Tratalos et al.: Modelling desert <strong>locust</strong> <strong>populations</strong>237<strong>rainfall</strong> lags more remote than lag 3 appear to be themost important predictors of future swarms, whereasfor the hopper b<strong>and</strong>s series, <strong>rainfall</strong> at lags 1 <strong>and</strong> 2 <strong>and</strong>swarms at lags 1, 2, 4 <strong>and</strong> 8 appeared to be the mostimportant factors. These results suggest a process inwhich swarms produced in the previous generationbreed on rains arriving approximately 2 or 3 mo later,to produce hopper b<strong>and</strong>s after approximately 4 mo.These in turn may give rise to a second swarminggeneration in subsequent months.Since the inclusion of <strong>rainfall</strong> variables improved thefit of purely endogenous ARIMA models, these analyseshave clearly shown that desert <strong>locust</strong> populationdynamics at an intercontinental scale are at least partlydriven by <strong>rainfall</strong>, but have also indicated that endogenouscontrol is important. However, as the time stepwas only 1 mo, which is less than the generation timeof the <strong>locust</strong>s, autocorrelations at lag 1, <strong>and</strong> perhapslags 2 to 3, would be expected. Nevertheless, therewas also evidence for a substantial degree of ‘memory’in the dynamics, with the ACF of the series showingsignificant lags up to 100 mo. The PACF is a measureof autocorrelation at lag k that takes account of autocorrelationsat lags
238Clim Res 43: 229–239, 2010that <strong>rainfall</strong> at remote lags (at 12 mo, for example) wasfound to be significant in models in which more recentdata on <strong>locust</strong> abundance were included. These resultsmay imply that rain falling 12 mo previously, may,through its effect on the abundance of successive generationsof solitary <strong>locust</strong>s, produce an effect on theabundance of gregarious <strong>populations</strong> in the currentmonth. This may constitute evidence against theswarm continuity hypothesis, the theory that breedingby a few gregarious, swarming <strong>populations</strong> remainingduring recession periods is responsible for <strong>locust</strong>upsurges, as opposed to a build-up <strong>and</strong> gregarisationof solitarious <strong>populations</strong> (Hemming et al. 1979, Rainey& Betts 1979). The relatively poor performance ofARIMA models during periods of upsurge also suggestsa role for solitarious <strong>populations</strong>. However, thefact that the dynamics of swarming <strong>populations</strong> couldbe modelled with a fair degree of success usingendogenous data only <strong>from</strong> swarming <strong>populations</strong> isconsistent with the swarm continuity hypothesis, butdoes not necessarily lend it support.In the swarms data models, <strong>rainfall</strong> at lags 0 <strong>and</strong> 1was negatively correlated with swarms data for thecurrent month. This may seem to be a surprisinglycounter-intuitive result, given that the survival of hopper<strong>populations</strong> may in some cases be due to the arrivalof <strong>rainfall</strong>. However, what is known about <strong>locust</strong> ecologysuggests that new swarms would most often beproduced as a result of <strong>rainfall</strong> at lags more remotethan lag 1 (Bennett 1976, Pedgley 1981). Secondly, it isknown that both hopper b<strong>and</strong>s <strong>and</strong> swarming <strong>populations</strong>tend to become increasingly solitary whenvegetation is dense, as they are no longer crowded intojust a few bushes <strong>and</strong> thus the gregarisation process isdisrupted, <strong>and</strong> therefore an increase in vegetation dueto <strong>rainfall</strong> may reduce gregarious <strong>populations</strong>. Thirdly,swarming <strong>populations</strong> are thought to be more sedentarywhen environmental conditions remain suitable,<strong>and</strong> would therefore be less likely to be observed.Finally, movements, growth rates <strong>and</strong> survivorship arelikely to be reduced by lower temperatures, which maybe brought about by higher <strong>rainfall</strong>.Taking into account these 4 points, a negative relationshipbetween <strong>rainfall</strong> at lags 0 <strong>and</strong> 1 <strong>and</strong> the numberof grid squares reported as infested with swarmsmight be expected. Non-significant relationships between<strong>rainfall</strong> at lags 2 <strong>and</strong> 3 <strong>and</strong> swarms in the currentmonth are perhaps due to a combination of thesenegative effects <strong>and</strong> the positive effect of <strong>rainfall</strong> on<strong>locust</strong> breeding <strong>and</strong> survivorship.This study suggests that desert <strong>locust</strong> dynamics areinfluenced by endogenous factors <strong>and</strong> <strong>rainfall</strong>, <strong>and</strong>that broad patterns of <strong>locust</strong> upsurges <strong>and</strong> declines canbe forecast with some degree of success using data ononly these factors. Also, once predictions of likely <strong>climate</strong><strong>change</strong>s throughout the recession area can bemade with more confidence than at present, our resultscould be helpful in forecasting whether <strong>locust</strong> plagueswill become more or less frequent. For instance, if theforecasts of increased precipitation over importantdesert <strong>locust</strong> habitats in the Sahara along a west–eastbelt at about 20° N on the basis of the AB1 scenario(Hulme et al. 2001) are realised, then <strong>locust</strong> upsurgesare likely to become more frequent.Acknowledgements. J.A.T. <strong>and</strong> R.A.C. thank the University ofGreenwich for support. We are grateful to J. I. Magor for providingaccess to the FAO SWARMS data set <strong>and</strong> advice on<strong>locust</strong> migrations. We also thank M. Hulme <strong>and</strong> colleagues atthe University of East Anglia Climate Change Unit for production<strong>and</strong> distribution of a global precipitation data set <strong>and</strong>3 anonymous referees for their helpful comments.LITERATURE CITED➤ Babah MAO, Sword GA (2004) Linking <strong>locust</strong> gregarizationto local resource distribution patterns across a largespatial scale. Environ Entomol 33:1577–1583➤ Bennett LV (1975) Development of a desert <strong>locust</strong> plague.Nature 256:486–487➤ Bennett LV (1976) The development <strong>and</strong> termination of the1968 plague of the desert <strong>locust</strong>, Schistocerca gregaria(Forskål) (Orthoptera: Acrididae). Bull Entomol Res 66:511–552Blackith RE, Albrecht FO (1979) Locust plagues, the interplayof endogenous <strong>and</strong> exogenous control. Acrida 8:83–94Box GEP, Jenkins GM (1976) Time series analysis: forecasting<strong>and</strong> control. Holden-Day, San Francisco, CAChatfield C (1997) The analysis of time series. Chapman &Hall, London➤ Cheke RA (1978) Theoretical rates of increase of gregarious<strong>and</strong> solitarious <strong>populations</strong> of the desert <strong>locust</strong>. Oecologia35:161–171➤ Cheke RA, Holt J (1993) Complex dynamics of desert <strong>locust</strong>plagues. Ecol Entomol 18:109–115Cheke RA, Holt J (1996) Chaos in desert <strong>locust</strong> plaguedynamics? In: Walter K, Mills N, Watt A (eds) Populations<strong>and</strong> patterns in biology. Intercept Press, Andover, p 42–45➤ Cheke RA, Tratalos JA (2007) Migration, patchiness <strong>and</strong>population processes illustrated by two migrant pests. Bioscience57:145–154Christensen JH, Hewitson B, Busuioc A, Chen A <strong>and</strong> others(2007) Regional <strong>climate</strong> projections. In: Solomon S, Qin D,Manning M, Chen Z <strong>and</strong> others (eds) Climate <strong>change</strong>2007: the physical science basis. Contribution of WorkingGroup I to the Fourth Assessment Report of the IntergovernmentalPanel on Climate Change. Cambridge UniversityPress, Cambridge, p 847–940➤ Claussen M, Brovkin V, Ganopolski A, Kubatzki C, PetoukhovV (2003) Climate <strong>change</strong> in northern Africa: tThe pastis not the future. Clim Change 57:99–118Diggle PJ (1990) Time series: a biostatistical introduction.Oxford University Press, Oxford➤ Farrow RA, Longstaff BC (1986) Comparison of the annualrates of increase of <strong>locust</strong>s in relation to the incidence ofplagues. Oikos 46:207–222➤ Greathead DJ (1966) A brief survey of the effects of bioticfactors on <strong>populations</strong> of the desert <strong>locust</strong>. J Appl Ecol
Change language