C S I R O P U B L I S H I N G

Wildlife ResearchVolume 26, 1999

© CSIRO Australia 1999

A journal for the publication of original scientific research in the biology and management of wild native or feral introduced vertebrates

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the Australian Academy of Science

Wildl. Res., 1999,26, 227–237.

Analysis of the impact of stoats,Mustela erminea,on northern brown kiwi, Apteryx mantelli,in New Zealand

B. BasseA , J. A. McLennanB and G. C. WakeA

A Mathematics and Statistics Department, University of Canterbury,Private Bag 4800, Christchurch, New Zealand.B Landcare Research, Private Bag 1401, Havelock North, New Zealand.

Abstract

An age-structured population analysis is used to determine recruitment levels and a condition forsurvival which can assist management decisions and hence improve the viability of populations ofnorthern brown kiwi,Apteryx mantelli, in forests on the New Zealand mainland. Currently, in theabsence of predator control, recruitment rates are less than 5% due to high levels of stoat,Mustelaerminea, predation on juvenile kiwi. Predation levels on adult kiwi are very low. The analysis predictsthat a recruitment rate of 19% is required to maintain population stability. To achieve this target, stoatpopulations have to be reduced by about 80% in some years, and maintained at a critical residualdensity estimated to be a value less than two animals per square kilometre for up to nine months untilimmature kiwi reach a safe size of about 1200 g (50% of their adult weight). Recent predator-controlinitiatives indicate that stoat numbers can be reduced and maintained at low levels in relatively smallareas of mainland forest (up to 1000 ha). New techniques are needed to protect kiwi over larger areas.

Introduction

All four species of kiwi (Apterygiformes) have declined significantly in range andabundance since human settlement. Little spotted kiwi (Apteryx oweniiGould) are nowprobably extinct on the mainland; great spotted kiwi (Apteryx haastiiPotts) are now mainlyconfined to high-rainfall regions of the north-western corner of the South Island; northernbrown kiwi (Apteryx mantelliBartlett) have disappeared from the lower third of the NorthIsland; and southern brown kiwi (Apteryx australisShaw & Nodder) are now largelyrestricted to Fiordland and Stewart Island.

Over the last century, kiwi abundance has probably declined by at least 90% in mostNorth Island forests. Buller’s (1887, 1888) historical accounts suggest former densities of40–100 adults km−2, whereas present densities seldom exceed 4 adults km−2 (McLennan andPotter 1992). Some parts of Northland and two offshore islands (Kapiti and Little Barrier)still support 50–100 adults km−2. Mainland populations, however, contain significantlyfewer juveniles (McLennan and Potter 1993) than do similar populations on predator-freeoffshore islands (Colbourne 1992).

Kiwi evolved in the absence of mammalian predators, but co-exist today with as manyas seven obligate and facultative carnivores introduced by Polynesians and Europeans(Wodzicki 1950). Recent studies show that a range of predators eat kiwi and their eggs,with different species being involved at different stages (McLennanet al. 1996). Impactsof predators on adults and eggs vary from place to place, but are often small and oflittle consequence. Fortunately, adult brown kiwi (2–3 kg) exceed the threshold prey sizeof cats and stoats, the largest of the common predators in mainland forests. Similarly,kiwi eggs benefit from their large size in that they are too big (mean length 129 mm)

q CSIRO 1999

10.1071/WR97091 1035-3712/99/020227$05.00

228 B. Basseet al.

and heavy (435 g) to be punctured or removed by rats. Immature kiwi, on the otherhand, consistently suffer heavy losses to stoats (Mustela erminea) and too few survive toreplace adult deaths in most years. This is the main cause of kiwi decline in mainlandforests (McLennanet al. 1996), though other factors (e.g. accidental poisoning in possum(Trichosurus vulpeculaKerr) control operations) accelerate the process in some areas.

Stoats were first introduced to New Zealand in 1855 to help control rabbits (Oryctolaguscuniculus) (Wodzicki 1950). They dispersed rapidly, aided by repeated liberations, and hadprobably spread throughout both the North and South Islands by the turn of the century(King 1990). Kiwi and stoats have therefore co-existed in mainland forests for approximately100–150 years. Stoat abundance varies between localities and years, apparently in responseto changes in the availability of their main foods (birds, rodents, lizards and invertebrates).These changes are particularly pronounced in beech (Nothofagusspp.) forests, where heavyseeding is followed by an irruption of mice, then stoats (King 1983). Measurements suggestthat even when stoats are at the low point of their cycle, they are still sufficiently abundantto prevent adequate recruitment of kiwi (McLennanet al. 1996). Other less-vulnerablespecies such as yellowhead (Mohoua ochrocephala) get a reprieve during low-stoat yearsand make good some of the losses incurred during an irruption (O’Donnellet al. 1992).

Here we identify: (1) the recruitment and predation rates needed to maintain kiwipopulations in mainland forests, and (2) the critical density that stoats cannot exceed toensure the desired recruitment rate is achieved.

Methods

Age-structure analysis of the population

The population is divided into two age classes, immature kiwi (differentiated by chicks andjuveniles) and adults (differentiated by gender) (Fig. 1). Chicks develop into independent juvenileswhen they leave the nest permanently, approximately 18–25 days after hatching (McLennan 1988).Juveniles become adults at an age of about 18 months (Reid and Williams 1975).

Fig. 1. Schematic diagram showing the age compartments of the population.

In particular, we are interested in the death rates due to predators of immature kiwi. Ifα1 andα2

are the (constant) natural mortality rate of chicks and juvenile kiwi per capita per year respectivelyand β1(s/S) and β2(s/S) are the (constant) mortality rate of chicks and juvenile kiwi per capita peryear due to predators then the rates of chicks and juvenile kiwi leaving the cohort due to death are−(α1 + β1(s/S)) and−(α2 + β2(s/S)) per capita per year respectively.

Impact of stoats on northern brown kiwi 229

We need to further clarify the predation rateβ(s/S) and the fraction part(s/S). Since stoats arethe main predators of immature kiwis (McLennanet al. 1996), we assume that the effect of otherpredators, besides stoats, on immature kiwi is negligible. The predation rate of immature kiwi percapita per year isβ(s/S) where s is the stoat density per square kilometre at timet (measured inyears) andS is the maximum density of stoats per square kilometre. (In practical terms,S is themaximum carrying capacity of stoats in any New Zealand forest.) The fraction(s/S) is a numberbetween 0 and 1 andβ(s/S) represents a predation rate that ranges between 0 (when there are nostoats, i.e.s = 0) and β (when s = S, that is, when stoats are at maximum density.) The scalingfactor, (s/S), is important (as opposed to having a single parameter to represent mortality) becausewe want to identify the critical densitysc at which β(sc/S) (the linear combination of the predationrates for chicks and juveniles) is low enough to allow kiwi to survive.

Let n1(t) and n2(t) be the number of male and female adult kiwi respectively at timet in years.Let f1 and f2 be the respective male and female mortality rates. Since adult kiwi are too large to bekilled by stoats, we treated their mortality rates as a constant. Ifb is the productivity rate per adultfemale per year then the number of chicks hatched in one year is given bybn2(t).

For survival, a female adult kiwi must produce at least one female chick that survives to adulthood.That is, each female must replace herself. We will use this principle to derive a survival threshold (acritical predation rate) at which juvenile recruitment equals adult mortality.

The parameters and variables used in the analysis are summarised in Table 1.

Table 1. Summary of parameters and variables

Description Parameter Value

The age (in years) when a chick becomes a juvenile 0·06The age (in years) when a juvenile becomes an adult 1·5The number of adult males at timet n1(t)The number of adult females at timet n2(t)Number of young produced per adult female per year b 0·85Natural death rate of chicks per capita per year α1 4·76Natural death rate of juvenile kiwi per capita per year α2 0·365Predation rate of chicks per capita per year β1(s/S) 3·97Predation rate of juvenile kiwi per capita per year β2(s/S) 3·1Death rate of adult males per capita per year f1 0·082Death rate of adult females per capita per year f2 0·082The stoat density per km2 present at timet sThe maximum possible density of stoats per km2 S 10The critical stoat density per km2 required for survival of kiwi sc

The data set and parameter values used in the analysis

The values for the parameters used in this analysis were taken from the data set compiled byMcLennanet al. (1996), the largest available for any species of kiwi. The productivity estimate ofb = 0·85 chicks per female per year was derived from 33 pairs in three different areas. The sexratio of adults in North Island forests varies from place to place but has no consistent bias, implyingthat average mortality rates are similar for males and females; thus, the adult mortality estimate off1 = f2 = 0·082 per capita per year was based on 122·1 radio-tracking-years of 171 individuals innine locations.

Mortality estimates of chicks (α1 = 4·76, andβ1(s/S) = 3·97 per capita per year) and juvenilekiwi (α2 = 0·365 andβ2(s/S) = 3·1 per capita per year) were derived by determining the fates of42 individuals in four locations. Deaths of immature kiwi were attributed to predators (64%) or othercauses (33%), according to criteria listed in McLennanet al. (1996).

Estimates of stoat densities in New Zealand forests were derived from: relative abundance indices(King 1983; Murphy and Dowding 1995); counts of animals removed during intensive kill-trappingoperations (Murphy and Bradfield 1992; McLennan 1997); mark and recapture studies (Murphy andDowding 1995); measurements of territory size and territory overlap (Murphy and Dowding 1994;1995); and biomass values for various predators in New Zealand forests (Brockie 1992).

230 B. Basseet al.

In beech forests following heavy seeding, stoats appear to reach densities of 7–9 resident animalskm−2. These estimates are based on a mark and recapture study (12 animals per 150 ha) andmeasures of the size of exclusive, core territories (20 ha for females, 25 ha for males). They do notinclude non-territorial and dispersing animals, so are conservative. Nevertheless, they are very similarto McLennan’s (1997) estimate of 9 animals km−2, derived by intensive kill-trapping on a 750-hapeninsula with restricted opportunities for immigration (65 animals removed over 3 months). Wetherefore assume that stoat densities in New Zealand forests reach a maximum ofS= 10 animalskm−2.

Trapping indices suggest that stoat densities in beech forests vary five-fold between years, dependingon the stage of the beech seeding-cycle (King 1983; Murphy and Dowding 1995). Natural fluctuationsin stoat density therefore appear to be within the range of 2–10 animals km−2. Densities may belower in forests where cats are plentiful (Brockie 1992) although, in such areas, the combined biomassof carnivores (0·032 kg ha−1) is equivalent to a stoat density of 10–11 adults km−2.

Results

Finding the critical recruitment rate required for survival

Assuming no stochasticity, the number of chicks that reach adulthood, is:

bn2(t − 1·5)e−(α+β(s/S))1·5

where

α = 1

1·5(

0·06×(

chick natural mortalityper year

)+1·44×

(juvenile natural mortality

per year

))= 1

1·5(0·06α1+ 1·44α2) = 0·5 per capita per year

βs

S= 1

1·5(

0·06×(

chick predation rateper year

)+1·44×

(juvenile predation rate

per year

))= 1

1·5(

0·06β1s

S+ 1·44β2

s

S

)= 3·1 per capita per year

and n2(t − 1·5) is the number of females in the kiwi population at time(t − 1·5), whichis when the juveniles reaching adulthood were hatched.bn2(t − 1·5) is the number ofchicks hatched at time(t − 1·5) and e−(α+β(s/S))1·5 represents the exponential decline(since immature kiwis leave the cohort at a rate proportional to numbers present) due tothe combined natural and predator rates of the chicks and juveniles.

Finding the threshold for survival

It is possible to find a series expansion for the number of adult males and femalesexplicitly and hence find out the asymptotic behaviour of the adults (Basseet al. 1997)as ert where r is explicitly determined andr = 0 corresponds to the threshold betweensurvival and extinction.

Here we show that the criterion for survival of female kiwi can be derived using theprinciple that each female must, in her lifetime, produce on average at least one femalechick that reaches maturity. A female has an average life expectancy of(1/ f2) years. Ofthe chicks hatched in her lifetime,(1/ f2)× (b/2)× e−(α+β(s/S))1·5 survive 1·5 years tobecome female adults. Thus, a survival condition for the whole kiwi population is:

b

2 f2e−(α+β(s/S))1·5 ≥ 1.

Impact of stoats on northern brown kiwi 231

The above inequality can be rearranged to give

βs

S<

1

1·5 ln

(b

2 f2

)− α

= 1

1·5 ln

(0·85

2× 0·082

)− 0·5

= 0·6 per capita per year.

This gives a critical value for the annual predation rate of immature kiwi ofβ(sc/S) = 0·6per capita per year. If the predation rateβ(s/S) falls below the critical valueβ(sc/S) = 0·6per capita per year then this will enable the population to sustain itself, while a predationrate above the critical value will eventually lead to extinction. Our criterion for survivalis therefore:

βs

S< 0·6 ⇒ SURVIVAL

βs

S> 0·6 ⇒ EXTINCTION.

The actual value ofβ(s/S) derived from field measurements isβ(s/S) = 3·1. Thisgreatly exceeds the critical valueβ(sc/S) = 0·6, and has to be reduced by a factor offive to ensure kiwi survival (Fig. 2).

Fig. 2. Immature recruitment versus predator mortality.

232 B. Basseet al.

Fig. 3. Sensitivity analysis ofβ(sc/S) = (1/1·5) ln((b/2 f2)) − α with α = 0·5. (a) β(sc/S)as a one-dimensional function off2 (with b = 0·85) and b (with f2 = 0·082) respectively.(b) β(sc/S) = (1/1·5) ln((b/2 f2)) − α as a two-dimensional function (with only positive functionvalues plotted) of f2 and b. The actual parameter values used in the modelling wereb = 0·85 andf2 = 0·082.

Recall that the number of chicks hatched that reach adulthood is

bn2(t − 1·5)e−(α+β(s/S))1·5.

In our data set, the number of kiwi hatched at time(t − 1·5) was bn2(t − 1·5) = 42.Given the threshold value ofβ(sc/S) = 0·6, the number that need to be recruited tomaintain population stability is42e−(0·5+0·6)×1·5 ≈ 8 or 19% of those hatched. Thepopulation can therefore sustain an 81% loss of juveniles without declining. In reality,the survival of immature kiwi is42e−(0·5+3·1)×1·5 ≈ 0. Clearly, the losses to stoats arethreatening the population with extinction.

Impact of stoats on northern brown kiwi 233

Sensitivity analysis of the threshold condition

The critical value for the predation rate per capita per year of immature kiwi is

βsc

S= 1

1·5 ln

(b

2 f2

)− α.

It is interesting to see how this critical value changes with small changes in eitherb orf2. It should be noted thatα is just a linear term soβ(sc/S) changes linearly withchanges inα. Since all parameters must be non-negative the feasible region forb and f2is b ≥ 2 f2e1·5α. If b is close to zero then the critical value is extremely sensitive tosmall changes inb but b = 0 is not in the feasible region. Fig. 3 shows graphicallyβ(sc/S) as a one- and two-dimensional function ofb and f2. Note that from McLennanet al. (1996), b can be in the range 0–1·72 per year andf2 is 0·04–0·14 per year.

Reducing the stoat population to find the threshold for survival

We have assumed that stoats are the main predator of young kiwi, and that reducingthe stoat population is the only way of reducing the predation rate. We also assume thatpredation losses change in direct proportion to stoat abundance. Thus, stoat populationshave to be reduced by 80% in order to reduce predation losses by 80%. Curvea in Fig. 4suggests that the survival threshold (19% recruitment) is reached when stoats decline toa density of 1·94 animals km−2. However, this critical density estimate is conservativebecause it assumes that stoats were at maximum density when the survival rates of immaturekiwi were measured in the field. In fact, the data were collected over a range of sitesand years, and so reflect average losses over an unknown range of stoat densities. If,

Fig. 4. Immature recruitment versus stoat density.

234 B. Basseet al.

at the time of the measurements, stoats were at an average density of 6 rather than 10animals km−2 (see curveb in Fig. 4) then the critical density for kiwi survival would becalculated as 1·16 animals km−2 rather than 1·94 km−2. We cannot find the exact valuefor the critical stoat density but we know it is between 0 and 2 animals km−2. Thus, toensure kiwi survival, stoat populations have to be reduced by at least 80% in years whenthey are abundant.

Discussion

Population declines of kiwi

Our results support the view of McLennanet al. (1996) that northern brown kiwi arefailing in mainland forests because of predation by stoats on immature kiwi. Current survivalrates of juveniles (1–5%) are well below the threshold required to maintain populations(19%). At the present rate of loss (about 6% per annum) many of the remaining populationsin the North Island will disappear over the next 40–50 years. Some have already done so(McLennan and Potter 1992; Miller and Pierce 1995). The estimate of time to extinctionis an approximation, based on the assumptions that the rate of loss is constant in timeand space, that demographic stochasticity and other chance events cause extinction whendensities fall below 0·2 individuals km−2, and that there are currently 2·5 kiwi km−2 inoccupied forests.

The first assumption is clearly not true, though it makes no difference to our estimate.Residual kiwi densities vary considerably within and between regions, and simple backprojections show that average rates of loss over the last 100 years must have been lessthan 6% in areas that currently support 1 or more kiwis km−2. In fact, it appears likelythat the decline started slowly, then accelerated as the birds became rarer. This patternwould be expected if predation losses diminish at high kiwi densities (Pechet al. 1995), apossibility now being investigated. King (1984) argued that predators are now unlikely tocause further avian extinctions in mainland habitats of New Zealand because the vulnerablespecies have already gone. However, she listed five species, all ancient endemics withrestricted distributions, that might be declining because of predation, and commented thatother ‘at-risk’ species could be identified following further research. King (1984) consideredthat sufficient time had elapsed for the full impacts of introduced predators to becomeapparent, a view that is not supported by our results or those of other recent investigations.

All of the five species on King’s (1984) list have continued to decline over the interveningdecade, with predation being confirmed as the main cause in at least three cases: kokako(Callaeas cinerea), black stilt (Himantopus novaezealandiae), kakapo (Strigops habroptilus).Other species now known or suspected to be declining because of predation includeyellowhead (Mohoua ochrocephala) (O’Donnell et al. 1992), kaka (Nestor meridionalis)(Beggs and Wilson 1991), northern brown kiwi (Apteryx mantelli) and great spotted kiwi(Apteryx haastii) (McLennan et al. 1996), New Zealand dotterel (Charadrius obscurus)(Dowding and Murphy 1993) and North Island weka (Gallirallus australis) (Bramley 1996).Remarkably, New Zealand pigeon (Hemiphaga novaeseelandiae), a relatively common speciesby today’s standards, also appears to be declining because of predation and (possibly)competition from introduced mammals (Cloutet al. 1995).

Other species currently regarded as being ‘safe’ may well be in a similar predicament,but few have been studied in sufficient detail to determine the factors regulating theirdistribution and abundance.

Clearly, predator impacts are far from over in mainland habitats of New Zealand. Speciesthat are still relatively common have not demonstrated an ability to co-exist indefinitelywith introduced mammals. Predator-induced declines can take much longer than 150 yearsto run their course. Certainly, the most vulnerable species have already gone, presumablybecause predator impacts were severe at all stages of their life cycle. Other species, suchas northern brown kiwi, have persisted for longer because predation impacts are either

Impact of stoats on northern brown kiwi 235

intermittent, restricted to one stage of the life cycle, restricted to particular habitats, orrestricted to one sex. Nevertheless, they are declining, but are just doing it more slowly.

Critical stoat density

Our analysis predicts that the critical stoat density, at which recruitment of juvenile kiwibalances adult losses, is estimated to be a value less than 2 animals km−2. To achievethis density, stoat populations have to be reduced by at least 80% in years when they areabundant. These management targets are tentative estimates based on limited measurementsof stoat density in New Zealand forests and the assumption that predation losses of youngkiwi are directly proportional to stoat abundance and independent of kiwi density (that is,it is a type I functional response). Nevertheless, two predictions of the analysis appearto be realistic: (1) that stoat populations have to be reduced substantially in order toproduce any measurable benefits, and (2) that in most habitats, stoat densities seldom, ifever, decline naturally to levels that allow adequate recruitment in kiwi.

The shape of each recruitment curve in Fig. 4 is such that small changes in stoatdensity of 0–5 animals km−2 greatly affect survival rates of juvenile kiwi. Once stoatdensities reach 5 animals km−2, further increases are largely irrelevant, because by thenchick survival rates are already close to zero. In ‘plague’ years, for example, the removalof 50% of the animals would have no significant effect on juvenile survival. The analysistherefore predicts that predation rates will not necessarily decline following the removalof large numbers of predators — the outcome of many mustelid-control operations in NewZealand (e.g. Reidet al. 1995). Indeed, if trapping operations generally remove only about50% of the stoats present, as (King and McMillan 1982) suggest, most will fail to reducepredation rates on young kiwi.

Trapping indices (captures per 100 trap-nights) suggest that densities of stoats in beech(Nothofagus) forests vary about five-fold between years (King 1983; Murphy and Dowding1995). Densities are both higher on average and less variable in mixed podocarp forestsand agricultural landscapes where food supplies are more constant (King 1990). Thesenatural variations in density appear to be within the range of 2–10 animals km−2, and thusseldom benefit immature kiwi. It is noteworthy, however, that kiwi are declining moreslowly in sub-alpine regions of the South Island than elsewhere (McLennan and McCann1994), possibly because in harsh, upland habitats stoats sometimes dip below the criticaldensity required for adequate recruitment.

Stoat densities vary seasonally within habitats, with a peak in midsummer. Mortalityof both pre-independent and newly-independent young is always very high, so the peak isshort-lived (King and McMillan 1982). Nevertheless, stoats are most plentiful in forestswhen young kiwi have either just become independent or are about to do so. At thesetimes, they outnumber kiwi chicks by as much as ten to one. Each stoat therefore has alimited opportunity to kill an immature kiwi, and most of them probably never do. Youngkiwi are merely an incidental item in their diet, a rare but nevertheless highly-vulnerableand easily-captured prey species. The general absence of kiwi remains in the digestivetract of stoats is therefore an expected result (King and Moody 1982; King 1983; Murphyand Dowding 1995), but one that belies the true relationship between the two species.

Significance of other predators

Our assumption that stoats are responsible for all predation losses of immature kiwi isunlikely to hold in all habitats. Stoats are the most widely distributed carnivore in NewZealand (King 1990), and are often the only large predator in forests dominated by beech(Nothofagus). Predator communities are more diverse in edge habitats where rabbits arepresent, and in forest tracts containing mixed hardwood and softwood assemblages. Someparts of the North and South Islands support sympatric populations of feral cats (Felis

236 B. Basseet al.

catus), ferrets (Mustela furo), weasels (Mustela nivalis vulgaris) and stoats, in variousproportions depending on habitat type (King 1990). All four species kill immature kiwi.

Our analysis may be applicable to mixed predator assemblages, using combined densitiesor biomass values, though we have not tested this. As it stands, it is applicable to alllarge forest tracts in both the North and South Islands, where stoats are invariably thedominant predator. It is probably of little or no use in small patches bordering farmland orriver-beds, where stoats are partially displaced by cats and ferrets. However, kiwi are nowrare in such habitats, except in parts of Northland and Taranaki (Reid and Williams 1975).

Future of kiwi in mainland forests

At present, immature kiwi are secondary prey and suffer excessive predation (Pechet al.1995). They are picked off easily by introduced predators, whose numbers are maintainedat relatively high levels by other more common and less vulnerable prey species. As ouranalysis indicates, the task of increasing recruitment rates of kiwi in mainland forests torequired levels is a daunting one, involving the removal of a high proportion of predatorsfrom large areas over a long time. Current methods of stoat control (intensive trapping) areonly occasionally effective (e.g. McLennan 1997) and too expensive and labour-intensiveto apply on a large scale (>1000 ha). Clearly, the persistence of kiwi on mainland NewZealand is now largely dependent on the development of new techniques for controllingstoats.

Acknowledgments

We thank Bill Lee and Tony Sinclair for commenting on the paper. We also thank thenumerous people who collected the data on kiwi upon which this study is based. Thisstudy was funded by a grant from the New Zealand Foundation of Research, Science andTechnology (contract No. C09405) to J. A. McLennan.

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Manuscript received 4 July 1997; accepted 2 July 1998

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