Inferring population structure of Pacific harbor seals using multivariate state space models

Background/Question/Methods The multivariate state-space model (MSSM) is a flexible approach to modeling the dynamics of multiple subpopulations.  The increased flexibility leads to a greater suite of hypotheses that may be tested – adjacent subpopulations may share similar growth rates, they may be affected by similar stochastic patterns, and there is the potential for subpopulations to have adverse effects on their neighbors (e.g. competition).  Previous approaches to MSSMs have been limited in assuming that time series do not contain missing data – we expand on Kalman-based approaches, showing that structure may be inferred even when time series are short and contain missing values.  To illustrate the sensitivity of the approach, we apply the model to 5000 simulated data sets, examining the role of survey design and sampling frequency on bias.  As a test case, we apply the model to 11 time series of Pacific harbor seals collected over the last 30 years.  For management purposes, these time series have been grouped into 3 management units or stocks, largely based on US state boundaries.  We examine whether the data provide support for the current boundaries, or whether there is more support for alternative boundaries based on geography and distance between subpopulations. 

Results/Conclusions

 In our simulated data sets, we applied the recent ‘data cloning’ technique to obtain maximum likelihood estimates of parameters.  These estimates are robust to missing data, even when 50% of the observations are missing.  We also explored four alternative sampling schemes, and illustrate how survey design might affect parameter bias – specifically, random missing data appears to perform better than situations where surveys are continuous, and then stopped for long periods of time.  To assess data support for our harbor seal models, we use a modified version of AICc.  The data provide the most support for a model with independent subpopulations with equal observation error CVs and nearly equal growth rates.  The magnitude of process errors is estimated to vary widely between subpopulations, but there is no support for the variation being correlated between subpopulations.  These results provide a contrast to existing management boundaries, and the limited genetic data available.  Finally, we illustrate how confidence intervals may be estimated using the results from data cloning and simulation.