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Keywords:

  • Ceratitis capitata;
  • Bactrocera tryoni;
  • power law;
  • negative binomial;
  • Diptera;
  • Tephritidae;
  • SIT

Abstract

Dispersion theory is applied to the distribution of two kinds of sterile insect, Mediterranean fruit fly (Medfly), Ceratitis capitata (Wiedemann), and Queensland fruit fly (Qfly), Bactrocera tryoni (Froggatt) (Diptera: Tephritidae). Dispersion theories are an essential basis of sampling theory and sampling plans, but this paper looks at them from another direction and uses data from arrays of sterile insect technique (SIT) monitoring traps to compare the utility of different measures such as coefficient of variation (CV), the exponent b of Taylor's power law, and exponent k of the negative binomial distribution and also derives predictions pertaining to the density (and hence release rate) of sterile insects that would be required to achieve effective coverage of the target area. This is far more useful than reliance on just the mean values of trap catches because such reliance takes no account of the fact that sterile flies distribute themselves unevenly with many patches inadequately covered despite the impression given by the mean. Data were used from recapture rates following either ‘roving releases’ of Medfly or releases from fixed points of Qfly. The relation of recapture rate to CV indicated that a doubling of release rate in order to double average recapture rate from 150 per trap per week to a value of 300 would have very little effect in terms of reducing CV and that there appears to be no practical prospect of reducing CV to below unity with the current methods of release without incurring a manifold increase in cost. Similarly, models derived from the negative binomial equation indicated that a law of diminishing returns applies in terms of the increase in the amount of adequate coverage (such as the percentage of traps catching >50 flies per week) that can be obtained by increasing release rates.