the evolution of self-fertilization when inbreeding depression is frequency-dependent pierre-olivier...

The Evolution of Self-FertilizationWhen Inbreeding Depression isFrequency-Dependent

Pierre-Olivier Cheptou and Ulf Dieckmann

Proc. R. Soc. Lond. B, in press

Primary Questions

What factors can drive the evolution of selfing rates in hermaphrodites?Cost of outcrossing: only 50% relatedness with offspringCost of selfing: inbreeding depression

Does it matter if inbreeding depression has frequency-dependent components?

What are the demographic conditions that lead to intermediate selfing rates?

Resident Dynamics and Inbreeding Depression

Resident population dynamicsttouttint NKNfRKNfRSN )]/exp()1()/exp()1([ 01

)1()( RcRaRf in )1()( RdRbRfout

)/)(exp()/)(exp()1(1 0 KNRf

KNRf

tout

tint

Resultant inbreeding depression

with and

Totalnumberof seeds

Fixed costof selfing

Variable costof selfing

Ricker-type density regulation

Mutant Dynamics and Evolutionary Singularity

Mutant population dynamics

)()(/))1(2log(

* 0

cbdadcN

R eq

*)1(**))1(log( 2

1

RdRbRS

N eq

ttouttnint NKNfRRKNfRSN )]/exp()11()/exp()1([ 2

101

Resultant evolutionary singularity

Three components: selfed zygotes outcrossed zygotes zygotes of other individuals produced by fertilization with exported male gametes

Selfed zygotes receive two gametes from their mother, whereas outcrossed zygotes receive only one.The number of male gametes used for self-fertilization is assumed to be negligible so thatthe selfing rate does not influence the export of male gametes.

with

Equilibrium Population Dynamics

General caseThe singular selfing rate is evolutionarily stable.

Density- and frequency-independent casea=b=c=d: No intermediate selfing rates.

Density-dependent casea=c, b=d: Intermediate selfing rates, but only ifinbreeding depression decreases with density.

Frequency-dependent caseE.g., b<a=d<c: Intermediate selfing rates, even ifinbreeding depression increases with density.

Intrinsic growth rate, S

Sing

ular

sel

fing

rate

Intrinsic growth rate, SSi

ngul

ar s

elfin

g ra

te

Conclusions

Considering frequency-dependent components of inbreeding depression drastically alters the predictions for the evolution of selfing rates.

In particular, intermediate selfing rates become evolutionarily feasible under equilibrium population dynamics.

Nonequilibrium population dynamics (deterministic demographic fluctuations and/or stochastic environmental fluctuations) resulting in fluctuating inbreeding depression further enhance the range of conditions that lead to intermediate selfing rates.