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Research Article
Estimating the Viability of a Reintroduced New Zealand
Robin Population as a Function of Predator Control
DOUG P. ARMSTRONG,
1
Wildlife Ecology Group, Institute of Natural Resources, Massey University, Palmerston North, New Zealand
ELIZABETH H. RAEBURN, Wildlife Ecology Group, Institute of Natural Resources, Massey University, Palmerston North, New Zealand
REBECCA M. LEWIS, Wildlife Ecology Group, Institute of Natural Resources, Massey University, Palmerston North, New Zealand
DON RAVINE, Department of Conservation, Palmerston North, New Zealand
Abstract
Wildlife managers often have a good understanding of the threats faced by populations, but they need to know the intensity of management
required for populations to survive. Managers therefore need quantitative projections for populations under different management regimes
rather than just qualitative comparisons. However, quantitative projections are subject to tremendous uncertainty, particularly for small
populations monitored for short time spans. We assess the level of predator control needed for a reintroduced population of North Island robins
(Petroica longipes) to grow, accounting for uncertainty associated with parameter estimation, model structure, and demographic stochasticity.
The robin population grew when exotic rats were reduced to low levels (,10%of footprint tunnels tracked in 24 hr) by regular maintenance of
poison bait stations. However, the population declined after baiting was stopped 3 years after the reintroduction (March 2002), and it had fallen
to 4 pairs by September 2004. We created a simulation model incorporating relationships between vital rates (survival and fecundity) of the robin
population and rat tracking rate estimated from 5 years of data. We ran the model 10,000 times at each rat tracking rate, with vital rates sampled
from distributions (defined by estimates and standard errors) at the start of each run. Output from a deterministic model suggested that k(finite
rate of increase) would be .1 if rat tracking were ,20%, and up to 1.2 with rat tracking at 1%. However, 95%confidence intervals for k
extended ,1 at any tracking rate. With demographic stochasticity added, there was .20%probability of further decline in 5 years even when
the expected kwas 1.2. With all forms of uncertainty included, 41%of simulations projected a further decline over 5 years if the rat tracking rate
were 10%. This proportion was reduced to 30%if initial population size was increased to 20 pairs. Our analysis therefore showed it was most
likely that the robin population would grow if intensive rat control were reinstated, particularly if the population was supplemented, but there was
substantial risk the population would continue to decline under such management. (JOURNAL OF WILDLIFE MANAGEMENT 70(4):1020–1027;
2006)
Key words
mainland islands, New Zealand, North Island robin, Petroica longipes, population viability, predator control, reintroduction,
tracking tunnels, uncertainty.
Population viability analysis (PVA) involves constructing models
that are used to assess survival prospects of populations (Reed et
al. 2002). The initial focus of PVA was to estimate the long-term
probability of extinction in small populations, taking into account
genetic, demographic, and environmental stochasticity (Shaffer
1981, Soule
´1987). This focus has shifted (Beissinger 2002) due to
the fact that many populations are faced with short-term driven
extinction rather than long-term stochastic extinction (Caughley
1994) and that the predictions of PVAs are subject to great
uncertainty, particularly when long time frames are considered
(Fieberg and Ellner 2000, Ellner et al. 2002). This uncertainty can
be acknowledged by keeping PVA projections to short time
frames and by using PVA to compare management strategies
rather than to estimate absolute probabilities of extinction
(Beissinger and Westphal 1998, Brook et al. 2002, Reed et al.
2002, McCarthy et al. 2003). However, restricting the role of
PVA to qualitative comparisons is often unsatisfactory for
managers. Managers may already know how they can reduce
threats to populations, but they need to know the intensity of
management required for the populations to persist.
The best approach for dealing with uncertainty is not just to
acknowledge it but to confront it, and this involves 2 processes.
First, PVA must be preceded by a sound analysis of the data,
allowing plausible models to be developed for the factors driving
vital rates and allowing uncertainty in model selection and
parameter estimates to be quantified (White 2000a, White et al.
2002). Second, PVA should produce a distribution of projections
for any management scenario, and these distributions should
account for uncertainty in model structure and parameter
estimates in addition to the uncertainty associated with stochas-
ticity (White 2000a, Taylor et al. 2002, Wade 2002).
Population projections can be summarized in terms of
probability of extinction or quasi-extinction, persistence time, or
population growth rate (Burgman et al. 1993). All can be difficult
to interpret, as extinction probability and persistence time both
depend on the initial population size, extinction probability
depends on the time frame, and growth rate depends on
population density. For reintroduced populations the finite rate
of increase, k, provides a good measure of initial viability, as
populations are usually reintroduced at low density and expected
to grow if conditions are suitable. Reintroduction sites are often
actively managed to redress the factors responsible for the
extirpation of the species, so the key question is whether the
population will grow (i.e., k.1) under any management regime.
In New Zealand, reintroduction or recovery of many native
species depends on management of exotic mammalian predators
(Clout 2001). Many reserves on the main islands now have
predator control programs, and these reserves are often termed
mainland islands (Saunders and Norton 2001). The term reflects
1
E-mail: D.P.Armstrong@massey.ac.nz
1020 The Journal of Wildlife Management 70(4)
the idea that it may be possible for managed mainland areas to
have dense native populations similar to those found on mammal-
free offshore islands. Unlike islands, however, unfenced mainland
areas are subject to continual reinvasion of predators, so predators
can only be controlled rather than eradicated. There is already
abundant evidence that predator control can improve survival and/
or reproduction of New Zealand bird species in mainland reserves
(James and Clout 1996, Innes et al.1999, Powlesland et al.1999,
Dilks et al.2003, Moorhouse et al. 2003). The relevant question is
not whether predator control is an appropriate management
strategy, but what level of control is needed to allow populations
to grow. This question can be addressed through an adaptive
management (Walters 1986) approach (i.e., by monitoring the
population under different levels of control and using the data to
predict the subsequent control needed).
Managers also need a tangible measure of the level of predator
control they are achieving. Footprint tracking tunnels are used
throughout New Zealand to monitor rodents and mustelids, and
tracking rates (proportion of tunnels tracked over 1–3 nights) are
used to assess the effectiveness of control programs targeted at
these mammals (Innes et al.1995). Exotic ship rats (Rattus rattus)
and mustelids appear to be the key predators of many native bird
species (Clout 2001). It would therefore be useful for managers to
know how low tracking rates need to be to allow reintroduced or
remnant populations to be viable.
We built a simulation model for the reintroduced North Island
robin (Petroica longipes) population at Paengaroa Mainland Island
and used it to assess the probability of growth and persistence at
different predator tracking rates. The population was ideal for this
purpose, as rat tracking rates had varied dramatically in the 5 years
after reintroduction and there were corresponding changes in the
vital rates of the robin population (Armstrong et al. 2006). The
reserve appeared to have good habitat for robins in terms of
vegetation structure, topography, and food availability (Raeburn
2001), and should have been able to support several hundred
robins in the absence of mammalian predators. We aimed to 1)
estimate the relationship between kand rat tracking rate; 2)
quantify the uncertainty in this relationship; 3) quantify
uncertainty due to demographic stochasticity, and therefore assess
the degree to which uncertainty could be reduced by increasing
the initial population size; and 4) obtain distributions for the
number of robins that would be present after 5 years with different
rat tracking rates, taking all these forms of uncertainty into
account.
Study Area
Paengaroa Mainland Island (398390S, 1758430E) is a 101-ha forest
remnant 8 km southwest of Taihape in the south-central portion
of New Zealand’s North Island. At the time of the robin
reintroduction (Mar 1999), ship rats and brush-tailed possums
(Trichosurus vulpecula) were controlled using brodifacoum cereal
baits placed in 97 permanent bait stations. This baiting was
discontinued briefly in 1999, continued until March 2002, then
stopped again, resulting in marked changes in rat abundance over
the first 5 years after robins were reintroduced to Paengaroa.
Further details are given by Armstrong et al.(2006).
Methods
Species
The North Island robin is a small (26–32 g), insectivorous, forest
passerine in the family Petroicidae. It is often considered a
subspecies of the New Zealand robin along with the South Island
robin (P. australis), but Holdaway et al. (2001) classified these as
separate species. North Island robins typically breed from
September to February (Armstrong et al. 2000, Powlesland et
al. 2000) and breed in monogamous pairs that occupy permanent
territories. Extra males are generally not involved in breeding,
although females may practice serial polyandry by switching
males between reproductive attempts (Armstrong et al.2000).
Extra females are often fertilized, but they receive no other help
from males and produce fewer young than paired females
(Armstrong et al.2006). Juveniles become independent about 4
weeks after fledging and are sexually mature by the start of the
next breeding season. Robins are highly susceptible to predation
by rats (Brown 1997, Powlesland et al. 1999) and probably by
other exotic mammals, and they are now absent from most of the
North Island. They were reintroduced to Paengaroa Mainland
Island in March 1999 when 40 robins were released there
(Raeburn 2001).
Data Collection and Analysis
We did tri-annual surveys of the Paengaroa robin population to
obtain survival data, and we monitored females throughout the
breeding season to obtain fecundity data. We measured fecundity
as the number of independent young produced per female, and we
usually color-banded birds when they reached independence (at
about 4 weeks of age). We ran tracking tunnels every 4 months to
monitor levels of rats and mustelids. However, mustelids rarely
tracked tunnels, so we only analyzed rat tracking rates. We
modeled functional relationships between the robin population’s
vital rates and the rat tracking rate (proportion of tunnels tracked).
We first nominated a set of candidate models, and we used
Akaike’s Information Criterion (AIC) to determine which models
best explained the data. We then used these models to estimate
the survival probability or mean fecundity expected at any tracking
rate and the standard errors associated with those estimates (Table
1; see Armstrong et al. [2006] for analyses). These functions
distinguish the survival rates of adult males, adult females, and
juveniles (from independence to start of the next breeding season),
and they distinguish the fecundity rates of paired versus unpaired
females.
We also required a model for sex allocation (i.e., the probability
of a bird being male or female). The robins recruited into the
Paengaroa breeding population from 2000 to 2004 had a female-
biased sex ratio (13 F, 7 M). However, this proportion was not
significantly different from 0.5 (95%profile likelihood confidence
interval ranged from 0.43 to 0.84), and the proportion of females
in 221 robin recruits on Tiritiri Matangi Island from 1993 to 2004
(Armstrong and Ewen 2002; D. P. Armstrong et al., Massey
University, unpublished data) was extremely close to 0.5 (95%
profile likelihood CI ranges from 0.47 to 0.55). As we have no
reason to expect a greater proportion of female recruits at
Paengaroa, we assumed a probability of 0.5 for a recruit being
male or female.
Armstrong et al. Population Viability versus Predator Control 1021
Population Modeling
We constructed a discrete-time population model (Table 2) that
could be applied to any population where 1) animals form
breeding pairs, 2) animals are sexually mature adults by the start of
the next breeding season after they are born or hatched, 3) survival
and fecundity do not change with age once animals reach
adulthood, and 4) survival and fecundity are not density depend-
ent. The first 3 conditions clearly apply to North Island robins,
and analyses of 12 years of data from the robin population on
Tiritiri Matangi Island suggest that survival and fecundity are not
age related in adult birds (Armstrong and Ewen 2002, Armstrong
et al.2002;D.P.Armstrongetal.,MasseyUniversity,
unpublished data). We did not incorporate density dependence,
as density of the simulated populations always remained low (,1.1
birds/ha, compared to .4 birds/ha on Tiritiri Matangi [Arm-
strong and Ewen 2002]) over the time frames we considered.
Our model tracked the number of males and females alive at the
start of the breeding season. There was no age structure in the
model, as we considered all males or females alive at that time to
have the same survival probabilities and expected fecundity rates.
We wrote the model as a spreadsheet in MicrosofttExcel
(Microsoft Office Professional 2003; Microsoft, Redmond,
Washington), where each row represented a different calculation
done in a year (Table 2) and each column represented a different
year. This spreadsheet approach offers many advantages for
modeling wildlife populations, the most important being that the
workings of the model are completely transparent and can be
explained to managers (White 2000b). We parameterized the
model using the functions obtained from analysis of the Paengaroa
data (Table 1).
Deterministic model with no uncertainty.—We first obtained
kvalues for different tracking rates assuming parameter estimates
(Table 1) were accurate and there was no demographic
stochasticity (see Deterministic Model in Table 1). We took k
to be the relative number of females from one year to the next
(F
t
/F
t1
), as is conventional when females are the limiting sex
(White 2000b). If females are always paired, then kis given by
k¼^
sfþ1
2^
sj^
fp;
Table 1. Models for predicting vital rates of North Island robins as a function of rat tracking rate, Paengaroa Mainland Island, New Zealand.
Estimate
a,b
Standard error
a,b
Distribution
c
^
f
p
¼2.26f1e
0.46[p/(1p)]
gSEð^
fpÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:05^
f2
pþ0:27 p
1p
ð2:26 ^
fpÞ
hi
2
0:09 p
1p
ð2:26 ^
fpÞ^
fp
rlnðfpÞ;Normal lnð^
fpÞ;SEð^
fpÞ
^
fp
^
f
u
¼1.03f1e
0.46[p/(1p)]
gSEð^
fuÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:39^
f2
uþ0:27 p
1p
ð1:03 ^
fuÞ
hi
2
þ0:001 0:09 p
1p
hi
ð1:03 ^
fuÞ^
fu
rlnðfuÞ;Normal lnð^
fuÞ;SEð^
fuÞ
^
fu
hi
^
s
f
¼0.64p
0.24
SEð^
sfÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:01^
s2
fþ0:027^
s2
flnðpÞ2þ0:011^
s2
flnðpÞ
qln sf
1sf
;Normal ln ^
sf
1^
sf
;SEð^
sfÞ
^
sfð1^
sfÞ
hi
^
s
m
¼0.64 SE(^
s
m
)¼0.065 ln sf
1sf
;Normalð0:57;0:28Þ
^
s
j
¼0.39 (A)
d
SE(^
s
j
)¼0.049 ln sf
1sf
;Normalð0:44;0:21Þ
^
s
j
¼0.49p
0.58
(B)
d
SEð^
sjÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:054^
s2
jþ0:211^
s2
jlnðpÞ2þ0:117^
s2
jlnðpÞ
qln sj
1sj
;Normal ln ^
sj
1^
sj
;SEð^
sjÞ
^
smð1^
sjÞ
hi
a
See Armstrong et al. (2006) for analyses used to select appropriate models and estimate standard errors.
b
^
f
p
, mean number of independent young per pair; ^
f
u
, mean number of independent young per unpaired female;
s
ˆ
f
, probability of an adult female surviving
1 yr;
s
ˆ
m
, probability of an adult male surviving 1 yr;
s
ˆ
j
, probability of a juvenile surviving from independence until the next breeding season; p, proportion of
tracking tunnels that are not tracked by rats in one night.
c
Used to incorporate uncertainty in vital rates when performing simulation modeling.
d
The juvenile survival model is ambiguous as these 2 models (A and B) have similar AIC weights when fitted to the data (Armstrong et al. 2006).
Table 2. Deterministic and stochastic models for projecting growth of North Island robin populations, Paengaroa Mainland Island, New Zealand.
Calculation
a
Deterministic model
b
Stochastic model
b,c
No. breeding females F¼F
1
þF
2þ
F¼F
1
þF
2þ
No. breeding males M¼M
1
þM
2þ
M¼M
1
þM
2þ
No. pairs P¼min(M,F)P¼min(M,F)
No. unpaired females U¼FPU¼FP
No. juveniles produced J¼f
p
Pþf
u
UJ
p
;Poisson(f
p
P), J
u
;Poisson(f
u
U)
No. first-year birds alive next year R¼s
j
JR;Binomial[(J
p
þJ
u
), s
j
]
No. first-year females alive next year F
1
¼½RF
1
;Binomial(R, 0.5)
No. first-year males alive next year M
1
¼½RM
1
¼RF
0
No. older females alive next year F
2þ
¼s
f
F
t
F
2þ
;Binomial(F
t
,s
f
)
No. older males alive next year M
2þ
¼s
m
M
t
M
2þ
;Binomial(M
t
,s
m
)
a
Each row of the table corresponds to a row in a spreadsheet model, and the complete set of rows represents 1 yr.
b
Functions for calculating vital rates are shown in Table 1.
c
Includes demographic stochasticity in fecundity, survival, and sex allocation, but does not include environmental stochasticity.
1022 The Journal of Wildlife Management 70(4)
where ^
s
f
is the annual survival of adult females, ^
f
p
is the number of
independent young per pair, and ^
s
j
is survival from independence
to adulthood. If females outnumber males at any stage, kwill also
depend on ^
s
m
(i.e., the annual survival probability of adult males)
and ^
f
u
(i.e., the number of independent young per unpaired
female) and will change over time until the sex ratio stabilizes. We
reported the kvalues for stable sex ratios.
Uncertainty in parameter estimates and model structure.—
To account for uncertainty in our estimates of vital rates, we
sampled each vital rate from a distribution (Table 1) at the start of
each run. We ran the model 10,000 times at each tracking rate to
generate a distribution for k(for discussion of this method, see
White 2000a, Taylor et al. 2002, and Wade 2002). We assumed
mean fecundity and survival probability to be log-normally
distributed and logit-normally distributed, respectively (Table 1).
We selected the transformed values using the Excel function
NORMINV(probability,mean,standard_dev), where probability is
a uniform random number from 0 to 1 (selected using the function
RAND()), and mean and standard_dev are the estimate and
standard error of the transformed value (shown in Table 1). We
then back-transformed the values selected to obtain the param-
eters used in the run.
Our analysis of juvenile survival data (Armstrong et al. 2006)
showed that it was ambiguous whether juvenile survival was
constant or declined with tracking rate (Table 1). We therefore
obtained distributions for kunder both juvenile survival models.
In contrast, there was unambiguous support for one adult survival
model and one fecundity model (Table 1), and we used these in all
simulations.
Demographic stochasticity.—We modified the spreadsheet
model to incorporate demographic stochasticity in survival, sex
allocation, and fecundity (Table 2). We sampled numbers of
survivors from the Binomial distribution using the function
CRITBINOM(trials,probability_s,alpha),wheretrialsisthe
maximum number, probability_s is the survival probability, and
alpha is a uniform random number from 0 to 1 (White 2000b).
We used the same function to determine the number of female
recruits, with probability_s set to 0.5. We sampled the total
number of independent young produced by paired or unpaired
females from the Poisson distribution using the Excel formula
ROUND(GAMMAINV(probability,alpha,beta)), where alpha is
the expected number based on the mean fecundity rate, and beta ¼
1 (the gamma distribution with b¼1 is a continuous analog to the
Poisson). We did not attempt to incorporate environmental
stochasticity, as it is impossible to estimate accurately from small
data sets (White 2000a), and its effects are swamped by
demographic stochasticity in small populations (Leigh 1981).
We initially ran the stochastic model using fixed values for vital
rates. This allowed us to assess the probability of the population
declining when kwas expected to be .1. Using 10,000 runs for
each tracking rate, we estimated the probability of the number of
females declining and the probability of the population becoming
extinct (0 M or 0 F) over a 5-year time frame. We first ran
simulations with an initial population of 4 males and 4 females,
the number present at the start of the 2004–2005 breeding season,
then did further simulations to assess the degree to which
uncertainty could be reduced by increasing population size.
Incorporating all forms of uncertainty.—Our final step was to
simultaneously incorporate uncertainty due to demographic
stochasticity, parameter estimation, and model selection. For
these simulations, we incorporated ambiguity in the juvenile
survival model by randomly selecting 1 of the 2 models at the start
of each run using the RAND() function. The AIC
c
weights for
the 2 models were almost identical (Armstrong et al.2006), hence
the probability of either model being selected was 0.5 (this is a
form of model averaging and produces similar results to the
analytical method given by Buckland et al.1997). We used these
simulations to obtain a distribution for the number of females that
would be present after 5 years at any tracking rate, accounting for
all forms of uncertainty.
Results
The Paengaroa robin population consisted of 18 birds (9 pairs) in
September 1999, at the start of first breeding season after
reintroduction (Fig. 1). The population had decreased to 11 birds
by September 2000, but it increased to 19 birds over the next 2
years when rats were at low levels. Rat tracking gradually increased
after brodifacoum baiting was stopped in March 2002, reaching
100%in September 2003, and there was a corresponding decline
in the robin population. The population consisted of 8 birds (4
pairs) in September 2004.
Deterministic calculations of ksuggest the rat tracking rate
needs to be less than approximately 20%for the population to
increase (i.e., for kto be .1). The ambiguity about the
appropriate juvenile survival model (Table 1) makes little differ-
ence to this calculation, as ^
k¼1.0 when tracking was 18%under
model A (where juvenile survival is constant) and when tracking
was 21%under model B (where juvenile survival declines as rat
tracking increases). However, model B predicted more generous
rates of increase when rat tracking was reduced to low levels (Fig.
2). For example, with tracking reduced to 1%, model B predicted
kto be 1.19, corresponding to a 138%increase in population size
over 5 years, whereas model A predicted kto be 1.08,
corresponding to a 47%increase over 5 years. The projected
Figure 1. Changes in the total population of North Island robins (black dots)
and number of females (white dots) in the 5 yr after reintroduction to
Paengaroa Mainland Island, New Zealand. Points show the numbers of birds
known to be alive at the start of each breeding season (Sep). The Department
of Conservation controlled rats and possums using brodifacoum cereal baits
until Mar 2002, except for Dec 1999 to May 2000.
Armstrong et al. Population Viability versus Predator Control 1023
growth was not much lower with rat tracking at 10%, with ^
k¼
1.06 under model A and 1.14 under model B.
When we accounted for uncertainty in parameter estimates, it
was unclear whether the population was likely to increase at any
tracking rate. With rat tracking held to 1%,the95%confidence
interval for kranged from 0.84 to 1.35 under model A and from
0.87 to 1.63 under model B (Fig. 2). However, the confidence
limits for kwere completely below 1 once tracking increased above
40%, suggesting that the robin population was guaranteed to
decline under those conditions.
Demographic stochasticity also created a lot of uncertainty with
an initial population of just 4 pairs. As noted above, if we treated
parameter estimates as known, using model B for juvenile survival,
and set tracking to 10%, then kwas expected to be 1.14, giving 8
females after 5 years. With demographic stochasticity, however,
the actual number of females ranged from 0 to 17, and there was
32%probability that the number of females declined from the
original 4 (Fig. 3). When we incorporated uncertainty in
parameter estimates and the juvenile survival model in addition
to demographic stochasticity, the 95%confidence interval for the
number of females after 5 years ranged from 0 to 24, and there was
a41%probability that the number of females would decline (Fig.
4).
The uncertainty due to demographic stochasticity can be
reduced somewhat by increasing the initial population size. If
we set the tracking rate at 10%and treated population parameters
as known, then an initial population of 20 pairs had a 7%
probability of declining over 5 years, as compared to 32%for an
initial population of 4 (Fig. 5). However, the effect of initial
population size was less pronounced when all forms of uncertainty
were incorporated. With an initial population of 20 pairs, there
was a 30%probability that the number of females would decline
after 5 years, as compared to a 41%probability of decline with an
initial population of 4 pairs (Fig. 6).
Discussion
Our analysis suggests that the rat tracking rate at Paengaroa
Mainland Island needs to be ,20%for the reintroduced North
Figure 2. Expected rates of increase (k) of the North Island robin population,
based on functional relationships between the population’s vital rates and the
rat tracking rate, Paengaroa Mainland Island, New Zealand. Solid lines show k
values calculated using the estimated values of the vital rates (Table 1), and
broken lines show 95%CI for kfrom 10,000 runs of a deterministic simulation
model (Table 2) where each parameter is selected from a distribution (Table 1)
at the start of each run. The black (model A) and gray (model B) lines are from
simulations using different juvenile survival models.
Figure 3. Effect of demographic stochasticity on viability of the North Island
robin population with an initial population of 4 pairs, Paengaroa Mainland
Island, New Zealand. Lines show the probabilities of the number of females
declining (solid line) or the population becoming extinct (broken line) over 5 yr
based on 10,000 runs of a stochastic simulation model. Expected kvalues
were calculated using the deterministic model (Fig. 2). If kis expected to be
.1, declines are due to demographic stochasticity.
Figure 4. Probability of the North Island robin population declining over 5 yr
starting with 4 pairs, accounting for all sources of uncertainty (parameter
estimates, juvenile survival model, demographic stochasticity), Paengaroa
Mainland Island, New Zealand. We obtained distributions for the numbers of
robins after 5 yr using a stochastic simulation model (Table 2), with the juvenile
survival model randomly selected at the start of run and the value of each
parameter selected from a distribution (Table 1). The probability shown is the
proportion of runs in which the number of females declined (solid line) or the
population became extinct (broken line).
1024 The Journal of Wildlife Management 70(4)
Island robin population to grow (i.e., for kto be .1). When
poison bait stations were maintained consistently, from 2000 to
2002, rat tracking rates at Paengaroa ranged from 0 to 9%. The
effectiveness of control may vary from year to year because of
natural fluctuations in rodent densities (Innes et al.1995).
However, our results suggest that it is quite feasible to maintain
rats at levels sufficiently low to allow the robin population to grow.
If rat tracking were maintained at about 10%, our analysis
suggested the robin population would be most likely to grow at
approximately 10%per year. If this were the case, the growth rate
would ultimately decline toward 1 through density dependence as
the population increased. Analysis of the reintroduced population
on Tiritiri Matangi (Armstrong and Ewen 2002, Armstrong et al.
2002) suggested that robin populations were regulated by density
dependence in juvenile survival in the absence of mammalian
predators, and were likely to maintain relatively stable densities.
There was considerable uncertainty about our projections,
however, as expected from data collected over 5 years for a small
population. Because of uncertainty in parameter estimates, it was
unclear whether the population was expected to grow at any
tracking rate, and because of demographic stochasticity it was
unclear whether the population would survive even if positive
growth was expected. The problem of demographic stochasticity
became even more acute following the deaths of 2 of the 4
remaining females during the 2004–2005 breeding season.
It is important to note that our uncertainty would be much
greater if we had not collected data on vital rates. We could have
calculated kjust from changes in the number of females each year
(Fig. 1), giving values of 0.44, 2.00, 1.63, 0.54, and 0.57 for the 5
years. A predictive model could be obtained by regressing ln(k)
against ln(p) (using average tracking rate for each year). The
resulting function would be ^
k¼1.44p
0.88
,suggestingthe
population will grow if the tracking rate (1 p) were ,34%.
However, the confidence intervals would be so huge that the
prediction would be meaningless. For example, with a 34%
tracking rate the confidence interval for ^
kwould range from 0.20
to 4.94, in comparison to the confidence interval of 0.67 to 1.06
that we generated using data on vital rates (Fig. 2). Although it
would save monitoring effort just to track population trends, many
years of monitoring (e.g., 30þ) are needed before reasonable
predictions can be made using this approach (Elkinton 2000,
Fieberg and Ellner 2000). If management decisions need to be
made over shorter time frames, it is imperative that data on vital
rates are collected.
Our projections are sufficiently precise to show that any robin
population at Paengaroa Mainland Island would be doomed to
extinction without predator control. Our modeling suggests a
population would be guaranteed to decline if rat tracking were
above 40%, and tracking rates have climbed to well over 40%
since poison baiting was discontinued in March 2002. This result
has implications for understanding the current distribution of
robins and other species that have been partially extirpated from
their former ranges following introduction of exotic mammals.
Given that robins survive in many locations in the absence of
predator control, and they tend to be found in large forest blocks,
their absence from other areas could be attributed to metapopu-
lation dynamics (Drechsler et al. 2003) rather than to differences
in predator levels or other aspects of habitat quality. Recent
research suggests that metapopulation dynamics are largely
responsible for explaining local distributions of robins among
small, unmanaged forest fragments in the central North Island (Y.
Richard and R. L. Boulton, Massey University, unpublished data).
However, our data for Paengaroa show that kwill be well below 1
if rats are not controlled, meaning the future absence of robins will
be due to driven extinction (sensu Caughley 1994) rather than to
stochastic extinction and failure to recolonize.
Populations can potentially be driven to extinction in small and
isolated fragments because of dispersal into surrounding sink
habitat (Basse and McLennan 2003). Such dispersal occurred to
some extent at Paengaroa, as one juvenile was found 10 km from
the reserve (dispersal is unlikely in adults, which are highly
sedentary). Our survival models estimate local survival, and it is
Figure 5. Effect of the initial number of pairs on the probability of the North
Island robin population declining due to demographic stochasticity, assuming
estimates of vital rates (Table 1) are accurate, Paengaroa Mainland Island, New
Zealand. Rat tracking rate is set at 10%. Otherwise as for Fig. 3.
Figure 6. Effect of the initial number of pairs on probability of the North Island
robin population declining, accounting for all sources of uncertainty,
Paengaroa Mainland Island, New Zealand. Rat tracking rate is set at 10%.
Otherwise as for Fig. 4.
Armstrong et al. Population Viability versus Predator Control 1025
unknown how much of the estimated juvenile mortality was due to
emigration. In the absence of emigration, the most optimistic
scenario would probably be for juvenile survival probability to
equal the annual survival probability of adult males. Under this
scenario, the maximum rat tracking rate that would allow positive
growth was estimated to be 34%under model 1 (constant juvenile
survival) or 28%under model 2 (juvenile survival declines from
intercept value as rat tracking rate increases). Given that rat
tracking rates at Paengaroa rose to .80%after cessation of
control, it seems unlikely that the extirpation of robins from
Paengaroa can be attributed to emigration alone. We therefore
suspect that aspects of the habitat at Paengaroa reduce vital rates
below those occurring at sites where robins are able to survive
without predator control. It is possible that this inferior habitat
quality was associated with edge effects (e.g., through increased
predation rates or greater exposure [Murcia 1995]), but there are
no New Zealand data available to assess this possibility.
It is also possible that the low density of the reintroduced
population at Paengaroa contributed to low vital rates (i.e., that an
Allee effect was operating). Allee effects can occur through several
mechanisms (Courchamp et al. 1999), including higher per capita
predation rates at low density. Such elevated predation may occur
through increased hunting effort by predators, resulting in the
classic Type II functional response of predator–prey theory.
Sinclair et al. (1998) noted that if predation by exotic predators on
native prey had a Type II functional response, then the level of
predator control required at low densities would be higher than
that required after populations recovered. It could also be argued
that reintroductions should involve large numbers of founders to
increase initial population density. However, we are skeptical
about Type II functional responses occurring in North Island
robins or other New Zealand birds threatened by exotic mammals.
These bird species make up a tiny portion of the food taken by any
predator species, so it is unlikely that predators would significantly
change their hunting effort in response to density of these prey.
We are also skeptical about other forms of Allee effects operating
in North Island robins, given that they are distributed as
individuals or pairs, meaning foraging and predator defense are
largely unaffected by density and that they have shown themselves
to be highly capable of seeking out mates. We therefore think it is
unlikely that vital rates of robins would have increased with
density, so we did not include such an effect in our simulation
model.
Although the Paengaroa robin reintroduction has been un-
successful at establishing a population, it has met Southgate’s
(1994) criterion for success in that it has provided information
that can be used to improve future management. The methods we
developed can be extrapolated to any population where the species
has a similar biology, and they can be used to relate population
viability to predator tracking rates. The methods are therefore
widely applicable to New Zealand mainland island programs
(Saunders and Norton 2001), where the primary management is
predator control, predator levels are measured by tracking rates,
and key management objectives include maintaining viable
populations of native forest birds.
Management Implications
Our analysis showed that the North Island robin population at
Paengaroa will inevitably decline to extinction if exotic predators
are not controlled. This case study therefore illustrates the risk
involved in reintroducing New Zealand species to mainland areas
where ongoing predator control cannot be guaranteed. Such
reintroductions may be justifiable on a local scale if there is reason
to believe that absences are attributable to chance extinction, and
therefore that reintroduction could provide a substitute for natural
dispersal to ameliorate the effects of habitat fragmentation
(Armstrong and McLean 1995, Lubow 1996). However, where
a reintroduction constitutes a range extension, as was the case with
Paengaroa, we suggest that policy needs to be in place to ensure
the necessary predator control is continued.
Our analysis also showed that a robin population would be most
likely to survive at Paengaroa if effective predator control were
reinstated, but that its persistence could not be guaranteed under
any level of control. It is not our role to decide whether predator
control should be reinstated in such circumstances. However, the
distributions of outcomes we reported provided the information
necessary for the managers responsible to make an informed
decision. If predator control is reinstated, translocation could be
used to again reintroduce robins to Paengaroa should the
remaining females die or to supplement the population to reduce
the substantial risk of extinction through demographic stochas-
ticity. The distributions of outcomes obtained under different
initial population sizes would then provide managers with the
information needed to make that decision. Our results therefore
illustrate how quantification of uncertainty can be imperative for
informed decisions about management of populations.
Acknowledgments
We thank H. Wittmer, I. Westbrooke, M. Maunder, K. Steffens,
W. Kendall, A. Powell, and an anonymous referee for comments
on our manuscript. Financial support for our research was
provided by the Department of Conservation, Massey University,
and the Marsden Fund.
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