Skip to main content
×
×
Home

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

  • K. E. F. Watt (a1)
Extract

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

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Canadian Entomologist
  • ISSN: 0008-347X
  • EISSN: 1918-3240
  • URL: /core/journals/canadian-entomologist
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed