Predicting Effects of Predation on Conservation of
Endangered Prey
A. R. E. SINCLAIR,* R. P. PECH,† C. R. DICKMAN,‡ D. HIK,§ P. MAHON,‡
AND A. E. NEWSOME†
*Centre for Biodiversity Research, Department of Zoology, University of British Columbia, Vancouver, V6T 1Z4,
Canada, email [email protected]
†CSIRO, Division of Wildlife and Ecology, P.O. Box 84, Lyneham, ACT 2602, Australia
‡School of Biological Sciences and Institute of Wildlife Research, University of Sydney, NSW 2006, Australia
§Division of Life Sciences, Scarborough College, University of Toronto, West Hill, Ontario M1C 1A4, Canada
Abstract: In parts of the world such as the Pacific Islands, Australia, and New Zealand, introduced vertebrate
predators have caused the demise of indigenous mammal and bird species. A number of releases for reestablishment of these mammal species in mainland Australia have failed because predators extirpated the new
populations. The nature of the decline of both extant populations and reintroduced colonies provides information on the dynamics of predation. Predator-prey theory suggests that the effects of predation are usually
inversely dependent on density (depensatory) when the prey are not the primary food supply of exotic predators. Thus, such predators can cause extinction of endemic prey species. Three types of evidence can be deduced from the predator-prey interactions that allow predictions for conservation: (1) whether per capita
rates of change for prey increase or decrease with declining prey densities, (2) whether predation is depensatory or density-dependent, and (3) the overall magnitude of predation. If this magnitude is too high for coexistence, then the degree of predator removal required can be predicted. If the magnitude of predation is sufficiently low, then the threshold density of prey that management must achieve to allow predator and prey to
coexist can also be predicted. We analyzed published reports of both declining populations and reintroduced
colonies of endangered marsupial populations in Australia. The observed predation curves conformed to the
predictions of predator-prey theory. Some, such as the black-footed rock-wallaby (Petrogale lateralis), were classic alternate prey and were vulnerable below a threshold population size. Others, such as the brush-tailed bettong (Bettongia penicillata), have a refuge at low numbers and thus offer the best chance for reintroduction.
Our predictions suggest a protocol for an experimental management program for the conservation of sensitive prey species: (1) determination of net rates of change of prey with declining population, (2) improvement
of survivorship through habitat manipulation, (3) improvement of survivorship through predator removal,
(4) determination of the threshold density above which reintroductions can succeed, and (5) manipulations
to change interactions from Type II to Type III. The task in the future is to determine how to change the vulnerability of the prey so that they can have a refuge at low numbers.
Predicción de los Efectos de la Depredación en la Conservación de una Presa en Peligro de Extinción
Resumen: En algunas partes del mundo como son las Islas del Pacífico, Australia y Nueva Zelandia, los veretebrados depredadores introducidos han ocasionado la desaparición de especies indígenas de mamíferos y
aves. Un gran número de liberaciones para el restablecimiento de estas especies de mamíferos en tierras continentales de Australia han fracasado debido a que los depredadores han extirpado las poblaciones nuevas.
La naturaleza de la declinación tanto de las poblaciones existentes como de las colonias reintroducidas
provee información de las dinámicas de la depredación. La teoría sobre depredador-presa sugiere que los
efectos de la depredación son usualmente inversamente densodependientes (depensatorios) cuando las presas no son el alimento principal de los depredadores exóticos. Por lo tanto, estos depredadores pueden causar
la extinción de especies de presas endémicas. Existen tres tipos de evidencia que pueden ser deducidas de las
Paper submitted January 17, 1997; revised manuscript accepted August 12, 1997.
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Sinclair et al.
Predicting Predation on Endangered Prey
565
interacciones depredador-presa y que permiten predicciones para la conservación: 1) que las tasas de cambio
per cápita de presas incremente o disminuya con la declinación de las densidades de presas, 2) que la depredación sea depensatoria o densodependiente, y 3) la magnitude total de la depredación. Si la magnitud es
muy alta para la coexistencia, entonces el grado de remoción del depredador requerido puede ser predecido.
Si la magnitud de la depredación es suficientemente baja, entonces la densidad umbral de la presa que debe
ser alcanzado mediante manejo y que permita al depredador y la presa coexistir tambien puede ser predecido. Analizamos reportes publicados tanto de declinaciones de poblaciones como de colonias reintroducidas
de poblaciones de marsupiales en peligro de extinción en Australia. Las curvas de depredación observadas se
conformaron a la teoría de depredador-presa. Albunas (i.e. el ualaby, Petrogale lateralis) fue una clasica presa
alternativa y fue vulnerable por debajo del tamaño poblacional umbral. Otras (i.e. Bettongia penicillata) tiene
un refugio de números bajos y ofrece la mejor de las opciones para reintroducciones. Nuestras predicciones
sugieren un protocolo para un programa de manejo experimental para la conservación de especies de presas
sensitivas: 1) determinación de tasas netas de cambio de presa con población en declive, 2) mejora de la supervivencia mediante la manipualción del hábitat, 3) mejora en la supervivencia mediante remoción de
depredadores, 4) determinación de la densidad umbral sobre la cual las reintroducciones podrían ser satisfactorias, y 5) manipulaciones para cambiar interacciones de tipo II y III. La tarea en el futuro será la de
identificar el como cambiar la vulnerabilidad de la presa, de tal forma que puedan obtener refugio aún con
números bajos.
Introduction
The successful reintroduction of rare and endangered
species has in many cases been attributed to the presence of suitable habitat at the core of the original range
of the species (Griffith et al. 1989; Gipps 1991). In various parts of the world, however, such as the Pacific Islands, Australia, and New Zealand, introduced vertebrate predators have caused or are causing the demise of
indigenous mammal, bird, and reptile species and are
preventing their successful reestablishment. Examples
of such exotic predators are the Indian mongoose (Herpestes auropunctatus) in Hawaii, the tree snake (Boiga
irregularis) on Guam, stoats (Mustela erminea) and feral cats (Felis catus) in New Zealand, and feral cats and
red foxes (Vulpes vulpes) in Australia. As a result numerous bird species have become extinct in Guam (Pimm
1987) and the Hawaiian Islands (Berger 1981; Pratt et al.
1987) and are declining in New Zealand (Clout & Craig
1994). In Australia endemic mammals in the range of
30–4000 g have been reduced to a fraction of their
former range, and some are now confined to outer islands where exotic predators are absent (Jarman &
Johnson 1977; Burbidge & McKenzie 1989; Johnson et
al. 1989; Robertshaw & Harden 1989; Dickman 1992;
Dickman et al. 1993; Serena 1994; Smith & Quin 1996).
A number of releases for reestablishment of these mammal species in mainland Australia have failed because
predators extirpated the new populations (Short et al.
1992, 1994; Serena 1994).
These events have led to the impression that all exotic
predators must be removed for the survival of such prey.
This may be so for some highly vulnerable species, but
in many cases it is not necessary for all predators to be
eradicated but merely that their numbers be reduced.
The task is to estimate how much reduction is needed.
The nature of decline of both extant populations and reintroduced colonies provides information on the dynamics of predation and the degree of predator control necessary for the survival of prey populations. We analyze
these declines and make predictions on the size of
founding populations necessary to overcome predation
and the degree of predator control necessary to allow
the escape of the prey population. These predictions
suggest the protocol for an experimental management
program for the conservation of sensitive prey species.
Predator-Prey Interactions and Models
for Extinction
The responses of predators to increasing prey numbers
have two components (Solomon 1949). The first is the
functional response, which represents what a single
predator eats and which takes two common forms
(Holling 1959, 1965). In the Type II response the predator eats more as prey density increases, but the curve
tends monotonically to an asymptote due to satiation
and handling time. The Type III response has a theoretical S shape where few if any prey are taken at low density but then are actively sought at higher density. The
second response of predators to increasing populations
of prey is the numerical response whereby the numbers
of predators increase through immigration and reproduction. Again the curve reaches an asymptote set by
social factors such as territoriality and dispersal, and
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Predicting Predation on Endangered Prey
this also results in depensatory predation at high prey
densities.
The total response of predators is the product of functional and numerical responses, and it differs according
to the types of functional and numerical responses exhibited by the predator (Ricklefs 1979; Sinclair 1989;
Pech et al. 1992, 1995; Messier 1994; Sinclair & Pech
1996). The stability properties of prey populations (N )
are determined by their rates of increase in the absence
of predation and the rates of mortality imposed by predators (i.e., the total response; Fig. 1a for Type II and Fig.
1b for Type III functional responses). To relate the theory in Fig. 1 to data, we used per capita rates of change
in Fig. 2 for Type II and Fig. 3 for Type III responses to illustrate the net change in prey population (rnet, the difference in Fig. 2a & Fig. 3a between prey rate of increase and predation rate) as a function of prey density.
These figures illustrate models, developed in the Appendix, for how net rates of change depend on predator
density (P).
For Type II functional responses there is a particular
density of predators, P *, representing the maximum
consistent with a viable prey population (equation 6 in
the Appendix). In this case there is only one solution for
N: the predator curve just touches the recruitment curve
(Fig. 2c). If predator density is greater than P *, then the
prey population can never persist (Fig. 2b). At low densities of predators (P , P *) there is a range of prey densities where rnet . 0 (Fig. 2d), and at very low densities of
predators (P , P 9, see Appendix) the net rate of increase
of prey is always positive (Fig. 2e). At these predator densities predation can never drive Type II prey species to
extinction. For Type III functional responses there is always one stable prey population. This is found at low
numbers (NA ) with very high predator populations (Fig.
3b). At slightly lower predator numbers, two stable prey
populations occur (NA, NC ) with a boundary between
them at NB (Fig. 3c). There is one density of predators, P *,
where NA 5 NB (Fig. 3d), and below P * the only stable
prey population is the high-density NC (Fig. 3e).
Predicting the Predation Interaction
for Conservation
We assume that it is known from other data that the cause
of decline or extinction is predation. The significance of
the predation models for conservation lies in the differences between Type II and Type III interactions. A Type
II response predicts that the per capita rate of increase
declines as the prey density decreases (i.e., is inversely
density dependent) at least at low densities, and that in
some cases it may become negative below a critical prey
density (NB). This would make the predator-prey system
potentially unstable at low prey numbers, and the prey
species could decline rapidly to extinction. If NB can be
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Sinclair et al.
Figure 1. The relationship between the total mortality
rate due to predation (thick line) and the rate of increase of prey population (N) in the absence of predators (thin line). Equilibria occur at prey densities NA,
NB, and NC. Type II functional response (A) is indicated by the predation curve increasing monotonically to an asymptote. Type III functional response (B)
is indicated by the S-shaped predation curve.
estimated, however, then it provides a measure of the
prey numbers that have to be achieved through conservation efforts to allow them to increase and coexist with
predators at a higher density (NC ).
A Type III response predicts that the per capita rate of
increase increases as the prey density declines below
some lower threshold (NB ), giving a lower stable prey
density (NA ) as a result of density-dependent predation.
These low prey densities may be so small that they are
prone to stochastic events and extinction. Nevertheless,
they provide a base from which such endangered popu-
Sinclair et al.
Predicting Predation on Endangered Prey
567
Figure 2. The net rate of increase (rnet ) of a prey population (N) when the predator has a Type II functional response. The growth rate without predation and the mortality due to predation (A) can be summed to give rnet
(B-E). The result depends on the density of predators relative to the threshold (P*) that occurs when rnet just reaches
zero at one point (defined by NB 5 NC in C, equation 6 in Appendix). Equilibria occur at prey densities NB and NC.
lations can be boosted by expeditious management of
predators or habitat.
In addition, the models in the form shown in Figs. 2
and 3 give an indication of the overall size of the predator population and whether it is higher than P *, the
threshold population, that determines possible coexistence between predator and prey in a Type II interaction
or predator regulation in a Type III interaction.
The type of conservation management required to
counteract predation requires an estimation of the degree of predation and whether the interaction is of Type
II or Type III, as shown in Figs. 2 and 3, because these
determine the stability of the system. Therefore, three
types of evidence can be deduced from the predatorprey interactions that allow predictions for conservation: (1) whether per capita rates of change increase or
decrease with declining prey densities, (2) whether predation is depensatory or density dependent, and (3) the
overall magnitude of predation to predict which curve
applies. If this magnitude is too high for coexistence
(Fig. 2b), then one can predict the degree of predator removal required to reduce predation so that coexistence
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Predicting Predation on Endangered Prey
Sinclair et al.
Figure 3. The net rate of increase (rnet ) of a prey population (N) when the predator has a Type III functional response. The growth rate without predation and the mortality due to predation (A) can be summed to give rnet
(B-E). The result depends on the density of predators relative to the threshold (P*, defined by equation 8 in Appendix). Equilibria occur at prey densities NA , NB , and NC.
can occur as in Fig. 2d or, better still, as in Fig. 2e. If the
magnitude of predation resembles Fig. 2d then it is possible, by extrapolation, to predict in addition the prey
density, NB, that management must achieve to allow for
predator and prey coexistence.
We have examined these predictions by analyzing examples of, respectively, (1) declining extant populations
of marsupials and native rodents in Australia and those
released from predation in predator removal experiments; (2) short-term declines in marsupial populations
reintroduced to the presence of predators, which can be
treated as experiments at the very-low-density range of
prey where Figs. 2 and 3 differ from each other; and (3)
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potential cases for experimental management. Because
the data are time series, they are inappropriate for statistical inferences for goodness-of-fit of curves. We use regression analysis merely to predict the population for
which the net rate of change is zero.
Rates of Change in Extant Populations
Type II Interactions
Changes in extant populations represent the net rate of
change resulting from the prey population growth rate
Sinclair et al.
and the predator depredation rate (Figs. 2 & 3). The eastern barred bandicoot (Perameles gunnii) is a l-kg omnivorous marsupial whose population in the state of Victoria declined in the twenty years from 1975 to 1994
(Backhouse et al. 1994), and this decline has been attributed entirely to exotic predators. Instantaneous rates of
change decline faster as population decreases (Fig. 4a), a
pattern resembling that of Fig. 2b with depensatory predation on secondary prey. On the basis of the information available there appears to be no stable point for
prey in the presence of predators.
Short et al. (1992) describe a reintroduction attempt
for quokka (Setonix brachyurus), a 2–3–kg macropod
in western Australia. Animals were released repeatedly
over several years, and some produced recruits. Predators were foxes and feral cats. Rates of change per year
(Fig. 4b) show depensatory predation, with the population eventually declining to extinction. The recruitment
Predicting Predation on Endangered Prey
569
curve, however, almost becomes positive at intermediate numbers, a situation that resembles that of Fig. 2c.
Predation in this case was too high to allow the natural
existence of quokkas, and they existed only because of
the repeated experimental release of animals. They died
out when these stopped. The density of predators appears to be close to the critical value P* (Fig. 2c). Any
reduction in the density of predators should generate
positive rates of increase for quokka densities in the intermediate range of 100–150. A similar result could be
obtained, in principle, by decreasing predator efficiency
(b21), for example, by improving shelter for the quokkas. Mathematically, this is equivalent to increasing b
and hence P * (Appendix equation 6) so that more predators are needed to prevent positive rates of increase for
the prey.
Black-footed rock-wallabies (Petrogale lateralis) were
examined in five small, rocky reserves in the western
Australian wheatbelt (Kinnear et al. 1988; Saunders et al.
1995). In two of these, foxes were removed after an initial 4-year study; in the remaining three areas foxes were
allowed to persist. Rates of change per year over three
time intervals from the five populations when foxes
were present (Fig. 4c) show a curve similar to that of
Fig. 2d, with a higher stable equilibrium lying in the
range of 20–40 animals and a lower instability boundary
in the region of 5–10 animals below which the population heads to extinction. In the two populations from
which foxes were removed, rates of change jumped up
and then declined toward a higher equilibrium, as illustrated for populations without predation in Fig. 2a. Extrapolation of these higher points suggests a carrying capacity in the region of 70–80 animals, double that when
foxes were present. These data suggest that foxes are
acting in a depensatory way, destabilizing the rock-wallaby populations when, as a result of habitat destruction
or weather, they fall below the threshold density (NB).
Type III Interactions
Figure 4. Examples of Type II interactions. Instantaneous rates of increase per year (r) with predation
(closed circles) and without predation (open circles)
plotted against numbers of eastern barred bandicoot
(A), quokka (B), and black-footed rock-wallaby (C).
Zero rate of increase is indicated by the dotted line.
Calculated from data in Backhouse et al. (1994) (A),
Short et al. (1992) (B), and Kinnear et al. (1988) and
Saunders et al. (1995) (C).
Both the spinifex hopping mouse (Notomys alexis) and
the sandy inland mouse (Pseudomys hermannsburgensis) are endemic rodents of arid regions in central Australia. Populations of both species in the Simpson Desert
declined precipitously in 1992 (C. R. Dickman & P. Mahon, unpublished data). This event followed a population increase in the long-haired rat (Rattus villosissimus), which was a response to high rainfall (Predavec &
Dickman 1994). High rat numbers resulted in the arrival
of the red fox, previously unrecorded in the area, and an
increase in feral cats, which had been resident possibly
for the past century. Subsequently, the rat population
declined, but the foxes have remained in the area. Instantaneous rates of change over 1990–1996 for both
the hopping mouse (Fig. 5a) and the sandy inland mouse
(Fig. 5b) show that there is a lower stable point in the
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Predicting Predation on Endangered Prey
Figure 5. Examples of Type III interactions. Instantaneous rates of increase per year (r) with predation
(closed circles) and without predation (open circles)
plotted against population indices. These are percent
trap success for A, B, D, E, and observations per 100
km of transect for 5c. The species are spinifex hopping
mouse (A), sandy inland mouse (with insert for population indices less than 1) (B), numbat (C), western
quoll (D), and brush-tailed bettong (E). Zero rate of increase is indicated by the dotted line. Calculated from
data in C. R. Dickman and P. Mahon (unpublished)
for A and B, Friend and Thomas (1994) for C, and
Morris et al. (1995) for D and E.
Sinclair et al.
The numbat (Myrmecobius fasciatus) is a 500-g marsupial termite eater. Once widespread over semiarid
Australia, it is now confined to two small populations in
western Australia. The population at Dryandra Woodland Reserve has been monitored periodically since
1955 (Friend & Thomas 1994). Predator removal was instituted in 1982. Regression of the instantaneous rates of
increase for this population before and after fox removal
estimates two stable states, one at a density index of 1.4
in the presence of predators, the other at a density index
of 5.9 without predators (Fig. 5c). This situation suggests a change in predation rates from that in Fig. 3b to
that in Fig. 3e with the removal of foxes. The lower state
is so low, however, that the population would probably
be in serious danger of extinction due to random events.
At Batalling in the extensive Jarrah forest of western
Australia, various small marsupial populations have been
monitored intermittently since 1985 (Morris et al. 1995).
In part of the area foxes were removed in 1990 for 4
years. Figures 5d and 5e show population changes for the
western quoll (Dasyurus geoffroii ), a 1.5-kg carnivore,
and the brush-tailed bettong (Bettongia penicillata), a
1.3-kg herbivore. In both cases there are lower and
higher stable points resembling those of Fig. 3c, and the
higher density is approximately six times that of the
lower. Again, the lower points are probably small
enough to be subject to stochastic extinction, but they
allowed the successful increase of the populations once
predators were removed. In summary, the examples in
Fig. 5 show that the populations tend to have positive
rates of increase at low density, which is the necessary
evidence for Type III interactions. But the variability of
these rates also increases at very low density, producing
some negative values indicating a higher vulnerability to
extinction.
Predation Rates on Reintroduced Populations
presence of foxes, indicated by the density-dependent
rates of change, and this suggests a Type III interaction
(Fig. 3). For the sandy inland mouse, predation appears
sufficient to create a “predator pit” (P . P *, Fig. 3c),
with a possibility of an “outbreak” from a low- to a highdensity state (NA to NC, Fig 3c). On the other hand, the
level of predation may allow only a low-density predatorregulated state (P .. P *, Fig. 3b) for the spinifex hopping mouse. Because both species coexisted with the
same number of predators, it is likely that foxes were
more efficient at capturing spinifex hopping mice. In
terms of equation 8 (Appendix), predator efficiency is
inversely proportional to b, so that greater efficiency
would lower the value of b—and hence P*—for hopping mice. Also, both species existed at much higher
densities before foxes appeared, with potential stable
equilibria at approximately five times the lower density.
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Attempted reintroductions in Australia include the rufous hare-wallaby (Lagorchestes hirsutus; Gibson et al.
1994), the burrowing bettong (Bettongia lesueur; Christensen & Burrows 1994), the brush-tailed phascogale
(Phascogale tapoatafa; Soderquist 1994), and the brushtail possum (Trichosurus vulpecula; Pietsch 1994). In
all these cases the population declined to extinction
within a few weeks, and observations indicated that almost all mortality was due to exotic predators. Because
of the short time scale involved, there was effectively no
recruitment to the prey population, so the decline reflected the total response of the predator. Furthermore,
it is unlikely that predator populations could have
changed substantially in such a short time, so the shape
of the total response largely reflects the type of functional response of the predators.
Sinclair et al.
The instantaneous rates of mortality due to predation
in the rufous hare-wallaby increased with decreasing
density of prey (Fig. 6a). This pattern suggests a Type II
functional response. The mortality curve of the brushtail
possum also suggests a constant, perhaps slightly increasing, predation rate as the population declines before dropping to low rates at small prey numbers (Fig.
6b). This pattern suggests a Type III functional response,
but the possum population size where the predation
rate declined was so low that it was effectively extinct.
Burrowing bettongs are 1.5-kg potoroid marsupials
that used to live in arid and semiarid shrublands but are
now largely confined to offshore islands. An attempt was
made to reintroduce them in the Gibson Desert within
their former range (Christensen & Burrows 1994). Their
population decline following release showed a mortality
rate that was both high and approximately constant.
There was no significant trend with prey density (Fig.
Figure 6. Comparison of the instantaneous mortality
rates (points) caused by predators and the intrinsic
rate of increase (rm ) for the prey (broken line) for the
same time interval plotted against population numbers: rufous hare-wallaby (A), brushtail possum (B),
burrowing bettong (C), and brush-tailed phascogale
(D). Calculated from data in Gibson et al. (1994) for
A, Pietsch (1994) for B, Christensen & Burrows (1994)
for C, and Soderquist (1994) for D.
Predicting Predation on Endangered Prey
571
6c). The mean instantaneous mortality rate per week
was 0.277, which was an order of magnitude greater
than the calculated weekly rm of 0.026. Thus, at very
low population sizes predation was high and constant.
The reintroduction of brush-tailed phascogales, a 200-g
marsupial carnivore, in Victoria showed a highly variable mortality, perhaps due to small population size (Fig.
6d). There was no significant trend, however, and mean
weekly instantaneous mortality was 0.428. Again this
was an order of magnitude above weekly rm of 0.048.
Experimental Management and the Magnitude
of Predation
For three of the reintroduced marsupial species, the observed rates of decline were at least an order of magnitude more than the maximum rate of increase possible for
the species (Table 1). Thus, irrespective of the shape of
the curve there is no alternative but to reduce predation
by about 90% until a substantial prey population has been
established. Then it should be feasible to reevaluate the
degree of predation that could be tolerated by the prey.
One species, the rufous hare-wallaby, showed a rate of
increase very close to the predation rate (Fig. 6a). Thus,
if this species could have been protected long enough to
allow breeding it may have been able to overcome predation and increase. This conclusion is supported by extrapolating the depensatory mortality curve. Regression
of the data in Fig. 6a allows us to predict that mortality
equals maximum recruitment at a population size around
30, which is roughly the same number of animals that
was originally released. The prediction is that if a few
more animals had been released—say two to three times
as many—they could have become established. This example illustrates how the boundary density (NB) may be
estimated and allows prediction of the size of population that should be released.
Analysis of extant populations also allows predictions
for conservation. The decline of the eastern barred
bandicoot suggests that a larger population may have
tolerated predation (Fig. 4a). Regression analysis of data
Table 1. Mean mortality rates and estimated intrinsic rates of
increase per week of marsupial species reintroduced in their
former range.
Species
Brush-tailed phascogale
Burrowing bettong
Brushtail possum
Rufous hare-wallaby
Instantaneous
mortality rate
Intrinsic rate
of increase
0.428
0.277
0.938
0.025
0.048
0.026
0.021
0.023
*Data from sources in Fig. 6; intrinsic rate calculated from Sinclair
(1996).
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Predicting Predation on Endangered Prey
in Fig. 4a allows the prediction that above a population
of 1200 the net rate of increase would have been positive. Thus, our analysis predicts that with a boost of population and even a modest control of predators there is a
good chance of reestablishment.
The rock-wallaby shows an upper stable population in
the presence of predators and a low unstable threshold
below which extinction occurs (Fig. 4c). This leads to
the prediction that active predator control is not necessary in principle until the population drops below about
20 individuals. Because the habitat is small, the upper
limit of the populations is also small—less than 100 individuals even without predators. Such small populations
are prone to stochastic events, so predator control
should be maintained to allow higher rates of increase
and greater resilience to random events. Alternatively,
the surrounding habitat should be cleared of predators
to enlarge the populations (rock-wallabies can live further away from rock outcrops but not with exotic predators). Although the quokka example (Fig. 4b) shows that
predation was too high at all densities, even a modest reduction of predation would change the predation curve
currently resembling that of Fig. 2c to one resembling
that of Fig. 2d. This should allow reestablishment of a
population above about 50 animals (the threshold density NB ).
The sandy inland mouse example (Fig. 5b) suggests
that there are both low and high stable states in the presence of predators. If this situation is confirmed, it would
lead to the prediction that predator reduction for a sufficient time should allow the build-up of prey numbers to
the higher stable point (Fig. 3c). The hopping mouse,
numbat, brush-tailed bettong, and quoll examples all
show higher average rates of increase at low densities in
the presence of predators, suggesting a lower stability
point (Fig. 3). These higher rates of increase at very low
numbers allow greater confidence that reestablishment
of such endangered species could succeed.
A Protocol for Experimental Conservation
We have analyzed these examples because they are
what is available. They suffer from the inherent problems of small samples and measurement error. We suggest that the examples be regarded as illustrations of an
approach that allows objective decisions for conservation to be made. Our analysis points to several aspects
that should be considered in a protocol for experimental
reintroductions.
First, it is necessary to establish whether the net rate
of change in the prey decreases as numbers decline
(Type II species), leading to potential instability and extinction, or whether these rates increase and become
positive with declining numbers, providing some chance
for a recovery.
Conservation Biology
Volume 12, No. 3, June 1998
Sinclair et al.
Second, the effects of predation can be counteracted
by improving the survival of endangered prey through
habitat manipulation. If survival can be improved, the
curves depicting net rate of increase in Figs. 2 and 3 shift
upward. For example, in Type II predator responses an
upward shift of rnet in Fig. 2b to that in Fig. 2d results in
a stable point appearing (NC ); the prey population can
then persist. In addition, the critical boundary density
(NB ) decreases so that smaller populations can exist. In
Type III predator responses, increasing survival results
in higher prey populations even in the presence of predators (NA moves to the right). If survival is sufficiently increased, as in Fig. 3e, the prey may even “outbreak” to a
much higher density. Survival can be improved by habitat manipulation at potential release sites so that reproduction improves, protection from environmental extremes improves, and refuges from predators increase.
Third, survival of the prey is also increased by the removal of predators, with the same consequences as described in the second point above. There can be strong
threshold effects, however, depending on the density of
predators relative to P* (defined by equation 6 for Type
II prey and by equation 8 for Type III prey in the Appendix). The important point is that it may not be necessary
to remove all predators. The degree of removal depends
on how close the net rate of increase curve is to the
boundary at which increase changes from negative to
positive. If net rate of increase is close to the boundary—as, in our examples, were the rufous hare-wallaby
(Fig. 6a) and the quokka (Fig. 4b)—only a modest removal should change the balance from extinction to reestablishment. If the net rate of increase is highly negative—as it was for burrowing bettongs (Fig. 6c) and
brush-tailed phascogales (Fig. 6d)—then near-total removal may be required.
Fourth, reintroduction attempts should take into account estimates of the boundary density (NB), if it exists,
above which successful establishment could occur and
below which failure is likely in Type II situations. This
could be done by a series of releases of different numbers of individuals and subsequent measurement of rates
of change. As initial release numbers become larger, rnet
should change from negative to positive, this transition
being the boundary number. In the absence of any prior
information, the safest policy is to release the largest
possible number. McCallum et al. (1995) recommend
this policy based on modeling reintroductions of the bridled nail-tail wallaby (Onychogalea fraenata). In addition, survivorship of released individuals should be measured (for example, by means of mortality radio collars)
as a function of population size. From this information
boundary, densities can be estimated as illustrated for
the rufous hare-wallaby (Fig. 6a). In Type III situations it
is still necessary to estimate NB because released populations lower than this will simply be held at the lower
predator-regulated point NA. Releases designed to sup-
Sinclair et al.
plement an already extant population at NA will succeed
only if NB is exceeded.
Fifth, any management that alters the predator-prey interaction from Type II to Type III allows the prey species to survive, if only at low numbers. This should be
one of the highest-priority objectives of management. It
could be accomplished by providing a refuge from predators. Predators have a number of sublethal effects because they alter the foraging behavior of prey. Refuges
reduce this risk and so improve both the reproduction
and survival of prey even in the presence of predators
(Hik 1995). Thus, habitat modification may cause a shift
from Type II to Type III interactions without reducing
predator numbers. Reducing the effectiveness of searching by the predator is another approach. For example,
large habitat patches containing endangered prey populations require predators to travel further from surrounding agricultural land than they would if commuting into
small patches. Thus, predators are less efficient in large
patches, so conservation efforts should focus on large
patches or re-create large patches as part of a renewal
program (Sinclair et al. 1995). A third approach is to reduce the primary prey of the predator so that predators
treat the endangered prey species in a Type III fashion.
Endangered prey can be driven to extinction only if they
are the alternate or secondary prey of the predators that
depend on some other, more common primary prey. For
example, foxes and cats in Australia often depend on the
exotic rabbit as primary prey (Newsome et al. 1989). Removal of rabbits, as is occurring through the spread of
the rabbit calicivirus disease, will test whether such a
change in total response occurs.
Conclusion
Predator-prey theory suggests that the effects of exotic
predators on endemic prey species are often inversely dependent on density (depensatory), and they can cause extinction of such prey. Several endangered marsupial populations in Australia show predation curves that conform
to the predictions of predator-prey theory. We show that
analysis of the pattern of decline in endangered prey and
the shape of the predation curve in failed reintroduction
experiments allow predictions of the degree of predator
control needed and the size of prey populations that
should be attained for successful reestablishment. These
predictions can be tested by experimental management,
and the protocol we have outlined can provide a basis
for an objective approach to reintroductions.
Acknowledgments
We thank H. Tyndale-Biscoe, R. Seamark, L. Hinds, and
G. Hood for considerable help, and K. A. Johnson and D.
Predicting Predation on Endangered Prey
573
G. Langford for showing us their experimental sites in
the Tanami. S. R. Morton and three referees provided
constructive comments on earlier drafts of the manuscript. A. R. E. S. was funded by a Sir Frederick McMaster
Fellowship from Australia. He thanks the Vertebrate Biocontrol Centre and the Commonwealth Scientific and Industrial Research Organization, Division of Wildlife and
Ecology, for providing facilities.
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Appendix
Interactions of Total Predation Rate and Prey Rate
of Increase
The effects of Type II and Type III total responses depend on their relationship to the rate of increase of the prey in the absence of predators. Without predation, rate of increase rises initially to a peak then
declines, through the effects of intraspecific competition. It reaches
zero at K, the equilibrium point where the prey are regulated by resources (Fig. 1). Superimposed on this are the responses using Type II
(Fig. 1a) and Type III functional responses (Fig. 1b). The overall rate of
change of a prey population with density N is
dN
------- = r ( N ) N – g ( N )P.
(1)
dt
The first term on the right-hand side of Equation 1 is determined by
the net recruitment rate without predators, r(N) (i.e., it includes nonpredation mortality). The second term is the total loss due to predation
which depends on the density of predators, P, and their functional response, g(N).
The interactions of predation rate and prey rate of increase are illustrated with commonly used forms of r(N ) and g(N ). If per capita consumption by predators is of the Type II form, then
g II ( N ) = a N ⁄ ( N + b II ) .
(2)
If it is of the Type III form, then
2
2
2
g III ( N ) = a N ⁄ ( N + b III ) .
(3)
In both cases a is the asymptotic upper limit to a predator’s consumption. The parameter b is inversely proportional to the foraging efficiency
of the predator. The higher the value of b the lower the mortality rate
at low prey densities, (i.e., b determines the slope of the functional response for small N).
A simple model for r(N) is the “linear” form of the logistic equation,
r ( N ) = r m ( 1 – N ⁄ K ),
(4)
where K is the carrying capacity and rm is the intrinsic rate of increase.
A more general form of Equation 4 is
θ
r ( N ) = r m [ 1 – ( N ⁄ K ) ],
where the exponent Q determines the degree of density dependence.
If Q ..1, population growth is exponential at low-to-medium densities, declining rapidly to zero as N approaches K. We use the simple
linear logistic equation because it is algebraically simpler. The results
are qualitatively similar for the more general model.
The rate of change is zero, and the prey population is at equilibrium, when mortality due to predation is balanced by the resourcedriven rate of increase. In Fig. 1 prey densities NA and NC are at stable
equilibria. For a Type III functional response, the density NB is an unstable equilibrium separating the low-density predator-regulated state
(N , NB) and the high density of an outbreaking prey population (N →
NC). In the case of a Type II functional response, the density NB is the
threshold below which predation can result in extinction of the prey
species.
Sinclair et al.
Predicting Predation on Endangered Prey
For a Type II functional response, simple analytic expressions can
be obtained for NB and for the maximum density of predators consistent with a viable prey population. Using Equations 1, 2, and 4, when
dN/dt = 0,
r m ( 1 – N ⁄ K ) = a P/ ( N + b II ).
(5)
Equation 5 is quadratic in N. For very low densities of predators (P' ,
rmbII /a) the predation curve starts below the prey rate of increase
and there is one solution corresponding to a high equilibrium (NC)
near K in Fig. 1a. At a particular high density of predators, P *, there are
no equilibria and there is only one solution of N given by
2
r m ( K + b II )
*
P = ------------------------------- .
4aK
(6)
P * represents the maximum density of predators consistent with a viable prey population. Between P' and P * there are two prey equilibria,
one unstable (NB) and one stable (NC) (Fig. 1a), corresponding to the
two roots of equation 5. Between prey densities NB and NC the prey
population has a positive rate of increase.
An approximate estimate of the lower, unstable prey equilibrium
(NB) can be obtained by assuming that N ,, K in Equation 4, in
which case r ø rm and NB is given by
aP
N B ≈ ------- – b II .
rm
This is the threshold density below which the net rate of increase of
the prey population is negative and predation will drive it to extinction (Fig. 1a). As the density of predators or their maximum offtake (a)
increases, NB increases, which means a larger initial prey population is
required for a viable reintroduction of the prey species. Alternatively, a
less efficient predator (large bII) and a high intrinsic rate of increase
for the prey (large rm) result in a lower value of NB.
To relate Fig. 1 to real data, it is helpful to consider the population’s
net per capita rate of increase in relation to density, with the effect of
the predator included. To this end both the net recruitment and predation rates in Fig. 1 are converted to per capita rates and one subtracted
from the other to give rnet,
1 dN
r net = ---- ⋅ ------- = r ( N ) – g ( N )P ⁄ N .
N dt
The results, for different levels of predation, are shown in Fig. 2. The
rate of increase, rnet, is the same as the instantaneous rate of change, ln
(Nt11/Nt), estimated directly from successive measurements of the
575
density of the prey species at times t and t11 in the presence of predators. Equation 6 shows that a prey species with a greater intrinsic rate of
increase, rm, can tolerate a higher density of predators. However, as the
upper limit to predators’ consumption (a) increases, P * decreases and
fewer predators are required to drive the prey population into decline.
For a Type III functional response (Equation 3) and the simple logistic form of Equation 4, the equilibrium condition is rnet 5 0 and
2
2
r m ( 1 – N ⁄ K ) = a PN/ ( N + b III ).
This is a cubic equation in N and the solutions are NA, NB, and NC in
Fig. 1b and in Fig. 3 (which shows the per capita rate of increase for a
Type III functional response).
At low densities, N ,, K, the prey will increase at the intrinsic rate,
r ø rm, in the absence of predators. With predation, equilibria (rnet 5
0) occur when,
2
N – ( a P ⁄ r m ) N + b III2 = 0.
(7)
The two solutions of Equation 7 correspond to NA and NB in Figs. 1B
and 3C. At densities less than NB the prey are in the so-called “predator
pit” and are regulated by predation. At very low densities, N2 → 0 so
that Equation 7 can be simplified to give an approximate solution for
NA. Then the predator-regulated equilibrium is
2
N A ≈ r m b III ⁄ aP.
The prey population has a positive net rate of increase for N , NA,
which means it can persist at low densities despite the presence of
predators. As the density of predators or their efficiency increases, NA
decreases and the prey population becomes increasingly susceptible
to stochastic events that could lead to extinction.
For a particular density of predators, P *, there is one solution for
Equation 7, (i.e., NA 5 NB) (Figs. 1b & 3d). This is given by
*
P = 2 b III r m ⁄ a.
(8)
If the density of predators is less than P *, rnet is always positive at lowto-medium prey densities and the population can increase to NC (Fig.
3e). When P . P *, there may be just sufficient predation for two stable states of the prey population: a low-density, predator-regulated
state and a high-density, “outbreak” state (Fig. 3c). At very high numbers of predators, P .. P *, predation always regulates the prey to a
low density (NA in Fig. 3b). As the maximum per capita offtake (a) or
predation efficiency (bIII21) increases, P * decreases, which means
fewer predators can successfully regulate the prey species.
Conservation Biology
Volume 12, No. 3, June 1998