1. Modeling the Re-invasion of Sea Otters along the Coast of California M.J. Krkosek J.S. Lauzon

2. A Little History… Thought extinct in the early 1900’s Small population of 50 found in 1914 Began to re-invade former range

3. Life History Occupies rocky coastline habitat less than 40 meters deep Live in “rafts” of 4 to 40 individuals Females have one pup a year, in the spring Pups wean after 4 months and take 5 years to reach reproductive maturity Feed primarily on sea urchins

4. Scale and Independence of Data Lubina & Levin’s Model Re-invasion Data Krkosek & Lauzon’s Model Independent Life-history & Dispersal data Re-invasion Data Models of California Sea Otters Re-invasion

5. Lubina and Levin’s Model One-dimensional Diffusion Model Rate of Invasion Growth function Diffusion r: intrinsic rate of increase D:diffusion coefficient Assumes random movement Rate of invasion is constant

6. Our Model Based on life history and spatial use data independent of invasion Begin with a stage structured growth model Eigenvalue = intrinsic growth rate Eigenvector = stable stage distribution Leslie Matrix

7. Incorporate Spatial Dynamics Stage-structured integro-difference equations Dispersal Kernel

8. What is a Dispersal Kernel? Frequency distribution of dispersal distances Types: Normal, leptokurtic, …

9. How do you parameterize a kernel?  2 = 2D, where D = M 2  /(4t) and M = mean displacement per time  = find by least squares fit to a density distribution of annual displacement

10. Results: How does the kernel affect the rate of spread? Gaussian Linear spread Fat Tailed Kernels exponential spread

11. A closer look at exponential spread  = 3.4598  = 3.7 (south)  = 5.2 (north) km

12. Results: Population growth Exponential growthLogistic growth

13. Carrying capacity and spatial distribution Exponential Logistic

14. So how do we compare? Lubina & Levin r = 0.056 D = 13.5 – 104 km 2 /yr Spread = piecewise linear Krkosek & Lauzon r = 0.0631 D J = 76.75 km 2 /yr D A = 15.55 km 2 /yr Spread = exponential Growth = logistic Population size vs time Population spread vs time

15. Conclusion We have shown that independent small scale data on sea otter life history and spatial movement can predict large scale patterns in population growth and dispersal. Due to their discrete nature, life history characteristics of sea otters are better described by integro-difference equations than by diffusion equations. Integro-difference equations appear to accurately predict growth and dispersal patterns of re-invading sea otters along the California coast.

16. References Eberhardt, L.L., 1995. Using the Lotka-Leslie model for sea otters. Journal of Wildlife Management, 59(2): 222-227. Kot, M., M.A. Lewis, and P. van den Driessche, 1996. Dispersal data and the spread of invading organisms. Ecology, 77(7): 2027-2042. Laidre, K.L., R.J. Jameson, and D.P. DeMaster, 2001. An estimation of carrying capacity for sea otters along the California coast. Marine Mammal Science, 17(2): 294-309. Lewis, M.A., 1997. Variability, patchiness, and jump dispersal in the spread of an invading population. in: Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions (D. Tilman and P. Kareiva, eds). Princeton University Press, Princeton, New Jersey. Lubina, J.A. and S.A. Levin, 1988. The spread of a reinvading species: Range expansion in the California sea otter. American Naturalist, 131(4): 526-543. Monnett, C., and L.M. Rotterman, 2000. Survival rates of sea otter pups in Alaska and California. Marine Mammal Science, 16(4): 794-810. Monson, D.H., and A.R. DeGange, 1995. Reproduction, preweaning survival, and survival of adult sea otters at Kodiak Island, Alaska. Canadian Journal of Zoology, 73(6):1161-1169. Ralls, K, T.C. Eagle, and D.B. Siniff, 1996. Movement and spatial use patterns of California sea otters. Canadian Journal of Zoology, 74(10): 1841-1849. Riedman, M.L., J.A. Estes, M.M Staedler, A.A. Giles, and D.R. Carlson, 1994. Breeding patterns and reproductive success of California sea otters. Journal of Wildlife Management, 58(3): 391-399. Udevitz, M.S., and B.E. Ballachey, 1998. Estimating survival rates with age-structure data. Journal of Wildlife Management, 62(2): 779-792.