Examining the interaction of density dependence and stochastic dispersal over several life history scenarios Heather Berkley Bruce Kendall David Siegel

Main Question How does stochastic dispersal & demography interact to affect spatial & temporal variability in populations?

Future additions to the F 3 model Types of density dependence:  Recruitment rate depends on adult density  Production rate depends on adult density  Adult mortality depends on adult density  Production rate depends on adult density Size & Age Structure  Increasing time to maturity  Increasing fecundity with age or size Adult movement Variability in habitat quality (spatial & temporal)

Characterizing the existing model Parameters that potentially impact variability in populations:  Type of density dependence: Recruitment rate depends on adult density  Mortality  Productivity  Dispersal Distance  Ndraw (number of draws from the kernel)

Equations Model without harvest: At equilibrium (N t = K): For stability analysis:

Set Parameters We chose the following values:  Mortality: 0.5, based on lifespan of 2 years 0.05, based on lifespan of 20 years  Fixed kernel dispersal distance based on PLD: 70 km, based on PLD of 5 days 230 km, based on PLD of 50 days

Calculated Parameters Productivity (P 0 ) is calculated from value of M & by setting Eqn. for stability to monotonic (+0.5) or oscillating (-0.5) approach to stability Density dependent term (c) is calculated by setting carrying capacity equation to 100 and given values of M and P 0

Parameter Combinations MPocDispDStability long lifespan, PLD ~ 5 days, monotonic short lifespan, PLD ~ 5 days, monotonic long lifespan, PLD ~ 50 days, monotonic short lifespan, PLD ~ 50 days, monotonic short lifespan, PLD ~ 5 days, oscillating short lifespan, PLD ~ 50 days, oscillating E long lifespan, PLD ~ 5 days, oscillating E long lifespan, PLD ~ 50 days, oscillating

Model Settings & Calculations Domain:  Absorbing boundaries  3000 km, used only middle section  Patches = 5km Spatial variance calculated at last time step (100 yrs) over 300 patches Temporal variance calculated for last 50 years  Local: for each patch  Total Population: for whole population (all 300 patches) Autocorrelation (lag 1 only)  Spatial  Temporal Local Total Population Over a range of Ndraw values Values averaged over 50 simulations

Stochastic Dispersal Ndraw  For small values of Ndraw, each patch only sends out a few groups of larvae to other locations At the receiving patch, the time between receiving larvae groups can be very long For short-lived adults, natural adult mortality can drive the population extinct until it receives a new group of larvae  For large values of Ndraw, each patch is interacting with almost all other patches Receiving patches should get larvae from many other patches each year

Adult Population Ndraw=10 Long-Lived Short-lived Short-lived, oscillating Distance (km)

Short-lived, oscillating Short-lived, monotonic Long-lived Short-lived, short PLD Short-lived, long PLD Long-lived, short PLD Long-lived, long PLD Short-lived, short PLD, oscillating Short-lived, long PLD, oscillating

Parameter Combination #4 Ndraw=20 Short-lived

Population Size Short-lived Long-lived Short-lived, oscillating

Spatial Variance Short-lived Long-lived Short-lived, oscillating

Spatial Coefficient of Variation Short-lived Long-lived Short-lived, oscillating

Temporal Variance (local) Short-lived Long-lived Short-lived, oscillating

Temporal Coefficient of Variation (local) Short-lived Long-lived Short-lived, oscillating

Temporal Variance (population) Short-lived Long-lived Short-lived, oscillating

Temporal Coefficient of Variance (population) Short-lived Long-lived Short-lived, oscillating

Spatial Autocorrelation Short-lived Long-lived Short-lived, oscillating

Temporal Autocorrelation (local) Short-lived Long-lived Short-lived, oscillating

Temporal Autocorrelation (population) Short-lived Long-lived Short-lived, oscillating

Next Steps Add other forms of density dependence Age/Size Structure Adult Movement Spatial/Temporal variability in habitat quality