2002. Effects of
grasslandplant species diversity, abundance, and composition on
foliar fun-gal disease. Ecology 83:1713–1726.
Newman, M. E. J. 2002. Spread of epidemic disease on
networks.Physical Review E 66:016128.
Norman, R., R. G. Bowers, M. Begon, and P. J. Hudson. 1999.
Per-sistence of tick-borne virus in the presence of multiple host
spe-cies: tick reservoirs and parasite mediated competition.
Journalof Theoretical Biology 200:111–118.
Ostfeld, R. S., and F. Keesing. 2000a. Biodiversity and disease
risk:the case of Lyme disease. Conservation Biology 14:722–728.
———. 2000b. The function of biodiversity in the ecology of
vector-borne zoonotic diseases. Canadian Journal of Zoology
2078:2061–2078.
———. 2012. Effects of host diversity on infectious disease.
AnnualReview of Ecology, Evolution, and Systematics 43:157–182.
Peixoto, I. D., and G. Abramson. 2006. The effect of
biodiversity onthe hantavirus epizootic. Ecology 87:873–879.
Power, A. G., and C. E. Mitchell. 2004. Pathogen spillover in
diseaseepidemics. American Naturalist 164:S79–S89.
Randolph, S. E., and A. D. M. Dobson. 2012. Pangloss revisited:
acritique of the dilution effect and the
biodiversity-buffers-diseaseparadigm. Parasitology 139:847–863.
Roche, B., A. P. Dobson, J.-F. Guégan, and P. Rohani. 2012.
Linkingcommunity and disease ecology: the impact of biodiversity on
path-ogen transmission. Philosophical Transactions of the Royal
SocietyB: Biological Sciences 367:2807–2813.
Rudolf, V. H. W., and J. Antonovics. 2005. Species coexistence
andpathogens with frequency-dependent transmission. American
Nat-uralist 166:112–118.
Salkeld, D. J., and R. S. Lane. 2010. Community ecology and
diseaserisk: lizards, squirrels, and the Lyme disease spirochete in
California,USA. Ecology 91:293–298.
Salkeld, D. J., K. A. Padgett, and J. H. Jones. 2013. A
meta-analysissuggesting that the relationship between biodiversity
and risk ofzoonotic pathogen transmission is idiosyncratic. Ecology
Letters16:679–686.
Schmidt, K. A., and R. S. Ostfeld. 2001. Biodiversity and the
dilutioneffect in disease ecology. Ecology 82:609–619.
Searle, C. L., L. M. Biga, J. W. Spatafora, and A. R. Blaustein.
2011. Adilution effect in the emerging amphibian pathogen
Batracho-
Disease-Diversity Relationship Framework 493
-
chytrium dendrobatidis. Proceedings of the National Academy
ofSciences of the USA 108:16322–16326.
Suzán, G., E. Marcé, J. T. Giermakowski, J. N. Mills, G.
Ceballos, R. S.Ostfeld, B. Armién, et al. 2009. Experimental
evidence for reducedrodent diversity causing increased hantavirus
prevalence. PLoSONE 4:e5461.
Venesky, M. D., X. Liu, E. L. Sauer, and J. R. Rohr. 2014.
Linkingmanipulative experiments to field data to test the dilution
effect.Journal of Animal Ecology 83:557–565.
Wood, C. L., and K. D. Lafferty. 2013. Biodiversity and disease:
asynthesis of ecological perspectives on Lyme disease
transmission.Trends in Ecology and Evolution 28:239–247.
Zhu, Y., H. Chen, J. Fan, Y. Wang, Y. Li, J. Chen, J. Fan, et
al. 2000.Genetic diversity and disease control in rice. Nature
406:718–722.
Associate Editor: C. Jessica E. MetcalfEditor: Susan Kalisz
“Vastness of size is so generally, and it may almost be
conceded, so naturally associated in the popular idea with the
whales, that some mayscarcely be able to realize at first the fact
that there are species no larger than ordinary porpoises; and yet
which agree so closely in all themore essential elements of
structure with some of the whales, that it is impossible, in a
natural system, to separate them from their giganticrelatives.”
Pictured: Two views of the skull of an adult Physeter
macrocephalus. From “The Sperm Whales, Giant and Pygmy” by
TheodoreGill (The American Naturalist, 1871, 4:725–743).
494 The American Naturalist