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Highlights • A model of engineered underdominance (UD) gene drive is proposed. • Numerical results suggest that UD could be an effective tool for disease control. • Success/failure of UD is affected by release strategy and fitness of mosquitoes. • A single release of only males with weakly suppressed lethals cannot succeed., Engineered underdominance is one of a number of different gene drive strategies that have been proposed for the genetic control of insect vectors of disease. Here we model a two-locus engineered underdominance based gene drive system that is based on the concept of mutually suppressing lethals. In such a system two genetic constructs are introduced, each possessing a lethal element and a suppressor of the lethal at the other locus. Specifically, we formulate and analyse a population genetics model of this system to assess when different combinations of release strategies (i.e. single or multiple releases of both sexes or males only) and genetic systems (i.e. bisex lethal or female-specific lethal elements and different strengths of suppressors) will give population replacement or fail to do so. We anticipate that results presented here will inform the future design of engineered underdominance gene drive systems as well as providing a point of reference regarding release strategies for those looking to test such a system. Our discussion is framed in the context of genetic control of insect vectors of disease. One of several serious threats in this context are Aedes aegypti mosquitoes as they are the primary vectors of dengue viruses. However, results are also applicable to Ae. aegypti as vectors of Zika, yellow fever and chikungunya viruses and also to the control of a number of other insect species and thereby of insect-vectored pathogens.

The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics.

Although evolution of sterile castes in social insects has been extensively studied, the differences between worker and soldier castes have not been addressed sufficiently. It is suggested here that the evolution of worker and soldier castes must be considered in terms of different trade-offs, specifically, the different relations between benefits and costs of sterility. An individual should be a sterile worker if the genetic gain of raising its sibling is higher than the genetic cost of losing its own offspring, while an individual should be a sterile soldier if the sacrifice of its own life is genetically compensated for by survival of other family members. Using these different conditions for evolution of sterility, caste distribution among existing eusocial insects can be explained by a difference in genetic systems: Aphids and a parasitic wasp with asexual reproduction have only the soldier caste; wasps, bees, and ants with male-haploidy have mainly the worker caste; and termites with diploidy have dominantly the soldier caste.

The evolution of dominance is both the simplest and best investigated example of the evolution of genetic systems. Nevertheless, there exists striking empirical material, e.g. industrial melanism, for which no satisfactory explanation could so far be provided. In this paper we take an approach to this classical problem based on a global analysis together with computer simulations. It reveals that during the evolution of dominance one has to distinguish a "nonequilibrium phase" and a "Fisherian phase". The non-equilibrium phase appears to be characterized by the fact that in general the selection intensity at the primary locus does not affect the degree of modifier selection but only the time necessary for passing through this phase. A further essential conclusion is that modifier evolution only obtains a reasonable amount of efficiency if the population reaches the Fisherian phase already with a high modifier frequency. Using these results, predictions on the population genetic prerequisites for the evolution of dominance are derived. From these we conclude that even in populations in which dominance evolution has occurred it cannot be expected that back-crosses into relics of the ancestral population lead to a breakdown of dominance within a few generations. These predictions are in accordance with empirical data on Biston betularia and Odontopera bidentata.

The properties of genetic networks based on a variant of Jacob-Monod type feedback-repression have been examined using digital computer simulation. Single gene loops do not seem feasible as oscillators, but networks with an odd number of genes connected cyclically oscillate over a wide range of conditions.

The effects of normalizing selection on populations containing inversions has been simulated for a six locus genetic model. The results show that co-adaptation to form a stable inversion polymorphism will only occur if the inversion is introduced at a frequency greater than 0·12. Over-dominance has been shown not to be a necessary feature of inversion polymorphism. The accession to stable polymorphism involves a newly-formed inversion having an additive advantage which is sufficient to result in an increase in frequency up to 12%, when the process of co-adaptation begins, resulting in the evolution of stable polymorphism.

A phenotype system is a mapping of a set of genotypes into a set of phenotypes. Two phenotype systems are permutationally equivalent if some permutation or combination of permutations of gene symbols or locus symbols makes them identical. A set of permutationally equivalent phenotype systems is called a phenogram . Two mappings of a set D into a set R are said to be equivalent and to belong to the same pattern if the first mapping performed on some permutation of D is identical to the second performed in conjunction with some permutation of R . Thus the number of phenotype systems which are identical under some permutation of gene or locus symbols is precisely the number of patterns of phenotype systems. De Bruijn's extension of Polya's fundamental counting theorem, which enumerates the number of patterns, is introduced in terms sufficiently general to allow its application to other biological enumeration problems. The theorem is used to solve the general phenogram enumeration problem, i.e. given any genetic system whatever, how many phenograms are there with exactly φ phenotypes? The results of calculations for several basic genetic systems are presented, along with some observations on these. A nomenclature which simplifies the presentation of two locus systems showing epistasis is suggested. Several applications of phenogram analysis are discussed.

The effects of intense normalizing selection have been studied, using computer simulation, for models of 3, 4, 5, 6, 8, 12 and 24 loci. The effectiveness of such selection in reducing heterozygosity decreases with increase of the number of loci to a limit that is only slightly greater than that consequent from random genetic dispersion, if the loci are freely recombining. Tight linkage markedly reduces the rate of loss of heterozygosity for small numbers of loci, but this effect of tight linkage decreases with increase of the number of loci.

The evolutionary dynamics in general two-sex two-phenotype frequency-dependent selection models are studied with respect to underlying multi-allele one-locus genetic systems. Two classes of equilibria come into play: genotypic equilibria, with equilibrium allelic frequencies independent of the phenotype, and phenotypic equilibria, which are characterized by equal mean phenotypic fitnesses. The exact conditions for genotypic equilibria to exist and be stable and for phenotypic equilibria to exist and be evolutionarily attractive are examined. Using adequate definitions of mean fitnesses in general contexts of frequency-dependent selection in dioecious populations, we show that two phenotypes, when they can coexist in the population, tend to balance their fitnesses as far as is allowed by the genetic system as more alleles responsible for phenotype determination are introduced into the population.