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Keywords:

  • fertility suppression;
  • Leslie-type population model;
  • Mastomys natalensis;
  • pest control;
  • rodenticides;
  • tropical rodents

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
  • 1
    Small rodents in general and the multimammate rat Mastomys natalensis in particular cause major economic losses in Africa through damage to crops. Attempts to develop dynamic population models for this and other pest rodents are ongoing.
  • 2
    Demographic estimates from a capture–mark–recapture (CMR) study in Tanzania were used to parameterize a population model for this species. This model incorporated three functional age categories (juveniles, subadults and adults) of both sexes and used density-dependent and density-independent factors, the latter represented by rainfall.
  • 3
    The model was used to analyse the effect of rodent control on the population dynamics and resulting number of rats. Control measures affecting survival as well as reproduction were considered.
  • 4
    The model showed that control measures reducing survival will only have long-term effects on population size if they are also applied when rodent densities are low. Control measures applied only when rodent densities are high will not have persistent effects, even at high mortality rates.
  • 5
    The model demonstrated that control measures reducing reproduction are likely to prevent Mastomys outbreaks, but will keep densities low over a long period only when the contraceptive effect is strong (> 75% reduction).
  • 6
    Provided that CMR data are available, we recommend developing Leslie-type population models for rodent pests on the basis of CMR-estimated demographic schedules. Such models have great potential in rodent management and allow the evaluation of different strategies.
  • 7
    Besides improving the ecological basis of the population modelling, economic considerations need to be incorporated into decisions about rodent control. We suggest that appropriate population models will provide important input into such decision making.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

Rodent damage is an important cause of harvest loss world-wide, and farmers often list rodents as one of their most significant crop pests (Singleton et al. 1999a). The need for ecologically based pest control actions has long been recognized: Charles Elton's (Elton 1942) description of the state of affairs in pest control is still applicable far beyond the problems of voles and mice:

‘In spite of sweeping changes in God and circumstances, Authority has for several thousand years continued to act in much the same way, even to the present day. The Bible story is, if you like, a parable. The affair runs always along a similar course. Voles multiply. Destruction reigns. There is dismay, followed by outcry, and demands to Authority. Authority remembers its experts or appoints some: They ought to know. The experts advise a Cure. The Cure can be almost anything: Golden mice, holy water from Mecca, a Government commission, a culture of bacteria, poison, prayers, denunciatory or tactful, a new trap, a Pied Piper. The cures have only one thing in common: with a little patience they always work.’

The most common rodents in sub-Saharan Africa belong to the genus Mastomys (Fiedler 1988). They occur all over the continent in natural grasslands, thicket, cultivated areas and human habitations. Population explosions happen at irregular intervals (Leirs et al. 1996) and crop losses of over 50% have been recorded during such outbreaks in Kenya (Taylor 1968; Makundi, Oguge & Mwanjabe 1999). In-between outbreak years, population densities, and consequently rodent damage, also vary considerably both within and between years. Mastomys are important pests in agriculture and post-harvest storage, and they are also implicated as reservoirs of many zoonoses such as Lassa fever, plague and leptospirosis (reviewed recently by Gratz 1997).

In cereal crops in the African savanna regions, most damage occurs during the sensitive young seedling stage and just before harvest (Fiedler & Fall 1994). At planting, even moderate rodent damage may necessitate late replanting, resulting in lower yields. Although efficient techniques exist to kill rodents, none of the traditional means has been able to control populations over the longer term (Singleton et al. 1999a). Short-lasting measures may be effective in order to protect the crop during the sensitive stages, but only if they are applied preventively before the damage is done (Myllymäki 1987).

The most commonly used control measure for rodent pests is rodenticides (reviewed by Buckle 1999). Killing rodents by trapping, hunting, flooding and gassing has been applied traditionally in many places but rarely has great effects on the population (Smith 1994). Fertility control has been a theoretical possibility for a long time, but with poor practical results (Bomford 1990; Smith 1994). Recent work on immunocontraception of house mice in the laboratory and in enclosed field populations has been promising (Chambers, Lawson & Hinds 1999) and has rekindled interest in fertility control of rodents.

Unfortunately, poor African farmers are by necessity risk-averse low-capital investors, which means that they cannot afford to apply effective (and usually more expensive) rodent control measures unless they are convinced that it will be economically beneficial on a short-term basis. As a result, they often apply control measures too late, and thus without much success and often with excessive quantities of rodenticides (Brown 1994).

A sound biological knowledge of the pest rodent species is a prerequisite for the development of more effective, ecologically based, rodent management strategies (Leirs, Singleton & Hinds 1999). Models are a way of linking bits and pieces of information together to provide ecological insights, formal representation and understanding. With the purpose of understanding and predicting fluctuations of African rodents, several models have been developed (Leirs 1999). Regression models describe patterns, and are often good at predicting phenomena, but do not provide an understanding of the underlying mechanisms (Leirs et al. 1996). Early biological models simply provided a concept, either described in words (Harris 1937; Telford 1989) or presented graphically (Taylor & Green 1972; Hubert & Adam 1983). Such models give a schematic representation of the different factors that could be important and which interactions between factors might be of consequence. However, they are of little use for practical applications because they are too vague and imprecise. Translating biological concepts into analytical formulae allows the investigation of population dynamic processes, but they only become useful for application if interactions and effects on demography are expressed as numerical estimates (French 1975; Hubert, Adam & Poulet 1978; Poulet 1985). The effects of environmental variation are difficult to include in such models. An approach focusing on population dynamics rates, as developed for house mice in Australia (Pech et al. 1999), is another possibility that is yielding useful models but the underlying demography remains hidden. In small mammal populations, survival and other demographic processes may differ between functional categories (Yoccoz et al. 1998; Julliard et al. 1999). Capture–mark–recapture (CMR) studies allow the synthesis of such detailed information, which can then be incorporated into a Leslie matrix-based population model, as we have done here. We believe this to be an optimal approach for modelling population ecological processes, because it allows us to simulate manipulations of several demographic processes separately, and then to investigate the consequences for population dynamics. The interactions of non-linear density-dependent and density-independent factors are too complicated to predict intuitively model outcomes. In any case, it is important that the interplay between models and field studies is as good as possible (Krebs 1999): modellers do not always take advantage of the ecological knowledge that exists, and too often field-orientated ecologists do not take full advantage of the benefit of having a good population model available.

In order to avoid rodent damage and the unnecessary use of rodenticides, there is a clear need for improving the capacity to predict when high rodent densities are likely to occur (Mwanjabe 1990; Brown & Singleton 1999; Leirs 1999; Pech et al. 1999). Population models are often useful tools for such predictions, as well as for evaluating the expected outcome of various control measures (Stenseth 1977, 1984). Such simulations are also a necessary tool for any economic decision analysis (Clark 1990; Hueth, Zivin & Zilberman 1999). Furthermore, if we have a population model providing predictions with high accuracy and precision, it may aid in timely intervention with an appropriate control measure for minimizing the build-up of high rat densities. The development of such population models obviously needs a solid ecological understanding of the biology of the pests species under consideration (Smith & Buckle 1994; Pech & Hood 1998; Singleton et al. 1999a).

In this study we used simulation models to evaluate the effectiveness of various control measures, including fertility control, for the multimammate rat Mastomys natalensis (Smith 1834). These analyses were done on the basis of an empirically based population model (Leirs et al. 1997a). We extended the original model presented by Leirs et al. (1997a) by including both sexes, and examined the likely effects of control measures on key demographic parameters, both with respect to survival and reproduction. We discuss our findings in the broader context of pest control and the modelling of rodent pest populations.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

Population dynamics background for the species under study

The population dynamics of M. natalensis are generally thought to be affected mainly by rainfall events; unusually abundant rainfall has been long considered a cause for outbreaks (Harris 1937; Taylor 1968; Fiedler 1988; Telford 1989; Brown & Singleton 1999). During the past decade, we have attempted to elucidate this relationship by studying the life history of the multimammate rat in Morogoro, Tanzania (Leirs et al. 1990; Leirs, Verhagen & Verheyen 1993). The link between rainfall and the onset of breeding (reviewed in Leirs 1995) is mediated by the stimulating effect of germinating grasses in the diet on sexual maturation (Leirs, Verhagen & Verheyen 1994; Firquet, Leirs & Bronner 1996).

Leirs (1995) summarized the population biology of M. natalensis in eastern Africa. Here we provide only a summary: breeding is highly seasonal and usually starts in April (1 month after the usual peak rainfall), lasting until September. Each female produces on average five to six litters, each consisting of around 11 young. New-borns grow slowly and normally do not mature before the next rainy period. Unless abundant rain appears before March and April the following year, they will be at least 6 months old before they begin to breed. However, if rainfall late in the year is abundant, subadults mature and may breed as early as January. Young born in such early breeding seasons grow fast and mature in their third month, starting to breed during the main breeding period. This additional generation allows the development of high densities later in the year. In fact, unusually abundant rainfall during the first months of the rainy season is a reliable predictor for the occurrence of an outbreak in the following year, as confirmed from analysis of a series of 40 years with and without rodent outbreaks in Tanzania (Leirs et al. 1996). Despite the obvious importance of rainfall in triggering reproduction and causing outbreaks, recent demographic analyses of M. natalensis also show a clear density-dependence for survival (Leirs et al. 1997a; Julliard et al. 1999).

Demography

Demographic estimates were obtained from CMR data (in total 6728 captures of 1410 females and 1071 males) collected between 1987 and 1989 in Morogoro, Tanzania, using a 1-ha fallow land grid and monthly capture sessions on 3 consecutive nights. Animals at each capture were categorized into a functional age class: juveniles (young and immature individuals are very rarely trapped because they are normally too small to trigger the traps), subadults (older but still non-reproducing, even though they are physiologically old enough) or adults (reproducing individuals). By using the multistate statistical model (ms-surviv; Hines 1994), we estimated both survival and transition probabilities between reproductive classes. This was necessary because sexual maturation in Mastomys does not occur in a deterministic way but depends on environmental conditions (Leirs, Verhagen & Verheyen 1994). For further details about the data and method of analysis, see Leirs et al. (1997a). The net reproductive rate was estimated from pregnancy rates and embryo counts obtained in the study population between 1981 and 1989; a total of 5196 individuals was used for this purpose (data from Telford 1989; Leirs, Verhagen & Verheyen 1993).

The population dynamics model

The population dynamics model is given as a Leslie-type model (Leslie 1945, 1948; for small rodent examples, see also Leirs et al. 1997a; Yoccoz et al. 1998):

  • image(eqn 1)

where Nt is the abundance vector including three stages of females and three stages of males (juveniles, subadults and adults), and M is a Leslie-type of transition matrix given as:

  • image(eqn 2)

with:

  • image(eqn 3a)
  • image(eqn 3b)
  • image(eqn 3c)
  • image(eqn 3d)

and where B(P,N) is the monthly net reproductive rate per adult female; s0 is the survival rate from newly born to subadults; sf1(P,N) and sm1(P,N) are the monthly survival rates of subadult females and males, respectively; ψf12(P,N) and ψm12(P,N) are the maturation rates from subadult to adult, for females and males, respectively; sf2(P,N) and sm2(P,N) are the monthly survival rates of adult females and males, respectively; and P and N refer to the precipitation and density categories, respectively, in which a month can be placed, implying that all demographic parameters except for juvenile survival and growth are affected in a non-linear way by both density-dependent and density-independent factors. The survival and recruitment of juveniles were discretionary and set at 0·5. For the other parameters, we used the estimates from the statistical modelling of the CMR data (see Table 2). While emigration was included in the local survival rates that we estimated, immigration was not incorporated into the model. Data for evaluating the bias due to this simplification were unavailable. We assumed that the population effect of immigration was negligible (Stenseth & Lidicker 1992). The model was implemented numerically using Stella Research Version 5.1.1 (High Performance Systems Inc., Hanover, NH), assuming discrete 1-month time steps.

Table 2.  Demographic parameter values used in the population dynamics model. The values were estimated in ms-surviv (point estimates ± SE), using the most parsimonious model out of several tested (see Table 1); notice that the model we have used in this paper is an extension of the model published by Leirs et al. (1997a), the difference being that the current model includes both sexes whereas the previous model included only females (female estimates as in Leirs et al. 1997a)
 Regimes
Regime definition
Rainfall in the past 3 months< 200< 200200–300200–300> 300> 300
Density per ha> 150< 150> 150< 150> 150< 150
Net monthly reproductive rate1·295·320·306·644·695·82
Survival rates
Females
Subadult survival0·629 ± 0·020·513 ± 0·0530·682 ± 0·0510·617 ± 0·1880·678 ± 0·0590·595 ± 0·146
Subadult maturation0·000 ± 0·0150·062 ± 0·0370·683 ± 0·1120·524 ± 0·1880·155 ± 0·111     1 ± 0·0
Adult survival0·583 ± 0·0660·650 ± 0·0780·513 ± 0·0740·602 ± 0·0920·505 ± 0·0740·858 ± 0·099
Males
Subadult survival0.677 ± 0·128     1 ± 0·2820·960 ± 0·3590·433 ± 0·4360·444 ± 0·2350·000 ± 0·000
Subadult maturation0·005 ± 0·0590·008 ± 0·0690·568 ± 0·2880·396 ± 0·5270·820 ± 0·2720·121 ± 0·187
Adult survival0·228 ± 0·3390·270 ± 0·3160·377 ± 0·2080·379 ± 0·3560·628 ± 0·2880·680 ± 0·376

We evaluated the realism of the model by making predictions 1 year ahead starting from known populations in December and using actual rainfall values. In order to do this, we used the 1987–89 data described above as well as CMR data collected at the same site on a 3-ha grid during the period 1994–98 (14 051 captures of 5473 individual M. natalensis). Population size was estimated for each month in program capture, using the jack-knife estimator M(h), which allows for individual heterogeneity in capture probability (Otis et al. 1978). We determined the population composition (number of adult and subadult males and females) in each December of the study period and used this as starting values for the model runs. The starting number of juveniles was always set to zero because December falls well outside the breeding season. We used the actual rainfall observed during the 12 months of each model run (Meteorological Station, Morogoro, Tanzania).

The spectral density of simulated population dynamics changes was quite similar to the observed spectrum (Stenseth 1999). This suggested that the model captured the general features of the observed population dynamics changes.

Modelling control measures

We incorporated two categories of control measures: increased mortality and decreased fertility. In the numerical model simulations, the modified survival rates were defined as the natural ones (given in Table 2) but multiplied by (1 – m), with m being the additional mortality imposed by the control measure. The reproductive rates were modified by multiplying the natural reproductive rate by a factor, q, less than one.

Efficient poisons exist but, in practice, limited access to baits, bait shyness or bait palatability problems make a complete kill of rodents in a field unlikely (Cowan & Townsend 1994). Moreover, due to recolonization, control results after 1 month (the time step in the model) will never be 100% effective (Myllymäki 1987). Therefore, we simulated control actions that decreased survival to 75%, 50% or 25% of the values when no control was applied. In a first series of numerical model simulations, survival was decreased permanently. In a second series, survival was decreased only when densities were higher than 150 ha−1. It should be noted that in all these simulations we reduced, as a first approximation, survival of the different functional groups by the same proportions. This is of great general interest even though it is not necessarily so in reality. For example, some groups may be targeted more efficiently by trapping or poisoning (Salmon & Marsh 1979), or different groups may have the same mortality rate due to control measures regardless of how different their survival is when no control is applied.

With approaches involving fertility control, it is also unlikely that all or even nearly all individuals in a population can be similarly affected by a treatment. Thus, we simulated fertility control by decreasing the number of young born in each time step to 75%, 50% or 25% of the value when no control is applied. In a first series of numerical simulations, fertility control was applied permanently. In a second series, fertility control was applied only in months following a month with more than one-third of the females being adults.

In order to study the general population dynamics under various assumptions, we ran all numerical model simulations over 180 months (corresponding to 15 years), starting from a realistic December population (no juveniles, 133 subadult females, 136 subadult males, no adult females, 7 adult males). For all runs, we used the same fictitious but realistic rainfall series. Because the patterns resulting from intermittent mortality and fertility control were more difficult to interpret, we repeated these numerical simulations 100 times, each time with a different bootstrapped rainfall series of 180 months. We plotted the frequency distribution of the average and maximum population size obtained.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

The demographic analyses, separately for males and females, showed that survival and maturation were both rainfall- and density-affected (Table 1). The parameter value estimates obtained from the most parsimonious statistical model in the CMR analysis are given in Table 2. The confidence intervals around the estimates were much larger for males than for females, but the point estimates for both sexes suggested inverse density-dependence of subadult survival and a rainfall effect on maturation. Female adult survival was density-dependent, while male adult survival was positively affected by rainfall but not by density. These results compared favourably with earlier results reported by Leirs et al. (1997a) and Julliard et al. (1999) as well as with findings for other species (McCarthy 1996).

Table 1.  The statistical models tested, denoted according to each model's time-specific variation in survival for each state (Sr), subadult-to-adult transition (ψ12) and capture probability (pr) in each state. Subscripts denote time-specific variation of the parameters: i denotes full time-specific variation (one value for each sampling month); DD denotes time-specific variation according to high or low density characterization of the sampling month (see Fig. 1); DID denotes time-specific variation according to rainfall characterization of the sampling month; DD/DID denotes a combined density–rainfall characterization; no subscript denotes no time-specific variation (one single value for all sampling months). The models were tested separately for the male and female parts of the population. The results for the female part were published earlier (Leirs et al. 1997a)
ModelModel specification (time-dependence)Number of parameters estimatedLog-likelihoodAICc*
  • *Akaike's information criterion; lower values indicate a more parsimonious model (Burnham & Anderson 1998).

  • Capture probability fully time-specific.

Females
(Sr,iψ12,ipr,i)Full model113−283·3 812·6
(Srψ12pr)None 5−661·71333·4
(Srψ12pr,i)Capture probability only 49−451·01003·7
(Sr,DDψ12,DDpr,i)According to density 52−447·21002·6
(Sr,DIDψ12,DIDpr,i)According to rainfall 55−354·3 823·1
(Sr,DD/DIDψ12,DD/DIDpr,i)According to rainfall and density 64−337·2 808·6
Males
(Sr,iψ12,ipr,i)Full model113−128·0 508·9
(Srψ12pr)None 5−501·51013·1
(Srψ12pr,i)Capture probability only 49−260·0 622·8
(Sr,DDψ12,DDpr,i)According to density 52−253·5 616·4
(Sr,DIDψ12,DIDpr,i)According to rainfall 55−206·0 528·1
(Sr,DD/DIDψ12,DD/DIDpr,i)According to rainfall and density 64−191·5 519·3

After incorporating the demographic estimates in the population dynamics model, the simulated trajectories for the a posteriori predictions starting in December and using actual rainfall (Fig. 1) generally followed the observed population dynamics rather well (except for 1998; see the Discussion). The fit was not perfect, but the demographic model created a realistic population dynamics pattern, suggesting that the model represented authentic processes.

image

Figure 1. Predicted and actual population size on 1 ha, using actual rainfall. Model simulation [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] results for 12-month ahead runs, starting in November or December, compared with observed population size estimates in the field. Start populations were based on the observed number of subadults and adults of both sexes in the population in the starting month. Rainfall values were the actual monthly values registered during the 12 months after the starting time.

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The numerical simulations including survival control are presented in Fig. 2. A control strategy that continuously lowered survival (Fig. 2a) showed a die-out of the population, but only at the higher mortality rates. If control was applied only at high rodent densities, however, the control did not have any obvious effects (Fig. 2b). In some months the population size reached densities higher than when no control was applied. The average and maximum population sizes decreased slightly but high densities still occurred (Fig. 3).

image

Figure 2. Model simulations [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] of mortality control strategies. (a) Permanently reducing survival; (b) reducing survival only when population size is more than 150 individuals. Thin curve shows population size without control. Black lines in graphs to the left: reduction to 75% of the normal value; centre: 50% of the normal value; right: 25% of the normal value. For all runs, the same starting conditions and bootstrapped monthly rainfall series were used; horizontal time axis 15 years.

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image

Figure 3. Frequency distribution of average (top) and maximum (bottom) population sizes obtained in simulation runs [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] with reduced survival to 100%, 75%, 50% and 25% of the normal value in periods with high rodent density. Each run was repeated 100 times, each time with different rainfall series. In order to avoid the transient effects of the initial population size, only estimates from months 60–180 are used.

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Permanently decreasing fertility had pronounced effects (Fig. 4a). Even at low efficiency, population size was generally lower and outbreaks were prevented. At higher efficiency, populations could be held at low levels or even exterminated. These effects were not due to a particular rainfall series: average population sizes were generally somewhat lower but remained in the same order of magnitude (Fig. 5, top). Outbreak densities, on the other hand, were only obtained when no fertility control was applied (Fig. 5, bottom). Reducing fertility only when many of the females were adults did not result in population extinction even at high efficiencies, but outbreaks were again avoided (Fig. 4b).

image

Figure 4. Model simulations [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] of reproduction control strategies. (a) Permanently reducing natality; (b) reducing natality only in months following a month with more than 33% adults. Thin curve shows population size without control. Black lines in graphs to the left: reduction to 75% of the normal value; centre: 50% of the normal value; right: 25% of the normal value. For all runs, the same starting conditions and bootstrapped monthly rainfall series were used; horizontal time axis 15 years.

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image

Figure 5. Frequency distribution of average (top) and maximum (bottom) population sizes obtained in simulation runs [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] with permanently reduced natality to 100%, 75%, 50% and 25% of the normal value. Each run was repeated 100 times, each time with different rainfall series. In order to avoid the effects of the initial population size, only estimates from months 60–180 are used.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

The mastomys model and rodent control

The observed rainfall effects in these simulations are consistent with all earlier observations about the importance of unusually long or abundant rainy seasons for outbreaks (Leirs et al. 1996). The density-dependent effects observed in the survival and maturation of M. natalensis (Table 2) allow, however, for some optimism in the development of population dynamics models. They also indicate that population dynamics are not completely dependent on environmental stochasticity and that we can design control strategies based on manipulation of the density-dependent structure of a population, for example through habitat changes and other mechanistic manipulations of the environment.

The earlier females-only version of our Mastomys population dynamics model (Leirs et al. 1997a) made acceptable predictions 1, 2 and 3 months in advance, compared with data for different months from an independent study (Leirs et al. 1997a). One-year ahead predictions based on the females-only model starting from known December populations and using actual rainfall values, showed populations dynamics that well resembled the observed population size fluctuations (Leirs 1999). Including a male component in the model, as we have done here, gives the same conclusion. This strongly suggests that the model captures the essential parts of the dynamics.

The aberrant result for 1998 remains to be explained. Rainfall in late 1997 was abundant and therefore one would expect high densities in 1998, particularly so since the first half of that year was not very dry. In fact, rainfall in January–February 1998 totalled 460 mm, which is more than twice the average rainfall for this period (192·15 ± 12·73 mm for 1971–99) and 28% more than the next highest value for this period in 1971–99; this anomaly was part of the 1997–98 El Niño. One possibility is that this extreme rainfall affected rodent mortality or reproduction directly, for example by flooding burrows. Preliminary numerical simulations performed by assuming an increased mortality during the first months of 1998 do indeed result in model predictions that are much closer to the observed pattern (Fig. 6). This scenario requires further investigation; however, the preliminary results reported in Fig. 6 suggest that such work might be highly rewarding.

image

Figure 6. Model simulation [using (Sr,DD/DIDψ12,DD/DIDpr,i) for both sexes; see Table 1] results as in Fig. 1 for a starting population in December 1997. Adult and subadult survival during the three first months of 1998 is set to 0·1 only to simulate heavy mortality due to flooding.

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We showed previously that the relative importance of environmental stochasticity for Mastomys population dynamics implies that predictions cannot be made very far ahead of the current conditions (Leirs 1999). Simulated population dynamics, however, are generally realistic in the sense that the model captures the general features of the population dynamic process. By performing a number of simulations with different rainfall conditions, the effects of different control operations may be investigated reliably through the general patterns that occur under specified assumptions.

Increasing mortality, or killing animals, is intuitively the most effective form of rodent control and is certainly the most widespread, through the use of poisons, traps and other lethal methods (Buckle & Smith 1994). The simulation results show that this indeed could be a useful strategy, but only when mortality can be increased considerably and continuously. This could represent situations where poisons would be applied permanently. This is an unrealistic scenario: farmers will probably not undertake poisoning actions when rodent densities are very low. Control that increases mortality solely under high density conditions corresponds with more realistic poisoning scenarios where farmers are likely to invest in rodenticides or other ways of killing rats, such as gassing and traps (Redhead 1988; Singleton et al. 1999b). Our numerical simulations show that no persistent effects can be expected from this strategy. This may not come as a surprise to many population ecologists, but the concept is still not generally accepted in pest control. Population ecologists nevertheless will be interested in observing the effects on the population dynamics of Mastomys following the various reductions in survival or reproduction.

Support for the concept of fertility control via immunocontraception is still restricted largely to experimental studies in the laboratory, although results from field studies simulating different levels of sterility are promising (Williams & Twigg 1996; Chambers, Lawson & Hinds 1999; for some caution based on a theoretical study, see Caughley, Pech & Grice 1992). At least for some species, like house mice in Australia, it can be expected that this approach will be practical in less than a decade from now. We simulated a permanent decrease in reproductive rate. This may superficially correspond to a situation where a viral-vectored immunocontraception method is applied and fertility reduction would be transferred to other individuals continuously. Such strategy has, according to our numerical simulations, long-term effects only when the realized fertility reduction is at least somewhere between 50% and 75%. This figure corresponds with results that were obtained in experiments with house mice (Chambers, Lawson & Hinds 1999). Our second series of simulations with fertility control could represent a strategy where a bait-delivered contraceptive is applied only when a monitoring programme shows a high proportion of females capable of reproduction. Our time lag of 1 month represents the delayed effect of a baiting in response to the monitoring, and we assume that the effect of the contraceptive would last a single month. According to our numerical simulations, such a strategy cannot keep populations at a low level, although it will prevent the population from reaching outbreak levels.

Summarizing, our findings show that a permanent and sufficiently large increase in mortality rate is an effective control strategy. This result is understandable by realizing that an increased mortality rate will result in fewer individuals reaching an age of reproduction. However, killing lots of individuals at high densities only will generally have little effect, at least in the long run. This is because of the density-dependent structure of the dynamics: if a population is artificially reduced to lower densities, adult survival, and consequently production of young in the population, may increase. This is particularly so as densities during the reproductive season are generally low and therefore, in this strategy, control is less likely to happen during this sensitive season. As a result, such a strategy may generally cause somewhat lower densities but it will not prevent population explosions. On the other hand, fertility control that is applied only during intensive periods of reproduction will not result in persistent low population densities but it will prevent the build up of outbreaks.

Further work

Much remains to be done to improve our understanding of the biology of M. natalensis and the modelling of its population dynamics. The lack of immigration events in the model is of concern. Recruitment in the model is based on local reproduction only, and this is only realistic if the model population is very large or isolated. This is not true for our study population (1 ha only) nor for the populations that we want to model (farmer fields). Although data about immigration and its effects are still lacking, we suspect that immigration will lead to higher population numbers than modelled. More information about immigration patterns is therefore urgently needed (for a relevant discussion see Fitzgibbon 1997).

The present model is based on data that were collected in fallow land. Even though traditional agriculture is being replaced by more intensive practices, African agricultural landscapes are still characterized by small-scale subsistence farming, with complex cropping systems (Ohigbo 1990). We know that individual animals can use different habitat patches (Leirs et al. 1997b) between which there may be demographic differences and exchange of individuals. Hence, a model incorporating dispersal in a patchy environment may be required (Stenseth 1981). Also, large-scale geographical differences should be investigated. Mastomys natalensis occurs in southern, eastern and probably western Africa (Granjon et al. 1997) and over this range reflects climatological and community variation. The results in Tanzania cannot be simply extrapolated, and therefore we recently started comparative work in Zambia, Tanzania, Kenya and Ethiopia.

The density-dependence observed in our population may be partly due to trophic interactions between the rodents and predators (or pathogens); suggestions for biological control can only be reliably investigated in the population dynamics model if the response functions within a community are better documented, over and beyond what happens in a situation without control. Field work is now in progress to collect data to complete such a model. Before these data are available, the present model must suffice.

It may be some time before African farmers can apply the kind of models used by their colleagues in Australia (Brown, Yare & Singleton 1998; Pech et al. 1999). An important factor will be how sensitive the model is to the quality of the input data, particularly the initial values of population density and age structure.

In a pest control framework, the population of the pest organism is only one part of the problem. At present, we are investigating the relationships between rodent densities and damage or yield loss. To decide how useful a strategy will be in practice, the cost of control measures (in terms of human resources, material input and probably also environmental effects) and their balance with the cost of damage is equally as important as the reduction of rodent numbers. In order to develop a model that can be used for practical decision making, such components need to be included. Finally, the results of the model need to be interpreted in the sociocultural setting where the problem occurs.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

We have shown that by integrating information derived from a CMR study, we can develop a population model that may be used for evaluating various pest control strategies. However, it should be remembered that models are not reality, but they are useful devices for providing insights into what might happen under the influence of density-dependent and density-independent factors (Stenseth 1984), particularly as rather complicated dynamics may emerge (May 1974).

In this paper we have addressed an applied problem, namely the control of tropical rodents in agricultural areas. This system, M. natalensis population biology, is interesting in its own right. Indeed, basic and applied ecology are often synergistic (Stenseth, Saitoh & Yoccoz 1998; Ormerod, Pienkowski & Watkinson 1999). As Paul & Robertson (1989) have noted:

‘Agronomists have for too long ignored ecology and the benefits from integrated research approaches. Ecologists have for too long considered agronomic systems inherently uninteresting. It's time to close the gap.’

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References

We appreciate all the field work efforts carried out by different Tanzanian and visiting staff at the Rodent Research Unit, Sokoine University of Agriculture, Morogoro, Tanzania. Financial support was provided by a variety of European, Belgian, Danish and Norwegian project grants, all of which is greatly appreciated. Comments provided by Laurent Crespin, Mauricio Lima, Grant Singleton and an anonymous referee on an earlier version of this paper are greatly appreciated.

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  4. Materials and methods
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgements
  9. References
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Received 1 September 1999; revision received 1 June 2001