1. 458 Meta-population models and movement Fish 458; Lecture 18

2. 458 What is a Meta-population? A set of populations of the same species, usually more or less isolated from one another in discrete patches of spatially separate habitat, that may exchange individuals through migration.

3. 458 Examples of Meta-populations Abalone, rock lobster, coral reef fishes – linked by larval dispersal. Seals and sea lions – linked by juvenile and adult migration. Mountain sheep, spotted owl ….. Meta-population structure is less recognized for highly mobile fish species.

4. 458 A General Model The number in population i at the start of time-period t+1 depends on the number in population i at the start of time- period t less the number of emigrants plus the number of immigrants. Note that we may wish to complicate this model with environmental impacts, deaths after migration, etc. As always, one needs to list the assumptions before building the model.

5. 458 Region 1 Region 2 Region 3 Each connection implies more parameters! Harvest

6. 458 Isolation by Distance Model (discrete logistic case) Notes: The boundary is “reflective” – we could have developed a model where animals die if they try to migrate somewhere other than to another patch (an “absorptive” boundary). mmmm

7. 458 An Example of the Discrete Logistic Model The meta-population consists of seven populations (sites) linked through migration. For all sites K=1000 and r=0.4 The movement rate m is constant Only site 7 is harvested Low movement leads to collapse

8. 458 An Example of the Discrete Logistic Model Harvest rate 0 0.9 The impact of movement is to prevent extirpation of site 7

9. 458 Specifying a Meta-Population Model (some of the key specifications) Site-specific birth / death / growth processes? Density-dependence – at the site or population level / on what population component? Migration: density-dependent, age-related, distance-related? Environmental variation (correlated among sites – how?) Harvesting, when?

10. 458 Extending the Logistic Model Include harvesting at all sites. Allow different sites to have different K and r. Allow movement among non-adjacent sites. What about density-dependent migration? What about a reserve – can this increase yield?

11. 458 Adding Density-Dependent Migration-I Lets assume that movement only occurs when the population is close to its carrying capacity, i.e.: We could restrict movement to sites that are not close to their carrying capacities (but we won’t this time).

12. 458 Adding Density-Dependent Migration-II Note the change at high exploitation rates Whoops, the discrete approximation seems to lead to oscillations – why?

13. 458 Adding Density-Dependent Migration-III We can attack this problem assuming a continuous model: The Runga-Kutta method was used to do the integration.

14. 458 Adding Density-Dependent Migration-IV These results are qualitatively different from those based on the discrete model!

15. 458 Some Meta-Population Structures (baleen whales) Panmixia Common Breeding ground Complicated!

16. 458 Modeling dispersal-I Dispersal may be a function of: Density on the “source” site. Density on the “target” site. Distance between sites. Homing: Do dispersers join the population to which they disperse? Do they return to their original site?

17. 458 Modeling Dispersal - II Dispersal proportional to density on the “source” site: Dispersal rate increases linearly (or non-linearly) with density on the “source” site:

18. 458 Modeling Dispersal – III (Homing) Lack of homing is a common assumption when dealing with larval movement / settlement of juveniles but may not be appropriate for adults. Example: Northern bluefin tuna Movement between the east and west Atlantic shown through tagging. Age at maturity is 4 in the eastern Atlantic but 8 in the western Atlantic!

19. 458 Protected Areas: Objectives We can use meta-population models to examine the extent to which alternative protected area definitions satisfy the need for: Biodiversity conservation. Protection of spawning aggregations. Reduction of fishing mortality. Habitat protection. (Unfished) controls for scientific study. (Unfished) reserves to “generate” large / old animals for trophy exploitation. Increased yield outside of the reserve.

20. 458 Readings Burgman et al. (1993); Chapter 5. Quinn and Deriso (1999); Chapter 10.