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

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

Transposition and deletion (i = 2) TE Element deletion TE Replicative transposition No transposition or deletion TE Diploid cell:

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

Production of gametes (i = 2) TE 1 TE 2 TEs Diploid cell: Gametes:

Population size changes of An. gambiae in Mali, West Africa

What this means mathematically Use to calculate: TE extinction probabilities Mean and variance of host counts over time

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

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

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

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