Successful conditions for the early spread of a TE in a disease vector population John Marshall, Department of Biomathematics, UCLA

transposasegene

effectorgene

IR 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)

v22

)1( 22 1

TE

Element deletion

TETE

TE

Replicative transposition

No transposition or deletion

22 2u

TE

TE

TE

TE

Diploid cell:

Repression of transposition

iu

))1(1( ibaui

i

Host fitness costs

dii 1

Sources:• Insertional mutagenesis• Ectopic recombination• Act of transposition

dii 1

i

Sources:• Self repression• Host repression

Transposition rate

TE copy number

Host death rate

iTE copy number

Production of gametes (i = 2)

0

2

2

12

2

2

2

12

TETE

TETE

TE

1 TE

2 TEs

0.5 -

0.25 -

0 -

Diploid cell:

Gametes:

1

2

2

12

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

What this means mathematically

}{1

1

11

2

1

)1(2

11

2

1

jii

ii

i

iii

iii

iij

j

i

j

i

j

if

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 < 1% for release size > 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 < 1 year for transposition rate > 0.0871 32

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