Download Integrating Epidemiology into Population Viability Analysis

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. Population
viability analysis (PVA) can be a useful tool for directing conservation management when decisions must be
made and information is absent or incomplete. Incorporating epidemiological dynamics explicitly into a PVA
framework is technically challenging, but here we make a first attempt to integrate formal stochastic models
of 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 remarkably stable and persistent. When rabies virus was introduced, epidemics, assumed to arise from sporadic dog-to-wolf transmission, caused extinction probabilities over 50 years to rise linearly with the force of
infection from the dog reservoir and particularly steeply in smaller populations. Sensitivity analysis revealed
that although the overall pattern of results was not altered fundamentally by small to moderate changes in
disease-transmission rates or the way in which interpack disease transmission was modeled, results were sensitive to the process of female recruitment to male-only packs. Completely protecting wolf populations from rabies through vaccination is likely to be impractical, but the model suggested that direct vaccination of as few as
20–40% of wolves against rabies might be sufficient to eliminate the largest epidemics and therefore protect populations from the very low densities that make recovery unlikely. Additional simulations suggested that the affect of periodic epidemics of canine distemper virus on wolf population persistence was likely to be slight, even
when modeled together with rabies. From a management perspective, our results suggest that conservation action 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 Representan
la Rabia y el Moquillo Canino en el Lobo Etíope.
Resumen: Las enfermedades infecciosas constituyen una amenaza sustancial contra la viabilidad de las especies en peligro. El análisis de viabilidad poblacional (PVA) puede ser una herramienta útil para dirigir la
conservación para el manejo cuando las decisiones deben ser tomadas y la información es escasa o incompleta. La incorporación de dinámicas epidemiológicas explícitamente dentro de una marco PVA es técnicamente un reto; sin embargo, llevamos a cabo el primer intento para integrar modelos estocásticos formales
de la dinámica de la rabia y del moquillo canino para un PVA del lobo etíope (Canis simensis), un cánido
críticamente amenazado. En ausencia de la enfermedad, las poblaciones que habitan parches de hábitat de
todos los tamaños fueron llamativamente estables y persistentes. Cuando se introduce el virus de la rabia, las
epidemias, que supuestamente surgen de transmisiones esporádicas de perro a lobo, hicieron que las probabilidades de extinción sobre 50 años se incrementaran linealmente con la fuerza de la infección del perro reservorio 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]
Paper submitted December 21, 2000; revised manuscript accepted October 31, 2001.
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PVA and Disease in Ethiopian Wolves
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que a pesar de que el patrón general de los resultados no haya sido alterado fundamentalmente por cambios
pequeños o moderados en las tasas de transmisión de la enfermedad ni por la forma en que la transmisión
de la enfermedad al interior del grupo fue modelada, los resultados fueron sensibles al proceso de reclutamiento de hembras en grupos de machos. La protección total de las poblaciones de lobos mediante vacunación contra la rabia probablemente no es práctica, pero el modelo sugiere que la vacunación directa de
por lo menos un 20-40% de los lobos podría ser suficiente para eliminar las epidemias más grandes y por lo
tanto proteger poblaciones con densidades muy bajas que harían poco probable una recuperación. Posteriores simulaciones sugirieron que las repercusiones sobre epidemias de moquillo canino en la persistencia de
poblaciones 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.
Introduction
Assessing risks for endangered species is an integral part
of conservation management and an essential prerequisite for deciding if, when, and where action should be
taken and how limited resources should be targeted
(Harwood 2000). Unfortunately, these decisions must
usually be made in the absence of adequate information
on the nature and severity of threats to endangered populations. Under such circumstances, accurate risk assessment will not be possible, and the best that can be done
is to consider all sources of information, appropriately
weighted by their dependability.
The most common form of risk assessment in conservation biology is population viability analysis (PVA),
which examines and analyzes the interacting factors that
place a population or species at risk ( Boyce 1992; Burgman et al. 1993). The limitations of PVA are increasingly
appreciated, and criticisms span the entire scope of its
applications (Caughley & Gunn 1996; Mills et al. 1996;
Beissinger & Westphal 1998; Reed et al. 1998). The statistical nature of many processes, particularly environmental factors that affect population demography and
that are usually modeled as stochastic “noise,” are poorly
understood ( Vose 2000). In addition, many models are
too simplistic. For example, many generic PVA programs omit potentially important autoecological features
of subject populations, such as social structure, reproductive suppression, and spatial factors (Mills et al.
1996; Beissinger & Westphal 1998; Reed et al. 1998; but
see Vucetich et al. 1997; Vucetich & Creel 1999).
Population viability analysis programs also frequently
omit a variety of extrinsic factors. The effect of disease is
a striking example of such an omission, despite a growing 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 management obviously is desirable, but it is difficult to identify the risk factors for pathogen invasion, spread, and effect. Indeed there is a general lack of objective or
quantitative decision-making tools available to assess dis-
ease risk, establish guidelines for instigating disease
management, or evaluate management effects on population processes.
A few PVA models include disease simply as an additional mortality factor, such as VORTEX-based models
oriented to the Ethiopian wolf (Canis simensis) (Mace
& Sillero-Zubiri 1997) and African wild dog (Lycaon pictus) (Ginsberg & Woodroffe 1997). In a similar but more
sophisticated approach, Vucetich and Creel (1999) explored disease effects in an individual-based model of
wild dogs by including additional mortality in patterns
characteristic of certain types of infection. To date, no
conservation-oriented models explicitly incorporate disease transmission dynamically as an infectious process,
despite the fact that epidemic size and interepidemic intervals can be acutely sensitive to the demography and
immunological status of populations. Furthermore, because disease can periodically bring populations to very
low numbers, traditional deterministic epidemiological
models are poorly suited for analysis of imposed extinction risk. In recent years there have been many advances
in human and veterinary epidemiology where models,
theory, and data have been combined in a powerful way
to provide insight into the dynamics and control of infectious disease within populations (Anderson & May
1991; Diekmann & Heesterbeek 2000). Similar approaches are required to understand the sometimes complex threat posed by disease to endangered populations.
Disease may be a particular conservation problem for
endangered carnivores (Alexander & Appel 1994; Young
1994; Murray et al. 1999). It has been identified as the
most immediate threat to the critically endangered Ethiopian wolf (Laurenson et al. 1997), found now in only
seven fragmented and isolated populations in the afroalpine highlands of Ethiopia. Remaining populations
consist of 15–250 individuals and total about 500 adults
in all (Marino 2000). Each of these habitat islands is surrounded by agricultural land occupied by farmers and
their livestock. Associated domestic dogs either live in
wolf habitat or make incursions into it and are the most
likely reservoir for wolves of diseases such as canine dis-
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PVA and Disease in Ethiopian Wolves
temper virus (CDV ), parvovirus, and infectious hepatitis
(Laurenson et al. 1998a).
A rabies outbreak in the largest population in the Bale
Mountains in the early 1990s caused a two-thirds decline
in this population (Sillero-Zubiri et al. 1996a); only now,
10 years later, are pack numbers and sizes approaching
pre-epidemic levels. Although dog vaccination was instigated there in 1996, we now need to make decisions
about where and what disease management strategies, if
any, should be adopted for other wolf populations and
how they should be prioritized. To assist in this, a more
objective and quantitative assessment of disease risk to
wolf populations is urgently required.
Despite its shortcomings, PVA may still play a useful
role in management decision-making (Beissinger &
Westphal 1998; Reed et al. 1998; Brook et al. 2000; Harwood 2000). It is relatively cheap and forces both a rigorous consideration of processes and an evaluation of
the state of knowledge of an endangered population.
Furthermore, its limitations may be minimized by appropriate interpretation, and it is likely to prove useful in assessment of relative risks such as evaluating alternative
management strategies, assessing the vulnerability of different-sized populations, and designing reserves.
Our objective was, first, to combine an explicitly epidemiological component within a conventional PVA
framework. Second, although our approach may have
general use, we examined its application as a decisionmaking tool to a particular endangered species, the Ethiopian wolf. In particular, we examined the following
questions relevant to the current status of Ethiopian
wolves: (1) What biological processes incorporated into
the model are least understood? (2) What does the
model predict about the relative persistence times of disease-free populations inhabiting areas of different size?
(3) What is the effect on population structure, size, and
risk indicators of the invasion of canine pathogens into
populations inhabiting areas of different size? (4) What
effect do management strategies that reduce disease incidence and transmission probability have on the relative population persistence and risk indicators associated with populations inhabiting areas of different size?
(5) Are the predicted effects of canine pathogens, and
management strategies to reduce their effect, sensitive
to identified uncertainties in model input?
Methods
Ethiopian Wolf Biology and Social Structure
The Ethiopian wolf is a diurnal, 15-kg canid that lives in
close-knit territorial packs but forages predominantly
alone on afroalpine rodents (Sillero-Zubiri & Gottelli
1995a). In optimal habitat, packs are male-biased and
consist of an average of six adults, one to six yearlings,
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Haydon et al.
and one to seven pups, although in poorer habitats
wolves live in smaller groups or pairs (Sillero-Zubiri &
Gottelli 1995b). Generally, dominance hierarchies within
packs ensure that only dominant females breed (SilleroZubiri et al. 1996b). Matings in the Bale Mountains generally occur between August and November, with pups
born 2 months later (Sillero-Zubiri et al. 1998). All pack
members help feed pups. Dispersal is constrained by a
scarcity of unoccupied habitat: males stay with their natal pack, whereas two-thirds of females disperse at 2
years of age and become “floaters,” occupying narrow
ranges between pack territories until a breeding vacancy
becomes available (Sillero-Zubiri et al. 1996b). Pack fission is a relatively rare event (3 successful events from
10 attempts during 7 years of intensive study of 9–11
packs) and occurs only when packs become very large,
subordinate females breed, and wolf densities are below
carrying capacity (Sillero-Zubiri 1994; Ethiopian Wolf
Conservation Programme [EWCP], unpublished data).
Alternatively, a group of subordinate males joins with
subordinate females from another pack to form a new
pack. Thus, although large litter sizes permit quick packsize recovery, pack structure reduces population growth
rates (Vucetich et al. 1997).
The Model
Our model, written in Pascal (Delphi V ), is an individually based, age- and pack-structured, spatially explicit,
stochastic representation of wolf population dynamics
based on the wolf population in the Bale Mountains.
Where available, model parameters were taken from the
existing literature. Where population parameters were
known with less confidence, we adopted a number that
in our opinion was biologically plausible.
Each patch was capable of maintaining wolf populations at a specified carrying density, K, initially set to
1/km2, which approaches the maximum observed in optimal habitat (Gotelli & Sillero-Zubiri 1992) before a variety of mechanisms arise to regulate pack dynamics. Each
pack was assumed to occupy a circular home range of
radius 1.4 km. Individuals were assigned to one of six
demographic classes: three age classes (0–1 years, juveniles; 1–2 years, subadults; and adult, 2 years) in each
sex. Each pack had a maximum size of 13 individuals
(excluding juveniles), only 2 of which could be adult females. Packs in which at least one adult of each sex
were present gave birth to litters of pups with probability F, which under baseline conditions is 0.63 (SilleroZubiri et al. 1996b). One female would give birth to a varying number of pups in December, with probability estimated from field data at 0.05, 0.11, 0.21, 0.16, 0.16, and
0.32 for one to six pups, respectively (Sillero-Zubiri et
al., unpublished data). Age classes were updated prior to
breeding. Between this updating and breeding a pack
could undergo one of four events, depending on pack
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PVA and Disease in Ethiopian Wolves
and population size, that we judged to be likely mechanisms underlying the regulation of pack numbers. All
these events have been observed in the wild (Sillero-Zubiri
et al. 1996a, 1996b). (1) If more than two adult females
were present in the pack, randomly selected “surplus”
adult females were removed to a nonbreeding “pool” population of floaters (assumed to exist at uniform density over
the habitat patch). (2) If the pack had more than 13 individuals and the total population was 75% of specified carrying density K, then randomly selected adult males were removed to the pool population until pack size was reduced
to 13 individuals. (3) If the pack had more than 13 individuals and the total population was 75% of K, then the pack
split and up to six randomly selected adult males were
transferred to a new and randomly located pack. (4) If the
pack lacked a single adult female but one was present in
the pool, then a female was recruited.
The entire wolf population was subjected to a continuous-time, demographically stochastic, age- and sex-specific mortality process, determined from field data, such
that adults and subadults had a probability of 0.15 of dying each year, with the equivalent probabilities for male
and female juveniles being 0.45 and 0.55, respectively
(Sillero-Zubiri 1994, EWCP, unpublished data). These
mortality rates included all agents of mortality except
disease. Mortality rates in the pool population were assumed to be D times higher than pack mortality rates.
Details of how demographically stochastic models can
be run with fixed parameters in continuous time are
available in many texts (e.g., Renshaw 1991).
Each individual wolf in the population was also subject
to a continuous-time, demographically stochastic susceptible-infectious-recovered (S-I-R) process. The summed
force of infection (Anderson & May 1991) calculated over
all infectious wolves and a randomly varying force of infection assumed to arise from the domestic dog reservoir
combine to determine the rate at which individuals become infectious. This rate is used to compute random
waiting times governing the stochastic transfer of individual animals from susceptible to infectious categories:
S i , x( t ) → S i , x( t ) – 1 = I i , x( t ) → I i , x( t ) + 1
 n
i 
=  ∑ β ij I j t + β ir Ir t ,
 j0

where Si ,x and Ii,x represent the numbers of susceptible
and infectious individuals in the xth demographic class of
the ith pack; n is the number of packs (the pool is referred to as the 0th pack); ij is the transmission coefficient between the ith and jth pack (see Table 1); Ij is the
number of infectious individuals in the jth pack; and ir is
i
the transmission coefficient between the I r infected individuals in the reservoir population in the ith pack’s home
range at time t and individuals of the ith pack. The interpack transmission coefficients are products of an underlying infectiousness parameter, ii and the proportion of the
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area of the ith pack’s circular home range that overlaps
with the jth pack’s home range, ij , calculated according to
the spatial locations of the home ranges (parameters are
given in Table 1).
The S-I-R process was run independently for rabies
and CDV, resulting in nine possible disease classes (SS,
SI, SR, IS, II, IR, RS, RI, RR ), making 54 different classes
in all for each pack: 2 sexes 3 age-classes 9 disease
states. Infection may result in recovery (with rate ) or
death (with rate ; Table 1). All packs were examined at
the end of each month; those containing two or fewer
individuals were broken up and individuals were transferred to the pool.
Disease incidence in the reservoir population was
modeled purely phenomenologically. Rabies incidence
was assumed to be spatially and temporally uniform on
average and was determined independently in each
wolf-pack home range on a weekly basis. Thus, with rabies incidence (denoted by i (rabies) ) equal to 0.025 per
home range per month, on average rabies could potentially be introduced to wolf packs independently every 4
months in a patch occupied by 10 packs. The observed
frequency of outbreaks arising will normally be lower,
however, because it is, of course, determined by the
transmission coefficients linking the wolf population to the
reservoir. Canine distemper virus was modeled as spatially
uniform but epidemic in nature. Each epidemic occurred
in three consecutive randomly chosen months, separated
by an interval that was either 3, 4, 5, or 6 years ( Table 1).
Collectively, we referred to this combination of demographic and epidemiological parameters as “baseline,” because we considered it to approximate the scenario in an
unmanaged wolf population in the Bale Mountains.
We performed simulations on 10 different-sized areas
of 25–250 km2 encompassing the range of sizes of remaining wolf populations ( Marino 2000). We also examined viability at eight different levels of dog reservoir disease incidence (0–140% of baseline incidence) and the
effect of directly vaccinating varying proportions of
wolves against both rabies and CDV or rabies alone.
Higher incidences of disease were considered unrealistic because the estimated incidence of dog rabies in our
study area (1.2–5.6% of dogs per year; Laurenson et al.
1998b) is among the highest in Africa (e.g., Cleaveland
et al. 1999; Kitala et al., 2000). For each scenario we performed 1000 simulations of 50 years, conditional on
populations remaining extant. Simulations were started
at a population density K, with age and pack structures
representative of baseline output.
Results
Disease-Free Populations
In the absence of disease, the model predicted that a population occupying a 250-km2 range of continuous habitat
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Haydon et al.
Table 1. Epidemiological parameter values used in the model of Ethiopian wolf populations.*
Parameter
Rabies
Canine distemper
virus (CDV)
Mean infection incidence in reservoir per home range per month—
k(disease)
Probability of CDV epidemic interval of j years ( j 3..6)
CDV epidemic duration (months)
Mean CDV interepidemic period (years)
00 (pool wolf to pool wolf)
0i (pack wolf to pool wolf)
0r (reservoir dog to pool wolf)
ir (reservoir dog to pack wolf)
ii (intrawolf pack)
ij (interwolf pack)
(per day)
(per day)
0.025
—
—
—
0.0006
1 00
6 00
4 00
0.1875
ij ii
0.2
0
4 (when present)
[0.1,0.2,0.4,0.3]
3
5.1
0.00018
1 00
1.5 00
1 00
0.1
ii ii
0.08
0.12
* Transmission rates ( ) are per infected individual wolf per susceptible individual per day. From field knowledge of likely contact probabilities, we considered intra–wolf pack-transmission most likely, followed by inter–wolf-pack transmission, whereas the likelihood of transmission
between a pool wolf and either another pool wolf or a pack wolf was much lower and similar. However, contacts between reservoir dogs and either pack or pool wolves may be slightly higher than pool wolves with either pack or pool wolves because interactions between dogs and wolves
are seen more often than between pool wolves and pack wolves (M.K.L., personal observations; Ethiopian Wolf Conservation Programme, unpublished data). Within-pack transmission rates were selected that resulted in approximately 90% of pack members contracting rabies (wild
dogs, Kat et al. 1995; Hofmeyr et al. 2000; Ethiopian wolves, Sillero-Zubiri et al. 1996a) and approximately 80% contracting canine distemper
virus (domestic dogs, Gorham 1966; Alexander & Appel 1994). Thus, although it is impossible to accurately quantify transmission rates, we anticipate 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 et
al. 1996; Cleaveland 1996), although the relative probability of interepidemic intervals were arbitrarily assigned. Those for rabies are from
Laurenson et al. 1997.
and conforming to our baseline set of demographic parameters should exhibit a high degree of population stability (Figs. 1 & 2d). No extinctions were observed in
1000 simulations each of 50-years duration or when simulations were extended to 200 years. The coefficient of
variation (CV) of population fluctuation was about 10%.
The populations were likely to be found slightly above
our defined carrying density (K ) (95% confidence interval[CI] 0.94–1.4K), 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 crashes
larger than 33% of population size), and pack extinction
probabilities were about 0.5% per year (95% CI 0.2–1.1).
Disease-free populations modeled in smaller patches
of habitat were similarly stable: no extinctions were observed in 1000 50-year simulation runs in 50-km 2
patches. The extinction rate increased to only 2% when
simulations were extended to 200 years. Even the smallest populations in 25-km2 patches suffered only a 2% extinction risk over 50 years, although this rose to 50%
over 200 years. In these smallest populations the CV of
population fluctuation increased to 22% ( Fig. 2d).
16% over 100 years and to 25% over 200 years. The populations were on average at about 40% of capacity after 50
years (95% CI 0.04–0.97K), divided into an average of
nine packs (95% CI 1–23) with an average pool size of
three (95% CI 0.5–5). Over 50 years, populations usually
experienced one or two crashes of at least 33%, with
half the populations experiencing a crash of more than
66%. Pack extinction probabilities were about 8% per
year (95% CI 2–32). Analysis of populations revealed
that if they dropped below 20 individuals, they had only
a 20% chance of recovering to twice that size. Rabies
deaths averaged seven per year, but with high variation
between years (95% CI 1.5–27.5).
Until habitat size dropped below 100 km2, modeled
populations exposed to baseline disease processes in
smaller areas appeared to be comparably viable (extinction probability over 50 years was 8–14%). For patch
sizes of 75 km2, extinction probability was 17% over 50
years but was 28% for 50-km2 patches and 46% for 25km2 patches (Fig. 2a). The average number of packs surviving this period decreased by progressively greater
amounts from just over nine for 250-km2 habitat patches
to just under three for 25-km2 patches ( Fig. 2b).
Baseline Disease Effect
When exposed to our baseline disease processes, the picture was different ( Fig. 1). For a population occupying
250 km2 of habitat, extinction probabilities evaluated
over a 50-year period were estimated to be 8–9%, rising to
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Responses to Variation of Disease Incidence
in the Reservoir Population
As disease incidence in the reservoir population decreased from 140% to 20% of baseline levels, 50-year ex-
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PVA and Disease in Ethiopian Wolves
1377
exceed 80%. High levels of disease reduced population
density in large habitat areas by as much as 60% of K,
but populations occupying smaller patches either persisted close to K or proceeded rapidly to extinction. The
frequency of population crashes of 33% did not vary
greatly between different-sized habitat patches and varied from about once every 50–60 years at 20% of baseline incidence to once every 25 years at the 140% incidence. Large population crashes (66%) occurred with
a probability of 65% and 26% in the largest and smallest
populations, respectively, over 50 years, about half as frequently as “one-third” crashes. The marked increase in extinction rates at higher disease incidences and in smaller
patches is reflected in the standard deviation of logged
population abundances ( Fig. 2d), which indicates substantially greater relative fluctuations in small populations and
those in which disease incidence is highest.
Effects of CDV or Rabies Alone
When rabies was excluded from simulations, CDV had
little effect on the persistence of any population and
pack numbers were only slightly reduced (Fig. 3a).
When CDV was excluded and only rabies was present,
however, extinction probabilities were greater than
those when both diseases were present (e.g., 250 km2,
13% vs. 9%; 50 km2, 39% vs. 28%) ( Fig. 3a). We suspect
that CDV acts as a mild population thinning agent in our
model, preventing the most damaging rabies outbreaks
and thereby actually enhancing population persistence.
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-jiggle 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 corresponding to 100% is indicated in Table 1, and reservoir disease incidence increases from 0 to 140% of this
level along the x-axis.
tinction probabilities in populations occupying a 250km2 habitat patch declined from 13% to 4% (Fig. 2a), the
average number of surviving packs increased from 8 to
18 (Fig. 2b), and annual pack extinction probabilities declined from 10% to 3% ( Fig. 2c). Rabies incidence in the
wolf population halved from an average of nine cases
per year to under four, but average CDV incidence decreased only slightly, from four to three.
Persistence of populations modeled in smaller patches
(100 km2) was particularly sensitive to variation in disease incidence (Fig. 2a), and only when disease incidence was 40% of baseline did persistence probability
Response to Direct Vaccination of Wolves
With vaccination of 20% of wolves in a population occupying a 250-km2 habitat patch exposed to baseline disease processes against both rabies and CDV, 50-year persistence probabilities rose from approximately 90% to
100%. In populations in 75-km2 patches, vaccination of
30% of wolves increased persistence probabilities from
83% to 100%, whereas in the smallest populations vaccinating 40% increased persistence probabilities from 54%
to 90% (Fig. 4a). The size of populations persisting in
smaller patches was again largely unaffected by vaccination, but in medium-sized and large patches, population
sizes increased rapidly with vaccination effort, much of
the potential increases realized by 40% coverage (results
not shown). The dramatic effect of 40% coverage was
also revealed by inspection of the annual pack-extinction probabilities, which fell to 2% in all habitat sizes.
Vaccinating populations occupying patches of 50 km2
or more against rabies alone provided an improvement
in persistence probabilities equivalent to that obtained
by vaccinating against both diseases together (results
not shown). In habitat patches of 50 km2 and less, however, CDV epidemics contributed a small but detectable
additional extinction risk over 50 years when rabies vac-
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Haydon et al.
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 simulations 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.
cination coverage was high (70%). Our simulations
suggest that our baseline CDV process added approximately 0.5% to the probability of extinction in 50-km2
habitat patches and approximately 5% in 25-km2 habitat
patches. When coverage was lower and rabies outbreaks
occurred, CDV presence again appeared to enhance persistence, presumably due to the population-thinning
process described previously.
Sensitivity of Simulation Results
The results of various parameter perturbations on simulation results for a 250-km2 habitat range under a range
of disease pressures are summarized in Appendix 1. No
perturbation reduced 50-year persistence probability below 70%, with only substantial perturbations (30% or
more) pushing 50-year persistence probability below
80%. When mortality parameters were treated as annually varying random variates (assumed to be uniformly
distributed from zero to twice the fixed parameter value,
thus ensuring a coefficient of variation in the realized parameters of approximately 40%), the probability of persisting over a 50-year period was reduced by 3–4% (Fig.
3a). Populations were particularly sensitive to the ab-
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Volume 16, No. 5, October 2002
sence of female recruitment to packs. When females
could not be recruited, pack-extinction rates rose from
8% to 12% per year under baseline disease conditions,
and the proportion of packs that failed to breed (because they contained individuals of only one sex) increased from 2% to 15%. Although the process of female recruitment from a pool population was essential
to population viability, persistence increased when pool
mortality rose (Fig. 3a). Although small pool populations
were essential, large ones appeared to constitute an
additional source of disease acquisition. Similar conclusions were drawn from a more limited sensitivity analysis applied to populations modeled in 50-km2 habitat
patches (Fig. 3b).
Our results were not overly sensitive to increases in interpack disease-transmission coefficients. If all non-zero
ij were set equal to ii, baseline 50-year extinction rates
increased by only 3% (because at baseline disease incidence, pack density is sufficiently low that range overlaps are uncommon). If interpack disease-transmission
coefficients were set to zero, then baseline 50-year extinction rates became zero.
Our results suggest that in large patches over 50-year
time periods pack numbers will decrease linearly in re-
Haydon et al.
Figure 3. (a) Results of parameter perturbations on
the proportion of 1000 simulations in which wolf populations modeled in 250-km2 habitat patches remained extant after 50 years. Attention is restricted to
the changes in pool mortality rate, inclusion of standard deviations on mortality rates, exclusion of female recruitment from the pool, and the effects of rabies and canine distemper virus (CDV) alone. (b)
Same analysis for 50-km2 habitat patches.
sponse to increases in mortality of up to 50% over baseline but that these decreases in population size do not
begin to affect observed persistence times until overall
mortality increases by 20% or more over baseline. In the
smallest populations (those occupying 25-km2 habitat
patches), any increase in mortality, and thus decrease in
population size, affected persistence probability ( Fig. 4b).
Discussion
In contrast to previous PVA models that incorporated
disease as an additional mortality factor (Ginsberg &
PVA and Disease in Ethiopian Wolves
1379
Figure 4. (a) Effect of vaccination on 50-year persistence 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 compartment of the underlying susceptible-infectious-recovered 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 mortality rates. Baseline epidemiological conditions applied.
Woodroffe 1997; Mace & Sillero-Zubiri 1997; Vucetich &
Creel 1999), our individual-based, stochastic, spatial population model for Ethiopian wolves explicitly incorporated disease transmission as a dynamic process. Our results suggest that, in the absence of disease, wolf
demography is impressively stable—even in populations
comprised of 25–50 individuals. The introduction of rabies and canine distemper caused substantial population
fluctuations and extinction risks, particularly when populations comprised 100 individuals. Over 50 years, ex-
Conservation Biology
Volume 16, No. 5, October 2002
1380
PVA and Disease in Ethiopian Wolves
tinction risk in wolf populations of all sizes rose linearly
with the force of rabies infection within the reservoir
population, but these risks could be reduced dramatically by directly vaccinating as few as 20–40% of wolves,
which stopped the largest epidemics. Canine distemper
alone had negligible effect on population persistence,
and the overall pattern of results appeared robust to
moderate parameter perturbations.
Generally, we used a 50-year time frame because we
consider it unlikely that parameters and processes assumed by our model would remain stationary even over
this period, let alone over 100 or 200 years. However,
the choice of this 50-year time horizon affected our results for smaller populations, because extinction rates
rose significantly for these populations over 100- and 200year time periods. Thus, although estimates of the increased extinction risk over longer periods will be inaccurate, it is probable that this relative increase in risk is considerable.
Parameter Estimation and Sensitivity Analysis
In an attempt to identify limitations of this model, we
subjected the most uncertain parameters and processes
to a sensitivity analysis to determine which have the
greatest effect on population persistence (Reed et al.
1998). Research can then be focused to provide more
accurate data for estimation of these parameters. Values
for parameters relating to nondisease sources of wolf
mortality, the probability of packs breeding, and average
litter sizes were chosen from available data. These data
are few, however, and representative of demographics
exhibited by only one stable and high-density population over only 4 years (or sometimes 7 years). Ongoing
studies of this and other populations will improve the
accuracy and knowledge of variation in these parameters and will determine whether density-dependent effects occur.
Our model, like other individual-based models of
other pack-living canids with reproductive suppression
(Gray wolves, Vucetich et al. 1997; Haight et al. 1997;
African wild dogs, Vucetich & Creel 1999), was sensitive
to demographic events such as pack fission, fusion, and
immigration frequency. We had to adopt relatively arbitrary rules for female recruitment, pack fission, and
shedding events, but these were based on data that
show that such events have occurred in the wild (for example, we know of three successful pack fissions in 7
years of study; Sillero-Zubiri et al. 1996b; EWCP, unpublished data), although the mechanism underlying these
events remains a source of considerable uncertainty.
Nevertheless, much more information on these phenomena is required for Ethiopian wolves and other species,
in particular, we need to determine how these phenomena vary with population size and density.
Conservation Biology
Volume 16, No. 5, October 2002
Haydon et al.
In contrast, the model was relatively insensitive to variation in pool wolf mortality, which is unknown, and to the
effects of varying interpack disease transmission. Thus,
our results may be viewed as applying to populations in
larger habitat patches with lower carrying capacity or in
smaller patches with higher carrying capacity.
Epidemiological parameters were also estimated with
considerable uncertainty. We estimated rabies incidence
in dogs through questionnaires, because official reports of
case incidence substantially underrepresent the true scale
of disease ( Laurenson et al. 1998b; Kitala et al. 2000). Preliminary data obtained from wolf ranges across Ethiopia
suggest that the current incidence of these diseases in
dogs falls within the range examined in our analysis; so
we considered an increase in disease incidence of more
than 140% of baseline to be unrealistic. We were primarily interested, however, in the response of population viability to changing disease incidence, so the absolute accuracy of incidence estimates is of limited importance.
Available field data suggest that when rabies infections
occur within packs, about 90% of pack members go on
to acquire the infection (Table 1). Our estimate of approximately 80% of pack members acquiring CDV infection is based on information from dogs, for which contact rates may be lower than those between closely knit
pack wolves and may be too low. Our selected values
for ii were based on the estimated pack sizes and durations of infectiousness of the two infections. Values of
00, 0r, 0i, and ir are unknown, however, and are chosen here only to generate plausible results, although we
expect that their relative magnitudes may be correct
( Table 1). Additional behavioral studies are required to
improve estimated contact rates between individuals
from pack, pool, and reservoir populations, although the
general trends revealed by our study are not overly sensitive to increases in these coefficients.
Generally, estimates of demographic and epidemiological parameters from field data are likely to reflect both
measurement error and genuine environmental variability, and these sources of uncertainty will be difficult to
decipher (Taylor 1995). There are few good estimates of
parameter variances within this system and no estimates
of parameter covariances, which are potentially important for understanding model robustness. In our main
analysis, parameters were used as constants, not as the
means of distributions with specified standard deviations from which random parameter values could be
drawn. In the sensitivity analysis, however, we did interpret disease-free mortality parameters in this way but
found that the inclusion of substantial standard deviations did not greatly alter results. This observation is perhaps not so surprising. A PVA process is quite similar to a
complex series of Bernoulli trials, in which the mean number of “successes” is equal to the number of trials (n), multiplied by the probability of success at each trial ( p). If the
constant probability of success for each trial is replaced by
Haydon et al.
an independent random probability that has the same average value p, it can be shown that the variance around
the expected number of successful trials is always greater
for the fixed probability of success than that for random
probabilities with the same average value. This reveals
the counter-intuitive result that ignoring variation in success probability in Bernoulli trials actually leads to an
overestimate of the variance in the number of successful
trials (Feller 1968). The extent to which this phenomenon might render PVA results based on invariant demographic parameters conservative remains unexplored.
Our analysis has not highlighted any single parameter
of obvious overriding importance, and although it identified a number of interesting and curious potential processes, these should not distract from the fact that the
basic demography of these wolves is really understood
only from a relatively short study of one population. Future studies must consider the basic demography of
more populations over longer time spans. An equally important objective for future research is to confirm the
role of domestic dogs as the major rabies reservoir for
wolves: current efforts to confirm this involve comparing viral RNA sequences obtained from sympatric carnivores and studying the effects of vaccine intervention in
domestic dogs.
Management Repercussions
We interpret our results to be informative more of relative rather than absolute population persistence probabilities. In addition, these results represent only one
component of the management decision-making process
(Reed et al. 1998) because other biological, social, economic, and political factors are important for determining the conservation actions to be taken.
Nevertheless, our results have a number of implications for the management of the seven fragmented and
isolated populations of Ethiopian wolves. Although all
but two of these populations may consist of 50 animals
or fewer (with the two smallest consisting of only 15–25
animals [ Marino 2000] ), it might appear that in the absence of catastrophes or other degrading events, even
these small populations may be relatively robust in the
short term. The model suggests, however, that any additional mortality in these small populations could be calamitous. Thus, conservation action aimed at safeguarding even the smallest habitat patches would appear to
be both worthwhile and urgently needed.
Disease appears to be a significant threat to these
smaller populations and could be a critical factor in determining their persistence. In a preliminary VORTEX–
based PVA of Ethiopian wolves, Mace and Sillero-Zubiri
(1997) also found that in a small population (50 individuals) persistence rapidly decreased when a rabies epidemic
occurred every 7 years, with or without CDV–related
mortality. In Ginsberg and Woodroffe’s (1997) model of
PVA and Disease in Ethiopian Wolves
1381
African wild dogs, even severe catastrophes (3% chance
per year of 50% mortality) such as disease affected persistence only of populations of 20 individuals, not those
of 50 or 100. However, this catastrophe probability is
considerably lower than the observed disease frequency
in the wild ( Vucetich & Creel 1999), so the persistence
of slightly larger wild dog populations also may be affected by more realistic estimates of disease outbreaks.
None of these studies include an Allee effect, which may
reduce the fecundity and consequent persistence of
packs still further at very low densities (Courchamp et
al. 2000).
Given the effect that disease appears to have on
smaller wolf populations, efforts to reduce disease in the
putative reservoir dog populations may be particularly
rewarding for Ethiopian wolf conservation. Over 50
years the relationship between wolf population persistence and disease reduction in dogs appears approximately linear; thus, even if incomplete rabies control in
dogs were achieved, any reduction in disease incidence
should have a beneficial effect on wolf persistence. Rabies
must be almost completely eradicated, however, before
these smaller populations are almost certain to persist,
which might require vaccination of at least 70% of the
dog population (Coleman & Dye 1996) in a band of up
to 15 km around wolf habitat. This will be both costly
and difficult because many of these populations are in
remote areas with difficult terrain and few access roads.
In contrast, the larger wolf populations (100 animals) appeared to be relatively persistent in the presence of a significant level of disease in the sympatric dog
population, although disease was a limiting factor for all
populations. Thus, efforts aimed at reducing disease levels
through dog vaccination may be better targeted at smaller
populations. However any population that crashed to
low numbers in the model frequently failed to recover
(e.g., only 20% of populations that dropped below 20 individuals recovered to twice this figure). Thus, management to prevent further disease outbreaks might be advisable after population crashes. A domestic dog
vaccination program in the Bale area in 1996 was in fact
instigated under this rationale (Laurenson et al. 1998a),
and the wolf population has recovered (EWCP, unpublished data).
The results of our model also suggest that canine distemper is of little importance in determining wolf population persistence. Similarly, in Mace and Sillero-Zubiri’s
(1997) simpler preliminary PVA for Ethiopian wolves,
extinction risk was not increased by CDV alone, although a slight increase was observed when rabies was
also present. Similarly, CDV decreased the persistence
probability of wild dog populations only when the annual probability of epidemics was higher than those normally observed in dog populations, or in our model, and
unlikely to occur in spillover species (Ginsberg & Woodroffe 1997;Vucetich & Creel 1999). Overall, there ap-
Conservation Biology
Volume 16, No. 5, October 2002
1382
PVA and Disease in Ethiopian Wolves
pears to be little advantage in putting many resources
into controlling canine distemper either in domestic
dogs or in wolves, particularly given the increased cost
of this vaccine over that for rabies. However, these models are sensitive to the mortality rate ascribed to CDV;
should that be higher than the 40% used, as it may be for
African wild dogs (perhaps 80%; Alexander et al. 1996),
then the effects of CDV should be reassessed.
Finally, wolf vaccination appears to be an effective
method of improving wolf population persistence. In
the largest populations (100 km2), vaccination of only
20% of wolves was sufficient to almost completely eliminate extinction of these populations, although in smaller
populations wolf vaccination rates of 40% were required
to substantially improve persistence. Although these
percentages should not be taken as absolute, it appears
that low levels of vaccination coverage in these compartmentalized host populations could prevent the largest epidemics and thus the frequency that populations
become dangerously small. Vaccinated animals should
also provide an epidemiologically secure nucleus for population recovery. Paradoxically, the resultant increase in
average population size could actually lead to more frequent, smaller outbreaks. No such rabies vaccine preparation is currently available for wolves, however, and considerable research and development must be carried out
before a safe and effective oral rabies vaccine could be administered by a logistically feasible method. A cost-benefit
analysis comparing this approach with dog vaccination
would inform future research requirements and planning.
Acknowledgments
We thank the Ethiopian Wildlife Conservation Organisation and the Council of Oromiya for their support for the
Ethiopian Wolf Conservation Programme, the Wellcome
Trust for financial support to both D.T.H. and M.K.L., and
the Born Free Foundation for supporting C.S.Z. and the
Ethiopian Wolf Conservation Programme. S. Cleaveland,
J. Marino, S. Thirgood, S. Williams, and two anonymous
reviewers gave us helpful comments on the manuscript.
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Conservation Biology
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Conservation Biology
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Baseline
ij ii if ij 0
ij 0
Pool mortality 32 (D 32)
Pool mortality 16 (D 16)
Pool mortality 4 (D 4)
No. female recruitment
100-year time horizon
With SDs where available
Rabies alone
Canine distemper virus alone
All mortality parameters down 10%
All mortality parameters down 20%
All mortality parameters down 30%
With SD on juv 0–1 mortality
With SD on juv 1–2 mortality
Juv 0–1 mortality doubled
K at 0.75 km2
K at 0.5 km2
K at 0.25 km2
All up 20%
All up 40%
All down 20%
Perturbationa
113.02
109.27
222.87
128.69
121.39
105.44
86.23
98.29
117.30
117.11
223.24
125.37
134.12
143.84
118.18
115.97
82.39
111.57
108.78
100.71
101.66
98.34
132.23
Average
population
size
0.91
0.88
1.00
0.95
0.92
0.84
0.78
0.84
0.88
0.87
1.00
0.89
0.89
0.84
0.92
0.90
0.82
0.90
0.88
0.88
0.84
0.78
0.96
2.44
2.41
4.79
0.31
0.86
5.61
2.49
2.15
3.30
2.50
4.94
3.24
4.13
5.41
2.64
2.59
1.68
2.44
2.43
2.27
2.24
2.14
2.88
9.23
9.27
22.13
11.00
10.19
8.22
3.59
9.62
9.90
9.63
22.94
11.06
12.94
14.12
10.27
10.00
4.18
9.06
7.74
5.77
7.67
6.23
11.98
No.
packs
b
Average after
P
(persispool
50
tence)
size
years
0.34
0.47
0.53
0.31
0.21
0.00
0.20
0.22
0.19
0.19
0.20
0.23
0.26
0.16
0.17
0.00
0.34
0.23
0.18
0.19
0.21
0.01
0.01
0.00
0.01
0.01
0.01
0.16
0.01
0.01
0.01
0.00
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.01
Pb
(recovery/
Nonpopulation breeding:
size
breeding
20)
packs
Table Results of sensitivity analysis of the baseline population viability analysis of Ethiopian wolves.
Appendix
0.18
0.18
0.16
0.23
0.20
0.15
0.13
0.20
0.22
0.18
0.12
0.24
0.32
0.38
0.22
0.22
0.02
0.14
0.09
0.03
0.16
0.12
0.22
Average
no.
fission
events
per
annum
0.33
0.37
0.24
0.41
0.41
0.35
0.54
0.34
0.39
0.35
0.32
0.40
0.35
0.42
0.36
0.34
0.47
0.33
0.37
0.30
0.43
0.74
0.31
Average
no. pack
breakups
per
annum
0.08
0.10
0.02
0.06
0.07
0.11
0.12
0.08
0.10
0.09
0.01
0.09
0.09
0.10
0.08
0.08
0.10
0.09
0.09
0.09
0.12
0.14
0.06
Pb
(pack
extinction)
per
annum
7.15
8.66
2.03
5.17
6.74
8.79
7.38
7.93
9.33
10.10
0.00
10.59
12.07
14.83
7.51
8.03
5.76
7.55
8.48
6.86
11.69
14.44
5.58
4.78
4.79
2.62
5.44
5.00
4.33
3.07
3.29
4.76
0.00
10.75
5.28
5.71
6.28
4.96
4.89
2.83
4.65
4.58
4.34
4.46
3.91
4.85
Canine
No.
distemper
rabies
virus
cases
cases
per
per
annum annum
1.77
1.74
0.08
1.52
1.68
1.90
2.01
2.47
1.90
1.79
0.08
1.76
1.85
2.01
1.74
1.80
1.66
1.68
1.63
1.73
1.94
2.08
1.40
No.
33%
crashes
in
50
years
continued
0.65
0.72
0.00
0.43
0.55
0.83
0.59
0.76
0.75
0.83
0.00
0.82
0.97
1.12
0.66
0.72
0.42
0.65
0.63
0.64
0.80
0.90
0.49
No.
66%
crashes
in
50
years
1384
PVA and Disease in Ethiopian Wolves
Haydon et al.
b
a
0.99
0.91
0.90
0.89
0.88
0.98
0.70
0.91
0.91
0.94
0.83
0.87
0.88
0.90
0.89
0.89
0.90
0.89
0.89
0.89
0.88
0.86
0.83
0.72
0.64
110.04
102.64
95.22
85.52
76.45
66.11
53.01
40.84
25.54
2.45
2.30
2.19
1.99
1.81
1.60
1.36
1.20
0.91
3.46
2.52
2.55
2.43
2.46
2.85
2.72
2.43
2.40
3.17
1.93
2.16
2.82
2.47
2.50
2.58
9.01
8.67
8.08
7.25
6.50
5.92
4.59
3.57
2.17
15.03
9.47
9.76
9.27
9.18
11.91
6.62
9.12
9.06
12.98
6.53
6.88
11.74
9.20
9.63
9.62
No.
packs
b
Average after
P
(persispool
50
tence)
size
years
158.68
114.87
115.84
111.40
111.71
130.16
127.71
111.48
110.51
145.10
87.22
96.86
126.74
112.34
113.12
119.09
Average
population
size
Parameters as defined in the text and Table 1.
Indicates probability of bracketed event.
All down 40%
ii down 20%
ii down 40%
ii up 20%
ii up 40%
oi halved
oi doubled
or halved
or doubled
ir halved
ir doubled
Prob. breeding (F ) down 20%
Prob. breeding (F ) up 20%
Canine distemper virus s up 20%
Canine distemper virus s up 40%
Canine distemper virus s down 20%
Habitat patch
225 km2
200 km2
175 km2
150 km2
125 km2
100 km2
75 km2
50 km2
25 km2
Perturbation
a
Appendix (continued)
0.18
0.21
0.17
0.21
0.15
0.15
0.11
0.10
0.03
0.26
0.17
0.19
0.19
0.20
0.26
0.19
0.21
0.22
0.24
0.18
0.05
0.41
0.19
0.18
0.18
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
Pb
(recovery/
Nonpopulation breeding:
size
breeding
20)
packs
0.17
0.16
0.14
0.11
0.10
0.07
0.05
0.02
0.00
0.22
0.19
0.18
0.18
0.18
0.25
0.10
0.19
0.18
0.19
0.15
0.12
0.26
0.18
0.19
0.19
Average
no.
fission
events
per
annum
0.38
0.29
0.29
0.23
0.18
0.15
0.13
0.11
0.06
0.30
0.36
0.42
0.36
0.38
0.31
0.96
0.34
0.36
0.35
0.47
0.41
0.36
0.40
0.37
0.37
Average
no. pack
breakups
per
annum
0.09
0.07
0.07
0.07
0.06
0.05
0.05
0.05
0.04
0.04
0.08
0.09
0.10
0.09
0.06
0.12
0.08
0.09
0.06
0.13
0.09
0.09
0.10
0.09
0.08
Pb
(pack
extinction)
per
annum
8.10
5.63
5.35
4.19
3.07
2.18
1.99
2.08
0.89
4.12
7.20
7.40
8.95
8.65
4.92
17.17
7.00
7.89
5.80
12.63
5.55
11.33
9.20
8.11
7.84
4.75
4.64
4.23
4.07
3.69
3.09
2.53
1.79
0.85
4.75
4.83
4.73
4.63
4.61
5.73
4.56
4.71
4.45
6.40
2.96
3.35
5.64
5.35
5.93
4.19
Canine
No.
distemper
rabies
virus
cases
cases
per
per
annum annum
1.73
1.66
1.63
1.75
1.74
1.52
1.59
1.49
1.56
1.08
1.73
1.69
1.79
1.80
1.45
1.80
1.77
1.78
1.25
2.21
1.70
1.83
1.75
1.77
1.72
No.
33%
crashes
in
50
years
0.62
0.58
0.54
0.52
0.46
0.38
0.39
0.34
0.26
0.33
0.66
0.68
0.66
0.70
0.39
0.90
0.66
0.70
0.51
0.82
0.53
0.86
0.66
0.62
0.66
No.
66%
crashes
in
50
years
Haydon et al.
PVA and Disease in Ethiopian Wolves
1385
Conservation Biology
Volume 16, No. 5, October 2002