Multi-gene-loci inheritance in resistance modeling

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 ED50-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.

► We model metabolic resistances by multi-gene-loci inheritance and growth in time.
► A new tensor-product approach for heredity matrices handles multiple gene loci.
► Resistance development is a shift in a continuum of stationary solutions.
► Polymorphic equilibria are isolated solutions, and shortterm resistances fade out.
► Numerical scenarios of multi-gene-loci inheritances give new types of resistances.