Rapid climate change:

• occurring over tens of generations
• different environment $\Rightarrow$ strong selective pressure

This talk: population genetics considerations.

What I'm not talking about:

• local adaptation
• plasticity
• genetic architecture
• population size dynamics
• interspecific interactions

What I am talking about:

• most organisms don't live on billiard tables

Questions

How does geography affect how adaptive variants

1. arise and

2. spread,

3. and how much variation is left afterwards?

Can adaptations spread?

• with moving environmental gradients
• or from locations of existing variants

Also relevant for:

• Do adaptive variants spread along wildlife corridors?
• What is the spatial resolution of adaptation?

Population genetics wants to know:

1. population size

   • availability of standing deleterious variation
   • influx of new mutations

2. strength of selection

   • probability of establishment of rare variants
   • rate of spread of adaptive variants

3. rate of genetic drift

   • rate of local loss of variation
   • probability of establishment of rare variants

these are affected by

geography ${}+{}$ dispersal ${}+{}$ temporal dynamics

Cal DFG; Todd Keeler-Wolf, CNPS (http://vegetation.cnps.org/)[http://vegetation.cnps.org/]

Zoomed-in (NVCS macrogroup):

Environmental niche models: (Biogeography Lab, UCSB)

Demographic model

• 200m grid
• equilibrium density: 0.4 (low) or 16 (high) / ha
• R package: github.com/petrelharp/landsim

demography(
    prob.seed = 0.2, fecundity = 100,
    pollen.migration = migration(
        kern = function (x) { exp(-sqrt(x)) },
        sigma = 300, radius = 1200, normalize = NULL ),
    seed.migration = migration(
        kern = "gaussian", sigma = 100,
        radius = 1200, normalize = 1 ),
    prob.germination = vital(
        function (N, ...) {
            out <- r0 / ( 1 + rowSums(N)/carrying.capacity )
            return( cbind( aa=out, aA=(1+s)*out, AA=(1+s)^2*out ) )
        },
        r0 = 0.01,  s = 0.05 ),
    prob.survival = 0.9,
    genotypes = c("aa","aA","AA")
 )

Wright's neighborhood size:

$$N_\text{loc} \propto \#\{ \text{ individuals within 1$\sigma$ } \},$$

where

• $\sigma$ is the dispersal distance
• individuals are haploid.

Local heterozygosity is $$H_0 \propto \frac{N_\text{loc}}{C + N_\text{loc}},$$ where $C$ depends on mutation rate and geometry.

(Barton, Depaulis, & Etheridge)

$N_\text{loc}$ at different scales depends on population density and amount of nearby habitat:

NVCS Macrogroup, central Mojave:

Creosote:

Blackbrush:

Wash:

Genetic drift:

$$\var[p_{t+1}|p_t]/p_t(1-p_t) \text{ against } N_\text{loc}$$

The probability of establishment of a single allele in a large population is $$p_\text{estab} \approx 2 s / \nu ,$$

• where $\nu$ is the strength of drift
• $s$ is growth rate when rare.

If $s < 1/N_\text{loc}$, local inbreeding may reduce $p_\text{estab}$.

Alleles that are advantageous when rare spread, like wildfire. (a "pulled" wave)

Continuous habitats

• speed: $\sigma \sqrt{2s}$ (Fisher/KPP)
  • $s$ is growth rate when rare
  • takes 1-10 generations to move a dispersal distance

• leptokurtic dispersal: patchy, accelerating (Mollison 1972)

• slowed by drift

Huygens principle: the wave has to go around barriers (Möbius, Murray, & Nelson 2015)

• tortuosity: ratio of length of curve to distance between its ends

Speeds in different habitats:

Spread in patchy habitats

• spread governed by arrival of migrants ${} \times p_\text{estab}$

• if gaps are totally uninhabitable (sparks carried by wind), depends on long distance dispersal

• if growth rate in gaps is $1-m$ (flammable but fire dies out) rate of migrant families is

  $$\propto e^{-x \sqrt{2m}/\sigma}$$

Both depend critically on dispersal mechanism.

• Adaptation in connected habitats depends on habitat shape, but only weakly.

• Adaptation is strongly affected by

  • connectivity
  • long-distance dispersal
  • population size
  • ecological interactions

Notes:

• Allee affects?
• Ubiquitous, polygenic variation?
• Many habitats are patchy: are they still connected?
• Shape of isolation by distance?

Thanks!

• Erik Lundgren (USC)
• Julie Evens (CNPS)
• Greg Suba (CNPS)

• R's GIS tools: sp, raster, rgeos, ...

• NSF: ABI

• Sloan Foundation

The R package: github.com/petrelharp/landsim