Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "Examining the interaction of density dependence and stochastic dispersal over several life history scenarios Heather Berkley Bruce Kendall David Siegel."— Presentation transcript:

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

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

3 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)

4 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)

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

6 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

7 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

8 Parameter Combinations MPocDispDStability 10.0511010.099997700.5long lifespan, PLD ~ 5 days, monotonic 20.51.360.01000632700.5short lifespan, PLD ~ 5 days, monotonic 30.0511010.0999972300.5long lifespan, PLD ~ 50 days, monotonic 40.51.360.010006322300.5short lifespan, PLD ~ 50 days, monotonic 50.510.0430.0300002370-0.5short lifespan, PLD ~ 5 days, oscillating 60.510.0430.03000023230-0.5short lifespan, PLD ~ 50 days, oscillating 70.055.34E+110.2999995670-0.5long lifespan, PLD ~ 5 days, oscillating 80.055.34E+110.29999956230-0.5long lifespan, PLD ~ 50 days, oscillating

9 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

10 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

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

12 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

13 Parameter Combination #4 Ndraw=20 Short-lived

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

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

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

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

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

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

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

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

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

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

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


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

Similar presentations


Ads by Google