Rate of increase as a function of rainfall for house mouse Mus domesticus populations in a cereal-growing region in southern Australia

Authors


Peter Brown (fax: + 61 26242 1505; e-mail p.brown@dwe.csiro.au).

Summary

1. Mouse plagues are a significant problem to agricultural areas of Australia, causing millions of dollars of damage. This study was conducted to determine if rainfall could explain the occurrence of mouse plagues.

2. On average, data on mouse abundance were collected every month, using mark-release-recapture techniques, from the Victorian Mallee cereal-growing region, from February 1983 to October 1994. No data were collected from December 1990 to September 1992. Three plagues of mice occurred during these 12 years. We examined the rate of increase of mouse populations as a function of antecedent rainfall.

3. The highest observed rate of increase per month was during 1986 (r = 1·86). The highest observed rate of decrease per month was during 1984 (r = –2·85). The maximum rate of increase of mouse populations used in the numerical response function was 1·16 month–1. The best estimate for the numerical response function was robs = –6·79 + 7·95 (1 – e–1·11V).

4. The numerical response of mouse populations to rainfall was examined against 6-month accumulated rainfall that was lagged by 0, 3 and 6 months. The best fit of the model was to lag rainfall by 3 months.

5. Two systems for the response of mouse populations to rainfall are described. The plague system occurred when mouse populations responded to rainfall: populations increased following high rainfall and decreased following low rainfall. The non-plague system occurred when the exponential rate of increase and rainfall were independent: populations crashed after a plague and were unable to respond to rainfall for at least 2 years thereafter.

6. The two systems suggest that there is ‘biological memory’ that masks the effect of rainfall for a minimum period after a mouse plague. This memory appears to be associated with the time since the last plague, the population response by mice (including shifts in age structure) in the previous year, and the abundance of mice after the spring decline. If rainfall is used to predict mouse plagues to assist in their management, the biology of the system must be known.

Introduction

Plagues of house mice Mus domesticus (Schwartz & Schwartz 1943) are a significant problem to agricultural areas of Australia. It has been estimated conservatively from a survey of grain-growers in Victoria and South Australia that the 1993 mouse plague cost AUD$64·5 million (Caughley, Monamy & Heiden 1994). A mouse plague occurs somewhere in Australia once every 4 years, but could be 1 year in 7 for any particular region (Redhead & Singleton 1988; Singleton 1989; Mutze 1991). Within the wheat belt of southern and eastern Australia there are a number of regions defined by different soil types, cropping systems and climate. Yet each is subject to mouse plagues. On the Darling Downs in southern Queensland, for example, winter and summer crops are grown on a continuous basis on self-mulching dark clay soils, whereas on the light sandy loam soils of the Victorian Mallee winter cereals are grown in the same paddock only once every 3 years. The mechanisms of plague formation in these regions differ markedly (Singleton 1989; Cantrill 1992).

Farmers generally do not perceive they have a mouse problem until densities are > 200 ha–1. It is then too late for cost-effective management because if mice are still breeding they will double their density every 4–6 weeks. Growers do not monitor numbers of mice on their property and only one state government (Queensland) has a regular monitoring programme. The monitoring programme conducted in Queensland uses 940 snap-traps along a 32-km transect four times a year. They consider a 1% trap success in September (early spring) to be the commencement of an increase that may lead to a mouse plague the following autumn. There is, however, large variation in mouse numbers across the region. Therefore, relying on such a low trap success for predicting plagues presents a high risk that a plague may be forecast but not materialize. Nevertheless, it is important to provide growers and governments with a warning of the likelihood of a mouse plague so that appropriate management strategies can be implemented early to reduce their impact. When mouse densities are high, state governments have given temporary registration to acute rodenticides such as strychnine for use over vast areas of land (up to 300 000 ha; Fisher 1996; Mutze 1998). There is limited evidence to show that broad-scale use of rodenticides reduces damage to growing crops or is cost-effective (Mutze 1989, 1993; Brown et al. 1997). The large amount of rodenticide used also creates a risk to non-target animals (Brown & Lundie-Jenkins 1999).

A regular system of plague prediction could be based on weather events such as rainfall. Saunders & Giles (1977) compared the relationship between prolonged dry weather on mouse numbers and suggested that plagues of mice were preceded by drought conditions at least 1 year prior. This association, however, would have predicted four plagues that did not occur. Redhead (1982) proposed a triphasic model of mouse plagues from a study in the Murrumbidgee Irrigation Area (New South Wales), and demonstrated the importance of good autumn rainfall (approximately 170% of the long-term average for autumn) that enhanced breeding in the following spring. Singleton (1989) postulated that a mouse plague is triggered by good autumn rainfall but that a sequence of rainfall events over the next 12 months is required for its development. Mutze, Veitch & Miller (1990) developed a stochastic model based on rainfall and grain production in South Australia that accounted for 41% of the variation in plague occurrence. Cantrill (1992) developed a computer model based on a regular annual cycle in mouse abundance. He provided forecasts of mouse densities from indices of population abundance and rainfall data obtained at particular times of the year. Twigg & Kay (1994) used linear multiple regression to develop a model using microhabitat features and short-term (3-month) climatic variables to identify important habitat characteristics for mice.

None of these studies has related rate of increase (r) of mouse populations to rainfall or food supply to predict plagues. The reason that there are plagues in some years and not others could be better explained if these population responses are considered.

This study examines the relationship between exponential rates of increase of mouse populations and antecedent rainfall using a numerical response function. Each model was considered over calendar years (January–December) and biological years (September–August) for accumulated (6-months) rainfall lagged by 0, 3 and 6 months, and the adjusted trap success of mice (for each month). We considered these responses in plague and non-plague years. The data were drawn from 12 years of live-trapping mice in the Mallee wheatfields of north-west Victoria, Australia. This is the first study to consider the numerical response of field populations of mice to rainfall.

Methods

Study area

Population data were collected from the Mallee cereal-growing area in north-western Victoria, Australia. All trapping sites were located on or within 5 km of the Mallee Research Station (MRS) at Walpeup (35°08′S, 142°01′E; altitude 115 m). The topography of the region is flat to mildly undulating. The soils are predominantly yellowish-brown sands and reddish-brown sandy loams (Newell 1961). The climate is mediterranean, with hot dry summers and cool wet winters. The average rainfall is 337 mm per year and the coefficient of variation is 30·3%. Rainfall at the MRS from 1981 to 1994 was above average for 4 of the years (1981, 1983, 1986 and 1993), below average for 4 of the years (1982, 1984, 1985 and 1994), and close to average for 6 of the years (within 10% of the long-term mean) (Fig. 1).

Figure 1.

(a) Mouse density (adjusted trap success) and (b) 6-month accumulated rainfall at MRS from February 1983 to October 1994. Trapping occurred irregularly from mid-1989 to mid-1992.

Live-trapping data

Mouse abundance was monitored from February 1983 to October 1994 using Longworth live-capture traps (Longworth Scientific, Abingdon, UK) baited with wheat. Singleton (1989) described the habitat types and the schedule for each trap session from February 1983 to January 1984 (on average a total of 50 traps in each of seven habitats over four consecutive nights every 6 weeks: 1400 trap nights (t.n.) per session) and from February 1984 to December 1985 (an average of 50 traps in seven habitats over three consecutive nights every third week: 1000 t.n. per session). The latter trapping schedule was followed from January 1986 to February 1989. Thereafter mouse populations were monitored intermittently: in April, November and December in 1989 (an average of 475 t.n. per session); in January, February, April, June and November in 1990 (an average of 510 t.n. per session); in October and December in 1992 (an average of 413 t.n. per session); and in March, April, May and August in 1993 (an average of 475 t.n. per session). No monitoring occurred during 1991. When trapping occurred twice within a month, the abundance of mice was averaged for that month.

From October 1993 to April 1994, mouse populations were monitored monthly for three consecutive nights from three sites within 5 km of the MRS (three sites × 117 traps across five habitats × 3 nights: 1053 t.n.). These sites were only trapped for two consecutive nights from May to October 1994 (138 traps across four habitats: 828 t.n. per session).

All mice captured were marked with a brass ear tag (Hauptner, Sieper and Co. Pty Ltd, 9 Beresford St, Strathfield, NSW, 2135), weighed, measured, sexed and assessed for breeding condition, then released at site of capture.

Mouse abundance from live-trapping is expressed as an adjusted trap success. This was calculated using the trap success per 100 trap nights adjusted using the frequency-density transformation of Caughley (1977).

A mouse plague (hereafter referred to as a plague) is defined as an upwelling of population numbers (increase in density) followed by a spread of animals into new habitats (= eruption; after Caughley 1981), with this occurring synchronously over large areas (greater than 50 000 ha). Mouse densities during a plague exceed 500 individuals ha–1 and are typically greater than 1000 individuals ha–1. For example, in southern New South Wales mouse densities were > 3500 mice ha–1 in 1980 (Saunders 1986) and > 2500 mice ha–1 in 1984 (Boonstra & Redhead 1994). The decline in mouse densities during early spring, which coincides with the onset of breeding, is termed the spring decline. The rapid decline in winter (over 1–2 months) from plague densities to densities of < 1 mouse ha–1 is termed a crash.

Exponential rate of increase per month

The exponential rate of increase per month (r) was calculated as the adjusted trap success for month t divided by the adjusted trap success for month t – 1, which was then logged using a natural logarithm.

Numerical response

Ivlev's (1961) inverted exponential function was used to model the numerical response of mice to changes in rainfall. Ivlev numerical response functions were fitted to the data points using SigmaPlot (Hearne Scientific Software Pty Ltd, Level 6, 552 Lonsdale St, Melbourne, Victoria, 3000, Australia) iterative regression procedures (Kuo 1994). The numerical response function in Ivlev form is:

r = – a + c (1 – edV)

where r is the exponential rate of increase, a is the maximum rate of decrease in the absence of food, c is the rate at which a is progressively decreased by increasing the amount of food until the animal is satiated, d is the measure of the demographic efficiency, or ability to multiply when V is sparse, and V is the available food. Both c and d were estimated from the data.

The maximum rate of increase (rmax) is defined by the relationship: rmax = c – a.

Rainfall was used here as a measure of food availability. Vegetative growth is important for mice because they depend on green or growing vegetation for reproduction (Redhead 1982; Bomford 1987a,b). In the Victorian Mallee, breeding by mice has been reported to commence after a pulse in the abundance of invertebrates and fresh grass seeds; breeding then peaked when fresh cereal grain became available (Tann, Singleton & Coman 1991). Rainfall has been used as an index of food availability for kangaroos in semi-arid environments (Bayliss 1985) and for ungulates in tropical environments (Sinclair 1979; Freeland & Boulton 1990; Skeat 1990; Caley 1993).

For each month, rainfall was accumulated over the previous 5 months, plus the current month (referred to as the rainfall in the previous 6 months). This provided an estimate of effective rainfall for sustained plant growth and evened out high and low rainfall events. To determine the best fit to a numerical response function, mouse abundance was plotted against accumulated rainfall with no lag and then against a lag of 3, 6 and 9 months.

The model that provided the best response curve was then examined further by (i) adjusting for the time interval between each trap session and converting to r per month (rt = [{ln(trapt/trapt – 1)}/n] × 30, where trap is the adjusted trap success and n is number of days interval between the first day of each trap session); and (ii) averaging the adjusted trap success over 3 months.

Results

Mouse numbers

Changes in mouse abundance from February 1983 until October 1994 are shown in Fig. 1. During this time there were three distinct plagues of mice.

Two different plague anatomies are evident in Fig. 1. In 1984 the mouse population built up and crashed within 1 year. In comparison, the 1987/88 and 1993/94 plagues were characterized by a population build up over 2 years interspersed with a decline during spring. However, in all cases populations crashed after each plague and mouse abundance remained low (< 10%) thereafter for at least a further 2 years.

Observed rate of increase

During the build-up of a plague, there was a succession of months when there was a positive exponential rate of increase. In 1984, there were 8 consecutive months when the rate of increase was positive, followed by 1 month when it was negative and another when it was positive. The population then crashed; the rates of increase for each of the next 2 months were r = –2·8 and –2·7.

During the plagues of 1987/88 and 1993/94, the mouse populations went through two stages. The first stage was characterized by an initial increase, then the spring decline. The second stage was an increase to higher population numbers, then a subsequent crash. These two stages are reflected in the exponential rates of increase over these periods. Initially they were positive, then negative for 2–3 months, positive again for a few months, then the populations crashed (Fig. 2).

Figure 2.

Observed rate of increase per month of mouse populations for each month from 1983 to 1994.

The highest rate of increase per month was during 1986 (r = 1·86). The lowest rate of increase per month was during 1984 (r = –2·85) (Fig. 2).

Numerical response

The best fit was provided by accumulated rainfall being lagged by 3 months (Pearson's correlation coefficients: no lag = 0·213, P < 0·05, n = 95; 3-month lag = 0·34, P < 0·001, n = 95; 6-month lag = 0·07, P > 0·05, n = 95). Biologically, this equates with the probable time for a mouse population to respond to increased food supply following good rainfall or to a lack of food following a period of little rain. Therefore we used a 3-month lag for subsequent analyses.

Adjusting the model for a standard time interval of 30 days or by smoothing adjusted trap success over 3 months did not improve the response curve.

The Ivlev numerical response model indicated two types of population response. The first response described mouse populations increasing when rainfall is high and decreasing when rainfall is low (Fig. 3a). This occurred when there were plagues of mice. We call this the plague system. The regression using derivative-free non-linear least squares [robs = –6·79 + 7·95 (1–e–1·11V)] explained 46·2% of the variation (d.f. = 2,50, P < 0·001).

Figure 3.

(a) Numerical response for a plague system, when a relationship existed between rainfall in the previous 6 months and the adjusted trap success of mice. Data combined for the 1984, 1986/87/88 and 1992/93/94 plagues. Curve fitted: robs = –6·79 + 7·95 (1 – e–1·11V) (r2 = 0·462, d.f. = 2,50, P < 0·001). (b) Numerical response for a non-plague system, when no relationship existed between rainfall in the previous 6 months and the adjusted trap success of mice. Data combined for the non-plague years 1983, 1985, 1986, 1989 and 1990.

Because the plague of 1987/88 was not as severe as other plagues, we analysed the numerical response for 1984 and 1993/94 only. The regression explained 56·1% of the variation (d.f. = 2,27, P < 0·001).

Although the standard errors associated with the estimates of a, d, c and rmax in the model were relatively large, the model demonstrated a substantial impact of rainfall on population density of house mice. The values generated and their standard errors were: a = 6·79 (± 2·97 SE); c = 7·95 (± 2·63 SE); d = 1·11 (± 0·43 SE); and rmax = 1·16.

The second response described a situation where mice did not respond to rainfall (Fig. 3b). The numerical response curve did not fit the combined data for 1983, 1985, 1986, 1989 and 1990 when rmax = 1·19 or rmax = 0·05 (Fig. 3b). This then indicates that mouse numbers were independent of rainfall (as shown by simple linear correlation: r = 0·069, t39 = 0·43, P > 0·05). This situation occurred for the 2 years following each of the three plagues of mouse populations. We call this the non-plague system.

Discussion

Maximum rates of increase

The maximum rate of increase for house mice in this study was approximately 1·16 month–1, which is equivalent to 13·92 year–1. This occurred in both the 1984 and 1993/94 plagues. In 1987/88 rmax was about 0·90 month–1, which is equivalent to 10·80 year–1. Caughley (1977) presented data on the maximum rate of increase for a range of mammalian species. The highest rate for a small mammal species was 4·56 year–1 and for larger species 0·40 year–1. Hansson (1987) gave an rmax estimate of 7·7 year–1 for a shrew Sorex araneus. Our rmax estimates are two or three times higher. However, it is likely that the annual rates of increase presented in Caughley (1977) were calculated from annual censuses and therefore dampen short-term variations in the rate of increase.

To determine whether our estimate for rmax is reasonable, we refer to the general formula for mammals described in Caughley & Krebs (1983): rmax = 18W–0·36, where W represents the average body weight of the species.

The average weight of wild mice in southern Australia from 10 000 captures was 13·5 g. This gives an estimate of rmax of 7·05. Our value of 13·92 is twice that expected. Therefore, perhaps the general allometric equation of Caughley and Krebs is not appropriate for an outbreaking population of small mammals. An estimate of rmax for mice in southern Australia generated from Krebs, Singleton & Kenney (1994), with a survival rate of 0·95 per 2 weeks and a recruitment of seven juveniles per pregnancy, was 10·40. Under these conditions, it appears an rmax of 13·92 is reasonable because it was estimated during the increase phase of a mouse plague when the average litter size is around nine (Redhead 1982; Singleton & Redhead 1990). If we calculate the maximum rate of increase over 9 rather than 12 months, which is equivalent to the average length of the breeding season (Singleton 1989), we obtain a value for rmax of 10·44. This shows that the demographic characteristics fed into a Leslie matrix by Krebs, Singleton & Kenney (1994) were appropriate.

The maximum rate of decrease of house mice in Australia, when food and shelter were scarce, was –81·48 year–1 (defined as a in the numerical response model). This value seems remarkable; however, it is largely a function of the rate of metabolization of stored reserves, mainly fat and protein (Caughley & Krebs 1983). As mice reserve little fat and protein, as reflected in their daily food consumption of approximately 20% of their body mass (Mutze, Green & Newgrain 1991), we contend that this decline is reasonable, particularly if food was in short supply during the previous 6 months.

An additional factor may be the impact of disease on field populations of mice. An increase in the prevalence of viral diseases was reported in mice during the population crash in 1987 from the MRS (Singleton et al. 1993). Therefore rapid decreases in mouse densities are not surprising when mice are confronted with the combination of nutritional stress, disease and social stress. Laboratory studies indicate that nutritional stress potentiates the progression of diseases (Teo, Price & Papadimitriou 1991).

Biological memory

Rainfall has been used in models for predicting mouse densities in Australia (Saunders & Giles 1977; Redhead 1982; Singleton 1989; Mutze, Veitch & Miller 1990; Cantrill 1992; Twigg & Kay 1994) but not to determine the numeric response.

Our analysis of the numerical response curve indicates that mice respond to rainfall during the plague response. When mouse numbers crash after a plague, mouse populations do not respond to rainfall for at least 2 years thereafter (the non-plague system).

Of interest is the trigger that flips mouse populations from the non-plague to the plague system. The two systems indicate that there may be ‘biological memory’ operating. This memory appears to be associated with the time since the last plague, the population response by mice (including shifts in age structure) in the previous year (Boonstra & Redhead 1994) and the abundance of mice after the spring decline.

To consider the trigger that flips the system, we need to look at the ecology of the wild house mouse in agricultural regions in Australia. Mus domesticus typically has a rapid generation time, a short gestation period, high litter size, and a high recruitment rate (Berry 1981; Sage 1981). During the main breeding season in the wheatfields of Australia, which typically extends for 7 months but can range from 5 to 9 months (G.R. Singleton, unpublished data), mice are capable of a high rate of increase. A ≥ 5-month non-breeding season is a long time for an animal that has an average survival of 3 to 5 months (Singleton 1989). Therefore, in general, mice born late in the previous breeding season form the nucleus of the next breeding season. The importance of this will be discussed below in the context of microtine cycles.

So why are there not plagues of mice every year? It is generally assumed, rightly or wrongly (Krebs et al. 1995), that mouse plagues are determined by extrinsic agencies such as predators (Newsome & Corbett 1975; Sinclair, Olsen & Redhead 1990), disease, food supply and weather. Social behaviour appears also to be important (Krebs et al. 1995), although there is insufficient field evidence to assess its role.

Rainfall promotes growth of weeds, grasses and crops that are the primary food items of mice in the Victorian Mallee (Tann, Singleton & Coman 1991). Having confirmed the role of rainfall and hence food supply in the years preceding a plague, we then hypothesized that rainfall and food supply have no effect on mouse numbers in the 2 years after a plague. This is an enigma that if unravelled could possibly lead to better management of mouse populations.

A similar enigma has beset small mammal ecologists in the northern hemisphere. Microtine populations in temperate and Arctic regions of the northern hemisphere fluctuate in regular 3–4-year cycles (Krebs & Myers 1974). These cycles appear to be self-regulatory, but the exact mechanism by which this is achieved is not certain (Lambin & Krebs 1991; Boonstra 1994). Mouse populations in southern Australia fluctuate, but not in regular 3–4-year cycles. In many regards, mouse plagues in Australia are similar in nature to microtine cycles (Krebs et al. 1995). In particular, after populations decline from peak densities there is a lag of at least 12 months before the population begins to recover. As with mouse populations, vole populations will not recover in the next year if they are provided with plentiful food (Krebs & DeLong 1965; Desy & Thompson 1983).

One interesting proposal for explaining declines in microtine populations and the maintenance of low densities thereafter is based on the occurrence of shifts towards an ageing population as the cycle progresses. Boonstra (1994) argues that population declines are inevitable once populations are composed of older animals. The proximate mechanism is the ageing of populations through delayed maturation (a density-dependent response) resulting in older animals at the commencement of the next breeding season. The ultimate mechanism is a decline in individual fitness with the onset of senescence.

Mouse plagues generally develop over 2 years (Redhead 1988; Singleton 1989), with a comparatively older dominant age cohort at the beginning of the second breeding season (Redhead 1982). These older animals have lower fecundity (Singleton & Redhead 1990). Furthermore, during a plague year breeding by mice typically ceases 2–3 months earlier than in the two preceding years (Singleton 1989; Singleton, Chambers & Spratt 1995). This leads to a further shift in the age structure during the peak and decline phase, resulting in older mice (the few that survive) at the commencement of breeding as mice enter the low phase. These results indicate that Boonstra's senescence hypothesis, which provides six testable predictions (Boonstra 1994), warrants testing in wild mouse populations.

The main difference between the dynamics of mouse and vole populations is that mouse plagues do not occur as frequently or as regularly as microtine cycles. Perhaps the mechanisms that drive these cycles are similar for the rodents of the northern hemisphere and Australian mice, but extrinsic factors such as extended periods of low rainfall, and hence poor food supply, may keep mouse populations at low densities for greater than 2 years.

Another possible explanation is that after mouse populations crash, avian predators maintain these populations at low densities (a predator pit). Mice can escape regulation by these predators only if environmental conditions favouring rapid growth of their populations persist sufficiently long or if predator numbers decline (Sinclair, Olsen & Redhead 1990). In our study region, the threshold density of mice required to escape predator regulation was estimated at around 30 mice per 100 trap nights (Sinclair, Olsen & Redhead 1990, based on Singleton 1989).

Rainfall – previous studies

The importance of rainfall and hence food supply in the development of mouse plagues has been emphasized in a number of previous studies. Basically there have been two approaches. The first approach focuses on the population processes following rainfall events (Newsome 1969a,b; Redhead 1988; Singleton 1989). Rainfall in this context provides a warning that conditions may be conducive for mouse populations to achieve a high rate of increase. This early signal switches the emphasis to the biology of the system; the focus is on monitoring specific changes in the breeding and population dynamics of mouse populations rather than rainfall events.

The second approach views rainfall and the response of mouse populations empirically (Saunders & Giles 1977; Mutze, Veitch & Miller 1990; Cantrill 1992). These rainfall-based models often include other indices such as soil type, temperature and grain production (Mutze, Veitch & Miller 1990). Cantrill (1992) assumed the rate of increase of mouse populations was the same within and between years. The success of these models for predicting mouse plagues has been variable. Saunders & Giles (1977) predicted four plagues that did not occur; Mutze, Veitch & Miller (1990) found rainfall could explain only 41% of the variance in plague occurrence.

Our findings highlight the importance of rainfall as a predictor of plagues but only if the rainfall data are viewed in the context of the biology of the system. We attest that deterministic models would have greater success at predicting mouse plagues if they too were used with stronger reference to the biology of mouse populations.

It would also be beneficial to know the effects of microhabitat and short-term weather events on mouse numbers. Using linear multiple regression analyses, Twigg & Kay (1994) revealed that the abundance of house mice in and around irrigated summer crops in NSW was associated with mild temperatures, adequate rainfall and an abundant ground cover and seed bank. This information can provide important information at a local scale, but does not provide information on a regional scale. Knowledge at the regional scale is required to plan and then implement management strategies. Redhead & Singleton (1988) demonstrate this clearly with their PICA (Predict, Inform, Control, Assess) strategy.

The model presented here could be improved further by examining the relationship between mouse abundance and food supply. Instead of using lagged rainfall as a surrogate of food supply, models of pasture and crop growth could be used. This approach has been used by Pech et al. (1999).

Prediction

The rates of increase and numerical response of mouse populations could be used to predict plagues of mice. The application of a numerical response was first undertaken for kangaroos (Macropus rufus and M. fuliginosus) by Bayliss (1985, 1987) and has subsequently been used for water buffalo Bubalus bubalis by Skeat (1990) and for feral pigs Sus scrofa in Australia (Caley 1993; Choquenot 1998); however, the numerical response was not used to predict when damage could occur. Knowledge of what system the mouse population is in (plague or non-plague) is important when considering mouse control and must be incorporated into a predictive model. A decision support system, or expert system, could be developed to predict mouse numbers if there was sufficient monitoring of both rainfall and changes in mouse population densities. Without a predictive ability, a decision support system will be able to provide only short-term, reactive advice.

A predictive model would assist managers in deciding whether it would be appropriate to take actions to control mice. Often the primary objective is to protect crops at sowing. The scale of control campaigns is important as well; areas of at least 5000–10 000 ha would be required (Twigg, Singleton & Kay 1991; Singleton, Chambers & Spratt 1995). If a mouse plague could be predicted well in advance (> 12 months warning) farmers could take early preventative management using farm management practices to reduce the impact of the increasing population (Brown et al. 1998; Singleton & Brown 1999). These practices may prevent the use of large amounts of rodenticides.

Conclusion

In comparison to previous studies of the numerical response of field populations of mammals to rainfall, mice in southern Australia exhibited a unique response. Mouse populations had a high rate of increase and decrease, plus a period when they responded to rainfall (the plague system) and a period after the crash of numbers when mice did not, or could not, respond to rainfall for at least 2 years thereafter (the non-plague system).

Further research is required during the non-plague system to identify factors that govern mouse numbers. This knowledge would be useful in managing the build-up of mouse numbers in order to prevent damage of the severity reported during 1993. For example, plagues could be prevented or their amplitude dampened if the food supply for mice is reduced during the 12–18 months development phase of a mouse plague.

Acknowledgements

We thank David Choquenot, Roger Pech and Charles Krebs for suggesting this analysis and encouraging us to pursue it. We owe gratitude to numerous people who have assisted with the mouse surveys over the last 12 years, to the farmers for access to their properties and to Geoffrey Stratford and his staff at the Mallee Research Station at Walpeup. In particular we wish to acknowledge the efforts of Colin Tann, Dean Jones and Stephen Day. Thanks also to Warren Müller for help in the analysis of the data. Drs Roger Pech and Jim Hone made comments on the manuscript. We thank three anonymous referees for their comments. This research was partially supported by funding from the Grains Research and Development Corporation.

Received 10 August 1998; revision received 27 February 1999

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