Predation by introduced foxes on native bush rats in Australia: do foxes take the doomed surplus?

Summary

1. Introduced vertebrate predators are one of the most important threats to endemic mammal species. Prey naivety can lead to heavy losses to alien predators, which may be additive to ‘natural’ sources of mortality that limit prey populations. Alternatively, predators may take only individuals that are surplus to the population, and hence predator control may have little benefit for susceptible native prey populations.

2. A field-based predator removal experiment was used to test the predator limitation and doomed surplus hypotheses on the impact of introduced red foxes Vulpes vulpes on populations of native bush rats Rattus fuscipes in south-eastern Australia.

3. Poison baiting was used in July 1993 to reduce fox numbers in two fox-removal sites from 2·8–3·4 km^–1 (spotlight counts) to less than 0·5 km^–1 within 6 months. Fox density in two non-removal sites remained typically five times higher than that in removal sites.

4. Bush rat numbers on replicated trapping plots showed no response to fox removal, and rodent numbers fluctuated seasonally in all sites over 22 months of fox control, which represented two breeding seasons for rats.

5. Fox removal also had no effect on rat persistence time, adult body weight, captures of juveniles or immature animals during the breeding season, nor captures of immigrant or transient animals.

6. The general lack of response by rat populations to fox removal supported the doomed surplus hypothesis, that fox predation operated as a compensatory source of mortality rather than an additive one. Consequently, there was no measured benefit to native rat populations of intensive short-term fox control.

7. The results suggest that where predation pressure is low, not all predation mortality will be additive to prey populations even if it results from a predator introduced to the ecosystem. Hence, indiscriminate control of introduced predators is unlikely to produce uniform benefits for all the species they prey upon. Feral predator control should therefore be targeted for native species known to be predation limited or for species where any mortality threatens persistence.

Introduction

Introduced vertebrate predators are one of the most important threats to endemic mammal species throughout a range of ecosystems (Courchamp, Langlais & Sugihara 1999). Their impact is thought to be pronounced because native prey are typically naive to the risks from alien predators (McLean, Lundie-Jenkins & Jarman 1995; Banks 1998), leading to potentially heavy losses. Losses from alien predators can be additive to ‘natural’ sources of mortality that, by definition, must limit prey populations (Sinclair & Pech 1996), and may be severe enough to cause local extirpation (Diamond & Case 1986). Consequently, the reduction of feral predator numbers is considered a key conservation action in the management of many native mammals vulnerable to feral predators (cf. Courchamp, Langlais & Sugihara 1999).

The basis of this action is probably associated with a plethora of work on native predator–prey systems that has emerged over the last two decades to implicate predation as a significant limiting or regulating factor for small mammal (< 500 g adult weight) populations (Korpimäki & Krebs 1996). Elaborate indirect approaches have been employed in the search for density-dependent processes in predator–prey interactions (reviewed by Boutin 1995; and Krebs 1995), producing correlative but not compelling evidence that predators can indeed suppress prey populations (Boutin 1995). As such, Errington's (1946) alternative ‘doomed surplus’ hypothesis, which suggests that predators take only the excess production of a prey population, is often dismissed as no longer relevant to predator–prey dynamics (Sinclair & Pech 1996).

In contrast, direct manipulative experiments critically testing the predator limitation hypothesis for small mammal populations are rare (Sih et al. 1985; Meserve et al. 1996; Norrdahl & Korpimäki 1996; Klemola et al. 1997; Korpimäki & Norrdahl 1998). Most have examined predation on cyclic microtine rodents in Fennoscandia and North America and have been carried out in small exclosures (cf. Norrdahl & Korpimäki 1995) removing all possible sources of predation (Taitt & Krebs 1983). Notably though, predator removal experiments have not universally rejected Errington's hypothesis that predation from a particular predator is surplus, i.e. a compensatory source of mortality rather than an additive one (Norrdahl & Korpimäki 1995).

In Australia, there is a conservation imperative to understand the impact of predation by red foxes Vulpes vulpes L. on the population ecology of native small mammals (Saunders et al. 1995). Terrestrial mammals within the critical weight range of 35 g–5·5 kg have experienced dramatic declines since European settlement, and these have coincided with the introduction and spread of the fox (Burbidge & McKenzie 1989). Patterns of habitat use by foxes and their prey (Catling & Burt 1994, 1995) also implicate fox predation as a potential limiting factor for many mammals. Where rabbits are foxes’ staple prey, native small mammals are important supplemental prey (reviewed by Newsome et al. 1997), and in the absence of rabbits, native small mammals are often the principal prey species, with foxes showing some dietary preferences for small mammals (Brunner, Lloyd & Coman 1975; Green & Osborne 1981). Fox predation, however, is one of a multitude of potential hypotheses to account for loss of mammal diversity in Australia (Dickman et al. 1993; Short & Smith 1994; Smith & Quin 1996), and the role of foxes in the continued suppression of any small mammal species has not been tested critically in any Australian environment.

This paper reports an experiment to test between the predator limitation and the doomed surplus hypotheses for the impact of fox predation on a relatively common small mammal prey species, the bush rat Rattus fuscipes Waterhouse. Bush rats are typically opportunistic prey for foxes in south-eastern Australia (Brunner, Lloyd & Coman 1975; Green & Osborne 1981; Barker, Lunney & Bubela 1994), and they are the most commonly preyed upon species of small mammals in forested areas of Australia (Newsome et al. 1997). Their populations fluctuate seasonally, declining substantially over winter (Wood 1971; Dickman 1983; Press 1986), but experimental food supplementation has failed to arrest seasonal declines (Press 1982; Banks 1991). Fox predation, however, appears to be most intense during cooler months when alternative ectothermic prey and rabbits decline in abundance (Green & Osborne 1981; Lin & Batzli 1995). Localized activity of foxes in habitats used by bush rats has coincided with winter population declines of this prey species (Banks 1991). Moreover, unlike small mammal prey where foxes are native, this Australian species shows no avoidance of fox odour (Banks 1998), suggesting that it may be naive to risks posed by foxes (McLean, Lundie-Jenkins & Jarman 1995). However, the importance of predation in the general population dynamics remains unknown.

The aim of this study was to determine if populations of bush rats are limited by fox predation, using a large-scale replicated fox-removal experiment. If fox predation limits population growth, a significant reduction in fox abundance and predation pressure should cause rodent populations to show population increases, as well as increases in other parameters likely to be indicative of a population response, including recapture rates, persistence times and juvenile recruitment. As bush rat populations typically undergo greater than twofold interannual fluctuations (Press 1986), in this paper it is proposed a priori that if fox removal does not cause populations to more than double within two breeding seasons then it can be accepted that the alternative doomed surplus hypothesis operates, whereby fox predation has no significant impact on this species.

Methods

Study species

The bush rat is a small (c.150 g) omnivorous rodent, common in a variety of forest habitats along the east coast of Australia (Lunney 1995). Juvenile mortality is generally high but adult individuals live for around 15 months, reaching maturity after 7 weeks. Breeding occurs in all months except winter (May–July) in coastal populations (Press 1976), but in mountain environments the winter hiatus in breeding is extended into October (P. Banks, personal observation). Litter size varies between three and five (Taylor & Horner 1973) and females can produce up to three litters in 93 days (Taylor & Horner 1971). Movements of males and females are extensive, and associated with dietary opportunism (Braithwaite & Lee 1979).

Study sites and experimental design

Four sites (approximately 10–18 km² each) were chosen for the fox-removal experiment in Namadgi National Park, an area of montane forest and repossessed cleared farmland in the Brindabella Ranges, 50 km south of Canberra, Australia. The methods and efficacy of the fox removal are reported by Banks, Dickman & Newsome (1998). In summary, a persistent campaign of 1080 baiting in two sites (R1, R2) commenced in July 1993 and reduced fox abundance from 2·8–3·4 km^–1 (spotlight counts) to less than 0·5 km^–1 within 6 months, and to almost zero for the next 12 months. Fox density in the two non-removal sites (C1, C2) remained comparatively stable over this period and was typically five times higher than in the fox-removal sites. Predation by foxes on rat populations in the study sites was confirmed by an analysis of 482 fox scats collected from roadsides adjacent to rodent habitat, of which 3% contained bush rat hair or bone (Banks 1997).

Monitoring rodent populations

Plots for monitoring small mammals were chosen in suitable habitat that was frequented by foxes (based on radio-tracking data; Banks 1997). All plots were located in moist habitat patches along small creek lines where rat density was highest; extensive preliminary trapping showed that densities elsewhere were very low (P. Banks, unpublished data). Outside the riparian strip, the forest was drier with a sparse and open understorey, which is generally avoided by bush rats (Hall & Lee 1982; Press 1982). However, suitable-sized riparian habitat patches able to support populations of bush rats were patchily distributed in the study area, which limited the number of replicate rodent populations available for monitoring. As a result monitoring was carried out on two plots spaced > 2 km apart in each of the non-removal sites, but on only one plot in each of the removal sites. No movements of marked individuals between plots were recorded during the study.

In each plot, two lines of 15 trap stations were established to survey the small mammals. Initial sampling using a 5 × 5 grid showed that all individuals and 85% of captures occurred in the two lines closest to the creek. Trap stations were placed in suitable microhabitats (e.g. animal runways, fallen logs; Norton 1987; Read, Malafant & Myers 1989) and spaced 12 ± 2 m apart to ensure the mean nightly movements of an animal would remain within the length of the trap line and would approximate 2–3 trap intervals (Wood 1971). The two lines of traps were spaced 25 m apart on either side of the creek. Trap success on any one night never exceeded 50% of available traps, thus ensuring minimal competition for traps (Banks 1991).

Each trap station comprised one Elliott folding aluminium trap (33 × 10 × 10 cm) baited with a mixture of rolled oats, peanut butter and honey, and provided with cotton wool bedding for insulation. Traps were checked each morning at first light. Male rats were scored as having abdominal or scrotal testes (Warneke 1971); female rodents were classified as mated if the vagina was open, bruised or bloody, as previously parous if possessing large obvious nipples, and as non-parous if nipples were small or invisible (Press 1982). All individuals were weighed and identified uniquely using a system of ear notching for juvenile bush rats and small numbered metal ear tags for adults. Rats were considered juvenile if less than 70 g, and immature if non-parous or with abdominal testes during the breeding season (December–March).

In all plots traps were set for three consecutive nights every 2 months from June 1993 to March 1995. Ninety per cent of captures on the third night were of individuals caught sometime on the previous two nights. Over the breeding season (spring–summer) trapping was conducted every month to capture and mark as many juvenile animals as possible.

The minimum numbers known to be alive (MKTA) were used as an index of bush rat population size and compared at each trapping period following fox removal by repeated Student's t-tests using plots as replicates (Soto & Hurlbert 1991). This approach does not partition the variance within sites (between trap plots in a site) but pools it within treatments. Similar analyses were performed for numbers of recaptures, numbers of juveniles, numbers of new immature animals captured during 1993–94 and 1994–95 breeding seasons, the number of immigrants and the total number of transient animals (never recaptured) captured during the experiment. Estimates of treatment effects ± 95% confidence limits for response variables were calculated on log_e-transformed values, which were then back-transformed to indicate the scale of predator reduction effect and the size of the effect likely to have been detected. The exponential rate of increase was used as an index of population growth over the course of the experiment and derived from the slope of a linear regression of log_e MKTA against time (Caughley & Sinclair 1994).

‘Survival’ of individuals over the period of the experiment was compared between fox-removal and non-removal sites and estimated from the mean persistence time of individuals (i.e. from date of first capture to date of last capture) (Meserve, Gutierrez & Jaksic 1993). Only recaptured individuals were included in the analysis to reduce the influence of mainly transient animals on estimates of resident survival associated with fox removal. Animals captured during the last trapping session were included in the analysis as right censored data, and data were pooled across sites to increase sample size. Analyses were performed using the JMP Statistical Package (SAS Inc., Carey, NC), and Kaplan–Meier survivorship functions were compared using Cox's proportional hazards.

Predator avoidance behaviour by small mammalian prey can result in restricted movements and loss of body weight due to presence of predators alone (Desy & Batzli 1989). To determine if rodent body weights were influenced by the presence of foxes, separate nested anova's were performed on the body weights of rats in three periods: the first summer after fox control and the following winter and summer. Data were pooled across the two trapping sessions in each season, but individuals were included only once in each season, scoring their weight at first capture. Data from trapping plots within sites were also pooled to achieve a balanced design for analysis. Sexes were separated and juveniles were excluded.

Results

Numerical responses to fox removal

From 6480 trap nights over 22 months, 252 bush rats were captured 739 times, with the sex ratio close to unity (1 : 0·9 males : females). In general, bush rat numbers at all sites increased during the summer due to an influx of juveniles into the population, and declined in winter (Fig. 1). These patterns have been reported for other unmanipulated populations (Wood 1971; Press 1982). There was no association of fox removal on these winter declines nor subsequent spring MKTA [treatment effect ± 95% confidence limits (CL) in October 1993 = 1·24 ± 2·09, and October 1994 = 1·30 ± 2·22]. Student's t-tests showed that on three occasions the MKTA did differ between treatments: August 1993 (t₄ = 3·08, P = 0·05), March 1994 (t₄ = 3·08, P = 0·05) and March 1995 (t₄ = 4·98, P = 0·03). In between these periods numbers fluctuated widely (Fig. 1a), hence these differences must be interpreted with caution.

Figure 1. Numbers of bush rats Rattus fuscipes in fox-removal sites [solid lines; R1 (×), R2 (+)] and non-removal sites [dashed lines; C1 (○,●) and C2 (□,▪)] in Namadgi National Park. Values represent (a) minimum numbers known to be alive (MKTA) and (b) the number of recaptured animals. Arrows represent significant differences between treatments (P < 0·05).

There was no association (P > 0·1) between fox removal and the numbers of recaptured individuals (Fig. 1b) (treatment effect ± 95% CL on mean monthly recaptures = 1·05 ± 1·31) nor the numbers of new animals captured (treatment effect ± 95% CL on mean monthly capture of new animals = 1·75 ± 2·07). Similarly, fox removal showed no association with the mean monthly numbers of transients captured (t₄ = 0·56, P = 0·60; treatment effect ± 95% CL = 1·06 ± 2·02).

Numbers of immature animals captured were similar in fox-removal and non-removal sites during the 1993–94 (t₄ = 1·64, P = 0·17; treatment effect ± 95% CL = 1·34 ± 1·66) and 1994–95 (t₄ = 1·37, P = 0·24; treatment effect ± 95% CL = 1·45 ± 1·69) breeding seasons (Fig. 2). Similarly there was no association between fox removal and the numbers of juveniles (< 70 g) captured during the 1993–94 (t₄ = 0·67, P = 0·54; treatment effect ± 95% CL = 1·46 ± 1·98) and 1994–95 (t₄ = 1·10, P = 0·33; treatment effect ± 95% CL = 1·41 ± 1·69) breeding seasons. Consequently, the exponential rate of change of rodent populations (on an annual basis) was similar (P > 0·30) between removal sites (R1 = –0·28, R² = –0·10) and non-removal sites (average of trap plots; C1 = –0·36, C2 = –0·18), with all plots showing decreases in MKTA over the duration of the experiment (treatment effect ± 95% CL = 1·5 ± 14·4).

Figure 2. Numbers (mean ± SE) of immature (non-reproductive and juvenile) bush rats Rattus fuscipes captured in fox-removal (black bars) and non-removal sites (white bars) during 1993–94 and 1994–95 breeding seasons.

Persistence times and body weights

Mean persistence times for rats ranged between 97 and 163 days in the non-removal sites, and between 88 and 119 days in the removal sites, but Kaplan–Meier survival functions did not differ significantly between treatments (Fig. 3; log-rank test; χ² = 1·53; P > 0·2; difference between treatments ± 95% CL on untransformed data = 0·11 ± 0·17). Sites with foxes had the longest persisting rats (3 individuals > 500 days) and 18% of individuals there lasted > 200 days, compared with 11% in the fox control sites. Similarly, 49% of individuals persisted for > 100 days in the sites with foxes compared with only 36% in the sites without foxes. Survival functions of male and female rats did not differ either, although males appeared to persist for less time than females (log-rank test; χ² = 3·99; 0·1 > P > 0·05) and the five longest persistence times were all for females. Animals captured as juveniles appeared to persist longer in the sites with foxes (log-rank test; χ² = 3·72; 0·1 > P > 0·05). However, at one trap plot with foxes, 85% of animals captured as juveniles persisted for > 200 days whereas only one individual in the other site had a persistence time > 200 days.

Figure 3. Kaplan–Meier survival functions for the persistence of individual bush rats Rattus fuscipes (males and females). Values are pooled across sites for fox-removal sites (––) and non-removal sites (–––). Only adults (> 70 g) are included.

Across all sites, females were generally heavier in summer than winter, while adult males showed no seasonal pattern of weight change (Fig. 4). However, anova showed that there was no association between fox removal and body weights of bush rats during any time period (P > 0·20), and the data both within and between sites were highly variable (average treatment effect ± 95% CL for the three periods = 1·1 ± 2·0 for males and 1·0 ± 1·4 for females).

Figure 4. Body weight (mean ± SE) of (a) female and (b) male adult bush rats Rattus fuscipes captured in fox-removal sites and non-removal sites. Values for non-removal sites represent pooled values for individual trapping plots.

Discussion

The experimental reduction in fox abundance had no impact on the population densities of bush rats over 22 months. Although rats were more abundant in sites without foxes during the last trap session, the preceding patterns of fluctuation did not indicate a gradual increase because of removal of foxes. Moreover, none of the demographic parameters suggested that bush rat populations would have necessarily increased with longer term fox control.

Variability between populations and between seasons was high, resulting in the power of the experiment being lower than desired. Nevertheless, this design was sufficiently powerful to detect an almost doubling in MKTA of rodent populations due to fox removal (with control site mean MKTA = 9·0 and upper 95% CL on treatment effect = 10·0 in October 1994). Similarly, confidence limits for other variables suggested that the experiment could have detected between two- and threefold increases due to fox removal. A greater than twofold increase in MKTA within the time-frame of the experiment was possible. Female bush rats produce on average three to five young per litter (Wood 1971) and in Namadgi females can produce at least two litters per season (Woodside 1983). Moreover, populations have increased greater than fivefold within only one to two breeding seasons following experimental food supplementation (Press 1982; Banks 1991) and have more than doubled over two breeding seasons following fire (Fox & McKay 1981). At Namadgi, rodent numbers at some sites showed more than threefold seasonal differences, while all sites differed by 100% in their minimum and peak numbers. Therefore, fox impact, if any existed, was considerably smaller than between-site variability and seasonal fluctuations.

In all sites more than 60% of females had bred by the end of the breeding season, resulting in no treatment differences in the numbers of juveniles or immature animals captured during the breeding seasons. Therefore, any difference in population size due to the removal of foxes could have resulted only from differential immigration or survival of juveniles and adults. Predator exclusion has previously resulted in enhanced survival of adult prairie voles Microtus ochrogaster Wagner (Desy & Batzli 1989) and field voles Microtus agrestis L. (Erlinge 1987; Norrdahl & Korpimäki 1998), which in turn produced significant population growth (Korpimäki & Norrdahl 1998). However, predator removal did not affect reproductive output, growth or survival of juvenile prairie voles (Desy & Batzli 1989). Similarly, predators (principally hawks Buteo lagopus Pontoppidan and red foxes) were responsible for significant adult and juvenile mortality in tundra lemmings Dicrostonyx kilangmiutak Anderson & Rana, and removal of predators kept populations stable while lemmings at non-removal sites continued to decline (Reid, Krebs & Kenney 1995). Importantly though, predator-free populations did not grow. Meserve, Gutierrez & Jaksic (1993) also found no difference in population size of degus Octodon degus Molina following predator control despite a difference in survival of adults, but concluded that predator limitation was occurring. In both cases, dispersal of juveniles from the study sites is thought to have influenced the lack of population growth (Reid, Krebs & Kenney 1995; Meserve, Gutierrez & Jaksic 1993).

Similarly, at Namadgi analysis of site-persistence time showed no differences between treatments, and fox removal did not influence the recruitment of young (based on the captures of immature animals). Together with the lack of a consistent response in densities, the data suggest strongly that fox predation had a negligible impact on rats despite the low power of the experiment. Theoretical models of predator impact suggest that even very low levels of predation can limit prey (cf. predator pit; Pech et al. 1992). However, the common prediction of this hypothesis and the predator limitation hypothesis, that prey should increase following predator removal, was not supported by the experimental evidence here. Instead, the data support the doomed surplus hypothesis that fox predation on bush rats is not an additive cause of mortality, but is compensatory for other causes of mortality in bush rat populations.

A source of potential compensatory mortality following fox removal is increased predation by other predators (Korpimäki & Krebs 1996). Compensatory predation was also thought to have buffered the population increases of voles and shrews following experimental raptor control (Norrdahl & Korpimäki 1995) and of lemmings following exclusion of foxes (Reid, Krebs & Kenney 1995). Similarly, native prey reintroduced into fox-free areas have been killed by cats (Felis catus L.), which increased in numbers in response to fox removal (Christensen & Burrows 1995). As the mean persistence time of bush rats was lower in the fox-removal sites, increased activity of another predator species may have compensated for fox removal. In the montane woodland of Namadgi, many native predator species may prey upon small native mammals. Red-bellied black snakes Pseudechis porphyriacus Cogger, brown snakes Pseudonaja textilis Krefft, tiger snakes Notechis scutatus Boulenger and native birds of prey are predators of small native mammals but all were encountered rarely in the study area. Similarly, the feral cat takes small mammals, but was encountered only rarely; foxes were therefore most likely to be the most abundant predator of small mammals in the survey areas. Whether these predators were the most significant consumers of small mammals is unknown and the issue of compensatory predation remains unclear. Thus fox control may have had mesopredator release benefits to other predators (Courchamp, Langlais & Sugihara 1999), but the extent of these benefits are not known.

Alternatively, density-dependent resource limitation may have prevented further population growth (Sinclair & Pech 1996). Local populations of bush rats can increase with supplemental food (Press 1982; Banks 1991). Without such provisioning it is possible that local densities were saturated and could not increase regardless of predator removal (Meserve et al. 1996; Reid, Krebs & Kenney 1995). While there were differences in MKTA due to fox removal in March, when numbers typically showed seasonal peaks (Press 1986), these differences were not sustained subsequently. It is possible that the excess individuals dispersed outside the narrow riparian areas, where their survival and reproduction prospects are not known. In open suboptimal habitats (Hall & Lee 1982) small mammals may be most vulnerable to predation, and the impact of foxes may be greater in these areas than in denser vegetation, which may provide refuge (Hansson 1989; Dickman, Predavec & Lynham 1991). Future studies would therefore benefit from examining the impact of predation in these suboptimal areas.

Thus Errington's (1946) doomed surplus hypothesis on the impact of fox predation was upheld for the populations of bush rats in Namadgi, with short-term (22 months) intensive fox control providing little conservation benefit for this native prey species. This result suggests that where predation pressure is low, not all predation mortality will be additive to prey populations even if it results from a predator introduced to the ecosystem. Hence, short-term control of introduced predators is unlikely to produce uniform benefits to all the native species they prey upon, and may well have adverse ecological costs (Banks, Dickman & Newsome 1998). During this study, fox control also led to dramatic increases of another introduced pest species (outside bush rat habitats), the European rabbit Oryctolagus cunniculus Lilljeborg, for which subsequent control measures had to be taken (Banks, Dickman & Newsome 1998). Thus, feral predator control should be targeted to particularly vulnerable species known to be limited by feral predators or to species whose persistence is threatened by any mortality.

Furthermore, it is proposed here that the doomed surplus hypothesis is not irrelevant, but is of particular application to the management of predation impact where evidence of predation alone is not sufficient to justify management action. The doomed surplus hypothesis need not mean that the individuals taken by predators are themselves doomed to die (Sinclair & Arcese 1995; Koivunen et al. 1996), but it will be supported whenever predator removal experiments with sufficient power do not lead to significant prey population growth. However, the extent of increases required to determine significance should be defined a priori, based on the importance of other potential limiting factors or some clear management objectives. The doomed surplus predation hypothesis will also be relevant to multipredator systems where compensatory predation by other predators is likely. This is of particular relevance when attempting to understand and manage the impact of an introduced predator in the context of predation by native species or other alien predators.

Acknowledgements

Many volunteers assisted with fieldwork during this research project, to whom I owe much appreciation. For multiple field trips and for working under typically arduous conditions, I offer special thanks to W.E. Maitz, A. Reid, R.J. Spencer, B. Tamayo, S.J. Parker, A.N. Banks and J.M. Tipping. Earlier drafts of this paper were greatly improved by comments from C.R. Dickman, A.E. Newsome, D.F. Hochuli, E.F. Sutherland, J.M. Tipping, D. MacDonald and E. Korpimäki and two anonymous referees. This research was funded by the Australian Alps National Parks and the Institute of Wildlife Research.

Received 18 December 1997; revision received 27 August 1999