Oecologia. Limits to predator regulation of rabbits in Australia: evidence from predator-removal experiments. Off~orint requests to: R.

Transcription

1 eclgia (1992) 89:1~112 eclgia 9 Springer-Verlag 1992 Limits t predatr regulatin f rabbits in ustralia: evidence frm predatr-remval experiments R.P. Pech 1,.R.E. Sinclair 2.E. Newsme 1, and P.C. Catling 1 CSIR, Divisin f Wildlife and Eclgy, P Bx 84, Lyneham, CT 262, ustralia 2 The Eclgy Grup, Department f Zlgy, University f British Clumbia, Vancuver V6T 1Z4, Canada Received February 11, 1991 / ccepted in revised frm ugust 2, 1991 Summary. Predatr-prey studies in semi-arid eastern ustralia demnstrated that ppulatins f rabbits (ryctlagus cuniculus) culd be regulated by predatrs. The functinal, numerical and ttal respnses f fxes ( Vulpes vulpes) t rabbits and the numerical respnse f feral cats (Felis catus) t rabbits, are described. Measurement f the rabbit cmpnent f fxes' stmach cntents indicates a Type III functinal respnse. The size f the fx ppulatin in summer was dependent n the availability f rabbits ver the immediately preceding rabbit breeding seasn but there appeared t be n density-dependent aggregatin f yung fxes in areas f surplus fd. The ttal respnse f fxes, estimated using the shrt-term numerical respnse f dispersing fxes, was directly density-dependent fr lw rabbit densities and inversely density-dependent fr high rabbit densities. Tw states are pssible with this frm f ttal respnse: a state with lw rabbit densities regulated by predatrs and a state with high rabbit densities which ccurs when rabbits escape predatr regulatin. The bundary between regulatin and nn-regulatin by predatrs was demnstrated by a predatr-remval experiment. In the treated areas, predatrs were initially culled and rabbits increased t higher densities than in an untreated area where predatrs were always present. When predatrs were allwed back int the treated areas, rabbit ppulatins cntinued t increase and did nt decline t the density in the untreated area. This is the critical evidence fr a tw-state system. When predatrs were present, rabbits culd be maintained at lw densities which were in the density-dependent part f the ttal respnse curve fr fxes. Exceptinally high rabbit recruitment, r artificially reduced predatin, culd result in rabbits escaping predatr-regulatin. Under these circumstances, rabbits culd mve int the inversely density-dependent regin f the ttal respnse curve fr fxes. Key wrds: Predatr remval - Predatr regulatin - Functinal respnse - Numerical respnse ff~rint requests t: R. Pech D predatrs regulate their prey? The answer t this questin depends n the ttal respnse f predatrs t changing prey ppulatins. This respnse has been divided int the tw cmpnents f functinal and numerical respnses (Slmn 1949). The functinal respnse describes the effect f individual predatrs in terms f the number f prey eaten per predatr at different prey densities. The numerical respnse describes hw the whle predatr ppulatin respnds t changes in prey density. Hlling (1959, 1965) examined the mechanism f functinal respnses and identified tw majr categries knwn as Type II and Type III functinal respnses. The first imprtant feature f bth functinal and numerical respnses is that they reach an asymptte as prey density increases, the frmer because (amngst ther things) animals becme satiated and s cannt eat mre prey even if mre becme available; and the latter because predatrs tend t reach sme scially impsed limit thrugh such factrs as interference r territriality. Whatever the mechanism, these asympttes in functinal and numerical respnses result in a decreasing prprtinal effect n prey numbers, when prey density is high and increasing. This means predatrs have an inverse density-dependent effect at high prey densities. The secnd feature f predatr respnses ccurs at lw prey densities. If the functinal respnse is Type II (a simple cnvex curve) then the effect n numbers is inversely density-dependent at all prey densities. If, hwever, there is a Type III functinal respnse (an S-shaped curve), then the accelerating part f this curve at lw prey density results in a density-dependent respnse, while the decelerating part at higher prey densities has the same effect as the Type II respnse. Similarly, the numerical respnse can prduce a unifrmly inverse density-dependent effect, r a dichtmus effect f direct densitydependence at lw prey density and inverse densitydependence at high prey density. Because f these alternative cmplex nn-linear respnses, the ttal respnse (the prduct f functinal and numerical respnses) f a predatr ppulatin t its prey ppulatin can result in varius stable and unstable

2 13 interactins. These have been extensively described elsewhere (Ricklefs 1979). ne pssible interactin, which is the subject f this paper, culd prduce multiple stable equilibria between predatr and prey ppulatins (Hlling 1973). This hypthesis is illustrated in Fig. la where the ttal respnse is shwn tgether with the net recruitment iscline fr the prey (i.e. recruitment after the effects f resurce limitatin have been impsed). Withut predatrs the prey stabilises at K, the carrying capacity, which is determined entirely by resurces. With predatrs there are equilibria where the tw lines intersect. This mdel prpses that the predatr ttal respnse can result in prey ppulatins being held at tw very different densities, a lwer ne (, Fig. 1) at which predatin is directly density-dependent and regulating the prey; and a higher ne (C, Fig. 1) where predatin is inversely density-dependent and nt regulating. Between these tw there is an unstable equilibrium (B, Fig. 1) which acts as a bundary between the dmains f attractin - belw B prey ppulatins mve t, abve B they mve t C (Sinclair 1989; Sinclair et al. 199). In practice, the mdel predicts that if prey numbers increase past B then they will "utbreak" rapidly t C. Cnversely, if prey numbers are reduced belw B, they will cllapse t.,,=, 12. a This tw-state mdel can be represented in an alternative frm (Fig. 1 b) by pltting the finite rate f change f prey (numbers at time t+l ver thse at time t) against prey density. s in Fig. la, prey cllapse ccurs t the left f B, and the density range between and B is referred t as the "predatr pit". Figure 1 predicts that if either (i) net recruitment f prey increases (higher reprductin, mre resurces as indicated by levels 1-3, Fig. 1), r (ii) predatr ttal respnse decreases (fewer predatrs) then the range f prey densities where predatrs can regulate (thse lwer than B) decreases, i.e. prey can "utbreak" at a lwer density if they were initially at. In the extreme case (level 3), the and B intersectins disappear and the prey "utbreaks" spntaneusly. The mdel als predicts that nce the prey ppulatin has erupted twards C, then a return t the riginal cnditins befre the utbreak (either lwer resurces r higher predatr numbers) will nt cause the prey ppulatin t return t its riginal density at. Instead, the prey ppulatin will merely be limited by predatrs (indicated by the difference between K and C, Fig. la). t C resurces are regulating prey density and predatrs are nt (Sinclair 1989). This mdel f tw stable states in a predatr-prey system has been tested using data frm a predatr remval experiment in semi-arid ustralia. The remval f fxes (Vulpes vulpes) and cats (Felis catus) that were preying upn rabbits (ryctlagus cuniculus) has been reprted by Newsme et al. (1989) and Catling (1988). This paper presents data btained subsequent t the remval t test the predictins f the mdel. Predictins frm the mdel rr 2: B C K PREY DENSITY There are five predictins frm this tw-state mdel: Predictin 1. Predatrs shuld shw a Type III functinal respnse r equivalent numerical respnse. ls, the lwer range f bserved prey densities shuld be where predatin is directly density-dependent r at least belw the bundary density B. P_ IT 2: LL PREY DENSITY Fig. 1. a Schematic ttal respnse frm a Type III functinal respnse and a density-invariant numerical respnse (thick line), and three pssible levels f net recruitment f prey (thin lines) pltted against prey density. Fr levels i and 2, tw stable equilibria ( and C) are pssible. B is the bundary separating regulatin and nn-regulatin by predatrs. t recruitment level 3, the prey species escapes predatr regulatin, b The finite rate f change (Nt+ I/N~) f the prey ppulatin is 1 at the hrizntal line. The ppulatin increases abve this line, decreases belw it. Three levels f recruitment are shwn. In years with prer recruitment (level 1 cmpared t level 2), the "predatr pit" between and B is deeper and predatrs are able t regulate their prey t higher densities. t level 3 the "predatr pit" disappears Predictin 2. In cntrast, the higher range f prey densities shuld be abve B and predatin shuld be inversely density-dependent. Predictin 3. n utbreak f prey shuld be induced experimentally by remval f predatrs while reprductin f prey des nt change. Predictin 4. In cntrast t (3), natural utbreaks f prey shuld be bserved in the presence f predatrs when net recruitment f prey increases thrugh imprved fd supply and reprductin. Predictin 5. The reintrductin f predatrs n terminatin f the remval experiment shuld result in the prey ppulatin remaining at the higher range f densities. Predatrs shuld nt be able t reduce the prey t their

3 14 riginal densities befre the remval began, r t densities in untreated areas. While all predictins are cnsistent with the mdel, predictins 3 and 5 tgether prvide the unique test fr a tw-state system as ppsed t a single-state system. Rabbits, fxes and feral cats in ustralia The Eurpean rabbit is a chrnic pest ver much f semi-arid ustralia. In general rabbit numbers are highest in spring and early summer; breeding ccurs at any time f the year but is cncentrated in late winter and early spring (Gilbert et al. 1987). Rabbit density can vary dramatically depending primarily n fd quality, quantity and persistence (Cke 1974), and n disease (especially myxmatsis) and predatin. Evidence frm semiarid New Suth Wales suggests that predatin, especially by fxes and feral cats, is an imprtant factr regulating rabbit ppulatins (Parer 1977; Wd 198; Newsme et al. 1989). Feral cats are established in a wide range f habitats thrughut ustralia. Fxes are widespread and abundant in all, except nrthern parts, f the mainland despite attempts in sme areas t cntrl them by shting and pisning. Their distributin is highly cincident with rabbits. Several studies shw that where rabbits are available they cnstitute an imprtant part f the diets f bth fxes and cats (Catling 1988 and references cited therein). There is verwhelming evidence fr a strng interactin between the three species. Methds The study was cnducted ver 5 years in Yathng Nature Reserve (3345 ' S; 1453 ' E) in semi-arid New Suth Wales, ustralia. The study area f abut 17 km 2 was basically a flat t undulating band f cleared grassland with scattered trees and flanked by wdlands. detailed descriptin f the vegetatin is given in Parer and Libke (1985) and the prevailing climatic cnditins in Newsme et al. (1989). Measurement f rabbit and predatr ppulatins Frm February 1979 t May 1983, the densities f rabbits, fxes and cats were assessed every 6 weeks r s by sptlight cunts (numbers f animals km -1) n standard transects ranging frm 8 t 32 km in length. Between June 1981 and January 1984, an index f rabbit density was als btained frm cunts f active (used) burrw entrances in grups f warrens. In (see Newsme et al. 1989), warren grups were larger than in when each cnsisted f fur adjacent warrens. The distributin f warren grups was essentially unchanged. Frm 1979 t 1982, the scial structure f rabbits was studied intensively n a grup f warrens centrally lcated in Yathng Nature Reserve (D.H. Wd and M. Stanger, unpublished data). The mst cmplete data set was cllected fr ne f the main warrens in the grup and was used here t assess rabbit recruitment during 1979, 1981 and Cunts were cnducted ver 2-11 days per mnth during the breeding seasn. ll rabbits n the warren were identifiable, with juvenile rabbits being trapped and tagged within a few days f their emergence at the surface f the warren. Predatr-remval experiments Three predatr-remval experiments were cnducted frm June 1981 t January 1984 and the results f tw f them are published in Newsme et al. (1989). Briefly, in the first experiment predatrs were remved frm ne blck () f 7 km 2 with n treatments n tw ther blcks (B and C) f 18 and 5 km 2. fter the first year, blck B was subdivided and predatrs als remved in the nrthern half (BI ; 9 km 2) fr a secnd experiment t examine repeatability and site specificity f the results. The third experiment reprted here began in mid In this experiment predatrs were sht intensively n blck as befre, but nly 3 cats and 3 fxes were remved frm blck B1. Shting f predatrs ceased in ugust 1983 and they were then allwed t reinvade the experimental blcks. Rabbit numbers were mnitred thrughut the remval and reinvasin perid until January 1984 by cunting active burrw en trances, but sptlight cunts f rabbits were discntinued because vegetatin grew t tall. During the predatr-remval experiments, shting was cnducted every night fr 2 weeks initially and then averaged 1 week in every 2-3. ttal f 288 fxes and 112 cats were sht. Stmach cntents were srted int prey species and weighed (Catling 1988). Results bundance f untreated rabbit and predatr ppulatins Sptlight cunts f rabbits, fxes and cats were cnducted regularly between February 1979 and May 1983 n areas where predatrs were nt remved (Fig. 2). Frm an already high density f 64 rabbits km-t in January 1979, rabbits increased spectacularly t 31 km-t by ctber, with the utbreak being curtailed by the nset f a severe drught in the summer f Rabbits then persisted at lw levels (< 3 rabbits km-1) with belw average rainfall (242 mm) in 198. Fllwing abve average rainfall in 1981, rabbit numbers increased with maximum densities (+_ SE) f 8.8+_3.2km -~ n blck C in 1981 and 13.2_+3.6 and km -1 n blcks C and B2 in Fxes and cats appeared in sptlight cunts in generally cmparable numbers. Fx densities were highest in 1979 at 7 E C t~ Y= t2~ l- :~.3 c~ 1. C rabbits.. -/)~\ /." "'... -"./ "LX - ~11 \~1 \\ l l /; , 198, 1981, Fig. 2. Sptlight cunts f rabbits, fxes and cats n areas where predatrs were nt remved (blcks B - -, B2... and C... ). Cunts were cnducted ver 32, 18 and 13 km respectively

4 km -~ in February and I km -~ in Nvember. Restricted activity f female fxes and their pups during denning may have cntributed t lw cunts f fxes in late winter and early spring (ugus~september 1979). The highest cat density, km -1, ccurred in Nvember Bth predatr species were mre abundant in 1979 and early 198 than in the fllwing 3 years. bundance f rabbits during predatr-remval experiments Predatr remval in the first and secnd experiments began in July 1981 and prduced a times greater rabbit density than in blcks B2 and C where predatrs were undisturbed. Rabbits reached a maximum density f km -~ in 1982 when predatrs were remved. 4.5-mnth drught at the end f 1982 reduced rabbits t lw abundance thrughut the remval and untreated areas (Newsme et al. 1981). The third predatr-remval experiment began in March 1983 and cntinued until ugust. Exceptinally heavy rains fell in autumn (frm March nwards) which prduced a flush f vegetatin in winter and spring (June-Nvember). ctive entrances t rabbit burrws were used t assess rabbit ppulatins thrughut T allw fr different-sized warren grups in 1983 and , the data were rescaled t the average number f active entrances per warren (Fig. 3). The number f rabbits is a linear functin f active entrances in the nn-breeding seasn (Parer 1982) but the relatinship may be variable when rabbits are breeding and nnlinear fr very high density ppulatins (Parer and Wd 1986). Hwever, valid cmparisns can be made between years fr equivalent perids in the breeding/nn-breeding cycle. In the pril-june (late autumn t early winter) perid f 1981, 1982 and 1983, prir t the main breeding seasn, rabbit ppulatins fr all blcks (except blck in 1982) were at the lw pint fr the year and in the cc 15- ~ 1- g experiment 1 experiment 2 experiment 5 I I I remval f : predatrs ceased.: Dec Jan Des Jan Dec Jan Fig. 3. Mean active entrances per warren during the three predatrremval experiments, June 1981 t January Data have been rescaled frm the number f active entrances per warren grup (Newsme et al. 1989) t the number f active entrances per warren. Predatrs were remved n blcks ( ) and B1 (... ). Blcks B ( -- - ) and B2 (... ) were untreated range active entrances per warren. Rabbit numbers were higher n the remval blck in autumn 1982 due t a cmbinatin f predatr cntrl and relatively lw lsses f rabbits during the mderate weather cnditins ver the summer (Newsme et al. 1989). Predatr remval prduced three respnses in rabbits during the breeding seasn, (i) Where predatrs were nt culled (blck B up t June 1982 and B2 thereafter), active entrance cunts never exceeded (mean + SE) per warren, even during the favurable cnditins f (ii) ctive entrances per warren reached peaks f (blck ) and (blck B1) n the remval areas in (iii) Between July and September 1983, bth remval blcks recrded temprary declines t () and (B1) active entrances per warren when predatr-remval ceased. Hwever by January 1984, active entrances per warren had reached n blck and n blck B1, despite the free access t predatrs ver the preceding 4 mnths. Functinal respnse f predatrs The functinal respnse f fxes t changes in rabbit density is shwn in Fig. 4. In the first tw remval experiments rabbit density was measured by sptlight cunts at intervals averaging 35 days. The technique did nt detect rabbits less than abut 5 days ld (Cke 197; I. Parer unpublished data) but this age class is a minr prtin (2%) f rabbits eaten by fxes (Catling 1988). Cnsumptin f rabbits was btained frm a sample f 281 stmach cntents f fxes cllected between June 1981 and May 1983 (Catling 1988). This sample was subdivided int the same time perids as thse used t estimate rabbit density. verage sample size was 11.1 fxes (tw perids were ignred due t insufficient samples). The weight f rabbit remains in the fx stmachs was taken as an index f number f rabbits eaten. The functinal respnse (Fig. 4) was calculated using the methd described in the appendix, with parameter values f T= 12 h fr the number f hurs fxes frage per day and ~ =.75 h fr the mean retentin time f fd in a fx's stmach. There are three main features: (i) few rabbits were eaten by fxes when the density f rabbits was lwer than 4-5 rabbits km-1, (ii) abve this density per capita cnsumptin increased with the density f rabbits, and (iii) at high rabbit densities, (> 17 rabbits km-1) cnsumptin appears t plateau. Unusual r systematic changes in the availability f alternative fd surces influenced the functinal respnse t rabbits. t Yathng, fxes ate mre carrin in the autumn-winter perid than in spring-summer (Catling 1988). This was the nly imprtant seasnal shift t an alternative fd item. The difference between thse tw perids appears t cntribute much f the variability in the data at high rabbit densities (Fig. 4). ne ther majr change in fd availability ccurred during a flush f insects in June f 17 fxes' stmachs 8 were full f caterpillars, mths and grass-

5 16 15,5-u 1 EQ- ~J X ~- ~- 5. [D 9 > ~ 9 -/-~, "., 1 2 5' rabbit density (sptlight cunts: rabbits km -1) Fig. 4. Functinal respnse f fxes t rabbits. Data are divided int spring-summer () and autumn-winter (9 perids, and each pint represents the mean amunt f rabbit per fx stmach per day. ne pint (*) crrespnds t a shrt-lived change in the diet f fxes during an eruptin f invertebrates. The curve is a Hlling Type III functinal respnse (see ppendix) >, 9 g ~ 2. q ~ 1.5.-~ ~ X~ 1. 5 is ~:.5 [D 9 E~.c 1; 2; s; Spring/summer peak in rabbit density (sptlight cunts: rabbits km -1) Fig. 5. The numerical respnse f fxes t rabbits. Sptlight cunts f fxes during dispersal in autumn are pltted against the maximum recrded rabbit density fr the immediately preceding rabbit breeding seasn T E S +8 _ U~ ,5, 8 Z~ 1; 2; s; Sptlight cunts: rabbits km -1 Fig. 6. The numerical respnse f feral cats t rabbits. The density f cats was estimated in summer () and autumn (~) and each estimate pltted against the maximum recrded density f rabbits in the preceding 3 mnths hppers and very little rabbit was fund. This sample was mitted in fitting a Type III functinal respnse f the frm y = bxz/(az-t-x2), where y is the average weight f rabbit in a fx's stmach and x is the rabbit density. Estimates (_+ SE) fr the saturatin level, b, and the nset f saturatin in a sigmid curve, a, are g d-1 and 7.9_+ 1.9 rabbits km -1 respectively. The curve accunts fr 8% f the variance in the data. The test fr using a Type III rather than a Type II respnse is explained in the appendix. The functinal respnse fr cats was nt measured because nly a few were sht, mst f these at the start f the predatr-remval experiments n blcks and B1, with few seen thereafter. Furthermre, cats fed upn very yung rabbits (< 5 days ld) (Catling 1988) whse densities were nt measured. Numerical respnse f predatrs Ttal number f fxes and cats. In semi-arid ustralia, fxes which survive t disperse in late summer and autumn (March-May) are the prduct f a breeding seasn beginning in the previus winter (June-ugust), prducing a delay in the numerical respnse. In Fig. 5, the peak in the density f fxes during the dispersal perid is pltted against the peak in rabbit densities fr the immediately preceding rabbit breeding seasn. This shws that the summer-autumn fx ppulatin was dependent n the size f the rabbit ppulatin ver the preceding 6 mnths. Fx numbers appeared t decline in the perid fllwing dispersal t an annual lw arund ugust (Fig. 2). The numerical respnse f cats is shwn in Fig. 6 frm the plt f cat density in mid-summer and autumn (determined frm sptlight cunts) against rabbit density 3-4 mnths earlier. The maximum rabbit density fr these perids was used as a measure f the fd supply fr each chrt f cats, ver the perid In sutheastern ustralia mst cats are brn in tw perids, September-ctber and December-January (Jnes and Cman 1982a). There was a 3-4 mnth lag in the bserved numerical respnse. The yungest cats in the sht sample were 94 days ld, as determined frm their weight (Rsenstein and Berman 1973 ; Jnes and Cman 1982a), and bth transect cunts and culling relied n detecting animals at night with sptlights. The relatinship between the sizes f the cat and rabbit ppulatins shwn in Fig. 6 is nt as clear as that fr fxes. This may be due partly t the difficulty f estimating the fd supply fr cats brn in December- January, when there were few yung rabbits t eat. Because adult rabbits were a minr cmpnent f the diet f cats, the survival f cats during late summer and autumn may be a functin f alternate prey including birds, reptiles and invertebrates (Catling 1988). Spatial distributin f fxes and cats. Mvements f predatrs, particularly when yung animals were dispersing, culd have changed the lcal density f the predatr ppulatin. s a result, the nn-resident prtin f the predatr ppulatin culd have been the mst respnsive

6 17 c.i e _ -8.2 ~ x (3D L ~.1 9..~ 9 1 ' 2' 3' Rabbit density (sptlight cunts: rabbits km -1) Fig. 7. The number f fxes remved frm blcks () and B1 (e) relative t the density f rabbits, as an index f fx dispersal >~ ~ 5- IDLQ Em ~_ 2 q) x ~ 1 ~ "6& E.~ a z Jan ~_.6- ~s._~.4-- &.2-13_. 1981, Dec Jan Dec Jan Jan Decdan Decdan Fig. 8. a Influx f fxes nt the remval blcks () and B1 (e), June 1981 t January b The prprtin f male fxes remved frm blcks and B1 cincide with lw r declining rabbit numbers in late summer. Fig. 7 shws that, fr the remval blcks and B 1, there appeared t be n density-dependent numerical respnse f incming fxes t an increasing rabbit ppulatin during the winter-spring perid. Higher numbers f fxes early in 1982 and 1983 (Fig. 8a) were due almst entirely t the arrival f juveniles less than 9 mnths ld (P.C. Catling, unpublished data). Fr the remainder f the year, fxes sht n the treated blcks were predminantly in the 9-24 mnth age class. Cnsequently, after resident fxes (mstly lder than 24 mnths) were remved in the first few weeks f the experiment, there appeared t be little r n expansin f territries nt the treated blck by neighburing lder fxes. This was despite a fld difference in the density f rabbits between treated and untreated areas in the spring f Frm the winter f 1981 t the winter f 1983, the rati f males t females was clse t parity except fr the autumn (March-pril) f 1982 (Fig. 8b) when fxes were dispersing (Fig. 8a). In this 2-mnth perid 28 males and 7 females were remved frm blcks and B1. By cntrast, during the main dispersal perid in early 1983, 44 males and 41 females were remved frm the same area. The difference in sex rati in the tw years may have been prduced by differences in fd supply. In 1982 there were high numbers f rabbits and yung female fxes may have remained n their natal territries, and nly males dispersed. In 1983, rabbit numbers crashed and all yung may have dispersed prducing a mre even sex rati f dispersers. This interpretatin is cnsistent with the mdel f Macdnald (1983) and Lindstrm (1989) which suggests that grup size rather than hme range is adjusted t fd supply. Mst cats were remved at the beginning f the experiments n blcks and B1, apart frm ne shrt perid during January and February 1982 n blck. Reclnizatin f blcks and B1 by cats f all age grups appeared t be slwer than that f fxes. Hwever, the higher numbers f cats remved frm blck early in 1982 may have been immigrants frm adjacent areas resulting frm a summer maximum in the cat ppulatin (Jnes and Cman 1982b; M. Izawa and T. Di, pers. cmm.). Ttal respnse t patchiness in fd supply. We cnsidered such mvements as part f the numerical respnse f predatrs [i.e. nt as aggregative mvements which cntribute t the functinal respnse (Murdch and aten 1975)]. The number f fxes remved during the experiment prvided an estimate f immigratin ver apprximately mnthly time intervals (average f 35 days) which culd be cmpared t rabbit abundance (Fig. 7). The number f fxes remved was mre variable fr lw rabbit densities (in the range 4-15 rabbits km-1) cmpared t high rabbit densities. Much f the variability in fx numbers was due t the dispersal f yung fxes which tended t The ttal respnse f fxes t rabbits is the percentage fftake f rabbits by all fxes as a functin f rabbit density. Changes in the ttal respnse within ne rabbit breeding seasn will depend n prcesses perating n a time scale f days r weeks. These prcesses include the daily cnsumptin f fd and the mvements f nnresident fxes. Frm the evidence presented abve, we can assume that the shrt-term numerical respnse is either (i) strictly density-invariant r (ii) apprximated by the dispersal rate f nn-resident fxes (Fig. 7). In the frmer case, the density-dependence in the ttal respnse will cme nly frm the functinal respnse as shwn in Fig. la. Then the maximum rabbit density fr a predatr

7 18 Z3 2~ ~2 -- E (D ~ , [] [] [] EW DD3 [] [] [] [] [] 1 2 Rabbit density (sptlight cunts: rabbits km -1) Fig. 9. Ttal respnse f fxes t rabbits fr the predatr-remval blcks and B1. ne pint (+) crrespnds t an eruptin f invertebrates E E 2 9 &.1= Rabbit abundance (number f juveniles and adults) Fig. 1. Rabbit recruitment rate fr 1979 (), 1981 (e) and 1982 () (D.H. Wd and M. Stanger, unpublished data) regulated equilibrium pint,, is given by the inflexin pint in the functinal respnse which is at rabbits km- 1. The ttal respnse was calculated using the secnd assumptin fr the numerical respnse f fxes. The ttal respnse in Fig. 9 is an index rather than an abslute measure because sptlight cunts were nt calibrated t estimate true density. Predatin increased rapidly with rabbit densities between 5 and 8 kin-1 then declined fr densities greater than 8 km- 1. This is cnsistent with the estimate fr the maximum value f based nly n the inflexin pint in the Type III functinal respnse. Thus, bth assumptins prvide similar estimates f the range f rabbit densities where predatrs culd be regulating rabbits. Rabbit recruitment Juvenile rabbits first appear at the surface f their warren when they are abut 21 days ld (Parer 1977). Fr the 1979, 1981 and 1982 breeding seasns, mnthly per capita recruitment was calculated as the number f newly emerged juvenile rabbits divided by the ttal number f rabbits (lder juveniles plus adults) in the warren at the start f the mnth (D.H. Wd and M. Stanger, unpub- [] 3' 3; lished data). The ttal number f rabbits n a warren was a measure f the lcal abundance f rabbits because n new warrens were excavated during the study. The number f newly tagged rabbits increased frm 13 t 46 ver the breeding seasn in Fr 1981 and 1982, per capita recruitment was much lwer and appeared t decline as the breeding seasn prgressed (Fig. 1). Discussin We nw cmpare these results with the predictins utlined in the intrductin fr a tw-state predatr-prey mdel. Predictin 1 Predatrs shuld shw a Type III functinal respnse r equivalent numerical respnse. ls, the lwer range f bserved densities shuld be where predatin is directly density-dependent in the ttal respnse curve, r at least lwer than the bundary density B (Fig. 1). The results in Fig. 4, tgether with the analysis described in the appendix, demnstrate a Type III respnse fr fxes. There was a lwer threshld density f rabbits belw which predatin by fxes was minimal, fllwed by a density range where the fx cnsumptin rate increased. The numerical respnses f fxes and feral cats were less clear because predatr ppulatins culd have respnded t the density f prey in different ways: a delayed respnse culd have ccurred thrugh recruitment because predatr and prey breeding seasns were ut f phase; but a mre immediate density-dependent respnse may have resulted frm the decline f prey numbers r frm dispersal f predatrs (Sinclair et al. 199). The ttal respnse curve (Fig. 9) suggests that predatin is density-dependent up t 8 rabbits km- 1 and that the bundary density B must lie in the range 8-15 rabbits km-1 bserved densities, therefre, when rabbits are nt in utbreak, shuld be lwer than 15 rabbits km-1 if the mdel is crrect. With a seasnal breeding cycle and large betweenseasn variatin in climate, ne shuld expect cnsiderable natural variatin in rabbit density. Nevertheless, a lng perid f quasi-equilibrium with cnsistently lw rabbit density ( < 3.4 kin- 1) was recrded ver 27 mnths frm pril 198 t June This was in the presence f predatrs (blcks B and C) and is cmpatible with the predictin frm the ttal respnse curve fr fxes (Fig. 9) f a predatr-regulated equilibrium at < 8 rabbits km - 1. Where predatrs were nt culled in experiments 1 and 2 (blck B in and B2 in ), rabbit densities were always less than km-1. Sptlight cunts are nt available fr blck B2 after mid-1983 but cunts f active entrances per warren in January 1984 were 6.4 =k.6 and less than 7.9 :k.6 which was the maximum bserved in 1982 (Fig. 3). These data are als cnsistent with an upper limit fr predatr-regulatin f abut 15 rabbits km- t.

8 19 Predictin 2 The higher range f prey densities shuld be abve B (i.e. > 15 rabbits km-1), and lie in the range where the ttal respnse is inversely density-dependent Naturally ccurring high densities in 1979 reached 31 rabbits km -1, well abve B. In 1982 n blcks and B1 where predatrs were remved, rabbits reached densities f and rabbits km-1 respectively, bth f which are greater than the estimated upper limit f 15 rabbits km -1 fr the bundary, B. Cunts f active warren entrances fr blck in 1981 (Fig. 3) suggests that rabbit abundance was similar t the remval blcks in Similarly, cmparisn f the maximum values in 1982 and January 1984 (Fig. 3) indicates that rabbit abundance n the remval blcks in the summer f was greater than 15 rabbits km-l These results, therefre, are cnsistent with the secnd predictin. Predictin 3 n utbreak f prey shuld ccur by remving predatrs experimentally, if prey were being regulated at (Fig. 1). Predatr remval caused an increase in rabbit density int the range where predatin was inversely densitydependent. The high numbers f rabbits were nt due t alternative causes such as gd fd because rabbits remained in lw density where predatr regulatin cntinued n the untreated blcks (B, B2, C). Predictin 4 Under natural cnditins, utbreaks f prey shuld ccur as a result f gd fd and high reprductin. This is represented in Fig. 1 by level 3. The utbreak f rabbits in 1979 was a natural event, and ccurred when predatrs were present at levels generally greater than thse in Data frm warrens in the centre f the study area indicate that the per capita recruitment f rabbits in 1979 was mre than duble that in (Fig. 1). This suggests that enhanced breeding in 1979, resulting frm favurable envirnmental cnditins, allwed rabbits t escape predatr-regulatin. Predictin 5 In a predatr-remval experiment which has allwed the prey t reach high densities, the system shuld remain in this state, and nt revert t lw prey densities, when predatrs are reintrduced. This predictin was tested when predatr remval ceased in ugust Despite gd rainfall prviding an abundance f fd in the winter and spring f 1983, rabbit numbers n the untreated blck B2 were always lwer than at equivalent stages in the rabbit breeding seasn in This implies that predatr-regulatin was pssible in and that cnditins were nt as favurable fr rabbits as in the lead-up t the 1979 plague. 5 c ~ 4 3 ~. /',. i_~ S~ " L 1...,E ' I 1 I Rabbit density (average active entrances per warren) Fig. ll. Finite rate f change (N~+ 1/N~) f rabbit ppulatins, June 1983 t January 1984, fr the remval blcks (--) and B1 (.) and the untreated blck B2 (z~--). Rabbit density was estimated using the mean number f active burrw entrances per warren. The rate f change fr each interval is pltted against the average density f rabbits, (N~ N~)/2. N change (N t + lint = 1) is indicated by the dashed line Up until ugust 1983, while predatrs were being culled n blcks and B 1, rabbits increased as in earlier years indicating n significant effect f ther pssible regulating factrs such as myxmatsis. The density f predatrs was nt mnitred after predatr cntrl ceased. Hwever, the experience f previus years indicates that fxes wuld have reccupied these areas rapidly (Newsme et al. 1989). Reclnizatin by cats wuld have als ccurred thugh pssibly t a lesser extent. Therefre, predatin shuld have been the mst imprtant cause f rabbit mrtality n blcks and B1 after ugust 1983, similar t that n the untreated blck B2. When predatrs were allwed unrestricted access t the treated areas after ugust 1983, there was an immediate drp in rabbit abundance clse t the upper limit fr predatr regulatin (B in Fig. la). Hwever, the decline after ugust was shrt-lived and by January 1984, rabbit abundances n blcks and B1 were greater than the maximum value reached n blck B1 during the predatr-remval experiment in The inability f predatrs n the treated blcks and B 1 t prduce a decline in rabbit abundance t the level n the untreated blck B2 demnstrates the existence f the bundary B (Fig. la) and is the evidence necessary t distinguish between a tw-state and a single-state system (Sinclair 1989). The results f the experiment can als be illustrated in the frm f Fig. 1 b. Finite rates f change in the number f active warren entrances were calculated fr the intervals between each f the five censuses between May 1983 and January The average time between censuses was 57.5 days. In Fig. 11 the finite rate f change fr each perid is pltted against the index f average rabbit density fr that perid. Fr the untreated blck B2, where predatrs were always present, the rate f change decreased as rabbits increased. The trajectry is equivalent t the segment f the graph fr densities less than in Fig. lb. Predatrs were initially cntrlled n blcks and

9 11 B1, which resulted in high rates f increase fr rabbits. fter shting stpped, the rabbit ppulatins declined due t the impact f predatrs and Nt+ lint fr the time interval when predatrs returned was less than 1. Rates f change were greater than 1 after this perid and the trajectries are equivalent t the apprach t the highdensity equilibrium, C, in Fig. lb. In summary, these results are cnsistent with predictin 5. Cmments There are a number f assumptins underlying these results. The primary cause f rabbit mrtality is assumed t be predatin by fxes and cats. Starvatin was prbably an imprtant cntributing factr during the severe drughts after 1979 and 1982 (Newsme et al. 1989). ther causes f rabbit mrtality included myxmatsis and predatin by raptrs. During the predatr-remval experiment, the effects f a virulent strain f myxma virus were bserved fr nly ne shrt perid in February 1982 (D.H. Wd and M. Stanger, unpublished data). few raptrs, mstly wedge-tailed eagles (quila audax), were present during the predatr-remval experiments. lthugh wedge-tailed eagles fed upn rabbits (Ridpath and Brker 1986; Rbertsn 1987), they had little impact n the rabbit ppulatin (Newsme et al. 1989). The bservatin f the interactins f predatrs and rabbits using census data was pssible with minimal disturbance t the system. In cntrast, the measurement f the functinal and numerical respnses using predatr-remval experiments required a majr perturbatin t the predatr ppulatin. Despite this, the cnclusins frm these tw sets f data are cnsistent. ne reasn may be that the diet f the predminantly yung, nnresident fxes cllected frm the remval areas was representative f neighburing fx ppulatins. Catling (1988) fund that the diet cmpsitin f yung and ld fxes was nt significantly different. The data fr the functinal respnse were cllected ver a series f 1-week shting perids during which little variatin in rabbit density was likely t have ccurred. This is a gd apprximatin t an ptimal experimental design where per capita predatin is measured ver a range f prey densities with prey density fixed fr each measurement. The functinal respnse shuld be a measure f the number f rabbits killed per predatr per unit time. The methd based n the cntents f fxes' stmachs apprximates this by estimating the bimass f rabbit eaten per fx per unit time. Therefre, ne surce f errr culd be frm fxes either caching their prey r discarding prtins f the carcase. Sargeant (1978) estimated that fx cubs cnsumed n average 8% f prey (mstly adult ducks) althugh this increased t 94% when the availability f prey was restricted. Cmparable figures fr prey cnsisting f jackrabbit (Lepus twnsendi) are 88% and 92% respectively. The remaining prtins f prey items were cnsidered t be nncnsumable parts. Surplus killing has been bserved fr red fxes (Kruuk 1972; Macdnald 1976) and a cntributing factr ap- peared t be a failure f prey t initiate anti-predatr behaviur. This situatin may ccur during a drught when rabbits are starving. Cnclusin Frm the abve results, we can pstulate that at Yathng the fx-cat-rabbit system can switch between the predatr-regulated state with lw rabbit densities and the state with high rabbit densities in several ways. pattern f predatr-regulatin with lw rabbit numbers culd be established if drught r myxmatsis caused rabbit numbers t crash, r if the perid when rabbits were nt breeding was sufficiently lng fr predatin and ther causes f mrtality t cull rabbits t a density less than the value at B. The rle f drught in this prcess lead t the cncept f "Envirnmentally Mdulated Predatin" described by Newsme et al. (1989). The system culd jump t high rabbit numbers and n predatr regulatin if rabbits experienced exceptinally gd breeding cnditins such as thse prir t the 1979 eruptin (level 3 in Fig. la), if predatrs were cntrlled (fr example by shting r pisning), r if fr sme ther reasn the density f rabbits at the start f the breeding seasn was greater than B. The results frm bth the experimental remval f predatrs and frm natural utbreaks f prey are cnsistent with all 5 predictins f the tw-state mdel and are incnsistent with a ne-state mdel. This is the first experimental study t indicate that predatrs, especially fxes, can regulate rabbits (Trut and Tittensr 1989). It is als ne f the few tests f the hypthesis that predatrs can regulate a mammal ppulatin (Sinclair et al. 199). cknwledgements. We wish t thank D. Wd and M. Stanger fr the use f unpunished data. The cntributins f W. Menzies, J. Libke, R. Burt, G. Pfitzner, L. Custer and H. Wakefield in cllecting data are als gratefully acknwledged. Thanks are due t I. Parer, L. Crbett and H. McCallum fr critical cmments n a draft f this manuscript..r.e. Sinclair was supprted in part by an Izaak Waltn Killam Research Fellwship frm Canada and research grants frm N.S.E.R.C., Canada and the Divisin f Wildlife and Eclgy, CSIR. The field study was supprted financially by the ustralian Wl Research Trust Fund. ppendix Calculatin f the functinal respnse ssuming fxes eat rabbits in a series f discrete meals, the cnsumptin f rabbit per fx per day can be estimated as fllws. In general, fxes feed predminantly at night (Llyd 198), a behaviur pattern in accrd with bservatins f fxes at Yathng. Therefre the number f hurs f fraging per day, T, is apprximately 12 h, althugh this culd be adjusted fr the varying perid f daylight thrughut the year. In a sample f n fx stmachs, n, cntain rabbit

10 111 remains. ssuming that the time perid when each sample was cllected is representative f the fraging behaviur f fxes and that this behaviur was nt influenced by sptlight shting, nr/n is the fractin f the fraging time, T, that a fx's stmach cntains enugh rabbit t be detected, i.e.t.(n,/n) is the average number f hurs per day that a fx has detectable levels f rabbit in its stmach. Because there is an expnential decline in the bimass in the stmach (Warner 1981), a meal f M grams remains in the stmach fr a perid z.ln(m) where is the mean retentin time. The average-sized meal f rabbit, :14, can be estimated frm the nr stmachs with rabbit remains. The mean bserved bimass (M*) f rabbit in these stmachs crrespnds t a fractin f f the mean meal size entering the stmach. The smallest amunt f meat which culd be reliably detected in a fx's stmach was 1 g. Therefre a meal f rabbit culd be detected at any time frm ingestin up t the pint when nly 1 g remained in the stmach. With a detectin threshld f 1 g, f ranges between.125 fr a 1-g meal t.197 fr a 1-g meal (a fx stmach can hld up t 1 kg f flesh: Lyd 198). Taking a mid-range value ff, M* is apprximately 16% f/17, r. Cmbining the abve results, the average ttal cnsumptin (Cttal) f rabbit per fx per day is: Ctta I = (mean meal size). (mean number f meals per day) = ~r (hurs per day with rabbit in the stmach) (detectin perid f an average-sized meal) T" (n/n) = m. r" In 7/) T. (n,./n) = (M*/.16) - (1) r. In (M*/. 16) The mean retentin time (r) f meat in a fx's stmach was estimated frm data summarized in Warner (1981). The transit times f fd thrugh the entire gut f a fx are t5=3 h and t9s = 12 h, where tp is the time required t excrete p% f a marker. The time r fr the stmach will be less than the mean retentin time fr the whle gut which is apprximately (ts + t9s)/2 = 7.5 h. The best estimate fr r fr meat in a dg's stmach is 2.4 h which is 1.1% f the time fr the whle gut. Therefre, assuming the dg and the fx have similar patterns f mvement f digesta thrugh the cmpartments f the gut (fr carnivres, there is a simple linear relatinship between transit times and bdy weight: Rbbins 1983), the mean retentin time f meat in a fx stmach wuld be abut 45 min (i.e.. I x 7.5). Test fr Type H r Type IIl functinal respnse Type II functinal respnse (see fr example May 1981) is nearly as gd a fit t the data as the Type III frm, The prblem arises frm the scatter in the data at medium t high densities rather than frm the lwdensity data which is imprtant fr distinguishing be- tween Type II and Type III respnses. ne methd fr reslving the difference between the tw types is as fllws (H. McCallum, pers cmm.). linear regressin was fitted t the data set f n = 24 pints in Fig. 4. Then the pint crrespnding t the highest rabbit density was deleted and a linear regressin fitted t the remaining data. This prcess was repeated until n = 5. Fr a Type I1 functinal respnse, the intercept fr the regressins shuld be psitive and apprach zer as n decreases; and the slpe f the regressins shuld increase mntnically. In cntrast, the intercept fr a Type III functinal respnse shuld initially be psitive then becme negative as n decreases; and the slpe shuld first increase then decrease, eventually appraching zer. In applying this methd t the data shwn in Fig. 4, the intercept is psitive fr 24 > n > 19 and is negative fr n < 19 (crrespnding t densities < 17 rabbits Mn-~). The slpe f the linear regressin increases as high-density pints are cumulatively deleted until n = 1, which crrespnds t data up t 8.2 rabbits km-1. s the data set is further reduced t very lw rabbit densities, the slpe f the regressin begins t decrease. With very small data sets, n < 5, the results are erratic. This test indicates that the functinal respnse fr fxes is f the Type III rather than the Type II frm. References Catling PC (1988) Similarities and cntrasts in the diets f fxes, Vulpes vulpes, and cats, Felis catus, relative t fluctuating prey ppulatins and drught. ust Wild Res 15: Cke BD (197) Factrs which influence the number f rabbits, ryctlagus cuniculus (L.), in natural ppulatins. M.Sc. thesis, Department f Zlgy, University f delaide Cke BD (1974) Fd and ther resurces f the wild rabbit ryctlagus cuniculus (L.). Ph.D. thesis, Department f Zlgy, University f delaide Gilbert N, Myers K, Cke BD, Dunsmre JD, Fullagar P J, Gibb J, King DR, Parer I, Wheeler SH, Wd, DH (1987) Cmparative dynamics f ustralasian rabbit ppulatins. ust Wild Res 14: Hlling CS (1959) The cmpnents f predatin as revealed by a study f small-mammal predatin f the Eurpean pine sawfly. Can EntmI 91 : Hlling CS (1965) The functinal respnse f predatrs t prey density and its rle in mimicry and ppulatin regulatin. Mem Entml Sc Can 45 : 1-6 Hlling CS (1973) Resilience and stability f eclgical systems. nnu Rev Ecl Syst 4 : 1-23 Jnes E, Cman BJ (1982a) Eclgy f the feral cat, Felis catus (L.), in suth-eastern ustralia. II. Reprductin. ust Wild Res 9: Jnes E, Cman BJ (1982b) Eclgy f the feral cat, Felis catus (L.), in suth-eastern ustraiia. III. Hme ranges and ppulatin eclgy in semiarid nrth-west Victria. ust Wild Res 9 : Kruuk H (1972) Surplus killing by carnivres. J Zl Lnd 166: Lindstrm E (1989) Fd limitatin and scial regulatin in a red fx ppulatin. Hlarct Ecl 12 : 7-79 Llyd HG (198) The red fx. Batsfrd, Lndn Macdnald DW (1976) Fd caching by red fxes and sme ther carnivres. Z Tierpsychl 42 : Macdnald DW (1983) The eclgy f carnivre scial behavinr. Nature 31:37%384

11 112 May RM (1981) Mdels fr tw interacting ppulatins. In: May RM (ed), Theretical Eclgy, Principles and pplicatins, 2nd edn. Blackwell Scientific Publicatins, UK, pp Murdch WW, aten (1975) Predatin and ppulatin stability. dv Ecl Res 9:1-131 Newsme E, Parer I, Catling PC (1989) Prlnged prey suppressin by carnivres-predatr-remval experiments. eclgia 78: Parer I (1977) The ppulatin eclgy f the wild rabbit, ryet~ lagus cuniculus (L.), in a Mediterranean-type climate in New Suth Wales. ust Wild Res 4: Parer I (1982) Eurpean rabbit (ustralia). In : Davis DE (ed), CRC Handbk f Census methds fr Terrestrial Vertebrates, CRC Press, Flrida, pp Parer I, Libke J (1985) Distributin f rabbit, ryctlagus cuniculus, warrens in relatin t sil type. ust Wild Res 12: Parer I, Wd DH (1986) Further bservatins f the use f warren entrances as an index f the number f rabbits, ryctlagus cuniculus. ust Wild Res 13: Ricklefs RE (1979) Eclgy, 2nd edn. Chirn Press, New Yrk Ridpath MG, Brker G (1986) The breeding f the wedge-tailed eagle quila audax in relatin t its fd supply in arid Western ustralia. Ibis 128: Rbbins CT (1983) Wildlife feeding and nutritin. cademic Press, New Yrk Rbertsn G (1987) Effect f drught n a breeding ppulatin f wedge-tailed eagles quila audax. Emu 87: Rsenstein L, Berman E (1973) Pstnatal bdyweight changes f dmestic cats maintained in an utdr clny. m J Vet Res 34: Sargeant B (1978) Red fx prey demands and the implicatins t prairie duck prductin J Wildl Manag 42: Sinclair RE (1989) Ppulatin regulatin in animals. In: Cherrett JM (ed), Eclgical Cncepts. (Sympsium f the British Eclgical Sciety), pp Sinclair RE, lsen P, Redhead TD (199) Can predatrs regulate small mammal ppulatins?: evidence frm huse muse utbreaks in ustralia. iks 59: Slmn ME (1949) The natural cntrl f animal ppulatins. J nim Ecl 18:1-35 Trut RC, Tittensr M (1989) Can predatrs regulate wild rabbit ryctlagus cuniculus ppulatin density in England and Wales? Mammal Rev 19: Warner CI (1981) Rate f passage f digesta thrugh the gut f mammals and birds. Nutr bstr Rev B 51 : Wd DH (198) The demgraphy f a rabbit ppulatin in an arid regin f New Suth Wales ustralia. J nim Ecl 49:55-79