Multi-gene-loci inheritance in resistance modeling.

Abstract:

:The ability of an organism to degrade harmful substances to less toxic compounds is referred to as metabolic resistance. The biochemical processes result in a shift of dose-response curves associated with the toxic substances. Hence, the development of metabolic resistance may cause great problems of managing pests and diseases by pesticides. We develop a polygenic fitness model capable of simulating the emergence of metabolic resistance. Within the model, polygenic inheritance is described by a new approach based on tensor products of heredity matrices. This is included as genetic submodel into the time-continuous population model for all possible biotypes. Evolution is acting on the parameters of dose-response curves, i.e., on the mortality rates and thus on the ED(50)-value. The resulting system of differential equations is analyzed with respect to polymorphic equilibria. Under a longterm application of only one mode of action the model produces a gradual shift of the mean dose-response curve of the population which is frequently observed in the field. Different scenarios of the development of metabolic resistance are demonstrated in numerical experiments.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Langemann D,Richter O,Vollrath A

doi

10.1016/j.mbs.2012.11.010

subject

Has Abstract

pub_date

2013-03-01 00:00:00

pages

17-24

issue

1

eissn

0025-5564

issn

1879-3134

pii

S0025-5564(12)00230-1

journal_volume

242

pub_type

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