A Theoretical Model to Determine the Degree of Trapping Required for Insect Population Contror By D. E. WEIDHAAS AND D. G. HAILE Insects Affecting Man and Animals Research Laboratory Agric. Res. Serv., USDA, Gainesville, FL 32604 growth to survival and progeny production is: Trapping devices designed to capture insects have been in use for many years, but they have usually been used as survey tools to determine the abundance and distribution of types and species. Nevertheless, they have also been considered as a potential means of control since large numbers can be caught. Hienton (1974) recently summarized methods of trapping based on attraction to electromagnetic radiation and reported their effect on insect control. Also, research involving attractants and chemicals that modify insect behavior has indicated that traps may be useful in insect control. (1) = mx relating the rate oviposition number of female eggs produced per live female at age x. = mean Since oviposition occurs in the adult stages, this equation can be modified to include other life history parameters by making certain assumptions concerning rate of adult survival and oviposition characteristics. We assumed that the rates of adult survival and oviposition are constant with age and that oviposition occurs at discrete intervals after a preoviposition time from emergence. The equation can then be written as: 00 (2) Ro = S.m 1: n=o d+cn S. where S, = probability of survival from egg to emerging adult s. average daily survival of adult female m = average number of female eggs per live female per oviposition d preoviposition time in days c = egg laying cycle in days. = = This equation forms a convergent can be written as : (3) Ro geometric series and = S,m s." . I-s: The immature survival term (S.) can be subdivided into survival values for stages in the immature cycle if desired. For example, if values for survival of eggs (S.), larvae (S,), and pupae (S.) are used, S, S.'SI'S" Also, if an avg daily survival of immature stages (5.) is assumed = for development time (I), then S. = I S,. The effects of trapping adult females can be considered as an additional survival factor in equation 3 if a constant proportion of females are removed from the population each day. We can describe the avg daily proportion of females removed by a trapping system as a trapping efficiency factor, et, and convert it to an avg daily survival factor after trapping, St = I-et. Then St can be included in our equation as follows: We therefore modified the basic population equation used to define the rate of population growth over generations to include common biological parameters and a factor for trapping efficiency. Then we used this equation to relate the degree of trapping required to obtain several levels of control with several insect species to illustrate both the methods and typical results. equation = }";lxmx Ro net reproduction rate per generation Ix = probability of survival to age x from birth or In our research with mosquitoes and flies we have been measuring and using population parameters that are associated with life history analyses in order to model and simulate growth and control of populations (Haile and Weidhaas 1977). This particular approach could also be used to relate the degree of trapping efficiency required to effect certain levels of population control. It occurred to us that such a relationship could provide a general rule of thumb on trapping efficiency vs. population control. The results of such a relationship would not provide information or help on the design of trapping systems that would capture large proportions of insect populations, but they would provide a means of determining whether existing systems were sufficiently effective to produce control over time. basic 1948) where In spite of the continued interest in insect control by attractants or trapping techniques, there has been little published relating the basic biology of a given insect and its population ecology and dynamics to the degree of trapping required for population control. Knipling (1966, 1970) discussed theoretical aspects of the potential of sex attractants for insect control and of the possibility of an oviposition trap for mosquitoes. His models are based on the available biological data for given species and assumptions on the effectiveness of the attractants. His general approach was to define the efficacy of attractants, attractive components, or systems as a ratio to what exists in nature (or in native populations) and then to determine the degree of control obtained when the attractive systems were applied at other ratios than those that occur naturally. The procedure allows one to compare the relative effectiveness of control strategies and to demonstrate theoretically how such strategies could be developed. The Ro (Birch of population (4) Rt The research reported in this manuscript was conducted in part with contract funds transferred from the Medical Research and Development Command, Office of the Surgeon General, U.S. Army. Received for publication Oct. 17, 1977. 1 = Slm(s.'s.)" I-(s.'s.)< Our interest 18 is in determining the trapping efficiency Vol. 24, nO.1 1978 19 ESA BULLETIN Table I.-Biological parameters used in calculations. S, for indicated Ro Insect species m c d s. IX 2X 3X A. albimanus 60 3 6 0.8 .85 0.03103 0.06205 0.09308 .80 .85 .8 .75 .80 .85 .80 .85 .98 .99 .8 .02327 .04654 .06981 .02959 .21068 .05890 .42139 .08878 .63212 5X lOX 0.08526 0.17052 .06018 .14710 .12037 .29593 C. p. quinquefasciatus 100 M. domestica S. calcitrans 3 7 16.5 5 M. autumnalis 4 5 8 G. morsitans .5 C. homnivorax 150 2 4 10 17 3 6 required to reduce Ro (growth rate without trapping) to specified levels. If values are known for each of the parameters necessary to determine Ro, then a trial and error solution of equation 4 can be used to determine the value of s. required to achieve a specified level of R •. We used a programmable calculator to perform this iterative solution. For many insects, it is relatively easy to find data concerning factors such as c, d, and m and to develop estimates of avg values of these parameters typical of populations in nature. Estimates of s. and S, typical of natural populations are more difficult to find. However, if one knows the general values of R. and s. that can be expected with such populations, equation 3 can be used to determine appropriate estimates of St. Then one can USe equation 4 to develop estimates of the trapping efficiency necessary to maintain Ro at 1 or reduce it to a level less than 1 (population reduction). We used this approach to make calculations for 2 mosquito species (Anopheles albimanus Wiedemann and CuTable 2.-Percent tial growth rates. .61032 .67617 .10987 .21974 .32960 .33226 .66449 .06206 .12409 .51578 .45730 .02482 .01241 .03723 lex pipiens quinquefasciatus Say) ; the house fly (Musca domestica L.) ; the stable fly (Stomoxys calcitrans (L.) ; the face fly (Musca autumnalis DeGeer); a tsetse fly (Glossina morsitans (Westwood»; and the screwworm (Cochliomyia homnivorex (Coquere1». The biological parameters used for various growth rates (Ro) are presented in Table 1 and represent averages of data based on the experience of workers. The calculated values for the trapping efficiency required to reduce the various Ro values to growth rates of 1, 0.5, and 0.1 (representing population reductions of 0, 50, and 90% per generation from the initial level) are presented in Table 2. To illustrate the density trends achieved with trapping, we used the dynamic life history model developed by Haile and Weidhaas (1977) that was based on the biological parameters for A. albimanus presented above. For an uncontrolled growth rate of 3X and trapping rates of 13, 21, and 380/0 (from Table 2), the simulation model produced the expected density trends (Fig. 1) resulting in growth rates of 1, 0.5 and O.1X per generation (18.6 of population to be trapped out each day to produce indicated rate of growth at different poten- Percent of population to be trapped out each day with indicated species Potential growth rate (no trapping) IX 2X 3X 5X lOX • A Growth rate with trapping' A. albimallus 0.5X 0.1X IX 0.5X O.1X 1X 0.5X O.1X IX 0.5X O.1X IX 0.5X O.1X growth rate with trapping of C. p. quinquefasciatus 7 23 7 14 30 11 18 34 15 22 36 22 28 42 8 26 8 16 34 13 21 38 17 24 40 24 32 47 IX, 0.5X and O.IX S. M. domestica is equivalent to calcitrans M. autumnalis 9 29 9 18 36 14 23 41 19 27 44 25 32 48 10 33 10 20 43 16 26 48 21 31 51 31 40 58 9 31 9 19 40 15 24 45 22 31 51 31 40 57 0, SO, and 90% G. moreitalls 1 7 1 2 7 reduction per generation, respectively. C. homnivorax 8 26 8 16 34 13 21 38 18 26 42 26 34 48 20 ESA Vol. 24, no. 1 1978 BULLETIN With 13%/day Trapping R = 1 FIG. 1.- Trends in population density for A. albimanus efficiencies of 0, 13, 21, and 38%/day. (potential day generation time). The oscillations in Fig. I resulted from the instability caused by the introduction of trapping in a normally stable population. These curves point out that equivalent results are obtained with a simulation model and the use of a mathematical model (equation 4) when both are based on the same biological parameters. The simulation model approach can be used to determine density trends resulting from the combined use of trapping and other methods of control, such as sterile males and insecticides. This analysis of trapping requirements is not concerned with making trapping systems work in total population contra\. However, it does provide guidelines and methods of evaluations. With specific insects and trapping systems, mark-release-recapture experiments could be used to determine whether the theoretical trapping requirements can be obtained. The calculations in Table 2 for flies and mosquitoes (with the exception of the tsetse fly) show some variation in the degree of trapping required to cause population reduction, but the differences are not large. Tsetse flies with their low reproductive capacity and long-lived adults show the lowest trapping requirements per day. Population growth rates influence the required degree of control as would be expected. For example, a 500/0 reduction per generation at a potential IX growth rate requires trapping out from 1-10% of the different species. To bring about the same reduction per generation with a potential growth rate of lOX requires trapping out 28-40% each day. The difficulty (relatively high proportion of insects that must be trapped) of using trapping systems for total population control is thus plain. growth rate of 3X/generation) REFERENCES Birch, L. C. with trapping CITED 1948. The intrinsic rate of natural increase of an insect population. J. Anim. Eco\. 17: 15-26. Haile, D. G., and D. E. Weidhaas. 1977. Computer simulation of mosquito populations (AnoPheles albimanus) for comparing the effectiveness of control technologies. J. Med. Entomol. 13; 553-67. Hienton, T. E. 1974. Summary of investigations of electric insect traps. USDA Tech. Bull. No. 1498. 136 pp. Knipling, E. F. 1966. Population models to test theoretical effects of sex attractants used for insect control. USDA Agric. Inform. Bull. 20 pp. 1970. A theoretical appraisal of the value of ovitraps for the suppression of container-breeding mosquitoes. WHO/VBC70.186. 14 pp.
© Copyright 2021 Paperzz