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

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

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

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

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

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

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

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

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

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

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

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

Results: Population growth Exponential growthLogistic growth

Carrying capacity and spatial distribution Exponential Logistic

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

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.