Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T18:39:30.541Z Has data issue: false hasContentIssue false
  • English
  • Français

THE COMPARATIVE STUDY OF FUNCTIONAL RESPONSES: EXPERIMENTAL DESIGN AND STATISTICAL INTERPRETATION

Published online by Cambridge University Press:  31 May 2012

Marilyn A. Houck  and
Richard E. Strauss
Marilyn A. Houck
Affiliation:
Museum of Zoology, University of Michigan, Ann Arbor 48109
Richard E. Strauss
Affiliation:
Museum of Zoology, University of Michigan, Ann Arbor 48109
Get access Rights & Permissions [Opens in a new window]

Abstract

Mathematical discussions of models of functional response (predation rate as a function of prey density) have usually emphasized description of the shape of the functional-response curve. However, lack of congruence between experimental design and data analysis and under-utilization of appropriate statistical methods of analysis have hindered an empirical synthetic treatment of such feeding behavior. Here we review existing experimental and statistical procedures with reference to Holling's generalized model of functional response, and describe: (1) an experimental design compatible with the assumptions of the model; (2) a maximum-likelihood method for fitting the model; (3) several methods for statistical comparison of sets of functional-response curves; and (4) an exploratory graphical method for examining patterns of variation among larger numbers of samples.

Résumé

Les discussions mathématiques des modèles de réponse fonctionnelle (intensité de prédation en fonction de la densité de proie) insistent généralement sur la description de la forme de la courbe de réponse fonctionnelle. Cependant, le manque de cohérence entre le plan expérimental et l'analyse des données, ainsi que la sous-utilisation de méthodes d'analyse statistique appropriées ont empêché le développement d'une synthèse empirique de ce type d'alimentation. On passe ici en revue les méthodes expérimentales et statistiques relatives au modèle général de Holling de réponse fonctionnelle, et on décrit : (1) un plan expérimental compatible avec les prémisses du modèle; (2) une méthode d'ajustement du modèle basée sur le maximum de vraisemblance; (3) plusieurs méthodes de comparaison statistique de séries de courbes de réponse fonctionnelle; et (4) une méthode exploratoire graphique permettant d'étudier les patrons de variation existant dans un nombre plus grand d'échantillons.

Type
Articles
Information
The Canadian Entomologist , Volume 117 , Issue 5 , May 1985 , pp. 617 - 629
Copyright
Copyright © Entomological Society of Canada 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akre, B.G. and Johnson, D.M. 1979. Switching and sigmoidal functional response curves by damselfly naiads with alternative prey available. J. Anim. Ecol. 48: 703–720.CrossRefGoogle Scholar
Banks, C.J. 1957. The behavior of individual coccinellid larvae on plants. Br. J. Anim. Behav. 1: 12–24.CrossRefGoogle Scholar
Chambers, J.M. 1973. Fitting nonlinear models: numerical techniques. Biometrika 60: 1–13.CrossRefGoogle Scholar
Conway, G.R., Glass, N.R and Wilcox, J.C. 1970. Fitting nonlinear models to biological data by Marquardt's algorithm. Ecology 51: 503–507.CrossRefGoogle Scholar
Curry, G.L. and DeMichele, D.W. 1977. Stochastic analysis for the description and synthesis of predator-prey systems. Can. Ent. 109: 1167–1174.CrossRefGoogle Scholar
Curry, G.L. and Feldman, R.M. 1979. Stochastic predation model with depletion. Can. Ent. 111: 465–470.CrossRefGoogle Scholar
Dixon, A.F.G. 1959. An experimental study of the searching behavior of the predatory coccinellid beetle Adalia decempunctata. J. Anim. Ecol. 28: 259–281.CrossRefGoogle Scholar
Dixon, A.F.G. 1970. Factors limiting the effectiveness of the coccinellid beetle Adalia bipunctata as a predator of the sycamore aphid Drepannosiphum platanoides. J. Anim. Ecol. 39: 739–751.CrossRefGoogle Scholar
Draper, N.R. and Smith, H.. 1966. Applied Regression Analysis. Wiley, NY. 347 pp.Google Scholar
Eveleigh, E.S. and Chant, D.A. 1981. Experimental studies on acarine predator-prey interactions: effects of predator age and feeding history on prey consumption and the functional response (Acarina: Phytoseiidae). Can. J. Zool. 59: 1387–1406.CrossRefGoogle Scholar
Everson, P. 1979. The functional response of Phytoseiulus persimilis (Acarina: Phytoseiidae) to various densities of Tetranychus urticae (Acarina: Tetranychidae). Can. Ent. 111: 7–10.CrossRefGoogle Scholar
Everson, P. 1980. The relative activity and functional response of Phytoseiulus persimilis (Acarina: Phytoseiidae) and Tetranychus urticae (Acarina: Tetranychidae): the effect of temperature. Can. Ent. 112: 17–24.CrossRefGoogle Scholar
Fleschner, C.A. 1950. Studies on searching capacity of the larvae of three predators on the citrus red mite. Hilgardia 20: 233–265.CrossRefGoogle Scholar
Geisser, S. and Eddy, W.F. 1979. A predictive approach to model selection. J. Am. Stat. Assoc. 74: 153–160.CrossRefGoogle Scholar
Gibbons, J.D. 1976. Nonparametric Methods for Quantitative Analysis. Holt, Rinehart and Winston, NY. 463 pp.Google Scholar
Glass, N.R. 1969. Discussion of calculation of the power function with special reference to respiratory metabolism in fish. J. Fish. Res. Bd Can. 26: 2643–2650.CrossRefGoogle Scholar
Hassell, M.P. 1978. The Dynamics of Arthropod Predator-Prey Systems. Princeton Univ. Press, Princeton, NJ. 229 pp.Google ScholarPubMed
Hassell, M.P., Lawton, J.H and Beddington, J.R. 1976. The components of arthropod predation. I. The prey death rate. J. Anim. Ecol. 45: 135–164.CrossRefGoogle Scholar
Hassell, M.P., Lawton, J.H and Beddington, J.R. 1977. Sigmoid functional responses by invertebrate predators and parasitoids. J. Anim. Ecol. 46: 249–262.CrossRefGoogle Scholar
Helwig, J.T. and Council, K.A. 1979. SAS User's Guide. SAS Institute, Raleigh, NC. 494 pp.Google Scholar
Hollander, M. and Wolfe, D.A. 1973. Nonparametric Statistical Methods. Wiley, NY. 503 pp.Google Scholar
Holling, C.S. 1959. Some characteristics of simple types of predation and parasitism. Can. Ent. 91: 385–398.CrossRefGoogle Scholar
Holling, C.S. 1966. The functional response of invertebrate predators to prey density. Mem. ent. Soc. Can. 48. 86 pp.Google Scholar
Houck, M.A. 1980. Predatory behavior of Stethorus punctum (Coleoptera: Coccinellidae) in response to the prey Panonychus ulmi and Tetranychus urticae (Acarina: Tetranychidae). Dissertation, The Pennsylvania State University. 154 pp.Google Scholar
Hull, L.A., Asquith, D. and Mowery, P.D. 1977. The functional responses of Stethorus punctum to densities of the European red mite. Environ. Ent. 6: 85–90.CrossRefGoogle Scholar
Kappenman, R.F. 1981. A method for growth curve comparison. Fish. Bull. 79: 95–101.Google Scholar
Kaddou, I.K. 1960. The feeding behavior of Hippodamia quinquesignata larvae. Univ. Calif. Publs Ent. 16: 181–232.Google Scholar
Livdahl, T.P. and Stiven, A.E. 1983. Statistical difficulties in the analysis of predator functional response data. Can. Ent. 115: 1365–1370.CrossRefGoogle Scholar
Longstaff, B.C. 1980. The functional response of a predatory mite and the nature of the attack rate. Aust. J. Ecol. 5: 151–158.CrossRefGoogle Scholar
Marquardt, D.W. 1963. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. indust. appl. Math. 11: 431–441.CrossRefGoogle Scholar
Marquardt, D.W. 1966. Least-squares estimation of nonlinear parameters. IBM SHARE Library Distribution No. 309401, NLIN 2, August 1966. 37 pp.Google Scholar
Mori, H. and Chant, D.A. 1966. The influence of prey density, relative humidity, and starvation on the predacious behavior of Phytoseiulus persimilis Athias-Henriot (Acarina: Phytoseiidae). Can. J. Zool. 44: 483–491.CrossRefGoogle Scholar
Morrison, D.F. 1976. Multivariate Statistical Methods. McGraw-Hill, NY. 415 pp.Google Scholar
Murdoch, W.W. and Oaten, A.. 1975. Predation and population stability. Adv. Ecol. Res. 9: 1–131.CrossRefGoogle Scholar
Nie, N.H., Hull, C.H, Jenkins, J., Sternbrenner, K. and Bent, D.. 1975. SPSS Statistical Package for the Social Sciences, 2nd ed. McGraw-Hill, NY.Google Scholar
Neter, J. and Wasserman, W.. 1974. Applied Linear Statistical Models. Richard D. Irwin, Homewood, IL. 842 pp.Google Scholar
Rasmy, A.H. and El-Banhawy, E.M. 1974. Behavior and bionomics of the predatory mite Phytoseius plumifer (Acarina: Phytoseiidae) as affected by physical surface of host plants. Entomophaga 19: 255–257.CrossRefGoogle Scholar
Rogers, D.J. 1972. Random search and insect population models. J. Anim. Ecol. 41: 369–383.CrossRefGoogle Scholar
Royama, T. 1971. A comparative study of models for predation and parasitism. Researches Popul. Ecol. Kyoto Univ. Suppl. 1. 91 pp.Google Scholar
Sandness, J.N. and McMurtry, J.A. 1970. Functional response of three species of Phytoseiidae (Acarina) to prey density. Can. Ent. 102: 692–704.CrossRefGoogle Scholar
Sandness, J.N. and McMurtry, J.A. 1972. Prey consumption behavior of Amblyseius largoensis in relation to hunger. Can. Ent. 104: 461–470.CrossRefGoogle Scholar
Santos, M.A. 1975. Functional and numerical responses of the predatory mite, Amblyseius fallacis, to prey density. Environ. Ent. 4: 989–992.CrossRefGoogle Scholar
Silvert, W. 1979. Practical curve fitting. Limnol. Oceanogr. 24: 767–773.CrossRefGoogle Scholar
Stubbs, M. 1980. Another look at prey detection by coccinellids. Ecol. Ent. 5: 179–182.CrossRefGoogle Scholar
Thompson, D.J. 1975. Towards a predator-prey model incorporating age structure: the effects of predator and prey size on the predation of Daphnia magna by Ischnura elegans. J. Anim. Ecol. 44: 907–916.CrossRefGoogle Scholar
Thomson, A.J. and Holling, C.S. 1976. Crowding and activity. Can. Ent. 108: 1417–1426.CrossRefGoogle Scholar
Werner, E.E. 1974. The fish size, prey size, handling time relation in several sunfishes and some implications. J. Fish. Res. Bd Can. 31: 1531–1536.CrossRefGoogle Scholar
Zar, J.H. 1968. Calculation and miscalculation of the allometric equation as a model in biological data. BioScience 18: 1118–1120.CrossRefGoogle Scholar