the evolution of self-fertilization when inbreeding depression is frequency-dependent pierre-olivier...
DESCRIPTION
Resident Dynamics and Inbreeding Depression n Resident population dynamics n Resultant inbreeding depression with and Total number of seeds Fixed cost of selfing Variable cost of selfing Ricker-type density regulationTRANSCRIPT
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.