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Successful conditions for the early spread of a TE in a disease vector population John Marshall, Department of Biomathematics, UCLA transposase gene effector gene IR
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Requirements for a successful control strategy: 1.Element loss probability: < 1% 2.Rate of element spread: reach 10% prevalence in < 1 year Question: What conditions satisfy these requirements? Replicative transposition rate Reduction of transposition rate with additional TE copies Fitness cost of TE copies Rate of population growth/decline Release size Time of release TE copy number of released mosquitoes
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Transposition and deletion (i = 2) TE Element deletion TE Replicative transposition No transposition or deletion TE Diploid cell:
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Repression of transposition Host fitness costs Sources: Insertional mutagenesis Ectopic recombination Act of transposition Sources: Self repression Host repression Transposition rate TE copy number Host death rate TE copy number
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Production of gametes (i = 2) TE 1 TE 2 TEs 0.5 - 0.25 - 0 - Diploid cell: Gametes:
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Population size changes of An. gambiae in Mali, West Africa
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What this means mathematically Use to calculate: TE extinction probabilities Mean and variance of host counts over time
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Optimal release time is end of dry season/beginning of rainy season Optimal release at beginning of population growth phase Bias towards release later rather than earlier
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TE loss probabilities vs. transposition rate vs. release copy no. vs. release size Release size has the greatest influence on TE loss probability Loss probability is 25
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No. transgenic hosts vs. time Almost all An. gambiae only have a single TE copy in the early stages of spread Transposition rate has the greatest influence on rate of TE spread TE reaches 10% prevalence in 0.087 132
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Model conclusions Transposition rate: Most efficient way to increase rate of element spread Recommend transposition rate > 0.1 per element per generation Release size: Most efficient way to reduce loss probability Recommend release size > 50 Fall off of transposition rate with increasing copy number: Recommend focus on transposition rate and fitness cost when there is only a single element in the genome
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