Inferring spatial structure from time‐series data: using multivariate state‐space models to detect metapopulation structure of California sea lions in the Gulf of California, Mexico

Summary 1. Understanding spatial structure and identifying subpopulations are critical for estimating population growth rates and extinction risk, and as such essential for e!ective conservation planning. However, movement and spatiotemporal environmental data are often unavailable, limiting our abilitytodirectlydefine subpopulations and theirlevel of asynchrony. 2. This study applies a recently developed statistical technique using time-series analysis of abundance data to identify subpopulations. The approach uses multivariate state-space models and Akaike’s Information Criterion-based model selection to quantify the data support for di!erent subpopulation numbers and configurations. This technique is applied to the population of CaliforniasealionsZalophuscalifornianusintheGulfofCalifornia, Mexico, distributedacross13breeding sites. 3. The abundanceof California sea lions in the Gulfof California has declinedover the lastdecade, though not all areas have been equally a!ected. In light of this variation, it is important to understandthepopulation structuretoensureaccurateviabilityassessmentsand e!ectivemanagement. 4. Ourdatasupportthehypothesisthatthe GulfofCaliforniasealion population hasfoursubpopulations, each with 2‐5 breeding sites. The dynamics between several adjacent subpopulations were correlated, suggesting that they experience similar environmental variation. For each subpopulation,weestimatedlong-termgrowthrates,aswell astheenvironmental andobservationvariation. 5. For most of the subpopulations, our estimates of growth rates were considerably lower than those previously reported. In addition, we found considerable variability across subpopulations in theirprojectedriskof severedeclineoverthe next 50 years. 6. Synthesis and applications. We illustrate a new multivariate state-space modelling technique that usestimeseriesofabundancetoquantifythedatasupportfordi!erentsubpopulationconfigurations. OuranalysisoftheCaliforniasealionpopulationintheGulfofCaliforniaindicatesthatthepopulationisspatiallystructuredintofoursubpopulations,eachexhibitingdistinctrisksofextinction.Based on our results, we recommend that conservation and management e!orts in the Gulf of California focus on the two subpopulations with high probabilities of extinction within the next 50 years (NorthernMidri!,SouthernMidri!).Multivariatestate-spacemodelsprovideapracticalapproach to determine the spatial structure of virtually any species; they may be particularly useful for species ofconservationconcernforwhichdataondispersalandenvironmentaldriversarelikelytobescarce.

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