Source-Sink Reconstruction Through Regularized Multicomponent Regression Analysis—With Application to Assessing Whether North Sea Cod Larvae Contributed to Local Fjord Cod in Skagerrak

Abstract

The problem of reconstructing the source-sink dynamics arises in many biological systems. Our research is motivated by marine applications where newborns are passively dispersed by ocean currents from several potential spawning sources to settle in various nursery regions that collectively constitute the sink. The reconstruction of the sparse source-sink linkage pattern, that is, to identify which sources contribute to which regions in the sink, is a challenging task in marine ecology. We derive a constrained nonlinear multicomponent regression model for source-sink reconstruction, which is capable of simultaneously selecting important linkages from the sources to the sink regions and making inference about the unobserved spawning activities at the sources. A sparsity-inducing and nonnegativity-constrained regularization approach is developed for model estimation, and theoretically we show that our estimator enjoys the oracle properties. The empirical performance of the method is investigated via simulation studies mimicking real ecological applications. We examine the transport hypothesis that Atlantic cod larvae were transported by sea currents from the North Sea to a few exposed coastal fjords along the Norwegian Skagerrak. Our findings of the spawning date distribution is consistent with results from previous studies, and the proposed approach for the first time provides valid statistical support for the larval drift conjecture. Supplementary materials for this article are available online.