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Bivariate stochastic modeling of functional response with natural mortality

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Faddy, M. J., Fenlon, John S. and Skirvin, David J.. (2010) Bivariate stochastic modeling of functional response with natural mortality. Journal of Agricultural, Biological, and Environmental Statistics, Vol.15 (No.1). pp. 38-48. ISSN 1085-7117

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Official URL: http://dx.doi.org/10.1007/s13253-009-0007-9

Abstract

A correction due to Abbott (1925) is the standard method of dealing with control mortality in insect bioassay to estimate the mortality of an insect conditional on control mortality not having occurred. In this article a bivariate stochastic process for overall mortality is developed in which natural mortality and predation are jointly modeled to take account of the competing-risks associated with prey loss. The total mortality estimate from this model is essentially identical with that from more classical modeling. However, when predation loss is estimated in the absence of control mortality the results are somewhat different, with the estimate from the bivariate model being lower than that from using Abbott’s formula in conjunction with the classical model. It is argued that overdispersion in observed mortality data corresponds to correlated outcomes (death or survival) for the prey initially present, while Abbott’s correction relies implicitly on independence.

Item Type:	Journal Article
Subjects:	Q Science > QL Zoology Q Science > QA Mathematics
Divisions:	Faculty of Science > Life Sciences (2010- ) > Warwick HRI (2004-2010)
Library of Congress Subject Headings (LCSH):	Abbott, W. S. (Walter Sidney) 1880-, Predatory insects -- Research, Competing risks -- Research, Mortality -- Statistics, Stochastic models
Journal or Publication Title:	Journal of Agricultural, Biological, and Environmental Statistics
Publisher:	Springer New York LLC
ISSN:	1085-7117
Date:	March 2010
Volume:	Vol.15
Number:	No.1
Page Range:	pp. 38-48
Identification Number:	10.1007/s13253-009-0007-9
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
References:	Abbott, W.S. (1925), “A method for computing the effectiveness of an insecticide”, Journal of Economic Entomology, 18, 265−267. Faddy, M.J. (1997), “Extended Poisson process modelling and analysis of count data”, Biometrical Journal, 39, 431−440. Faddy, M.J. and Fenlon, J.S. (1999), “Stochastic modelling of the invasion process of nematodes in fly larvae”, Applied Statistics, 48, 31−37. Faddy, M.J. and Smith, D.M. (2005), “Modelling the dependence between the number of trials and the success probability in binary trials”, Biometrics, 61, 1112−1114. Fenlon, J.S. and Faddy, M.J. (2006), “Modelling predation in functional response”, Ecological Modelling, 198, 154−162. Hewlett, P.S. and Plackett, R.L. (1979), The Interpretation of Quantal Responses in Biology, London: Edward Arnold. Hoekstra, J.A. (1987), “Acute bioassays with control mortality”, Water, Air and Soil Pollution, 35, 311−317. Holling, C.S. (1959), “The components of predation as revealed by a study of small mammal predation of the European pine sawfly”, Canadian Entomologist, 91, 293-320. Kuenen, D.J. (1957), “Time mortality curves and Abbott’s correction in experiments with insecticides”, Acta Physiologica et Pharmacologica Neerlandica, 6, 179–196. Morgan, B.J.T. (1992), Analysis of quantal response data, London: Chapman & Hall. Preisler, H.K. (1989), “Fitting dose-response data with non-zero background within generalized linear and generalized additive models”, Computational Statistics and Data Analysis, 7, 279−290. Skirvin, D.J. and de Courcy Williams M. (1999), “Differential effects of plant species on a mite pest (Tetranychus urticae) and its predator (Phytoseiulus persimilis): implications for biological control”, Experimental and Applied Acarology, 23, 497−512. Skirvin, D.J. and Fenlon. J.S. (2001), “Plant species modifies the functional response of Phytoseiulus persimilis (Acari: Phytoseiidae) to Tetranychus urticae (Acari: Tetranychidae): implications for biological control”, Bulletin of Entomological Research, 91, 61−67. Skirvin, D.J., de Courcy Williams, M.E., Fenlon, J.S. and Sunderland K.D. (2002), “Modelling the effects of plant species on biocontrol effectiveness in ornamental nursery crops”, Journal of Applied Ecology, 39, 469−180.
URI:	http://wrap.warwick.ac.uk/id/eprint/3008