Computation of fish larvae self-recruitment in using forward- and backward-in-time particle tracking in a Lagrangian model (SWIM-v2.0) of the simulated circulation of Lake Erie (AEM3D-v1.1.2)

Abstract. Accurately estimating self-recruitment (SR), which is the fraction of recruits at a location that originated locally, is fundamental to understanding population connectivity. Biophysical models typically compute SR by releasing larval particles from source locations and tracking them forward in time. However, forward-tracking studies employ a variety of particle-release strategies (random, constant, area-scaled or production-scaled), which often leads to ambiguous SR estimates. Using theoretical analysis supported by numerical simulations of Lake Whitefish (Coregonus clupeaformis) larvae in Lake Erie, we show that SR is inherently dependent on larval production at all source locations. As a result, SR cannot be computed unambiguously in forward-tracking models unless the true larval production is known and released from every source location. In contrast, empirical parentage-analysis studies estimate SR directly as the fraction of locally produced juveniles among those sampled at a settlement location, without quantifying larval production at all sources. Motivated by this, we computed SR using backward-in-time particle tracking from the settlement location. We demonstrate that SR estimated using backtracking is independent of the number of particles released, which provides considerable benefit; namely the use of any magnitude of particles released and eliminating the need to identify all contributing sources or their larval output. This reduces the effort required to estimate SR and provides a theoretically consistent basis for its calculation. Our findings provide a theoretical framework for estimating SR and highlight the advantages of applying backtracking models for studying larval dispersal and recruitment.