Journal of Animal Cats protecting birds] modelling the mesopredator 0888\ 57\ 171Ð181 release effect

FRANCK COURCHAMP \ MICHEL LANGLAIS$ and GEORGE SUGIHARA Scripps Institution of Oceanography\ University of California San Diego\ 8499 Gilman Drive Ð La Jolla\ CA 81982Ð9191\ USA^ and $ERS CNRS 012 {Mathematiques Appliquees de Bordeaux|\ Universite Victor Segalen Bordeaux 1\ 035 rue Leo Saignat\ F!22965 Bordeaux Cedex\ France

Summary 0[ Introduced predators account for a large part of the extinction of endemic insular species\ which constitutes a major component of the loss of biodiversity among vertebrates[ Eradication of alien predators from these is often considered the best solution[ 1[ In some ecosystems\ however\ it can generate a greater threat for endemic prey through what is called the {mesopredator release|[ This process predicts that\ once superpredators are suppressed\ a burst of mesopredators may follow which leads their shared prey to extinction[ 2[ This process is studied through a mathematical model describing a three species system "preyÐmesopredatorÐsuperpredator#[ Analysis of the model\ with and without control of meso! and superpredators\ shows that this process does indeed exist and can drive shared prey to rapid extinction[ 3[ This work emphasizes that\ although counter!intuitive\ eradication of introduced superpredators\ such as feral domestic cats\ is not always the best solution to protect endemic prey when introduced mesopredators\ such as rats\ are also present[ Key!words] bird conservation\ feral cats\ introduced mammals\ control strategy\ rats[ Journal of Animal Ecology "0888# 57\ 171Ð181

or by from or destruction by Introduction introduced grazers such as rabbits "Oryctolagus cun! Most contemporary worldwide extinctions have iculus\ Lilljeborg# or goats "Capra hircus\ L[# "Moors occurred\ or are currently occurring in island eco! + Atkinson 0873^ Atkinson 0878^ Williamson 0885#[ systems[ As an example\ of the 29 species of reptiles According to King "0874#\ by introduced and amphibians that have gone extinct since 0599\ animals has been a major cause of 31) of island more than 89) are island forms "Honnegger 0870#^ bird extinctions in the past\ and is a major factor 82) of 065 species or subspecies of birds "King 0874#\ endangering 39) of currently threatened island bird and 70) of 54 mammal species extinctions "Ceballos species[ In particular\ introduced feral cats "Felis + Brown 0884# that have occurred during this period catus\ L[# are known to be a major threat to many have occurred on islands[ island bird species[ They are known to have been The introduction of vertebrate species is one of the introduced into at least 54 island groups where they most important threats to many endemic species in are responsible for the loss of many large land and many islands "Moors + Atkinson 0873^ Atkinson seabird colonies\ populations or even species "e[g[ Jou! 0878#[ Numerous rare or endemic vertebrate species ventin et al[ 0873^ Rodriguez!Estrella et al[ 0880^ Mon! are currently endangered because of predation by teiro\ Ramos + Furness 0885#^ for example\ a few introduced invertebrates\ reptiles\ birds or mammals\ cats "around _ve# were introduced to the Kerguelen Islands in the mid!century[ They are now responsible for the decline or extinction of several bird popu! Correspondence] Franck Courchamp\ Department of Zoology\ University of Cambridge\ Downing Street\ Cam! lations in these islands\ killing more than 2 million Þ 0888 British bridge\ CB1 2EJ\ UK[ E!mail fc108Ýcam[ac[uk[ Tel] 90112! petrels per year "Chapuis 0884#[ Cats also constitute Ecological Society 225532[ Fax] 90112!225565[ a major threat to many endemic reptile species or

171 172 subspecies "e[g[ Iverson 0867^ Case + Bolger 0880^ gerald 0877#[ When both bird and mammal prey are F[ Courchamp\ Arnaud et al[ 0882# and mammals "Spencer 0880^ Mel! available\ it is believed that the domestic cat diet will M[ Langlais + link 0881#[ Their impact has also been demonstrated include mainly mammals "e[g[ Konecny 0876^ Nogales G[ Sugihara through competition towards endemic mammalian et al[ 0881^ Nogales + Medina 0885#[ In some island predators such as island foxes "e[g[ Urocyon littoralis ecosystems\ these cats maintain rodent populations dickeyi\ Baird#\ which they replace when uncontrolled at low levels[ Although they also often prey upon "Steve Kovach\ personal communication#[ endangered species\ it is believed that\ in some eco! Eradication of those alien cat populations is systems at least\ the bene_cial e}ects of reducing the required in many cases\ has often been tried\ some! rodent population could outweigh the damage done times achieved "Rauzon 0874^ Veitch 0874^ Domm to the endemic prey species "Fitzgerald et al[ 0880^ + Messersmith 0889^ Cooper 0884# and several cat Tidemann\ Yorkston + Russack 0883#[ The threat eradication programmes are currently underway[ posed by introduced cats to the kakapo "Strigops hab! Paradoxically\ in some particular situations\ the pres! roptilus\ Gray# on Stewart Island is a striking example[ ence of a controlled population of cats might be\ at Here\ cats prey lightly on this highly endangered bird least temporarily\ more bene_cial to their endemic species "remains were found in 4=0) of 007 collected prey than its eradication[ Such is the case on many scats\ Karl + Best 0871#\ but even low predation pres! islands where rodents have also been introduced[ sure may be detrimental for fragile species "Rod! Indeed\ it has been shown that the di}erent species riguez!Estrella et al[ 0880#[ However\ rat remains were of introduced rats "Kiore or Polynesian or Paci_c rat found in 82=9) of these 007 scats "Karl + Best 0871#\ Rattus exulans\ F[\ Black or Roof or Ship rat\ showing the indirect role cats might play in preserving R[ rattus\ F[ and Brown or Norwegian rat R[ nor! native fauna through reduction of rat predation pres! vegicus\ F[# have an extremely deleterious e}ect on sure on the kakapo[ Moreover\ the elimination of feral numerous species of amphibians "e[g[ Thurley + Ben cat populations from such ecosystems could lead to a 0883^ Towns + Daugherty 0883#\ reptiles "e[g[ Mac! more severe negative impact on the endemic species\ Callum 0875^ Newman + McFadden 0889^ Case\ as a result of expansion of rodent populations once Bolger + Richman 0881^ Cree\ Daugherty + Hay their predators are removed[ Attempted reduction of 0884#\ birds "e[g[ Atkinson 0874^ Konecny 0876^ the cat population of Amsterdam Island is alleged to Bertram + Nagorsen 0884# and even mammals "e[g[ have caused a compensating rise in the number of rats Brosset 0852^ Bell 0867^ Atkinson 0874#[ This e}ect and mice\ and so has been abandoned "Holdgate + can be indirect\ such as through competition for shel! Wace 0850#[ This process\ termed {mesopredator ter\ nest!sites "Seto + Conant 0885# or food\ as the release|\ had been described in fragmented insular eco! diet of rats comprises mainly berries\ leaves\ seeds and systems "Soule et al[ 0877# and applies well to many invertebrates "Clark 0879\ 0870#[ Rats can also have insular foodwebs "e[g[ Schoener + Spiller 0876#[ Con! a direct e}ect\ through predation[ Indeed\ these three versely\ the eradication of rodents _rst "which has of rat are known to prey on eggs\ now proven feasible\ even on relatively large islands\ chicks\ juveniles and even adults of ground!nesting Taylor + Thomas 0878\ 0882^ Towns 0885# might seabirds and land birds "e[g[ Kepler 0856^ Bertram induce cats to switch prey\ resulting in a brutal 0884^ Brooke 0884^ Lovegrove 0885# and even tree! increase in predation pressure on the threatened nesting birds "e[g[ Campbell 0880^ Seitre + Seitre 0881^ endemic species\ as experienced for stoats and rats in Amarasekare 0882#[ In total\ R[ exulans predation is New Zealand "Murphy + Brad_eld 0881#[ Unfor! documented on at least 04 di}erent bird species\ tunately "from the theoretical point of view#\ there is R[ rattus predation on at least 28 bird species\ and little _eld evidence from island management either of R[ norvegicus on at least 42 bird species "for a review\ mesopredator release following superpredator eradi! see Atkinson 0874#[ Not only do rats have a potential cation\ or of predators switching prey following meso! impact on numerous species throughout the world predator eradication[ "they are known to have colonized at least 71) of the As the optimal control strategy is neither simple to 012 major island groups\ Atkinson 0874#\ but they _nd nor intuitive\ it is studied through the analysis of sometimes cause extremely rapid extinctions on newly a mathematical model which mimics the dynamics of colonized islands[ A well!known example is the estab! the three species in this system[ In the study reported lishment around 0853 of black rats on Big South Cape here\ the interactions of a prey species\ such as a bird Island\ New Zealand\ causing the local loss of three species\ a threatening alien mesopredator\ such as a New Zealand endemic birds\ and the complete extinc! rat\ and an alien superpredator species\ such as the tion of two more\ and of one species of bat\ in less feral domestic cat\ were examined through their than 1 years "Bell 0867#[ Introduced house mice "Mus coupled dynamics[ Through this model\ the theor! musculus\ L[# also have a potential negative impact on etical existence of {mesopredator release| and the e}ect vertebrate species\ by competition or direct predation of the presence of a superpredator on the prey will be Þ 0888 British Ecological Society "e[g[ Moors + Atkinson 0873^ Johnstone 0874^ New! investigated[ It is assumed that the superpredator Journal of Animal man 0883#[ preys both upon the prey and the mesopredator[ For Ecology\ 57\ 171Ð181 The domestic cat is an opportunist predator "Fitz! the sake of simplicity\ reference will sometimes be 173 made to them as bird\ rat and cat\ instead of prey\ The prey:mesopredator "bird:rat# system is given Mesopredator mesopredator and superpredator\ respectively[ by] release in insular FdB B B ecosystems rbB 0− − hbR eqn 0 G dt K S¦B j 0 b1 The models J dR hbhsR G rrR 0− eqn 1 f dt 0 hbS¦hsB1 THE PRELIMINARY MODELS There are several equilibrium points[ The _rst two For the sake of simplicity\ models are _rst presented equilibrium states\ extinction of both populations ð9\ taking into account only two species\ and only then is 9Ł and extinction of the rat only ðK \ 9Ł are always the third species added and its implied complications b unstable[ The third state\ extinction of the bird only\ analysed[ The construction and analysis of the models "9\ S:h # is globally asymptotically stable if and only are based on previous work "Courchamp + Sugihara s if r ¾ h :h [ These three points always exist[ When 0888#\ to which the reader can refer for additional b b s both populations coexist\ the system reaches "B \ details[ The _rst two systems consist of two simple S:h ¦ B :h #[ B is given in the Appendix with the coupled di}erential equations\ each representing the s b analysis of the system[ dynamics of one population[ Each population is The prey:superpredator "bird:cat# system is given described by a simple logistic equation\ modi_ed to by] take into account its relationship with the other spec! FdB B ies[ The other possible prey species populations are r B 0− −m C eqn 2 G dt b K b not taken into account^ it is assumed that all the prey j 0 b1 species form a single {bird| population\ with average J dC mbC characteristics[ The realism of these assumptions has G rcC 0− eqn 3 f dt 0 B 1 been discussed previously "Courchamp + Sugihara 0888#[ The number of individuals at time t in the prey\ It is the same for the mesopredator:superpredator

mesopredator and superpredator populations are B\ "rat:cat# system "B is replaced by R and b indices are

R and C\ respectively[ The intrinsic growth rates of replaced by r indices#[ They have three stable equi! the prey\ mesopredator and superpredator popu! librium points only\ as the predator cannot survive

lations are rb\ rr and rc\ respectively[ The predation alone] ð9\ 9Ł\ ðKb\ 9Ł and ðKb"0−0:rb#\

rate of the superpredator is mb on the prey and mr on Kb"0−0:rb#:mbŁ[ the mesopredator[ The predation rate of the meso! THE COMPLETE MODEL predator is hb on the prey and hs on other food items "seeds\ leaves\ invertebrates#[ The of To take the three species into account simultaneously\ the environment for the prey population is Kb[ The one needs to make further assumptions[ First of all\ carrying capacities of the environment for the meso! like the rat\ the domestic cat is an opportunist pred! predator and the superpredator populations are not ator\ which switches prey species according to their constants\ but depend partially "rats are # or availability "Fitzgerald 0877#[ Accordingly\ the num! totally "cats are # on the number of available ber of birds and rats preyed upon by cats will depend individual prey on which their populations can feed on their respective numbers[ Instead of mbC and mrC\ at time t[ For the mesopredator\ the carrying capacity one will _nd] mbBC:"B¦R# and mrRC:"B¦R# for the of the environment is the number of mesopredators bird and the rat populations\ respectively[ Potential that can live on food other than birds when there is preferences of the cat for the indigenous prey over the no prey\ to which is added the number of meso! introduced predator are not taken into account "see predators that can be fed by the total of available prey Courchamp\ Langlais + Sugihara\ in press#[ The cat at time t[ The carrying capacity is thus the quantity of carrying capacity is] B:mb ¦ R:mr[ The compartmental non!avian food S divided by the consumption rate hs\ representation of the model is given in Fig[ 0[ plus the number of prey B divided by the meso! One has the following system] predator predation rate hb]S:hs¦B:hb\ that is FdB B B B "hbS¦hsB#:hbhs[ For the sake of simplicity\ it is G rbB 0− − hbR− mbC assumed that S is a constant "the carrying capacity in G dt 0 Kb1 S¦B B¦R the absence of prey is kept under the form S:h instead G s G eqn 4 of a constant\ say K \ to conserve homogeneous s GdR h hR R notation#[ Rats are opportunistic predators\ and their G rR 0− b s − mC dt r h hB B¦R r diet "proportion of avian and non!avian food con! g 0 bS¦ s 1 G sumed# depends on relative availability of food items G eqn 5 "Clark 0879#[ Accordingly\ instead of h R\ the pre! G Þ 0888 British b dC m mC G rC 0− b r Ecological Society dation rate of rats on birds is] BhbR:"S¦B#[ In the c G dt 0 mrB¦mbR1 Journal of Animal two!species models\ the rat:cat system is not G Ecology\ 57\ 171Ð181 presented\ because it is the same as the bird:cat system[ f eqn 6 174 F[ Courchamp\ M[ Langlais + G[ Sugihara

Fig[ 0[ Compartmental representation of the mathematical model with three species "eqns 6\ 7\ 8#[ Each box represents one population\ symbolized by a letter and an animal] superpredator "C\ cats#\ mesopredator "R\ rats# and prey "B\ birds#[ The arrows represent the ~ux within and are between compartments] curved arrows are intrinsic growth rates^ straight arrows are

predation rates[ The intrinsic growth rates of the superpredator\ the mesopredator and the prey are rc\ rr and rb\ respectively[

The predation rates of the superpredator on the mesopredator and on the prey are mr and mb\ respectively^ the predation rate

of the mesopredator on the prey is hb[

There are several states with this system] all popu! predators are present by controlling rat "c#\ or even

lations go extinct ð9\ 9\ 9Ł\ only the prey survives ðKb\ by extirpating the rat "d#[

9\ 9Ł\ only the mesopredator survives ð9\ S:hs\ 9Ł\ only One can see that\ in some cases\ the presence of the

the superpredator disappears ðB \ S:hs ¦ B :hb\ 9Ł "B superpredator can indirectly protect a shared prey has the same value than in system "0Ð1##\ only the prey from a mesopredator[ Even in circumstances where

disappears ð9\ S:hs"0−0:rr#\ S:mrhs"0−0:rr#Ł\ only the this is not the case\ the elimination of the super!

mesopredator disappears ðKb "0−0:rb#\ 9\ predator might be more harmful to the prey\ through

Kb"0−0rb#:mbŁ\ and\ _nally\ no species disappears ðB5 \ the {mesopredator release|\ which arises when the pres!

R5 \ C5 Ł[ There can be between 9 and 4 stationary sure on mesopredators by superpredators is states with the equilibrium value of B between 9 and suppressed[ To mimic this process\ the e}ect of the

Kb\ as solutions of an equation of the _fth degree[ As suppression of the superpredator when the three spec! its expression is very long and complex for the last ies are present in equilibrium is studied[ First one has point\ it will not be presented here\ but the authors to _nd values for which the bird population does not will provide the Maple _le upon request[ For the same go extinct when the two other species are introduced[ reason\ the comparison between di}erent points is A range of parameters must be de_ned at which all too complex to be presented here analytically[ The three populations persist and reach an equilibrium deterministic nature of the model allows\ however\ a state[ This range of parameters implies high values of numerical study[ intrinsic growth rate of the prey "×0=2# if it is to It can be noted that the fourth\ _fth and sixth equi! survive the presence of the two predators[ From this

librium points are equivalent to some from the models equilibrium state "ðB5 \ R5 \ C5 Ł#\ the extinction of 0Ð1 and 2Ð3[ The conditions of existence of these the superpredator population can be simulated and points are described in the Appendix[ the outcome of the two remaining populations moni! tored] new simulations are run with the following

initial conditions] ðB5 \ R5 \ 9Ł[ This is repeated for SUPERPREDATOR PRESENCE AND di}erent values of sensible parameters\ to obtain a MESOPREDATOR RELEASE pattern displayed Fig[ 2[ This shows that prey extinc! The behaviour of the model is studied analytically "see tion through mesopredator release does occur in this Appendix#\ but simulations are presented for heuristic system[ Moreover\ it is avoided only for higher values purposes[ It can be seen from Fig[ 1 that\ under some of prey intrinsic growth rate "×0=5#[ These correspond Þ 0888 British Ecological Society conditions\ while the rat alone would extirpate the to values too high to be biologically realistic\ and will Journal of Animal bird "a# and the cat alone would not "b#\ the cat pre! not often be reached in natura by insular bird species[ Ecology\ 57\ 171Ð181 vents extinction of the bird by the rat when both Indeed\ in the absence of similar predation pressure\ 175 Mesopredator release in insular ecosystems

Fig[ 1[ Simulations showing the dynamics of the three population sizes plotted against time] "a# the model with only prey and mesopredator "system 0Ð1#^ "b# the model with only prey and superpredator "system 2Ð3#^ "c# and "d# the model with prey and both mesopredator and superpredator "system 4Ð6#[ The values used for the simulations show that the superpredator can lower the mesopredator population\ to such a point that it prevents the prey elimination ðsimple mesopredator control in "c#\

total mesopredator eradication in "d#Ł[ Values used are 0=4\ 3=9 and 9=64 for rb\ rr and rc\ respectively\ 099 999 for Kb and 09999

for S\ 43 for mb and 199 for mr\ 5 for hb and 254 for hs[ Initial conditions are in all cases 099 999 birds\ 099 rats and 0 cat "which corresponds to the introduction of 099 rats and:or 0 cat into a healthy population of 099 999 birds#[ The scale is di}erent for the three species[

Fig[ 2[ Phase portrait of the bird vs[ the rat populations\ displaying the e}ect of the eradication of the superpredator on the prey\ for di}erent values of the prey intrinsic growth rate[ Initial conditions are here the equilibrium point of the model where Þ 0888 British all three species are present "cat population is set to zero to simulate its eradication#[ This point changes because di}erent Ecological Society values are used for the prey intrinsic growth rate leading to di}erent equilibrium values[ Elimination of the superpredator Journal of Animal without elimination of the mesopredator results in elimination of the prey population through {mesopredator release|\ when Ecology\ 57\ 171Ð181 the prey intrinsic growth rate is lower than 0=5 "curves in light grey#[ 176 these endemic species seldom have developed anti! were taken as examples[ Indeed\ as Diamond "0878# F[ Courchamp\ predator life history traits\ such as a high intrinsic stated\ {rats and cats are the most notorious killers M[ Langlais + growth rate[ These results show that the only endemic and island birds the most notorious victims\ in this G[ Sugihara species with intrinsic growth rates high enough to regard ðextinctions due to introduced predatorsŁ[| This survive the introduction of both a superpredator and work shows several interesting features of direct con! a mesopredator will normally be extirpated through cern to conservation biology[ First\ the result of this mesopredator release if the control strategy implies theoretical work shows that the presence of one pred! only the superpredator eradication[ The strategy of ator only is su.cient to induce the extinction of the control therefore appears essential in these particular endemic prey[ This is not new\ as indicated by too ecosystems[ many examples in natura[ Second\ when both the mesopredator and the superpredator are present\ seven di}erent situations may arise\ among which is CONTROL STRATEGY the case where the three species are present with stable Mesopredator release can occur following eradication dynamics[ Interestingly\ there is another case where of the superpredator and the presence of the super! both predator species can coexist inde_nitely\ even predator also has negative e}ects on the prey popu! after the eradication of the prey species[ Finally\ and lation\ therefore a study of control strategies is neces! most interestingly\ is the case where the superpredator sary to determine an optimal strategy[ If one applies causes the extinction of the mesopredator\ but not of the prey[ a control e}ort of lr on the rat population and of lc on the cat population\ the model "4Ð6# becomes] It has been shown here that presence of a super! predator may have a global positive e}ect in insular FdB B B B ecosystems in which an introduced mesopredator G rbB 0− − hbR− mbC G dt 0 Kb1 S¦B B¦R threatens an endemic prey[ Indeed\ in the model pre! G sented here the presence of the superpredator may eqn 7 G preclude the elimination of the prey by the meso! G dR hbhsR R predator "or allow a larger prey population size#[ In G rrR 0− − mrC−lrR g dt 0 hbS¦hsB1 B¦R addition\ it has been demonstrated that superpredator G eradication should be avoided\ as a means to prevent G eqn 8 what has been termed {mesopredator release| "Soule GdC m mC b r et al[ 0877#] a sudden burst of mesopredators\ once G rcC 0− −lcC G dt 0 mrB¦mbR1 the superpredator pressure is suppressed[ Rats have a G f eqn 09 lower predation rate on birds than cats\ but they are much more numerous and can have a higher impact This provides the same number of equibrium points on the prey "Newman + McFadden 0889#[ Moreover\ as model "4Ð6#\ although with di}erent values[ Values as they are omnivores\ they can maintain a high popu! of these points are provided in the Appendix\ together lation and a high predation pressure\ even when the with their conditions of existence and stability[ prey population size is low\ which the cat cannot[ This Analysis of this model shows that when super! explains why rats alone eliminate the prey more easily predator control is high enough "lc × rc#\ the super! than cats alone in the model "Fig[ 1#\ and why the cat predator disappears[ As a result\ the prey also dis! presence is sometimes bene_cial to shared prey[ In appears when the mesopredator control is not high fact\ over the last 399 years\ rats and cats are said to enough ðlr ³ rr"0 − rbhs:hb# ³ rr#\ because of meso! be responsible for 43) and 15) of island extinctions predator release[ In contrast\ and surprisingly\ the caused by predators\ respectively "King 0874#[ The prey does not disappear when the superpredator con! study of the control strategies clearly shows that the trol is below a certain threshold ði[e[ rc"0 − rb# ³ fate of the prey will depend on the superpredator lc ³ rcŁ\ provided the mesopredator control is high control level[ Although counterintuitive\ if the super! enough ðlr × rr − mr"0 − lc:rc#:mbŁ[ This illustrates the predator control is too high\ the prey will disappear[ importance of the presence of the superpredator in This may be a further argument in favour of the use the system\ and the need to take it into account in of biological control\ especially with pathogens with a control programmes[ steady long!term impact "see Courchamp + Sugihara 0888#\ which are unlikely to be too brutal[ Despite its mathematical complexity\ this model Discussion remains very simple in its representation of the bio! This study examined\ through a mathematical model\ logical reality[ In particular\ spatial and temporal the fate of a prey species in an insular into population heterogeneities\ which are important com! which both a mesopredator and a superpredator have ponents of insular ecosystems\ were not taken into Þ 0888 British Ecological Society been introduced[ Although other species could have account[ Similarly\ the fact that di}erent prey species Journal of Animal been considered\ such as mongooses and reptiles "Case are present in these ecosystems has not been taken Ecology\ 57\ 171Ð181 et al[ 0881#\ the rat\ feral cat and endemic bird species into account[ Instead\ only one species\ which is sup! 177 posed to represent the {average| of all prey species\ was son 0877^ Towns 0880\ 0883^ Newman 0883^ Cooper Mesopredator considered[ As the rats and the cats are opportunistic et al[ 0884#[ Fourth\ in the cases where alien species release in insular predators\ which switch prey species according to their induced the complete extinction of the population\ ecosystems relative availability "Clark 0879^ Fitzgerald 0877#\ it local populations were often concerned^ species or would be interesting to study the e}ect of the presence subspecies extinctions are less frequent "Moors + of several prey species[ This model is robust enough Atkinson 0873#[ Moreover\ seabird populations are to be extended to other ecosystems that can be well not dependent on the land for food\ and breeding described by the preyÐmesopredatorÐsuperpredator can continue on isolated islets and stacks free from trophic web[ It therefore holds for systems where sev! predators "Atkinson 0874#[ In most cases of colony or eral prey species are present "e[g[ landbirds\ seabirds population extinctions as a result of alien predators\ and lizards# provided that they are prey of both the there are\ in nearby islets\ populations able to re! mesopredator and the superpredator[ Some changes colonize the ecosystem once the predator eradication may occur in the solutions of the model according to is achieved "Moors + Atkinson 0873^ Case et al[ 0881^ the characterics of the species "e[g[ if they have di}er! Jouventin + Micol 0884#[ Last\ in some cases "as in ent antipredation response#\ but the general con! the well known case of the kakapo\ Clout + Craig clusions should remain the same[ Similarly\ the results 0884^ Powlesland et al[ 0884# it is suspected that only will be the same if another superpredator\ say a bird a small number of individuals "cats as well as rats# of prey\ is present[ Di}erent e.ciencies in hunting have learned to kill the prey or eat the eggs "Grant\ di}erent preys would here again add more complexity[ Pettit + Whittow 0870^ Moors + Atkinson 0873#[ In In contrast\ the model results will undoubtedly be these cases\ when heavy programmes\ such as com! di}erent if another species is present which does not plete eradication or long!term control\ are not poss! fully _t into one of these three trophic levels\ because ible\ selective control to eliminate these particular it would describe a totally di}erent system[ It is the individuals may be su.cient in the short term\ and case\ for example\ if a prey species "e[g[ the rabbit# is should thus be implemented[ present which is not preyed upon by both the super! However\ the situation is critical in many cases\ and predator and the mesopredator] islands where cats\ the media and scienti_c coverage of the situation on rats and rabbits have been introduced should there! most islands does not seem to be proportionate to fore be described by a di}erent model[ Despite these the problems faced by these often unique ecosystems possible improvements\ this theoretical work shows "Crystal 0878#[ Despite numerous indications of cata! that it is crucial to take into account the presence of strophic e}ects of introduced mammals on most oce! other alien species when designing control pro! anic islands\ politically organized policies to resolve\ grammes for one introduced species "see also Cour! or even prevent these e}ects remain comparatively champ et al[\ in press for another example#[ Emphasis few[ Recent examples\ and other older ones\ show is placed on the following important distinction that that solutions do exist[ It is often the high _nancial should be understood from this work] in some eco! constraints on eradication programmes that preclude systems where rats are present\ introduced cats might them "Powlesland et al[ 0884#\ or that impose unde! play a positive role "implying that their removal could sired priorities in the order of their attainment "Bro! have negative aspects on local fauna#^ however\ their thers + Copson 0877#[ In these cases\ a predictive introduction cannot be recommended\ whatever the study on the feasibility of the eradication and its circumstances[ potential e}ects on the ecosystem is needed\ especially Several points allow optimism about this particular when there is more than one introduced species\ in area of conservation biology[ First\ the recovery order to maximize the e.ciency of eradication pro! and:or preservation of the ecosystems involved is not grammes[ Theoretical studies\ such as mathematical in con~ict with local economic or politic interests\ modelling could ful_l this task[ This study shows that even if the governments of many concerned islands the intuitively evident need for feral cat eradication can hardly a}ord costly programmes such as mammal may not be the best solution in some speci_c cases\ eradications[ Second\ eradication of introduced mam! such as when introduced rodents are present[ This is mals such as domestic cats "Bloomer + Bester 0881#\ well illustrated by the case of Raoul Island\ where it rabbits "Flux 0882#\ rats "Taylor + Thomas 0882#\ has been said that eradication of feral cats might bring possums "Cowan 0881#\ foxes "Bailey 0881#\ goats little bene_t to bird populations\ because Norway rats "Parkes 0889# or others\ once thought impossible\ is are present on this island and constitute a major part now known to be feasible^ for example\ 019 successful of the diet of the cats "Fitzgerald et al[ 0880#[ Empirical {pest| eradications have already been conducted on examples remain\ however\ scarce regarding the e}ects New Zealand islands "Veitch et al[ 0881#[ Third\ many of eradication of predators "top predators or meso! studies show that\ when the introduced species has predators# on population dynamics of coexisting been successfully removed from the whole ecosystem\ species[ Þ 0888 British Ecological Society the threatened species "plant or animal# generally The idea that top predators may be important spec! Journal of Animal recovers\ sometimes rapidly\ from the e}ects of these ies for conservation biology is not new[ It has been Ecology\ 57\ 171Ð181 alien species "e[g[ Cruz + Cruz 0876^ Brothers + Cop! suggested that they have a disproportionate importance 178 in food webs because their extinction can gen! van Aarde\ R[J[ "0872# Demographic parameters of the feral F[ Courchamp\ erate a cascade of unexpected secondary extinctions cat Felis catus population at Marion Island[ South African Journal of Wildlife Research\ 02\ 01Ð05[ M[ Langlais + "Paine 0855^ Pimm 0879#[ For example\ the extinction Amarasekare\ P[ "0882# Potential impact of mammalian nest G[ Sugihara of several prey species has been attributed to the predators on endemic forest birds of Western Mauna Kea increase of generalist and:or medium!sized predatory Hawaii[ Conservation Biology\ 6\ 205Ð213[ mammals because of the lack of top predators in Arnaud\ G[\ Rodriguez\ A[\ Ortega!Rubio\ A[ + Alvarez! di}erent ecosystems "Terborgh + Winter 0879^ Dia! Cardenas\ S[ "0882# Predation by cats on the unique endemic lizard of Socorro Island Urosaurus auriculatus mond + Case 0875^ Wilcove\ McLellan + Dobson Revillagigedo Mexico[ Ohio Journal of Science\ 82\ 090Ð 0875^ Diamond 0878^ BoÃhning!Gaese\ Taper + 093[ Brown 0882^ Goodrich + Buskirk 0884#[ With the Ashmole\ N[P[\ Ashmole\ M[J[ + Simmons\ K[E[L[ "0883# example of lynx\ mongooses and rabbits\ it has been Seabird conservation and feral cats on Ascension Island\ shown\ both theoretically and empirically\ that top South Atlantic[ Seabirds on Islands\ Threats\ Case Studies and Action Plans "eds D[ N[ Nettleship\ J[ Burger + M[ predators actually bene_t their prey through intra! Gochfeld#\ pp[ 28Ð56[ Birdlife Conservation Series no[ 0\ predation on other smaller predators which Hamilton[ share the prey "Palomares et al[ 0884#[ What is new Atkinson\ I[A[E[ "0874# The spread of commensal species of here is rather the application of this idea to an already Rattus to oceanic islands and their e}ect on island perturbed ecosystem\ a rather counter!intuitive idea] avifaunas[ Conservation of Island Birds "ed[ P[ J[ Moors#\ pp[ 24Ð70[ ICBP Technical Publication no[ 2[ Cambridge[ in some cases the removal of one of the causes of Atkinson\ I[A[E[ "0878# Introduced animals and extinctions[ perturbation may lead to increased damage[ This is Conservation for the Twenty!First Century "eds D[ Western the case with the mesopredator release "Soule et al[ + M[ C[ Pearl#\ pp[ 43Ð64[ Oxford University Press\ 0877#[ In some systems\ only the direct negative e}ects Oxford[ of the top predator on endemic threatened prey have Bailey\ E[P[ "0881# Red foxes\ Vulpes vulpes\ as biological control agents for introduced arctic foxes\ Alopex lagopus\ been examined\ while in some cases greater positive on Alaskan Islands[ Canadian Field Naturalist\ 095\ 199Ð e}ects may be present on the same species[ Obviously\ 194[ outcomes of changes of these already perturbed tro! Bell\ B[D[ "0867# The Big South Cape Island rat irruption[ phic webs are not intuitive\ and intervention as dra! The Ecology and Control of Rodents in New Zealand Nature matic as species eradication should always be pre! Reserves "eds P[ R[ Dingwall\ I[ A[ E[ Atkinson + C[ Hay#\ pp[ 22Ð35[ Dept[ Land and Surveys\ Private Bag\ ceded by careful empirical and theoretical studies of Wellington[ Inf[ Ser[ 3[ the whole ecosystem[ Indeed\ in the present case\ era! Bertram\ D[F[ "0884# The roles of introduced rats and com! dicating the rats before the cats "at _rst a seemingly mercial _shing in the decline of ancient murrelets on Lan! sound strategy# might in fact lead to another case of gara Island\ British Columbia[ Conservation Biology\ 8\ mesopredator release\ as shown by the recent example 754Ð761[ Bertram\ D[F[ + Nagorsen\ D[W[ "0884# Introduced rats\ of Bird Island in the Seychelles[ Here\ a recent eradi! Rattus spp[\ on the Queen Charlotte Islands] Implications cation of the introduced black rat population led to an for seabird conservation[ Canadian Field Naturalist\ 098\ explosion of the exotic crazy ant Anoplolepis longipes\ 5Ð09[ Jerdon\ which has been shown to be threatening the Bloomer\ J[P[ + Bester\ M[N[ "0881# Control of feral cats bird colonies which rat eradication was intended to on sub!Antarctic Marion Island\ Indian Ocean[ Biological Conservation\ 59\ 100Ð108[ protect "Feare 0887#[ As complete removal of those BoÃhning!Gaese\ K[\ Taper\ M[L[ + Brown\ J[H[ "0882# Are alien predators is most of the time "and often rightly# declines in North!American insectivorous songbirds due the only envisaged solution "Veitch 0874^ Ashmole\ to causes on the breeding range< Conservation Biology\ 6\ Ashmole + Simmons 0883^ Rainbolt + Coblentz 65Ð74[ Brooke\ M[ de L[ "0884# The breeding biology of the gad~y 0886#\ this idea of possible positive e}ects of top pred! petrels Pterodroma spp[ of the Pitcairn Islands] Charac! ators should be kept in mind in conservation biology[ teristics\ population sizes and controls[ Biological Journal of the Linnean Society\ 45\ 102Ð120[ Acknowledgements Brosset\ A[ "0852# Statut actuel des mammifeÁres des¼ (les Galapagos[ Mammalia\ 16\ 212Ð227[ This work was supported by a Lavoisier fellowship Brothers\ N[P[ + Copson\ G[R[ "0877# Macquarie Island from the French Foreign O.ce\ by Biological Ocean! ~ora and fauna management Ð interpreting progress and predictions for the future[ Papers and Proceedings of the ography Grant ONR] N99903!84!0!9923\ and endow! Royal Society of Tasmania\ 011\ 018Ð024[ ment funds from the John Dove Isaacs Chair in Natu! Campbell\ E[W[ "0880# The e}ect of introduced roof rats on ral Philosophy\ and was part of the IFRTP Program bird diversity of Antillean cays[ Journal of Field Orni! No[ 168[ We thank Professor T[ Clutton!Brock\ Doc! thology\ 51\ 232Ð237[ tors M[ de L[ Brooke\ S[ Lingle and P[ Rohani for Case\ T[J[ + Bolger\ D[T[ "0880# The role of introduced species in shaping the distribution and abundance of island their helpful comments on the manuscript[ reptiles[ \ 4\ 161Ð189[ Case\ T[J[\ Bolger\ D[T[ + Richman\ A[D[ "0881# Reptilian References extinctions] the last ten thousand years[ Conservation Þ 0888 British Biology\ the Theory and Practice of Nature Conservation Ecological Society van Aarde\ R[J[ "0867# Reproduction and population ecol! Preservation and Management "eds P[ L[ Fielder + K[ J[ Journal of Animal ogy in the feral house cat\ Felis catus on Marion Island[ Subodh#\ pp[ 80Ð014[ Chapman + Hall\ London[ Ecology\ 57\ 171Ð181 Genetics Newsletter\ 2\ 177Ð205[ Ceballos\ G[ + Brown\ J[H[ "0884# Global patterns of mam! 189 malian diversity\ endemism and endangerment[ Con! traditional control or competitors in removing rabbits Mesopredator servation Biology\ 8\ 448Ð457[ from islands[ New Zealand Journal of Zoology\ 19\ 02Ð07[ Chapuis\ J[L[ "0884# Alien mammals in the French Sub! Goodrich\ J[M[ + Buskirk\ S[W[ "0884# Control of abundant release in insular antarctic Islands[ Progress in Conservation of the Sub! native vertebrates for conservation of endangered species[ ecosystems antarctic Islands "ed[ P[ R[ Dingwall#\ pp[ 016Ð021[ IUCNÐ Conservation Biology\ 8\ 0246Ð0253[ The World Conservation Union[ Conservation of the Sou! Grant\ G[S[\ Pettit\ T[N[ + Whittow\ G[C[ "0870# Rat pre! thern Polar Region No 1[ Paimpont[ dation on Bonin petrel eggs on Midway atoll[ Journal of Clark\ D[A[ "0879# Age! and sex!dependant stra! Field Ornithology\ 41\ 225Ð227[ tegies of a small mammalian [ Journal of Animal Holdgate\ M[W[ + Wace\ N[M[ "0850# The in~uence of man Ecology\ 38\ 438Ð453[ on the ~oras and faunas of Southern Islands[ Polar Record\ Clark\ D[A[ "0870# Foraging patterns of black rats across a 09\ 364Ð382[ desert!montagne forest gradient in the Gualapagos Honnegger\ R[E[ "0870# List of amphibians and reptiles Islands[ Biotropica\ 02\ 071Ð083[ either known or thought to have become extinct since Clout\ M[N[ + Craig\ J[L[ "0884# The conservation of criti! 0599[ Biological Conservation\ 08\ 030Ð047[ cally endangered ~ightless birds in New Zealand[ Ibis\ 026\ Iverson\ J[B[ "0867# The impact of feral cats and dogs on S070ÐS089[ populations of the west Indian rock iguana\ Cyclura Cooper\ J[ "0884# Conservation status of the Prince Edward carinata[ Biological Conservation\ 03\ 52Ð62[ Islands[ Progress in Conservation of the Subantarctic Johnstone\ G[W[ "0874# Threats to birds on subantarctic Islands "ed[ P[ R[ Dingwall#\ pp[ 10Ð29[ IUCNÐThe World islands[ Conservation of Island Birds "ed[ P[ J[ Moors#\ pp[ Conservation Union[ Conservation of the Southern Polar 090Ð010[ ICBP Technical Publication no[ 2[ Cambridge[ Region No\ 1[ Paimpont[ Jouventin\ P[ + Micol\ T[ "0884# Conservation status of the Cooper\ J[\ Marais\ A[V[N[\ Bloomer\ J[P[ + Bester\ M[N[ French Subantarctic Islands[ Progress in Conservation of "0884# A success story] breeding of burrowing petrels "Pro! the Subantarctic Islands "ed[ P[ R[ Dingwall#\ pp[ 20Ð41[ cellariidae# before and after the eradication of feral cat IUCN*The World Conservation Union[ Conservation of Felis catus at subantartic Marion Island[ Marine Orni! the Southern Polar Region No 1[ Paimpont[ thology\ 12\ 22Ð26[ Jouventin\ P[\ Stahl\ J[C[\ Weimerskirch\ H[ + Mougin\ J[L[ Courchamp\ F[ + Sugihara\ G[ "0888# Biological control of "0873# The seabirds of the French Subantarctic Islands + introduced predator populations to protect native island Adelie Land\ their status and conservation[ Status and species from extinction[ Ecological Applications\ in press[ Conservation of the World|s Seabirds "eds J[ P[ Croxall\ P[ Courchamp\ F[\ Langlais\ M[ + Sugihara\ G[ "in press# Rab! G[ H[ Evans + R[ W[ Schreiber#\ pp[ 598Ð514[ ICBP bits killing birds] modelling the hyperpredation process[ Technical Publication no[ 1[ Cambridge[ Journal of Animal Ecology "in press#[ Karl\ B[J[ + Best\ H[A[ "0871# Feral cats on Stewart Island] Cowan\ P[E[ "0881# the eradication of introduced Australian their foods and their e}ects on kakapo[ New Zealand Jour! brushtail possums\ Trichosurus vulpecula\ from Kapiti nal of Zoology\ 8\ 176Ð183[ Island\ a New Zealand nature reserve[ Biological Con! Kepler\ C[B[ "0856# Polynesian rat predation on nesting Lay! servation\ 50\ 106Ð115[ san Albatrosses and other Paci_c seabirds[ Auk\ 73\ 315Ð Cree\ A[\ Daugherty\ C[H[ + Hay\ J[M[ "0884# Reproduction 329[ of a rare New Zealand reptile\ the Tuatara Sphenodon King\ W[B[ "0874# Island birds] will the future repeat the past< Conservation of Island Birds[ ICBP Technical Pub! punctatus\ on rat!free and rat!inhabited islands[ Con! lication no[ 2 "ed[ P[ J[ Moors#\ pp[ 2Ð04[ Cambridge[ servation Biology\ 8\ 262Ð272[ Konecny\ M[J[ "0876# Food habits and energetics of feral Cruz\ J[B[ + Cruz\ F[ "0876# Conservation of the dark! house cats in the GalaÁpagos Islands[ Oikos\ 49\ 13Ð21[ rumped petrel Pterodroma Phaeopygia in the Galapagos Lovegrove\ T[G[ "0885# A comparison of the e}ects of pre! Islands\ Ecuador[ Biological Conservation\ 31\ 292Ð201[ dation by Norway "Rattus norvegicus# and Polynesian rats Crystal\ L[ "0878# American Broadcast journalism] its cover! "R[ exulans# on the saddleback "Philesturnus carunculatus#[ age of conservation crises[ Conservation for the Twenty! Notornis\ 32\ 80Ð001[ First Century "eds D[ Western + M[ C[ Pearl#\ pp[ 178Ð MacCallum\ J[ "0875# Evidence of predation by kiore upon 182[ Oxford University Press\ Oxford[ lizards from the Mokohinau islands[ New Zealand Journal Derenne\ P[ "0865# Notes sur la biologie du chat haret de of Ecology\ 8\ 72Ð76[ Kerguelen[ Mammalia\ 39\ 420Ð484[ Mellink\ E[ "0881# The Status of Neotoma anthonyi Rod! Diamond\ J[ "0878# Overview of recent extinctions[ Con! entia Muridae Cricetinae of Todos Santos Islands Baja servation for the Twenty!First Century "eds D[ Western + California Mexico[ Bulletin Southern California Academy M[ C[ Pearl#\ pp[ 26Ð30[ Oxford University Press\ Oxford[ of Sciences\ 80\ 026Ð039[ Diamond\ J[ + Case\ T[ "eds# "0875# Overview] introductions\ Monteiro\ L[R[\ Ramos\ J[A[ + Furness\ R[W[ "0885# Past extinctions\ exterminations and invasions[ Community and present status and conservation of the seabirds breed! Ecology\ pp[ 54Ð68[ Harper + Row Publishers\ New York[ ing in the Azores Archipelago[ Biological Conservation\ Domm\ S[ + Messersmith\ J[ "0889# Feral cat eradication on 67\ 208Ð217[ a barrier reef island\ Australia[ Atoll Research Bulletin\ Moors\ P[J[ + Atkinson\ I[A[E[ "0873# Predation on seabirds 227\ 0Ð3[ by introduced animals\ and factors a}ecting its severity[ Feare\ C[ "0887# The sustainable exploitation of sooty tern Status and Conservation of the World|s Seabirds[ "eds J[ P[ eggs in the Seychelles[ 5th annual unpublished report to Croxall\ P[ G[ H[ Evans + R[ W[ Schreiber#\ pp[ 556Ð589[ the Division of Environment\ Government of the Republic ICBP Technical Publication no[ 1[ Cambridge[ of Seychelles[ Murphy\ E[ + Brad_eld\ P[ "0881# Change in diet of stoats Fitzgerald\ B[M[ "0877# Diet of domestic cats and their following poisoning of rats in a New!Zealand forest[ New impact on prey populations[ The Domestic Cat\ the Biology Zealand Journal of Ecology\ 05\ 026Ð039[ of its Behaviour "eds D[ C[ Turner + P[ Bateson#\ pp[ 012Ð Newman\ D[G[ "0883# E}ects of a mouse\ Mus musculus\ 036[ Cambridge Academic Press\ Cambridge[ eradication programme and habitat change on lizard Þ 0888 British Fitzgerald\ B[M[\ Karl\ B[J[ + Veitch\ C[R[ "0880# The diet populations of Mana Island\ New Zealand\ with special Ecological Society of feral cats "Felis catus# on Raoul Island\ Kermadec reference to McGregor|s skink\ Cyclodina macgregori[ Journal of Animal group[ New Zealand Journal of Ecology\ 04\ 012Ð018[ New Zealand Journal of Zoology\ 10\ 332Ð345[ Ecology\ 57\ 171Ð181 Flux\ J[E[C[ "0882# Relative e}ect of cats\ myxomatosis\ Newman\ D[G[ + McFadden\ I[ "0889# Seasonal ~uctuations 180 of numbers\ breeding\ and food of kiore "Rattus exulans# Mercury Islands\ New Zealand\ to removal of an intro! F[ Courchamp\ on Lady Alice Island "Hen and Chickens group#\ with duced rodent] The kiore "Rattus exulans#[ Journal of the a consideration of kiore] Tuatara "Sphenodon punctatus# Royal Society of New Zealand\ 10\ 008Ð025[ M[ Langlais + relationships in New Zealand[ New Zealand Journal of Towns\ D[R[ "0883# The role of ecological restoration in the G[ Sugihara Zoology\ 06\ 44Ð53[ conservation of Whitaker|s skink "Cyclodina whitakeri#\ Nogales\ M[ + Medina\ F[M[ "0885# A review of the diet of a rare New Zealand lizard "Lacertilia] Scincidae#[ New feral domestic cats "Felis silvestris L[ catus# on the Canary Zealand Journal of Zoology\ 10\ 346Ð360[ Islands\ with new data from the laurel forest of La Towns\ D[R[ "0885# Changes in habitat use by lizards on a Gomera[ Zeitschrift fuÃrSaÃugetierkunde\ 50\ 0Ð5[ New Zealand island following removal of the introduced Nogales\ M[\ Rodriguez\ J[L[\ Delgado\ G[\ Quilis\ V[ + Paci_c Rat Rattus exulans[ Paci_c Conservation Biology\ Trujillo\ O[ "0881# The diet of feral cats "Felis catus#on 1\ 175Ð181[ Alegranza island "north of Lanzarote\ Canary islands#[ Towns\ D[R[ + Daugherty\ C[H[ "0883# Patterns of range Folia Zoologica\ 30\ 198Ð101[ contractions and extinctions in the New Zealand her! Paine\ R[T[ "0855# complexity and species diver! petofauna following human colonisation[ New Zealand sity[ American Naturalist\ 099\ 54Ð64[ Journal of Zoology\ 10\ 214Ð228[ Palomares\ F[\ Gaona\ P[\ Ferreras\ P[ + Delibes\ M[ "0884# Veitch\ C[R[ "0874# Methods of eradicating feral cats from Positive e}ects on game species of top predators by con! o}shore islands in New!Zealand[ Conservation of Island trolling smaller predator populations] an example with Birds "ed[ P[ J[ Moors#\ pp[ 24Ð70[ ICBP Technical Pub! lynx\ mongooses and rabbits[ Conservation Biology\ 8\ lication no[ 2[ Cambridge[ 184Ð294[ Veitch\ C[R[\ Fitzgerald\ B[M[\ Innes\ J[ + Murphy\ E[ "0881# Parkes\ J[P[ "0889# Feral goat control in New Zealand[ Bio! Proceedings of the National Predator Management Work! logical Conservation\ 43\ 224Ð237[ shop\ Threatened Species Occasional Publication[ No 2[ Pimm\ S[L[ "0879# Food web design and the e}ect of species Wilcove\ D[S[\ McLellan\ C[H[ + Dobson\ A[P[ "0875# Habi! deletion[ Oikos\ 24\ 028Ð038[ tat fragmentation in the temperate zone[ Conservation Powlesland\ R[G[\ Roberts\ A[\ Lloyd\ B[D[ + Merton\ D[V[ Biology\ the Science of Scarcity and Diversity[ "ed[ M[ "0884# Number\ fate\ and distribution of kakapo "Strigops E[ Soule#\ pp[ 126Ð145[ Sinauer Assoc[ Inc[\ Sunderland\ habroptilus# found on Stewart Island\ New Zealand\ 0868Ð Massachusetts[ 81[ New Zealand Journal of Zoology\ 11\ 128Ð137[ Williamson\ M[ "0885# Biological Invasion[ Chapman and Rainbolt\ R[E[ + Coblentz\ B[E[ "0886# A di}erent per! Hall\ London[ spective on eradication of vertebrate pests[ Wildlife Society Bulletin\ 14\ 078Ð080[ Received 07 February 0887^ revision received 05 June 0887 Rodriguez!Estrella\ R[\ Arnaud\ G[\ Cardenas\ S[A[ + Rod! riguez\ A[ "0880# Predation by feral cats on birds at Isla Socorro Mexico[ Western Birds\ 11\ 030Ð032[ Appendix Schoener\ T[W[ + Spiller\ D[A[ "0876# E}ect of lizards on spider populations] manipulative reconstruction of a natu! SYSTEM "0Ð1# ral experiment[ Science\ 125\ 020Ð023[ Seitre\ R[ + Seitre\ J[ "0881# Causes of land!bird extinction There are several stationary states for the _rst system in French Polynesia[ Oryx\ 15\ 104Ð111[ "eqns 0\1#[ The _rst two equilibrium states ð9\ 9Ł and Seto\ N[W[H[ + Conant\ S[ "0885# The e}ects of rat "Rattus rattus# predation on the reproductive success of the Bonin ðKb\ 9Ł are always unstable[ The third state ð9\ S:hsŁis Petrel "Pterodroma hypoleuca# on Midway Atoll[ Colonial globally asymptotically stable if and only if rb ¾ hb:hs[ Waterbirds\ 08\ 060Ð074[ These three points always exist[ When no populations Soule\ M[E[\ Bolger\ D[T[\ Alberts\ A[C[\ Wright\ J[\ Sorice\ go extinct\ the system reaches ðB \ S:hs ¦ B :hbŁ\ M[ + Hill\ S[ "0877# Reconstructed dynamics of rapid where B \ the bird population size at equilibrium\ is extinctions of chaparral!requiring birds in urban habitat islands[ Conservation Biology\ 1\ 64Ð81[ the solution of a quadratic equation and therefore one Spencer\ P[B[S[ "0880# Evidence of predation by a feral cat\ can have 9\ one or two equilibria with both popu! Felis catus "Carnivora] Felidae# on an isolated rock!wall! lations present between 9 and Kb] B ð−t¦ aby colony in tropical Queensland[ Australian z"t1−3hr u#Ł:1h r \ with t  h K − h r "K − S#\ Mammalogy\ 03\ 032Ð033[ s b s b s b s b b Taylor\ R[H[ + Thomas\ B[W[ "0878# Eradication of Norway and u "hb−hsrb#"SKb#[ Numerically\ when there are rats "Rattus norvegicus# from Hawea island\ Fiordland\ two points with admissible coexistence\ one only\ at

using Brodifacoum[ New Zealand Journal of Ecology\ 01\ most\ is stable[ If 9 ³ hb ¾ hs\ then there are two cases] 12Ð21[ if hb:hs ¾ rb\ the point is stable\ otherwise it does not Taylor\ R[H[ + Thomas\ B[W[ "0882# Rats eradicated from exist[ If 9 ³ h ¾ h \ then there are two cases] if rugged Breaksea Island 069 ha Fiordland New Zealand[ s b Biological Conservation\ 54\ 080Ð087[ hb:hs ³ rb\ it is stable\ if rb ¾ 0 ³ hb:hs it does not exist[ Terborgh\ J[ + Winter\ B[ "0879# Some causes of extinction[ If 0 ³ rb ³ hb:hs\ then if hb × hb \ it does not exist\ if

Conservation Biology] an EvolutionaryÐEcological Per! hb  hb \ it is stable\ if hb ³ hb there are two values spective "eds M[ E[ Soule + B[ A[ Wilcox#\ pp[ 008Ð022[ 1 for this point[ hb "hsBmax ¦ rbhbSKb#:KbS\ with Sinauer Assoc[ Inc[\ Sunderland\ Massachusetts[ B ð"r − 0#K − r SŁ:1r × 9[ Thurley\ T[ + Ben\ B[D[ "0883# Habitat distribution and max b b b b predation on a western population of terrestrial Leiopelma "Anura] Leiopelmatidae# in the northern King Country\ SYSTEM "2Ð3# New Zealand[ New Zealand Journal of Zoology\ 10\ 320Ð 325[ The second system "eqns 2\ 3# has 2 stationary states[ Þ 0888 British Tidemann\ C[R[\ Yorkston\ H[D[ + Russack\ A[J[ "0883# r Ecological Society The diet of cats\ Felis catus\ on Christmas Island\ Indian P023] ð9\ 9Ł\ P123]ðKp\ 9Ł\ and P223]ðKp"0−0: p#\ Journal of Animal Ocean[ Wildlife Research\ 10\ 168Ð175[ "0:mp#Kp"0−0:rp#Ł[ The dynamic behaviour of this Ecology\ 57\ 171Ð181 Towns\ D[R[ "0880# Response of lizard assemblages in the system is given by four cases[ 181 0 Case 0] rc × 0] if rp ¾ 0 the system reaches P023\ SYSTEM "7Ð09# Mesopredator otherwise it reaches P2 [ 23 Several equilibirum points arise[ Only the prey sur! release in insular 1 Case 1] 9 ³ r ¾ r ³ 0] the system reaches P0 [ p c 23 vive] ðK \ 9\ 9Ł[ This point is stable if l × r and l × r [ ecosystems 2 Case 2] 9 ³ r ³ 0\ r ¾ r ] in this case\ the dynamics b r r c c c c p Only the mesopredator survives] ð9\ "0 − l :r #S:h \ 9Ł[ depend on the initial proportion of prey and predator[ r r s This point is stable if l ³ r \ l × r and l ³ r "0 − If C"9#:P"9# × m "r − r #:"0 − r #\ then the system r r c c r r p p c c r h :h #[ Only the mesopredator disappears] ðK "0 − reaches P0 [If9³r¾r³0\ then the system b s b b 23 c p 0:r ¦ l :r r #\ 9\ K "0−0:r ¦l:r r#"0−l :r #:m Ł[ reaches P0 [If0³r\ then] "i# if r ¦ r × 1\ then b c b c b b c b c c c b 23 p c p This point is admissible if] r × l × r "0 − r #[ It is the system reaches P2 ^ "ii# if r ¦ r  1\ then this c c c b 23 c p stable if r × l × r "0 − r #\ l × r − m :m "0 − l :r # stationary state becomes a centre\ all nearby trajectory c c c b r r r b c c and l × "1 − r − r #:"1 − r #[ The last condition being periodical^ "iii# if r ¦ r ³ 1\ then this point is c c b c c p implies r ³ 1\ which is ful_lled by studied cat popu! unstable[ c lations in natura "e[g[ r  9=32Ð9=44] Derenne 0865^ 3 Case 3] r 0]if9³r ¾0\ the system reaches P0 \ c c p 23 or 9=122Ð0=060] van Aarde 0867\ 0872#[ If not\ one otherwise it reaches P223[ would have to replace it by] "1 − rc#lc × "1 − rc − rb#[

Only the prey disappears] ð9\ "0 − 0:rr ¦ lc:rrrc − lr:

rc#S:hs\ "0−0:rr¦lc:rrrc−lr:rc#"0 − lc:rc#S:mrhsŁ[

This point is admissible if] rc × lc × rc"0 − lrrr: SYSTEM "4Ð6# rc − rr#[ It is stable if rc × lc × rc"0 − lrrr:rc − rr#\

There are several equilibrium points for this system[ rb ³ mb"0 − lc:rc#:mc ¦ hb"0−0:rr¦lc:rrrc−lr:rc#:hs

The two equilibrium points ðKb\ 9\ 9Ł and ð9\ S:hs\9Ł and lc × rc"lr¦1 − rc −rr#:"1 −rc#[ The same com!

always exist but are never stable[ There are 9\ one or ment holds for the last condition "rc × 1#[ Only the two equilibrium points where only the cat population superpredator disappears] as in the case without disappears\ since it is the solution of an equation of control\ there are 9\ 0 or 1 points\ given by the solu!

the second degree ðB \ S:hs ¦ B :hb\ 9Ł[ These points tions of an equation of the second degree[ 1 are never stable when they exist[ The point where only ð−t 2 z"t −3rrhshbu#:1rrhshb\S:hs¦ B :hb\ 9Ł\ with

the prey disappears ð9\ S"0 − 0:rr#:hs\ "0:mr# "S:hs# here t  lrhsKb ¦ rr ðhsKb − hsrb "Kb − S#Ł\ and

"0−0:rr#Ł is admissible if rr × 0 and is stable if u  lrhbSKb ¦ rr "hb − hsrb#"SKb#[ The point where

rb ³ ðmb:mr ¦ hb"0−0:rr#:hsŁ and rc ¦ rr × 1[ The the superpredator disappears is unstable if lc ³ rc point where only the mesopredator disappears "new introductions lead to other states#[ Numerically\

ðKb"0−0:rb#\ 9\ "0:mb#Kb"0−0:rb#Ł is admissible if this point can be stabilized by increasing the value of

rb × 0 and is stable if rr ³ mr:mb and rc ¦ rb × 1[ In lc "increasing the control of the superpredator#[ In numerical simulations\ at least one equilibrium point numerical simulations\ at least one equilibrium point

with persistence of the three species ðB5 \ R5 \ C5 Ł is with persistence of the three species ðB5 \ R5 \ C5 Ł is found if the above conditions are not ful_lled[ found if the above conditions are not ful_lled[

Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 171Ð181