A model of complete underdominance that applies to population replacement for insect control by compound autosomes or compound; free arm strains, has been used to develop a new technique for estimating fitness and generation time in continuously-breeding competing populations, without resorting to measurement of birth rate, survivorship etc. The method is statistical and uses successive intervals of various sizes in an estimation equation. Estimates of fitness and generation time are revealed as a result of convergence of data from competitions in which a strain either becomes fixed or is eliminated in a mixed population. The technique has been applied to data from Drosophila melanogaster cage competitions with believable results. Difficulties resulting from the frequency dependence of the estimates over time and the inherent cyclicity of the population competition data are evaluated. Fitness estimates from this method of successive intervals are lower than those from another unstable equilibrium method. The former technique measures fitness in population at carrying capacity in which density-dependence is prominent, whereas the latter method is applicable only to populations in which density-dependence is negligible. The implications to insect control of an estimation procedure which yields fitness values for continuously-breeding populations under conditions of density dependence are discussed.
The possible role of cytoplasmic sex ratio (SR) distortion in insect population control has been assessed experimentally.In Drosophila melanogaster the agent responsible for SR distortion is a male-killing spiroplasma and SR strains are characterized by females producing daughters but few, if any, sons. Populations were constructed of wildtype and SR females (of various malekill effectivenesses) plus males, in different proportions.The frequency of females in the populations was monitored regularly.Under some circumstances the frequency of females increased but not to fixation or population collapse. In most instances the frequency of females declined (to as low as 25% in some cases), then went through cycles of increase and decrease, with gradually reduced amplitude over time. This pattern of fluctuations was repeatable over cages.Independently, it was shown that SR females persisted in the cages for the length of the experiments. The unexpected extremely low frequencies of females found in cages established with an excess of females, raised the possibility of distorting a population by SR releases, and then when the female frequency is at its lowest point to add sterile male or similar load inducers to suppress the population. The possible role of density dependence is discussed.
A new model for use in theoretical and practical studies of egg production is derived: N(t) = (1−e−ξ(t–to))e−α(t–tq), where N(t) is the number of eggs laid on day t; ξ is the rate of increase in egg production; α is the rate of decrease in egg production; to is the day of initiation of egg-laying; tq is the day of cessation of egg-laying. Egg production curves for Drosophila melanogaster strains were fitted using non-linear least squares regression analyses such that all parameters in the model and their errors were generated simultaneously. The goodness-of-fit of the model to the observed data was precise. The experimental evidence showed that parameters α and tq were basically describing the genetic components of egg production in females whereas parameters ξ and to exhibited additional components, the interactions between males and females. Expressions derived from the model, tmax, the time of maximum production, N(tmax), the maximum production at this time and T(to,tq), the production over lifetime, gave results consistent with the observations.
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