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A Mathematical Model for the Effect of Densities of Attacked and Attacking Species on the Number Attacked

Published online by Cambridge University Press:  31 May 2012

K. E. F. Watt
Statistical Laboratory, Science Service, Ottawa


Any realistic mathematical model of insect pest population dynamics to be used in maximizing control efficiency must mimic the effects of weather, the habitat, other organisms of various specles, food, and chemicals applied by man. However. before such a model can be constructed. suitable mathematical formulations for the mechanismof each type of factor must be developed.

Copyright © Entomological Society of Canada 1959

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Allee, W. C., Emerson, A. E., Park, O., Park, T. and Schmidt, K. P.. 1949. Principles of Animal Ecology. W. B. Saunders Company, Philadelphia.Google Scholar
Anderson, R. L., and Bancroft, T. A.. 1952. Statistical theory in research. McGraw-Hill, New York.Google Scholar
Andrewartha, H. G., and Birch, L. C.. 1954. The distribution and abundance of animals. U. Chicago Press, Chicago.Google Scholar
Bailey, V. A. 1931. The interaction between hosts and parasites. Quart. J. Math. 2: 6877.CrossRefGoogle Scholar
Beverton, R. J. H., and Holt, S. J.. 1957. On the dynamics of exploited fish populations. Fishery Investigations, Ser 2, Vol. 19. Her Majesty's Stationery Office, London.Google Scholar
Bodenheimer, F. S., and Schiffer, M.. 1952. Mathematical studies in animal populations, I: A mathematical study of insect parasitism. Ser. A. Acta Biotheoretica 10: 2356.CrossRefGoogle Scholar
Burnett, Thomas. 1951. Effects of temperature and host density on the rate of increase of an insect parasite. Am. Nat. 85: 337352.CrossRefGoogle Scholar
Burnett, Thomas. 1953. Effects of temperature and parasite density on the rate of increase of an insect parasite. Ecology 34: 321328.CrossRefGoogle Scholar
Burnett, Thomas. 1954. Influences of natural temperatures and controlled host densities on oviposition of an insect parasite. Physiological Zoology 27: 239248.CrossRefGoogle Scholar
Burnett, Thomas. 1956. Effects of natural temperatures on oviposition of various numbers of an insect parasite (Hymenoptera, Chalcididae, Tenthredinidae). Annals Entomological Society of Amer. 49: 5559.CrossRefGoogle Scholar
Burnett, Thomas. 1958a. Effect of host distribution on the reproduction of Encarsia formosa Gahan (Hymenoptera: Chalcidoidae). Can. Ent. 90: 179191.CrossRefGoogle Scholar
Burnett, Thomas. 1958b. Effect of area of search on reproduction of Encarsia formosa Gahan (Hymenoptera: Chalcidoidea). Can. Ent. 90: 225229.CrossRefGoogle Scholar
Burnett, Thomas. 1958c. Dispersal of an insect parasite over a small plot. Can. Ent. 90: 279283.CrossRefGoogle Scholar
David, F. N., and Neyman, J.. 1938. Extension of the Markoff theorem on least squares. Stat. Research Mem. 2: 105116.Google Scholar
DeBach, P., and Smith, H. S.. 1941. The effect of host density on the rate of reproduction of entomophagous parasites. J. Econ. Ent. 34: 741745.CrossRefGoogle Scholar
DeBach, P., and Smith, H. S.. 1947. Effects of parasite population density on rate of change of host and parasite populations. Ecology 28: 290298.CrossRefGoogle Scholar
Dethier, V. G. 1957. Chemoreception and the behavior of insects. In. Survey of Biological Progress, 3: 149183. Academic Press, Inc., New York.Google Scholar
Edwards, Roy L. 1954. The host-finding and oviposition behavior of Mormoniella vitripennis (Walker) (Hym., Pteromalidae), a parasite of muscoid flies. Behavior 7: 88112.CrossRefGoogle Scholar
Ezekiel, M. 1941. Methods of correlation analysis. Wiley (2nd ed.).Google Scholar
Gause, G. F. 1934. The struggle for existence. Williams and Wilkins, Baltimore.CrossRefGoogle ScholarPubMed
Hald, A. 1952. Statistical theory with engineering applications. Wiley.Google Scholar
Ivlev, V. S. 1945. The biological productivity of waters. Uspekhi Sovremennoi Biologii 19: 98120.Google Scholar
Laing, J. 1937. Host finding by insect parasites. 1. Observations on the finding of host of Alysia manducator, Mormoniella vitripennis, an. Trichogramma evanescens. J Animal Ecol. 6: 298317.CrossRefGoogle Scholar
Lotka, A. J. 1923. Contribution to quantitative parasitology, J. Wash. Acad. Sci. 13: 152158.Google Scholar
Miller, C. A. 1955. A technique for assessing spruce budworm larval mortality caused by parasitism. Canadian J. Zool. 33: 517.CrossRefGoogle Scholar
Milne, A. 1957. The natural control of insect populations. Can. Ent. 89: 193213.CrossRefGoogle Scholar
Morris, R. F., and Miller, C. A.. 1954. The development of life tables for the spruce budworm. Can. J. Zool. 32: 283301.CrossRefGoogle Scholar
Nicholson, A. J., and Bailey, V. A.. 1935. The balance of animal populations. Part I. Proc. Zool. Soc. London 1935: 551598.CrossRefGoogle Scholar
Salt, G. 1932. Superparasitism by Collyria calcitrator, Grav. Bull. Ent. Res. 23: 211215.CrossRefGoogle Scholar
Smirnov, E., and Wladimirow, M.. 1934. Studien über die Vermehrungsfähigkeit der Pteromalide Mormoniella vitripennis Wlk. Z. Wiss. Zoologie 145: 507522.Google Scholar
Smith, Frederick D. 1952. Experimental methods in population dynamics: A critique Ecology 33: 441450.CrossRefGoogle Scholar
Solomon, M. E. 1949. The natural control of animal populations. J. Animal Ecol. 18: 135.CrossRefGoogle Scholar
Stanley, J. 1932. A mathematical theory of the growth of populations of the flour beetle Tribolium confusum Duval. Can. J. Res. 6: 632671.CrossRefGoogle Scholar
Stevens, W. L. 1951. Asymptotic regression. Biometrics 7: 247267.CrossRefGoogle Scholar
Stoy, R. H. 1932. Appendix to “Superparasitism by Collyria calcitrator, Grav.” by George Salt. Bull. Ent. Res. 23: 215216.Google Scholar
Thompson, W. R. 1922. Théorie de l'action des parasites entomophages. Les formules mathématiques du parasitisme cyclique. C. R. Acad. Sci. Paris 174: 12011204.Google Scholar
Thompson, W. R. 1924. La théorie mathématique de l'action des parasites entomophages et le facteur du hasard. Ann. Fac. Sci. Marseille 2: 6989.Google Scholar
Thompson, W. R. 1939. Biological control and the theories of the interactions of populations. Parasitology 31: 299388.CrossRefGoogle Scholar
Ullyett, G. C. 1936. Host selection by Microplectron fuscipennis Zett. (Chalcididae Hymenoptera). Proc. Roy. Soc (B) 120: 253291.CrossRefGoogle Scholar
Ullyett, G. C. 1943. Some aspects of parasitism in field populations of Plutella maculipennii Curt. J. Ent. Soc. South Africa 6: 6580.Google Scholar
Ullyett, G. C. 1947. Mortality factors in poulations of Plutella maculipennis Curtis (Tineidae: Lep.), and their relation to the problem of control. Ent. Mem. Union S. Afr. Dept. Agric. Forestry 2: 77202.Google Scholar
Ullyett, G. C. 1949a. Distribution of progeny by Chelonus texanus Cress. (Hymenoptera: Braconidae). Can. Ent. 81: 2544.CrossRefGoogle Scholar
Ullyett, G. C. 1949b. Distribution of progeny by Cryptus inornatus Pratt (Hymenoptera: Ichneumonidae). Can. Ent. 81: 285299.CrossRefGoogle Scholar
Ullyett, G. C. 1953. Biomathematics and Insect Population problems. A critical review. Memoirs Ent. Soc. Southern Africa 2: 189.Google Scholar
Varley, G. E. 1941. On the search for hosts and egg distribution of some Chalcid parasites of the knapweed gallfly. Parasitology 33: 4766.CrossRefGoogle Scholar
Volterra, V. 1926. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. Acad. Lincei (6) 2: 31113.Google Scholar
Walker, M. G. 1937. A mathematical analysis of superparasitism by Collyria calcitrator Grav. Parasitology 29: 477503.CrossRefGoogle Scholar
Walker, M. G. 1940. Notes on the distribution of Cephus pygmaeus, Linn., and of its parasite Collyria calcitrator, Grav. Bull. Ent. Res. 30: 551573.CrossRefGoogle Scholar
Watt, K. E. F. 1956. The choice and solution of mathematical models for predicting and maximizing the yield of a fishery. J. Fish. Res. Bd. Can. 13: 613645.CrossRefGoogle Scholar
Watt, K. E. F. 1958. Mathematical fish population dynamics (book review) Ecology, 39: 777.CrossRefGoogle Scholar
Watt, K. E. F. 1959. Studies on population productivity. II. Factors governing productivity in a population of smallmouth bass. Ecol. Monog. (in press).CrossRefGoogle Scholar