Post on 17-Jan-2016
description
Brian KinlanUC Santa Barbara
Integral-difference model simulations of marine population genetics
Population genetic structure
-Analytical models date back to Fisher, Wright, Malecot 1930’s -1950’s
-Neutral theory
-Can give insight into population history and demography
-Many simplifying assumptions
-One of the most troublesome – Equilibrium
-Simulations to understand real data?
Glossary
Allele
Locus
Heterozygosity
Polymorphism
Deme
Marker (e.g., Allozyme, Microsatellite, mtDNA)
Hardy-Weinberg Equilibrium
Genetic Drift
Measuring population structure
-F statistics – standardized variance in allele frequencies among different population components (e.g., individual-to-subpopulation; subpopulation-to-total)
FST = 1 - (HS/HT)
Population structure
vs.
t=0; no structuret=500; structure
Inferring Migration from Genetic Structure: Island Model
Fst = 1/(1+4Nm)
Nm = ¼ (1-Fst)/Fst
Limitations
I. Assumptions must be used to estimate Nm from Fst
For strict Island Model these include:
1. An infinite number of populations 2. m is equal among all pairs of populations 3. There is no selection or mutation 4. There is an equilibrium between drift and migration
“Fantasy Island?”
Lag Distance
Sta
nd
ard
ized
Var
ian
ce
Am
on
g P
op
ula
tio
ns
-Differentiation among populations increases with geographic distance (Wright 1943)
-Dynamic equilibrium between drift and migration
Inferring Migration from Genetic Structure: Isolation-by-Distance (IBD)
Palumbi 2003 - Simulation Assumptions
Palumbi, 2003, Ecol. App.
1. Kernel
3. Effective population size
2. Gene flow model
Ne = 1000 per deme
Linear array of subpopulations
Pro
bab
ility
of
dis
per
sal
Distance from source
Laplacian
Calibrating the IBD Slope to Measure Dispersal
Palumbi 2003 (Ecol. App.)
-Simulations can predict the isolation-by-distance slope expected for a given average dispersal distance (Palumbi 2003 Ecol. Appl., Kinlan and Gaines 2003 Ecology)
Kinlan & Gaines (2003) Ecology 84(8):2007-2020
Genetic Estimates of Dispersal from IBD
Genetic Dispersion Scale (km)
Mod
ele
d D
isp
ers
ion
Sca
le,
Dd
(km
)
From Siegel, Kinlan, Gaylord & Gaines 2003 (MEPS 260:83-96)
But how well do these results But how well do these results hold up to the variability and hold up to the variability and complexity of the real-world complexity of the real-world
marine environment?marine environment?
Basic Integro-difference model of population dynamics
A Adult abundance [#/km]
M Natural mortality
H Harvest mortality
F Fecundity
P Larval mortality
L Post - settlement recruitment
K Dispersion kernel
xt
x
x'
x
x x'
[spawners / adult]
[larvae / spawner]
[adult / settler]
[(settler / km) / total settled larvae]
A 1 M A A F K L dxxt 1
xt
xt
x x x x
( ) '' ' '
A Adult abundance [#/km]
M Natural mortality
F Fecundity
K Dispersion kernel
xt
x'
x x'
[spawners / adult]
[(settler / km) / total settled larvae]
L Post - settlement recruitmentx [adult / settler]
(Ricker form L(x) e-CA(x))
Avg Dispersal = 10 km; Domain = 1000 km; Spacing = 5 km; 1000 generations; Ne=100
…Add genetic structure
Model Features
-Coupled population dynamics & genetics
-Temporal variation – mortality, fecundity, dispersal, settlement
-Spatial heterogeneity – barriers, variable mortality, fecundity, dispersal, settlement
-Timescales of adult & juv. movement & reproduction flexible (larval pool, discrete or overlap generations)
-Initial distribution flexible; can study range expansions or stable pops, founder effects
-Different genetic markers – effect of mutation rate, mutation model, number of loci, selection (future)
Avg Dispersal = 12 km
Domain = 1000 km
Spacing = 5 km
1000 generations
Ne~100
Q1: How fast does IBD slope approach equilibrium?
Avg Dispersal = 10 km; Domain = 1000 km; Spacing = 5 km; 1000 generations; Ne=100
t=20
t=200
t=1000
Avg Dispersal = 12 km; Domain = 1000 km; Spacing = 5 km; 1000 generations; Ne=100
Palumbi model prediction
Dd= 12.6 km
t=20
t=200
t=1000
Avg Dispersal = 12 km; Domain = 1000 km; Spacing = 5 km; 1000 generations; Ne=100
Palumbi model prediction
Dd= 38 km t=20
t=200
t=1000
Avg Dispersal = 2 km; Domain = 100 km; Spacing = 5 km; 800 generations; Ne=100
t=20
t=400
t=800
Avg Dispersal = 2 km; Domain = 100 km; Spacing = 5 km; 800 generations; Ne=100
t=20
t=400
t=800Palumbi model prediction
Dd= 1.6 km
Diverging Currents
Spatial Pattern of AbundanceT=300 years; Mortality = 0.5 (mean lifespan = 2 years); Reproduction every year; 75 populations spaced 20 km apart over 1500 km of coast
U= 10 cm/s; σu=12 cm/s
U= 10 cm/s; σu=12 cm/s
Dispersal: approximates an organism with 30 day PLD in a mean flow of 10 cm/s with a velocity variance of 12 cm/s (based on Siegel et al. 2003)
Currents diverge at the midpoint (but there is some exchange across this point due to eddies and flow reversals represented by the velocity variance).
Pairwise Fst vs. DistanceAfter T=10 (green), 50 (red), and 300 (black) yearsMean ± 1 SE of Fst across all possible pairs at each distance lag
T=300
T=50
T=10
Spatial Pattern of Allelic RichnessAfter T=300 years1 Microsatellite Locus (mutation rate = 1e-03; initial number of alleles = 10; symmetric stepwise mutation model)
Spatial Pattern of Genotype Presence/AbsenceAfter T=300 years1 Microsatellite Locus (mutation rate = 1e-03; initial number of alleles = 10; symmetric stepwise mutation model)
Converging Currents
Strong Convergent Flow
LOCUS 1 (3 alleles) LOCUS 2 (2 alleles)
Unidirectional Currents
Current
Mean drift = +15km
Std = 5 km
Strong Unidirectional Mean Flow
2 km spacing on 300 km domain
t=20,60,100
Ne~1000
LOCUS 1 (2 alleles) LOCUS 2 (2 alleles)
Dispersal Barriers
Dispersal Barriers
X (km) Lag distance (km)
Nu
mb
er o
f in
div
idu
als
Abundance vs. Space IBD
Dispersal Barriers
Figure 1: Using a numerical gene-tracking integro-different model with a step-wise stochastic mutation rate at 3 loci, pairwise genetic distance (GST, (Nei 1973) patterns after stability for a 500-km coastline allowing for panmixia (A), and asymmetrical dispersal across a “border” placed in the center of the coastline (B). As expected (Rousset 1997b), pairwise genetic distance plateaus over large distances. The decline at greater distance lags is likely attributable to the asymmetrical barrier.
-100 -50 0 50 100 150 200 250 300 3500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
U = 5 Ustd = 15 To = 14 T
f = 21
tota
l set
tlers
= 1
3 t
otal
par
t =
100
alongcoast (km)
-Next stepsNext steps Spiky kernels?Spiky kernels?Fishing effects?Fishing effects?
MPA’s?MPA’s?