The coevolution of host resistance and parasite virulence in Yersenia pestis infection in black-tailed prairie dogs (Cynomys ludovicianus)

Michael Buhnerkempe1

1Department of Biology, Colorado State University

*Corresponding Author: Michael Buhnerkempe, Department of Biology, 1878 Campus Mail, Colorado State University, Fort Collins, CO, 80523-1878, U.S.A. Phone number: (970) 491-2133, Fax number: (970) 491-0649, E-mail address: [email protected]

Abstract

Plague, caused by the bacterium Yersinia pestis, is a highly virulent pathogen in hosts like the black-tailed prairie dog (Cynomys ludovicianus). However, over a century of selective pressure has not led to increased immunity to plague infection in prairie dog towns leaving many to ask why resistance has failed to develop. Here, we present a model of the coevolution of plague virulence and prairie dog resistance to plague to study this phenomenon. Analysis of this model indicates that resistance can coevolve with virulence in prairie dog populations, but resistance only increases to the point where extinction due to plague is avoided leaving small remnant populations. Further study on life-history tradeoffs for both virulence and resistance in prairie dog hosts and eventually flea vectors will be needed to further illuminate this coevolutionary arms race.

Introduction The ability of a pathogen to cause damage to its host, known as virulence, is an important life history trait in the study of host-parasite interactions and infectious disease dynamics. As a trait of a pathogen, virulence is capable of undergoing evolution. Previous studies on the evolution of virulence have predicted that intermediate levels of virulence will develop in pathogens that are directly transmitted due to transmission tradeoffs at high levels of virulence (i.e., high virulence limits host movement which in turn limits transmission) (Anderson and May 1982; Ewald 1995). However, parasites transmitted through an environmental reservoir or that are vector-borne are not subject to such constraints. In this case, virulent parasites can develop since they are not dependent on host movement for transmission (Ewald 1995). In nature, examples of these highly virulent pathogens abound. Plague, caused by the bacterium Yersinia pestis, is a flea-borne disease characterized by high virulence. In hosts like the black-tailed prairie dog (Cynomys ludovicianus), the infection is nearly always fatal with no evidence of reduced virulence over the century since its introduction to these hosts (Cully and Williams 2001). Similarly, when the vector-borne myxoma virus was introduced into Australia to control rabbit populations, it showed high levels of virulence with high host mortality (Dwyer et al. 1990). However, Australian strains of the virus have shown decreased virulence since their introduction over a half century ago (Dwyer et al. 1990). The decreasing virulence has been accompanied by an increase in host immunity to the virus (Dwyer et al. 1990). The question then becomes: what accounts for this difference in evolutionary trajectories between these two seemingly similar host-pathogen systems? When considering this question, we must take into account not only the evolution of pathogen virulence but also the evolution of host resistance. The coevolutionary “arms-race” between pathogen and host is evident in the myxoma virus-rabbit system (Dwyer et al. 1990). In this case, highly virulent pathogens should evolve to be less virulent to achieve sustained chains of transmissions without driving the host population extinct. This in turn allows the host to begin to evolve resistance to the parasite beginning the coevolutionary arms race. However, no such dynamics are seen in the plague-prairie dog system with plague causing massive extinction events on prairie dog towns (Stapp et al. 2004). To study the coevolution of virulence and host resistance in the plague and prairie dog system, we use a coevolutionary model of quantitative traits that couples an ecological system with an evolutionary system. By analyzing this model, we hope to determine if the development of resistance to plague is possible in natural populations of black-tailed prairie dogs. If the evolution of resistance is possible, we also hope to determine under what conditions we would expect to see significant increases in plague resistance in these populations.

The Model

General Fast-Slow Dynamical System

The model we used was based on the fast-slow dynamical systems described by Khibnik and Kondrashov (1997). In this framework, variables are separated into fast (ecological, Eq. 1) and slow (genetical, Eq. 2) variables.

dx i = x f (x ,..., x ,α ,...,α ) (1) dt i i 1 n 1 m dα ∂ j = ε f (x ,..., x ,α ,...,α ) ( 2) j ∂α i 1 n 1 m dt j

α Here, the xi represent the ecological variables, while the j represent the quantitative traits of τ = ε ε interest. The time scale of the slow system is given by jt , where j describes the genetic variance of the jth trait and is assumed to be small. The mean Malthusian fitness of each (⋅) population is given by fi . Thus, the change in the quantitative traits of interest is determined by their contribution to the mean fitness of ecological variables. The choice of ecological (⋅) variable, fi , to maximize over is based on knowledge of each trait’s impact on each population’s mean fitness. To be included in the slow system, a population’s fitness must be directly impacted by the trait of interest.

Ecological subsystem

The ecological system used in our model (Eqs. 3-7) is a modified version of the Susceptible-Exposed-Infectious-Recovered (SEIR) model described in Buhnerkempe et al. (in prep). In the ecological subsystem, we define five classes of individuals: (1) Susceptibles, S; (2) Exposed, E (i.e., those individuals who are infected but not yet symptomatic); (3) Infected, I; (4) Recovered, R; (5) Infectious reservoir, M (i.e., infectious carcasses and associated fleas from plague fatalities). We also define N to be the total number of live hosts in the system (S+E+I+R). General disease dynamics are given in Figure 1. dS  N  M = r(1 − xp z )( S + E + R)1 −  − β S − µS + φR (3) dt  K  R B dE M = β S − E(σ + µ ) (4) dt R B dI = σ (1 − p) E − αI (5) dt dR = pσE − R(φ + µ ) (6) dt dM − σ = αI − λ (1− e b )M − DM (7) dt

Susceptible (S) Resistant (R)

Exposed (E)

Infected (I)

Infectious Reservoir (M) Figure 1: General disease dynamics for plague infection in prairie dog towns. Here, susceptible individuals (S) become exposed to plague via the infectious reservoir (M) denoted by the gray arrow. The exposed class (E) represents individuals that are not yet symptomatic but who harbor plague bacteria. Exposed individuals can either develop immunity to plague (R) or can become infected (I), where they show symptoms of plague infection. Individuals that develop resistance to plague gradually lose their resistance over time and become susceptible again. Infection is always fatal, and infected individuals enter the infectious reservoir.

Reproduction in this system is assumed to only occur amongst healthy individuals (i.e. S, E, and R) according to a logistic growth function. Transmission of plague occurs only from the infectious reservoir, M, and is modeled as a density-dependent process (Webb et al. 2006). Specific parameter definitions and values are given in Table 1. Parameter values were obtained from field and lab studies as well as from the literature. However, when data was not available for a particular species, we substituted for data on the most closely related species available.

Genetical Subsystem

The two traits that we allowed to evolve are the probability a host gains resistance, p, and a measure of virulence, σ . Our measure of virulence describes the time until the onset of disease. While this measure is not identical to disease-induced mortality that is commonly used in these studies, it is similar to alternative measures of virulence (Day 2002; Koella and Boëte 2003). To determine the genetical subsystem, we must determine which fitness functions must be maximized with respect to our traits. For the pathogen, fitness is determined by the number of infected hosts produced. Thus, we maximize the fitness of infected hosts with respect to σ . For hosts, fitness is maximized by the production of individuals unaffected by plague. This leads us to maximize the total fitness of both susceptible and resistant individuals with respect to p. Using Eq. 2, we can then define our genetical subsystem (Eqs. 8-9). dp   S + E + R  N  − E  = ε r 1 − (− xzp z 1 ) + σ  (8) dt 1   S  K  R 

σ   d = ε − E 2 (1 p)  (9) dt  I 

Life-History Tradeoffs

The genetical subsystem describes the evolution of two life-history traits. Life-history evolution is frequently assumed to be accompanied by a tradeoff, usually between reproduction and some other component of fitness. We introduce tradeoffs in our model for both increasing resistance and virulence, which prevents these traits from increasing continuously (Khibnik and Kondrashov 1997). For host resistance, we assume increased allocation to immune responses will lead to decreased reproduction. Thus, in Eq. 3, the intrinsic rate of increase, r, which governs host reproduction is reduced by the term (1− xp z ) (Koella and Boëte 2003). Here, x determines the maximum reduction in reproduction possible, and z determines nonlinearities in the cost of developing resistance. The tradeoff for pathogens evolving increased virulence is usually assumed to be a reduction in transmissibility (Ewald 1995). However, this tradeoff does not apply to pathogens that are transmitted from a reservoir (Ewald 1995). Generally, the longer a pathogen can survive outside of a host, the more virulent it can become. For our system, however, neither of these cases applies. In our model, the plague bacterium is transmitted from a reservoir, but Y. pestis is still dependent on host resources (i.e., tissues in decaying carcasses or questing fleas) for survival. This dependency allows us to assume that highly virulent Y. pestis strains may deplete host resources quickly leading to decreased survival times in the reservoir. Thus, we assume that increasing virulence comes at the cost of decreasing pathogen survival in the reservoir. This tradeoff is represented in Eq. 7 by the term (1− e−bσ ) . This reduction is bounded by 0 and 1 with the parameter b determining the rate at which pathogen survival in the reservoir decreases with virulence.

Table 1: Parameter definitions and values. These values describe plague infection in black-tailed prairie dogs. All rates are measured in units of (days)-1. Parameter Value Description Reference r 0.087 Intrinsic rate of increase Hoogland 1995 x 0.75 Maximum cost of resistance in None terms of reproduction z 1 Nonlinearity of cost of resistance None K 200 Carrying capacity Hoogland 1995 μ 0.0002 Natural mortality rate Hoogland 1995

βr 0.073 Transmission rate from infectious Webb et al. 2006 reservoir B 20 Number of burrows host enters Webb et al. 2006 σ 0.22 (Exposed period)-1 Cully and Williams 2001 α 0.5 Disease induced mortality rate Webb et al. 2006 λ 0.091 Infectious reservoir decay rate due Ber et al. 2003 to virulence b 1 Rate at which pathogen survival in None the reservoir decreases with virulence D 0.006 Background infectious reservoir Webb et al. 2006 decay rate p 0.01 Probability of gaining resistance Cully and Williams 2001 φ 0.011 Rate resistance is lost Williams et al. 1979

ε1 0.001 Genetic variance for host None resistance

ε2 0.001 Genetic variance for pathogen None virulence

Analysis To analyze this model, we first consider the case where no evolution is occurring (i.e., ε = ε = 1 2 0 ). This simplification leaves us with only the ecological system. Setting equations 3-7 equal to zero and solving for the ecological variables allows us to find three equilibria. The first is at [0 0 0 0 0] , hereafter referred to as the extinction equilibrium. Here both the disease agent and the host go extinct. The next is a plague-free equilibrium that occurs at   µ   K1 −  0 0 0 0 . At this equilibrium, the disease is absent leaving us with   r(1 − xp z )   only susceptible hosts. The last equilibrium is the coexistence equilibrium. Here both plague and hosts coexist in an enzootic state. Unfortunately, we can not find an analytical expression for this equilibrium, but numerical analysis verifies its existence for the default parameter values found in Table 1 (Fig. 2).

Figure 2: Coexistence equilibrium for the case with no evolution. Parameter values are specified in Table ε = ε = 1 except 1 2 0 . Notice there is no change in host resistance or plague virulence over time.

To determine the linear stability of these equilibria, we linearize about each equilibrium by finding the Jacobian for the ecological system (Eqs. 3-7) evaluated at each equilibrium. We then find the eigenvalues of these Jacobians. If all the eigenvalues have negative real parts, we have a linearly stable equilibrium. Since we do not have an expression for our coexistence equilibrium, we numerically solve for this equilibrium to determine its stability. Using the default parameter values for the prairie dog system (Table 1), we find the coexistence equilibrium to be linearly stable. The extinction and plague-free equilibria are both saddle points (i.e., the Jacobian evaluated at these equilibria has a mixture of both positive and negative eigenvalues) . We are able to expand on the analysis at the extinction equilibria however. At this equilibrium, we find a bifurcation at µ = r(1 − xp z ) . When the death rate of the host is greater than the birth rate (i.e., µ > r(1 − xp z ) ), the extinction equilibrium is stable. However, when the death rate of the host is smaller than the birth rate (i.e., µ < r(1− xp z ) ), this equilibrium is a saddle point. Through this bifurcation, we find that the plague-free equilibrium is always a saddle point. Typically, to analyze the system with evolution, these ecological equilibria would be inserted into the genetical subsystem since ecological changes occur at a much higher rate than evolutionary changes. However, the genetical subsystem is undefined for the extinction and plague-free equilibria. Fortunately, we can ignore these two cases since no evolutionary pressure exists at these points. We can, however, look at model dynamics for the coexistence equilibrium. To visualize these dynamics, we use numerical analysis (Fig. 3). When evolution is occurring, we find an increase in both host resistance and plague virulence, and stable coexistence of prairie dogs and plague.

Figure 3: Coexistence equilibrium when hosts and the plague bacterium are allowed to evolve.

Finally, we would like to consider the effect of varying the cost of life-history tradeoffs of both prairie dog resistance and plague virulence on the coevolution of resistance and virulence. To do this, we vary z and b over a biologically realistic range. In this case, we find that the equilibrium level of resistance increases with z, which controls the resistance- reproduction tradeoff (Fig. 4). Large values of z indicate that there is a low cost to developing resistance when there is none, but high costs to increasing resistance when the population is already mostly resistant. The probability of developing resistance is insensitive to changes in b, which controls the virulence-reservoir decay tradeoff (Fig. 4). Large values of b indicate large costs to developing virulence. The equilibrium value of virulence, however, is not sensitive to changes in the cost structure of either of these tradeoffs and evolves to a consistent level regardless (Fig. 5). resistance-reproduction tradeoff, z, and virulence-reservoir decay, b. The initial value of was of p 0.01. value The anddecay, z,virulence-reservoir initial tradeoff,b. resistance-reproduction 4: Figure and virulence-reservoir decay, b. The initial value ofvalue decay, initial virulence-reservoirb. The and 5: Figure 2.9 2.9 2.3 b 2.3 b Host resistance at equilibrium in the evolutionary system across differing costs ofthe across differing systemcosts equilibrium evolutionary in the at resistance Host Plague virulence at equilibrium across differing costs of the resistance-reproduction tradeoff, z, tradeoff, costs of resistance-reproduction across the differing virulence equilibrium at Plague 1.7 1.7 1.1 1.1 0.5 0.5

0.6 0.6

0.9 0.9

1.2 1.2

1.5 1.5

1.8 1.8

2.1 2.1 z z σ 2.4 2.4 was 0.22. 2.7 2.7

3 3 1 1.05 1.1 1.15 1.2 0 1.25 1.3 0.05 1.35 0.1 1.4 1.45 0.15 1.5 0.2 0.25 of Virulence, sigma ofVirulence, Equilibrium Value Value Equilibrium Equilibrium Value Value Equilibrium ofProbability of Resistance, p Resistance,

Discussion

Our model predicted that black-tailed prairie dogs, in the absence of evolution, virtually go extinct in the presence of plague. This result agrees closely with observations of plague epizootics on prairie dog towns (Stapp et al. 2004). However, when we allowed evolution to occur in prairie dog populations, our model predicted that resistance in prairie dogs would increase, and a small population of prairie dogs would persist despite the presence of plague. The level of resistance observed at equilibrium for these populations is similar to a previously observed resistance threshold for prairie dog extinction (Buhnerkempe et al. in prep). This fact may indicate that prairie dogs will develop immunity to overcome this threshold and avoid extinction, but tradeoffs with reproduction will prevent further increases in immunity. The evolution of resistance, however, is not supported in nature. Despite nearly a century of evolutionary pressure, black-tailed prairie dogs exhibit little or no resistance to Y. pestis infection (Cully and Williams 2001). What then accounts for this difference between prediction and observation? Most notably, our model predicts that only small populations (<50 individuals) will persist in the presence of plague. These small populations are subject to the effects of demographic stochasticity and face increased extinction risk that threatens the continued existence of plague resistance genes. Prairie dogs also may face higher costs to the development of resistance than we have considered here. We found the evolution of resistance to be highly sensitive to these costs. Thus, the development of plague resistance could potentially be too costly to maintain for prairie dogs. Little information exists on the evolution of plague virulence within prairie dog hosts. Our model predicted that plague would increase in virulence regardless of the cost we imposed on this development. This insensitivity may indeed indicate that there is little cost to increasing virulence in this system. The nature of life-history tradeoffs for pathogens, however, is not well understood. Much of the work on the evolution of virulence has focused on transmission tradeoffs for directly transmitted, vector-borne, and environmentally reservoired pathogens (Ewald 1995). Our model of transmission does not fit neatly into any of these categories leaving the potential life-history tradeoffs for the evolution of plague virulence in our model up for debate. To remedy this shortcoming, future models of the coevolutionary arms race between prairie dog resistance and plague virulence should employ a more community-based approach. Transmission of plague by fleas is the dominant transmission mechanism for plague and has not been addressed here. To incorporate flea-borne transmission, knowledge of the costs of virulence and resistance in flea vectors will be important. Extensions of the model in this way could provide an example of community level feedback in coevolutionary systems beyond just pathogen-host interactions. References

Anderson, R.M. and R.M. May. 1982. Coevolution of hosts and parasites. Parasitology 85: 411-426.

Ber, R., E. Mamroud, M. Aftalion, A. Tidhar, D. Gur, Y. Flashner, and S. Cohen. 2003. Development of an improved selective agar medium for isolation of Yersinia pestis. Applied and Environmental Microbiology 69(10): 5787-5792.

Buhnerkempe, M.G., Eisen, R.J., K.L. Gage, B. Godell, M.F. Antolin, and C.T. Webb. In preparation. Species-specific responses to Yersinia pestis infection: the role of hosts, fleas, and early-phase transmission.

Cully, J.F. and E.S. Williams. 2001. Interspecific comparisons of sylvatic plague in prairie dogs. Journal of Mammalogy 82(4): 894-905.

Day, T. 2002. On the evolution of virulence and the relationship between various measures of mortality. Proceedings of the Royal Society: Series B 269: 1317-1323.

Dwyer, G., S.A. Levin, and L. Buttel. 1990. A simulation model of the population dynamics and evolution of myxomatosis. Ecological Monographs 60(4): 423-447.

Ewald, P.W. 1995. The evolution of virulence: a unifying link between parasitology and ecology. Journal of Parasitology 81(5): 659-669.

Hoogland, J.L. 1995. The Black-Tailed Prairie Dog. Chicago, IL: University of Chicago Press.

Khibnik, A.I. and A.S. Kondrashov. Three mechanisms of Red Queen dynamics. Proceedings of the Royal Society: Series B 264: 1049-1056.

Koella, J.C. and C. Boëte. 2003. A model for the coevolution of immunity and immune evasion in vector-borne diseases with implications for the epidemiology of malaria. American Naturalist 161(5): 698-707.

Stapp, P., M.F. Antolin, and M. Ball. 2004. Patterns of extinction in prairie dog metapopulations: plague outbreaks follow El Ninõ events. Frontiers in Ecology and the Environment 2(5): 235-240.

Webb, C.T., C.P. Brooks, K.L. Gage, and M.F. Antolin. 2006. Classic flea-borne transmission does not drive plague epizootics in prairie dogs. PNAS 103(16): 6236-6241.

Williams, J.E., M.A. Moussa, and D.C. Cavanaugh. 1979. Experimental plague in the California Ground Squirrel. Journal of Infectious Diseases 140(4): 618-621.