integrating epidemiology into population viability analysis: managing the risk posed by rabies and...

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Conservation Biology, Pages 1372–1385Volume 16, No. 5, October 2002

Integrating Epidemiology into Population Viability Analysis: Managing the Risk Posed by Rabies and Canine Distemper to the Ethiopian Wolf

D. T. HAYDON,*‡ M. K. LAURENSON,* AND C. SILLERO-ZUBIRI†

*Centre for Tropical Veterinary Medicine, University of Edinburgh, Easter Bush, Roslin, Midlothian, EH25 9RG, United Kingdom†Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, United Kingdom

Abstract:

Infectious disease constitutes a substantial threat to the viability of endangered species. Populationviability analysis (PVA) can be a useful tool for directing conservation management when decisions must bemade and information is absent or incomplete. Incorporating epidemiological dynamics explicitly into a PVAframework is technically challenging, but here we make a first attempt to integrate formal stochastic modelsof the combined dynamics of rabies and canine distemper into a PVA of the Ethiopian wolf (

Canis simensis

),a critically endangered canid. In the absence of disease, populations in habitat patches of every size were re-markably stable and persistent. When rabies virus was introduced, epidemics, assumed to arise from spo-radic dog-to-wolf transmission, caused extinction probabilities over 50 years to rise linearly with the force ofinfection from the dog reservoir and particularly steeply in smaller populations. Sensitivity analysis revealedthat although the overall pattern of results was not altered fundamentally by small to moderate changes indisease-transmission rates or the way in which interpack disease transmission was modeled, results were sen-sitive to the process of female recruitment to male-only packs. Completely protecting wolf populations from ra-bies through vaccination is likely to be impractical, but the model suggested that direct vaccination of as few as20–40% of wolves against rabies might be sufficient to eliminate the largest epidemics and therefore protect pop-ulations from the very low densities that make recovery unlikely. Additional simulations suggested that the af-fect of periodic epidemics of canine distemper virus on wolf population persistence was likely to be slight, evenwhen modeled together with rabies. From a management perspective, our results suggest that conservation ac-tion to protect even the smallest populations of Ethiopian wolves from rabies is both worthwhile and urgent.

Integración de la Epidemiología dentro del Análisis de Viabilidad Poblacional: Manejo del Riesgo que Representanla Rabia y el Moquillo Canino en el Lobo Etíope.

Resumen:

Las enfermedades infecciosas constituyen una amenaza sustancial contra la viabilidad de las es-pecies en peligro. El análisis de viabilidad poblacional (PVA) puede ser una herramienta útil para dirigir laconservación para el manejo cuando las decisiones deben ser tomadas y la información es escasa o incom-pleta. La incorporación de dinámicas epidemiológicas explícitamente dentro de una marco PVA es técnica-mente un reto; sin embargo, llevamos a cabo el primer intento para integrar modelos estocásticos formalesde la dinámica de la rabia y del moquillo canino para un PVA del lobo etíope (

Canis simensis

), un cánidocríticamente amenazado. En ausencia de la enfermedad, las poblaciones que habitan parches de hábitat detodos los tamaños fueron llamativamente estables y persistentes. Cuando se introduce el virus de la rabia, lasepidemias, que supuestamente surgen de transmisiones esporádicas de perro a lobo, hicieron que las proba-bilidades de extinción sobre 50 años se incrementaran linealmente con la fuerza de la infección del perro res-ervorio y particularmente de manera abrupta en poblaciones pequeñas. El análisis de sensibilidad reveló

‡

Current address: Department of Zoology, University of Guelph, Guelph, Ontario, N1G 2W1 Canada, email [email protected] submitted December 21, 2000; revised manuscript accepted October 31, 2001.

Conservation BiologyVolume 16, No. 5, October 2002

Haydon et al. PVA and Disease in Ethiopian Wolves

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Introduction

Assessing risks for endangered species is an integral partof conservation management and an essential prerequi-site for deciding if, when, and where action should betaken and how limited resources should be targeted(Harwood 2000). Unfortunately, these decisions mustusually be made in the absence of adequate informationon the nature and severity of threats to endangered pop-ulations. Under such circumstances, accurate risk assess-ment will not be possible, and the best that can be doneis to consider all sources of information, appropriatelyweighted by their dependability.

The most common form of risk assessment in conser-vation biology is population viability analysis (PVA),which examines and analyzes the interacting factors thatplace a population or species at risk ( Boyce 1992; Burg-man et al. 1993). The limitations of PVA are increasinglyappreciated, and criticisms span the entire scope of itsapplications (Caughley & Gunn 1996; Mills et al. 1996;Beissinger & Westphal 1998; Reed et al. 1998). The sta-tistical nature of many processes, particularly environ-mental factors that affect population demography andthat are usually modeled as stochastic “noise,” are poorlyunderstood ( Vose 2000). In addition, many models aretoo simplistic. For example, many generic PVA pro-grams omit potentially important autoecological featuresof subject populations, such as social structure, repro-ductive suppression, and spatial factors (Mills et al.1996; Beissinger & Westphal 1998; Reed et al. 1998; butsee Vucetich et al. 1997; Vucetich & Creel 1999).

Population viability analysis programs also frequentlyomit a variety of extrinsic factors. The effect of disease isa striking example of such an omission, despite a grow-ing appreciation of its threat to many populations (e.g.,May 1988; Thorne & Williams 1988; Murray et al. 1999;Daszak et al. 2000). Instigating proactive disease man-agement obviously is desirable, but it is difficult to iden-tify the risk factors for pathogen invasion, spread, and ef-fect. Indeed there is a general lack of objective orquantitative decision-making tools available to assess dis-

ease risk, establish guidelines for instigating diseasemanagement, or evaluate management effects on popu-lation processes.

A few PVA models include disease simply as an addi-tional mortality factor, such as VORTEX-based modelsoriented to the Ethiopian wolf (

Canis simensis

) (Mace& Sillero-Zubiri 1997) and African wild dog (

Lycaon pic-tus

) (Ginsberg & Woodroffe 1997). In a similar but moresophisticated approach, Vucetich and Creel (1999) ex-plored disease effects in an individual-based model ofwild dogs by including additional mortality in patternscharacteristic of certain types of infection. To date, noconservation-oriented models explicitly incorporate dis-ease transmission dynamically as an infectious process,despite the fact that epidemic size and interepidemic in-tervals can be acutely sensitive to the demography andimmunological status of populations. Furthermore, be-cause disease can periodically bring populations to verylow numbers, traditional deterministic epidemiologicalmodels are poorly suited for analysis of imposed extinc-tion risk. In recent years there have been many advancesin human and veterinary epidemiology where models,theory, and data have been combined in a powerful wayto provide insight into the dynamics and control of in-fectious disease within populations (Anderson & May1991; Diekmann & Heesterbeek 2000). Similar ap-proaches are required to understand the sometimes com-plex threat posed by disease to endangered populations.

Disease may be a particular conservation problem forendangered carnivores (Alexander & Appel 1994; Young1994; Murray et al. 1999). It has been identified as themost immediate threat to the critically endangered Ethi-opian wolf (Laurenson et al. 1997), found now in onlyseven fragmented and isolated populations in the afro-alpine highlands of Ethiopia. Remaining populationsconsist of 15–250 individuals and total about 500 adultsin all (Marino 2000). Each of these habitat islands is sur-rounded by agricultural land occupied by farmers andtheir livestock. Associated domestic dogs either live inwolf habitat or make incursions into it and are the mostlikely reservoir for wolves of diseases such as canine dis-

que a pesar de que el patrón general de los resultados no haya sido alterado fundamentalmente por cambiospequeños o moderados en las tasas de transmisión de la enfermedad ni por la forma en que la transmisiónde la enfermedad al interior del grupo fue modelada, los resultados fueron sensibles al proceso de re-clutamiento de hembras en grupos de machos. La protección total de las poblaciones de lobos mediante vacu-nación contra la rabia probablemente no es práctica, pero el modelo sugiere que la vacunación directa depor lo menos un 20-40% de los lobos podría ser suficiente para eliminar las epidemias más grandes y por lotanto proteger poblaciones con densidades muy bajas que harían poco probable una recuperación. Posteri-ores simulaciones sugirieron que las repercusiones sobre epidemias de moquillo canino en la persistencia depoblaciones de lobos serían probablemente ligeras, aún cuando se modelaran conjuntamente con la rabia.Desde la perspectiva del manejo, nuestros resultados sugieren que las acciones de conservación para proteger

aún a las poblaciones más pequeñas de lobos etíopes de la rabia son importantes y urgentes.

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PVA and Disease in Ethiopian Wolves Haydon et al.


temper virus (CDV ), parvovirus, and infectious hepatitis(Laurenson et al. 1998

a

).A rabies outbreak in the largest population in the Bale

Mountains in the early 1990s caused a two-thirds declinein this population (Sillero-Zubiri et al. 1996

a

); only now,10 years later, are pack numbers and sizes approachingpre-epidemic levels. Although dog vaccination was insti-gated there in 1996, we now need to make decisionsabout where and what disease management strategies, ifany, should be adopted for other wolf populations andhow they should be prioritized. To assist in this, a moreobjective and quantitative assessment of disease risk towolf populations is urgently required.

Despite its shortcomings, PVA may still play a usefulrole in management decision-making (Beissinger &Westphal 1998; Reed et al. 1998; Brook et al. 2000; Har-wood 2000). It is relatively cheap and forces both a rig-orous consideration of processes and an evaluation ofthe state of knowledge of an endangered population.Furthermore, its limitations may be minimized by appro-priate interpretation, and it is likely to prove useful in as-sessment of relative risks such as evaluating alternativemanagement strategies, assessing the vulnerability of dif-ferent-sized populations, and designing reserves.

Our objective was, first, to combine an explicitly epi-demiological component within a conventional PVAframework. Second, although our approach may havegeneral use, we examined its application as a decision-making tool to a particular endangered species, the Ethi-opian wolf. In particular, we examined the followingquestions relevant to the current status of Ethiopianwolves: (1) What biological processes incorporated intothe model are least understood? (2) What does themodel predict about the relative persistence times of dis-ease-free populations inhabiting areas of different size?(3) What is the effect on population structure, size, andrisk indicators of the invasion of canine pathogens intopopulations inhabiting areas of different size? (4) Whateffect do management strategies that reduce disease in-cidence and transmission probability have on the rela-tive population persistence and risk indicators associ-ated with populations inhabiting areas of different size?(5) Are the predicted effects of canine pathogens, andmanagement strategies to reduce their effect, sensitiveto identified uncertainties in model input?

Methods

Ethiopian Wolf Biology and Social Structure

The Ethiopian wolf is a diurnal, 15-kg canid that lives inclose-knit territorial packs but forages predominantlyalone on afroalpine rodents (Sillero-Zubiri & Gottelli1995

a

). In optimal habitat, packs are male-biased andconsist of an average of six adults, one to six yearlings,

and one to seven pups, although in poorer habitatswolves live in smaller groups or pairs (Sillero-Zubiri &Gottelli 1995

b

). Generally, dominance hierarchies withinpacks ensure that only dominant females breed (Sillero-Zubiri et al. 1996

b

). Matings in the Bale Mountains gen-erally occur between August and November, with pupsborn 2 months later (Sillero-Zubiri et al. 1998). All packmembers help feed pups. Dispersal is constrained by ascarcity of unoccupied habitat: males stay with their na-tal pack, whereas two-thirds of females disperse at 2years of age and become “floaters,” occupying narrowranges between pack territories until a breeding vacancybecomes available (Sillero-Zubiri et al. 1996

b

). Pack fis-sion is a relatively rare event (3 successful events from10 attempts during 7 years of intensive study of 9–11packs) and occurs only when packs become very large,subordinate females breed, and wolf densities are belowcarrying capacity (Sillero-Zubiri 1994; Ethiopian WolfConservation Programme [EWCP], unpublished data).Alternatively, a group of subordinate males joins withsubordinate females from another pack to form a newpack. Thus, although large litter sizes permit quick pack-size recovery, pack structure reduces population growthrates (Vucetich et al. 1997).

The Model

Our model, written in Pascal (Delphi V ), is an individu-ally based, age- and pack-structured, spatially explicit,stochastic representation of wolf population dynamicsbased on the wolf population in the Bale Mountains.Where available, model parameters were taken from theexisting literature. Where population parameters wereknown with less confidence, we adopted a number thatin our opinion was biologically plausible.

Each patch was capable of maintaining wolf popula-tions at a specified carrying density,

K

, initially set to1/km

2

, which approaches the maximum observed in op-timal habitat (Gotelli & Sillero-Zubiri 1992) before a vari-ety of mechanisms arise to regulate pack dynamics. Eachpack was assumed to occupy a circular home range ofradius 1.4 km. Individuals were assigned to one of sixdemographic classes: three age classes (0–1 years, juve-niles; 1–2 years, subadults; and adult,

�

2 years) in eachsex. Each pack had a maximum size of 13 individuals(excluding juveniles), only 2 of which could be adult fe-males. Packs in which at least one adult of each sexwere present gave birth to litters of pups with probabil-ity

F

, which under baseline conditions is 0.63 (Sillero-Zubiri et al. 1996

b

). One female would give birth to a vary-ing number of pups in December, with probability esti-mated from field data at 0.05, 0.11, 0.21, 0.16, 0.16, and0.32 for one to six pups, respectively (Sillero-Zubiri etal., unpublished data). Age classes were updated prior tobreeding. Between this updating and breeding a packcould undergo one of four events, depending on pack


Haydon et al. PVA and Disease in Ethiopian Wolves

1375

and population size, that we judged to be likely mecha-nisms underlying the regulation of pack numbers. Allthese events have been observed in the wild (Sillero-Zubiriet al. 1996

a

, 1996

b

). (1) If more than two adult femaleswere present in the pack, randomly selected “surplus”adult females were removed to a nonbreeding “pool” pop-ulation of floaters (assumed to exist at uniform density overthe habitat patch). (2) If the pack had more than 13 individ-uals and the total population was

�

75% of specified carry-ing density

K

, then randomly selected adult males were re-moved to the pool population until pack size was reducedto 13 individuals. (3) If the pack had more than 13 individu-als and the total population was

�

75% of

K

, then the packsplit and up to six randomly selected adult males weretransferred to a new and randomly located pack. (4) If thepack lacked a single adult female but one was present inthe pool, then a female was recruited.

The entire wolf population was subjected to a contin-uous-time, demographically stochastic, age- and sex-spe-cific mortality process, determined from field data, suchthat adults and subadults had a probability of 0.15 of dy-ing each year, with the equivalent probabilities for maleand female juveniles being 0.45 and 0.55, respectively(Sillero-Zubiri 1994, EWCP, unpublished data). Thesemortality rates included all agents of mortality exceptdisease. Mortality rates in the pool population were as-sumed to be

D

times higher than pack mortality rates.Details of how demographically stochastic models canbe run with fixed parameters in continuous time areavailable in many texts (e.g., Renshaw 1991).

Each individual wolf in the population was also subjectto a continuous-time, demographically stochastic suscep-tible-infectious-recovered (S-I-R) process. The summedforce of infection (Anderson & May 1991) calculated overall infectious wolves and a randomly varying force of in-fection assumed to arise from the domestic dog reservoircombine to determine the rate at which individuals be-come infectious. This rate is used to compute randomwaiting times governing the stochastic transfer of individ-ual animals from susceptible to infectious categories:

where

S

i

,

x

and

I

i,x

represent the numbers of susceptibleand infectious individuals in the

x

th demographic class ofthe

i

th pack;

n

is the number of packs (the pool is re-ferred to as the 0th pack);

�

ij

is the transmission coeffi-cient between the

i

th and

j

th pack (see Table 1);

I

j

is thenumber of infectious individuals in the

j

th pack; and

�

ir

isthe transmission coefficient between the infected indi-viduals in the reservoir population in the

i

th pack’s homerange at time

t

and individuals of the

i

th pack. The inter-pack transmission coefficients are products of an underly-ing infectiousness parameter,

�

ii

and the proportion of the

Si x, t( ) Si x, t( )→ 1– Ii x, t( ) Ii x, t( ) 1+→=

βijIjt βirIrit+

j�0

n

∑

= ,

Iri

area of the

i

th pack’s circular home range that overlapswith the

j

th pack’s home range,

�

ij

, calculated according tothe spatial locations of the home ranges (parameters aregiven in Table 1).

The S-I-R process was run independently for rabiesand CDV, resulting in nine possible disease classes (

SS,SI, SR, IS, II, IR, RS, RI, RR

), making 54 different classesin all for each pack: 2 sexes

�

3 age-classes

�

9 diseasestates. Infection may result in recovery (with rate

�

) ordeath (with rate

; Table 1). All packs were examined atthe end of each month; those containing two or fewerindividuals were broken up and individuals were trans-ferred to the pool.

Disease incidence in the reservoir population wasmodeled purely phenomenologically. Rabies incidencewas assumed to be spatially and temporally uniform onaverage and was determined independently in eachwolf-pack home range on a weekly basis. Thus, with ra-bies incidence (denoted by

i

(

rabies)

) equal to 0.025 perhome range per month, on average rabies could poten-tially be introduced to wolf packs independently every 4months in a patch occupied by 10 packs. The observedfrequency of outbreaks arising will normally be lower,however, because it is, of course, determined by thetransmission coefficients linking the wolf population to thereservoir. Canine distemper virus was modeled as spatiallyuniform but epidemic in nature. Each epidemic occurredin three consecutive randomly chosen months, separatedby an interval that was either 3, 4, 5, or 6 years (Table 1).Collectively, we referred to this combination of demo-graphic and epidemiological parameters as “baseline,” be-cause we considered it to approximate the scenario in anunmanaged wolf population in the Bale Mountains.

We performed simulations on 10 different-sized areasof 25–250 km

2

encompassing the range of sizes of re-maining wolf populations ( Marino 2000). We also exam-ined viability at eight different levels of dog reservoir dis-ease incidence (0–140% of baseline incidence) and theeffect of directly vaccinating varying proportions ofwolves against both rabies and CDV or rabies alone.Higher incidences of disease were considered unrealis-tic because the estimated incidence of dog rabies in ourstudy area (1.2–5.6% of dogs per year; Laurenson et al.1998

b

) is among the highest in Africa (e.g., Cleavelandet al. 1999; Kitala et al., 2000). For each scenario we per-formed 1000 simulations of 50 years, conditional onpopulations remaining extant. Simulations were startedat a population density

K

, with age and pack structuresrepresentative of baseline output.

Results

Disease-Free Populations

In the absence of disease, the model predicted that a pop-ulation occupying a 250-km

2

range of continuous habitat

1376

PVA and Disease in Ethiopian Wolves Haydon et al.


and conforming to our baseline set of demographic pa-rameters should exhibit a high degree of population sta-bility (Figs. 1 & 2d). No extinctions were observed in1000 simulations each of 50-years duration or when simu-lations were extended to 200 years. The coefficient ofvariation (CV) of population fluctuation was about 10%.The populations were likely to be found slightly aboveour defined carrying density (

K

) (95% confidence inter-val[CI] 0.94–1.4

K

), divided into 25 packs (95% CI 21–29),and with an average pool population of six (95% CI 4.6–6.8). Sudden population crashes were absent (no crasheslarger than 33% of population size), and pack extinctionprobabilities were about 0.5% per year (95% CI 0.2–1.1).

Disease-free populations modeled in smaller patchesof habitat were similarly stable: no extinctions were ob-served in 1000 50-year simulation runs in 50-km

2

patches. The extinction rate increased to only 2% whensimulations were extended to 200 years. Even the small-est populations in 25-km

2

patches suffered only a 2% ex-tinction risk over 50 years, although this rose to 50%over 200 years. In these smallest populations the CV ofpopulation fluctuation increased to 22% ( Fig. 2d).

Baseline Disease Effect

When exposed to our baseline disease processes, the pic-ture was different ( Fig. 1). For a population occupying250 km

2

of habitat, extinction probabilities evaluatedover a 50-year period were estimated to be 8–9%, rising to

16% over 100 years and to 25% over 200 years. The popu-lations were on average at about 40% of capacity after 50years (95% CI 0.04–0.97K), divided into an average ofnine packs (95% CI 1–23) with an average pool size ofthree (95% CI 0.5–5). Over 50 years, populations usuallyexperienced one or two crashes of at least 33%, withhalf the populations experiencing a crash of more than66%. Pack extinction probabilities were about 8% peryear (95% CI 2–32). Analysis of populations revealedthat if they dropped below 20 individuals, they had onlya 20% chance of recovering to twice that size. Rabiesdeaths averaged seven per year, but with high variationbetween years (95% CI 1.5–27.5).

Until habitat size dropped below 100 km

2

, modeledpopulations exposed to baseline disease processes insmaller areas appeared to be comparably viable (extinc-tion probability over 50 years was 8–14%). For patchsizes of 75 km

2

, extinction probability was 17% over 50years but was 28% for 50-km

2

patches and 46% for 25-km

2

patches (Fig. 2a). The average number of packs sur-viving this period decreased by progressively greateramounts from just over nine for 250-km

2

habitat patchesto just under three for 25-km

2

patches ( Fig. 2b).

Responses to Variation of Disease Incidencein the Reservoir Population

As disease incidence in the reservoir population de-creased from 140% to 20% of baseline levels, 50-year ex-

Table 1. Epidemiological parameter values used in the model of Ethiopian wolf populations.*

Parameter RabiesCanine distemper

virus (CDV)

Mean infection incidence in reservoir per home range per month—

k

(disease)

0.025 4 (when present)Probability of CDV epidemic interval of

j

years (

j

�

3..6) — [0.1,0.2,0.4,0.3]CDV epidemic duration (months) — 3Mean CDV interepidemic period (years) — 5.1

�

00 (pool wolf to pool wolf) 0.0006 0.00018�0i (pack wolf to pool wolf) 1 � �00 1 � �00

�0r (reservoir dog to pool wolf) 6 � �00 1.5 � �00

�ir (reservoir dog to pack wolf) 4 � �00 1 � �00

�ii (intrawolf pack) 0.1875 0.1�ij (interwolf pack) �ij �ii �ii �ii

(per day) 0.2 0.08� (per day) 0 0.12

* Transmission rates ( �) are per infected individual wolf per susceptible individual per day. From field knowledge of likely contact probabili-ties, we considered intra–wolf pack-transmission most likely, followed by inter–wolf-pack transmission, whereas the likelihood of transmissionbetween a pool wolf and either another pool wolf or a pack wolf was much lower and similar. However, contacts between reservoir dogs and ei-ther pack or pool wolves may be slightly higher than pool wolves with either pack or pool wolves because interactions between dogs and wolvesare seen more often than between pool wolves and pack wolves (M.K.L., personal observations; Ethiopian Wolf Conservation Programme, un-published data). Within-pack transmission rates were selected that resulted in approximately 90% of pack members contracting rabies (wilddogs, Kat et al. 1995; Hofmeyr et al. 2000; Ethiopian wolves, Sillero-Zubiri et al. 1996a) and approximately 80% contracting canine distempervirus (domestic dogs, Gorham 1966; Alexander & Appel 1994). Thus, although it is impossible to accurately quantify transmission rates, we an-ticipate that the ratios of transmission types to one another are correctly ranked. Estimates of incidence of canine distemper, mortality rates,and epidemic parameters in reservoir dogs are based on published accounts (e.g., Gorham 1966; Blixenkrone-Moller et al. 1993; Alexander etal. 1996; Cleaveland 1996), although the relative probability of interepidemic intervals were arbitrarily assigned. Those for rabies are fromLaurenson et al. 1997.


Haydon et al. PVA and Disease in Ethiopian Wolves 1377

tinction probabilities in populations occupying a 250-km2 habitat patch declined from 13% to 4% (Fig. 2a), theaverage number of surviving packs increased from 8 to18 (Fig. 2b), and annual pack extinction probabilities de-clined from 10% to 3% ( Fig. 2c). Rabies incidence in thewolf population halved from an average of nine casesper year to under four, but average CDV incidence de-creased only slightly, from four to three.

Persistence of populations modeled in smaller patches(�100 km2) was particularly sensitive to variation in dis-ease incidence (Fig. 2a), and only when disease inci-dence was �40% of baseline did persistence probability

exceed 80%. High levels of disease reduced populationdensity in large habitat areas by as much as 60% of K,but populations occupying smaller patches either per-sisted close to K or proceeded rapidly to extinction. Thefrequency of population crashes of 33% did not varygreatly between different-sized habitat patches and var-ied from about once every 50–60 years at 20% of base-line incidence to once every 25 years at the 140% inci-dence. Large population crashes (�66%) occurred witha probability of 65% and 26% in the largest and smallestpopulations, respectively, over 50 years, about half as fre-quently as “one-third” crashes. The marked increase in ex-tinction rates at higher disease incidences and in smallerpatches is reflected in the standard deviation of loggedpopulation abundances (Fig. 2d), which indicates substan-tially greater relative fluctuations in small populations andthose in which disease incidence is highest.

Effects of CDV or Rabies Alone

When rabies was excluded from simulations, CDV hadlittle effect on the persistence of any population andpack numbers were only slightly reduced (Fig. 3a).When CDV was excluded and only rabies was present,however, extinction probabilities were greater thanthose when both diseases were present (e.g., 250 km2,13% vs. 9%; 50 km2, 39% vs. 28%) ( Fig. 3a). We suspectthat CDV acts as a mild population thinning agent in ourmodel, preventing the most damaging rabies outbreaksand thereby actually enhancing population persistence.

Response to Direct Vaccination of Wolves

With vaccination of 20% of wolves in a population occu-pying a 250-km2 habitat patch exposed to baseline dis-ease processes against both rabies and CDV, 50-year per-sistence probabilities rose from approximately 90% to100%. In populations in 75-km2 patches, vaccination of30% of wolves increased persistence probabilities from83% to 100%, whereas in the smallest populations vacci-nating 40% increased persistence probabilities from 54%to 90% (Fig. 4a). The size of populations persisting insmaller patches was again largely unaffected by vaccina-tion, but in medium-sized and large patches, populationsizes increased rapidly with vaccination effort, much ofthe potential increases realized by 40% coverage (resultsnot shown). The dramatic effect of 40% coverage wasalso revealed by inspection of the annual pack-extinc-tion probabilities, which fell to �2% in all habitat sizes.

Vaccinating populations occupying patches of 50 km2

or more against rabies alone provided an improvementin persistence probabilities equivalent to that obtainedby vaccinating against both diseases together (resultsnot shown). In habitat patches of 50 km2 and less, how-ever, CDV epidemics contributed a small but detectableadditional extinction risk over 50 years when rabies vac-

Figure 1. Simulations of Ethiopian wolf populations based on baseline demographic parameters in habitat patches of 250 km2. The dots, with a small added x-jig-gle factor, and the line (with open circles) indicate the distribution and mean number of packs extant in the simulation after 50 years, based on 1000 simulations The inset figure is the proportion of 1000 simulations remaining extant. The reservoir disease incidence cor-responding to 100% is indicated in Table 1, and reser-voir disease incidence increases from 0 to 140% of this level along the x-axis.

1378 PVA and Disease in Ethiopian Wolves Haydon et al.


cination coverage was high (�70%). Our simulationssuggest that our baseline CDV process added approxi-mately 0.5% to the probability of extinction in 50-km2

habitat patches and approximately 5% in 25-km2 habitatpatches. When coverage was lower and rabies outbreaksoccurred, CDV presence again appeared to enhance per-sistence, presumably due to the population-thinningprocess described previously.

Sensitivity of Simulation Results

The results of various parameter perturbations on simu-lation results for a 250-km2 habitat range under a rangeof disease pressures are summarized in Appendix 1. Noperturbation reduced 50-year persistence probability be-low 70%, with only substantial perturbations (30% ormore) pushing 50-year persistence probability below80%. When mortality parameters were treated as annu-ally varying random variates (assumed to be uniformlydistributed from zero to twice the fixed parameter value,thus ensuring a coefficient of variation in the realized pa-rameters of approximately 40%), the probability of per-sisting over a 50-year period was reduced by 3–4% (Fig.3a). Populations were particularly sensitive to the ab-

sence of female recruitment to packs. When femalescould not be recruited, pack-extinction rates rose from8% to 12% per year under baseline disease conditions,and the proportion of packs that failed to breed (be-cause they contained individuals of only one sex) in-creased from �2% to �15%. Although the process of fe-male recruitment from a pool population was essentialto population viability, persistence increased when poolmortality rose (Fig. 3a). Although small pool populationswere essential, large ones appeared to constitute anadditional source of disease acquisition. Similar conclu-sions were drawn from a more limited sensitivity analy-sis applied to populations modeled in 50-km2 habitatpatches (Fig. 3b).

Our results were not overly sensitive to increases in in-terpack disease-transmission coefficients. If all non-zero�ij were set equal to �ii, baseline 50-year extinction ratesincreased by only 3% (because at baseline disease inci-dence, pack density is sufficiently low that range over-laps are uncommon). If interpack disease-transmissioncoefficients were set to zero, then baseline 50-year ex-tinction rates became zero.

Our results suggest that in large patches over 50-yeartime periods pack numbers will decrease linearly in re-

Figure 2. Population simulations using baseline demographic parameters for wolf populations in habitat patches of different areas exposed to different levels of disease incidence in the dog reservoir: (a) proportion of 1000 simula-tions in which populations remained extant after 50 years; (b) average number of packs in extant populations after 50 years; (c) probability of a pack going extinct each year; and (d) standard deviation of log10 population size.



sponse to increases in mortality of up to 50% over base-line but that these decreases in population size do notbegin to affect observed persistence times until overallmortality increases by 20% or more over baseline. In thesmallest populations (those occupying 25-km2 habitatpatches), any increase in mortality, and thus decrease inpopulation size, affected persistence probability ( Fig. 4b).

Discussion

In contrast to previous PVA models that incorporateddisease as an additional mortality factor (Ginsberg &

Woodroffe 1997; Mace & Sillero-Zubiri 1997; Vucetich &Creel 1999), our individual-based, stochastic, spatial pop-ulation model for Ethiopian wolves explicitly incorpo-rated disease transmission as a dynamic process. Our re-sults suggest that, in the absence of disease, wolfdemography is impressively stable—even in populationscomprised of 25–50 individuals. The introduction of ra-bies and canine distemper caused substantial populationfluctuations and extinction risks, particularly when pop-ulations comprised �100 individuals. Over 50 years, ex-

Figure 3. (a) Results of parameter perturbations on the proportion of 1000 simulations in which wolf pop-ulations modeled in 250-km2 habitat patches re-mained extant after 50 years. Attention is restricted to the changes in pool mortality rate, inclusion of stan-dard deviations on mortality rates, exclusion of fe-male recruitment from the pool, and the effects of ra-bies and canine distemper virus (CDV) alone. (b) Same analysis for 50-km2 habitat patches.

Figure 4. (a) Effect of vaccination on 50-year persis-tence of Ethiopian wolf populations. Simulations are based on baseline demographic and epidemiological parameters for wolf populations in habitat patches of different areas but assume that varying proportions of pups are born directly into the recovered compart-ment of the underlying susceptible-infectious-recov-ered model (i.e., vaccinated) and are thus immune to disease. ( b) The results of steadily increasing overall mortality rates on persistence and surviving pack numbers after 50 years of simulations in populations modeled to occupy habitat patches of different sizes. The x-axis is a multiplier by which baseline mortality rates in Table 1 are multiplied; thus, the x-axis spans mortality rates from baseline to twice baseline mortal-ity rates. Baseline epidemiological conditions applied.



tinction risk in wolf populations of all sizes rose linearlywith the force of rabies infection within the reservoirpopulation, but these risks could be reduced dramati-cally by directly vaccinating as few as 20–40% of wolves,which stopped the largest epidemics. Canine distemperalone had negligible effect on population persistence,and the overall pattern of results appeared robust tomoderate parameter perturbations.

Generally, we used a 50-year time frame because weconsider it unlikely that parameters and processes as-sumed by our model would remain stationary even overthis period, let alone over 100 or 200 years. However,the choice of this 50-year time horizon affected our re-sults for smaller populations, because extinction ratesrose significantly for these populations over 100- and 200-year time periods. Thus, although estimates of the in-creased extinction risk over longer periods will be inaccu-rate, it is probable that this relative increase in risk is con-siderable.

Parameter Estimation and Sensitivity Analysis

In an attempt to identify limitations of this model, wesubjected the most uncertain parameters and processesto a sensitivity analysis to determine which have thegreatest effect on population persistence (Reed et al.1998). Research can then be focused to provide moreaccurate data for estimation of these parameters. Valuesfor parameters relating to nondisease sources of wolfmortality, the probability of packs breeding, and averagelitter sizes were chosen from available data. These dataare few, however, and representative of demographicsexhibited by only one stable and high-density popula-tion over only 4 years (or sometimes 7 years). Ongoingstudies of this and other populations will improve theaccuracy and knowledge of variation in these parame-ters and will determine whether density-dependent ef-fects occur.

Our model, like other individual-based models ofother pack-living canids with reproductive suppression(Gray wolves, Vucetich et al. 1997; Haight et al. 1997;African wild dogs, Vucetich & Creel 1999), was sensitiveto demographic events such as pack fission, fusion, andimmigration frequency. We had to adopt relatively arbi-trary rules for female recruitment, pack fission, andshedding events, but these were based on data thatshow that such events have occurred in the wild (for ex-ample, we know of three successful pack fissions in 7years of study; Sillero-Zubiri et al. 1996b; EWCP, unpub-lished data), although the mechanism underlying theseevents remains a source of considerable uncertainty.Nevertheless, much more information on these phenom-ena is required for Ethiopian wolves and other species,in particular, we need to determine how these phenom-ena vary with population size and density.

In contrast, the model was relatively insensitive to varia-tion in pool wolf mortality, which is unknown, and to theeffects of varying interpack disease transmission. Thus,our results may be viewed as applying to populations inlarger habitat patches with lower carrying capacity or insmaller patches with higher carrying capacity.

Epidemiological parameters were also estimated withconsiderable uncertainty. We estimated rabies incidencein dogs through questionnaires, because official reports ofcase incidence substantially underrepresent the true scaleof disease (Laurenson et al. 1998b; Kitala et al. 2000). Pre-liminary data obtained from wolf ranges across Ethiopiasuggest that the current incidence of these diseases indogs falls within the range examined in our analysis; sowe considered an increase in disease incidence of morethan 140% of baseline to be unrealistic. We were primar-ily interested, however, in the response of population via-bility to changing disease incidence, so the absolute accu-racy of incidence estimates is of limited importance.

Available field data suggest that when rabies infectionsoccur within packs, about 90% of pack members go onto acquire the infection (Table 1). Our estimate of ap-proximately 80% of pack members acquiring CDV infec-tion is based on information from dogs, for which con-tact rates may be lower than those between closely knitpack wolves and may be too low. Our selected valuesfor �ii were based on the estimated pack sizes and dura-tions of infectiousness of the two infections. Values of�00, �0r, �0i, and �ir are unknown, however, and are cho-sen here only to generate plausible results, although weexpect that their relative magnitudes may be correct( Table 1). Additional behavioral studies are required toimprove estimated contact rates between individualsfrom pack, pool, and reservoir populations, although thegeneral trends revealed by our study are not overly sensi-tive to increases in these coefficients.

Generally, estimates of demographic and epidemiolog-ical parameters from field data are likely to reflect bothmeasurement error and genuine environmental variabil-ity, and these sources of uncertainty will be difficult todecipher (Taylor 1995). There are few good estimates ofparameter variances within this system and no estimatesof parameter covariances, which are potentially impor-tant for understanding model robustness. In our mainanalysis, parameters were used as constants, not as themeans of distributions with specified standard devia-tions from which random parameter values could bedrawn. In the sensitivity analysis, however, we did inter-pret disease-free mortality parameters in this way butfound that the inclusion of substantial standard devia-tions did not greatly alter results. This observation is per-haps not so surprising. A PVA process is quite similar to acomplex series of Bernoulli trials, in which the mean num-ber of “successes” is equal to the number of trials (n), mul-tiplied by the probability of success at each trial ( p). If theconstant probability of success for each trial is replaced by



an independent random probability that has the same av-erage value p, it can be shown that the variance aroundthe expected number of successful trials is always greaterfor the fixed probability of success than that for randomprobabilities with the same average value. This revealsthe counter-intuitive result that ignoring variation in suc-cess probability in Bernoulli trials actually leads to anoverestimate of the variance in the number of successfultrials (Feller 1968). The extent to which this phenome-non might render PVA results based on invariant demo-graphic parameters conservative remains unexplored.

Our analysis has not highlighted any single parameterof obvious overriding importance, and although it identi-fied a number of interesting and curious potential pro-cesses, these should not distract from the fact that thebasic demography of these wolves is really understoodonly from a relatively short study of one population. Fu-ture studies must consider the basic demography ofmore populations over longer time spans. An equally im-portant objective for future research is to confirm therole of domestic dogs as the major rabies reservoir forwolves: current efforts to confirm this involve compar-ing viral RNA sequences obtained from sympatric carni-vores and studying the effects of vaccine intervention indomestic dogs.

Management Repercussions

We interpret our results to be informative more of rela-tive rather than absolute population persistence proba-bilities. In addition, these results represent only onecomponent of the management decision-making process(Reed et al. 1998) because other biological, social, eco-nomic, and political factors are important for determin-ing the conservation actions to be taken.

Nevertheless, our results have a number of implica-tions for the management of the seven fragmented andisolated populations of Ethiopian wolves. Although allbut two of these populations may consist of 50 animalsor fewer (with the two smallest consisting of only 15–25animals [Marino 2000]), it might appear that in the ab-sence of catastrophes or other degrading events, eventhese small populations may be relatively robust in theshort term. The model suggests, however, that any addi-tional mortality in these small populations could be ca-lamitous. Thus, conservation action aimed at safeguard-ing even the smallest habitat patches would appear tobe both worthwhile and urgently needed.

Disease appears to be a significant threat to thesesmaller populations and could be a critical factor in de-termining their persistence. In a preliminary VORTEX–based PVA of Ethiopian wolves, Mace and Sillero-Zubiri(1997) also found that in a small population (50 individu-als) persistence rapidly decreased when a rabies epidemicoccurred every 7 years, with or without CDV–relatedmortality. In Ginsberg and Woodroffe’s (1997) model of

African wild dogs, even severe catastrophes (3% chanceper year of 50% mortality) such as disease affected per-sistence only of populations of 20 individuals, not thoseof 50 or 100. However, this catastrophe probability isconsiderably lower than the observed disease frequencyin the wild ( Vucetich & Creel 1999), so the persistenceof slightly larger wild dog populations also may be af-fected by more realistic estimates of disease outbreaks.None of these studies include an Allee effect, which mayreduce the fecundity and consequent persistence ofpacks still further at very low densities (Courchamp etal. 2000).

Given the effect that disease appears to have onsmaller wolf populations, efforts to reduce disease in theputative reservoir dog populations may be particularlyrewarding for Ethiopian wolf conservation. Over 50years the relationship between wolf population persis-tence and disease reduction in dogs appears approxi-mately linear; thus, even if incomplete rabies control indogs were achieved, any reduction in disease incidenceshould have a beneficial effect on wolf persistence. Rabiesmust be almost completely eradicated, however, beforethese smaller populations are almost certain to persist,which might require vaccination of at least 70% of thedog population (Coleman & Dye 1996) in a band of upto 15 km around wolf habitat. This will be both costlyand difficult because many of these populations are inremote areas with difficult terrain and few access roads.

In contrast, the larger wolf populations (�100 ani-mals) appeared to be relatively persistent in the pres-ence of a significant level of disease in the sympatric dogpopulation, although disease was a limiting factor for allpopulations. Thus, efforts aimed at reducing disease levelsthrough dog vaccination may be better targeted at smallerpopulations. However any population that crashed tolow numbers in the model frequently failed to recover(e.g., only 20% of populations that dropped below 20 in-dividuals recovered to twice this figure). Thus, manage-ment to prevent further disease outbreaks might be ad-visable after population crashes. A domestic dogvaccination program in the Bale area in 1996 was in factinstigated under this rationale (Laurenson et al. 1998a),and the wolf population has recovered (EWCP, unpub-lished data).

The results of our model also suggest that canine dis-temper is of little importance in determining wolf popu-lation persistence. Similarly, in Mace and Sillero-Zubiri’s(1997) simpler preliminary PVA for Ethiopian wolves,extinction risk was not increased by CDV alone, al-though a slight increase was observed when rabies wasalso present. Similarly, CDV decreased the persistenceprobability of wild dog populations only when the an-nual probability of epidemics was higher than those nor-mally observed in dog populations, or in our model, andunlikely to occur in spillover species (Ginsberg & Wood-roffe 1997;Vucetich & Creel 1999). Overall, there ap-



pears to be little advantage in putting many resourcesinto controlling canine distemper either in domesticdogs or in wolves, particularly given the increased costof this vaccine over that for rabies. However, these mod-els are sensitive to the mortality rate ascribed to CDV;should that be higher than the 40% used, as it may be forAfrican wild dogs (perhaps 80%; Alexander et al. 1996),then the effects of CDV should be reassessed.

Finally, wolf vaccination appears to be an effectivemethod of improving wolf population persistence. Inthe largest populations (�100 km2), vaccination of only20% of wolves was sufficient to almost completely elimi-nate extinction of these populations, although in smallerpopulations wolf vaccination rates of 40% were requiredto substantially improve persistence. Although thesepercentages should not be taken as absolute, it appearsthat low levels of vaccination coverage in these com-partmentalized host populations could prevent the larg-est epidemics and thus the frequency that populationsbecome dangerously small. Vaccinated animals shouldalso provide an epidemiologically secure nucleus for pop-ulation recovery. Paradoxically, the resultant increase inaverage population size could actually lead to more fre-quent, smaller outbreaks. No such rabies vaccine prepara-tion is currently available for wolves, however, and con-siderable research and development must be carried outbefore a safe and effective oral rabies vaccine could be ad-ministered by a logistically feasible method. A cost-benefitanalysis comparing this approach with dog vaccinationwould inform future research requirements and planning.

Acknowledgments

We thank the Ethiopian Wildlife Conservation Organisa-tion and the Council of Oromiya for their support for theEthiopian Wolf Conservation Programme, the WellcomeTrust for financial support to both D.T.H. and M.K.L., andthe Born Free Foundation for supporting C.S.Z. and theEthiopian Wolf Conservation Programme. S. Cleaveland,J. Marino, S. Thirgood, S. Williams, and two anonymousreviewers gave us helpful comments on the manuscript.

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