Random walk models for the movement and recruitment of reef fish larvae

Abstract

The factors influencing the movement and recruitment of settlement stage larvae are investigated using random walk models. Individual-based sensing and orientating abilities are included explicitly in the model. We consider 2 simple reef environment models consisting of a simple circular reef with and without a constant cross-current. The sensing ability of the larvae is modelled as either fixed or spatially dependent, together with a fixed orientating ability. The survival probability is found to be highly sensitive to both the sensing and orientating abilities of the larvae, as well as to the properties of the reef environment itself. KEY WORDS: Reef fish settlement · Larval swimming ability · Biased random walksResale or republication not permitted without written consent of the publisher

Modelling the dispersal of riverine fish larvae: from a raster-based analysis of movement patterns within a racetrack flume to a rheoreaction-based correlated random walk (RCRW) model approach

“…Instead of the bias introduced in Codling et al (2004), representing navigation to a specific target (e.g., reef), here a newly developed, rheoreactive bias of movement has been implemented in the new model concept. Vertical swimming has not yet been considered.…”

“…The model inherits four larval movement patterns, and larval durations within these patterns, which were evaluated within the flume experiment, and it estimates these movement patterns and their durations for individual larvae over simulation time T. For the RCRW model, we also modified the concept of the BCRW model, developed by Codling et al (2004), to enable accordance with the actual movement patterns (rheoreaction). The RCRW model was coded in JAVA as an additional tool within the software of the 3D hydrodynamic model RSim-3D (Tritthart 2005; Tritthart and Gutknecht 2007).…”

“…Vertical velocity fluctuations u3=(t) in the direction of z were not considered. Codling et al (2004) introduced a BCRW model for the movement and navigation of fish larvae toward a reef. A Poisson distribution (1/ s ϳ P( ), 1/ s ʦ Z ϩ ) regulates the frequency of changing movement directions, where s represents the instantaneous time period between direction changes.…”

“…For horizontal swimming, the BCRW approach according to Codling et al (2004) was modified with respect to movement direction and magnitude of swimming speed |S|͑t͒ to account for rheoreaction over longer time periods and greater extents (10 s to minutes and areas with a minimum size of grid cells (0.10 m × 0.10 m), respectively). Instead of the bias introduced in Codling et al (2004), representing navigation to a specific target (e.g., reef), here a newly developed, rheoreactive bias of movement has been implemented in the new model concept.…”

“…The latter have become a focus in studies on biased and correlated random walk (BCRW) models by using either fixed compass directions (Béguer-Pon et al 2015) or environmental cues, for example, ambient reef sound (Staaterman et al 2012;Codling et al 2004;Werner et al 1993) or prey occurrence (Matanoski and Hood 2006). Relating to reef sounds, Staaterman et al (2012) linked the navigation approach from Codling et al (2004) with a three-dimensional (3D), coupled biophysical model (Paris et al 2013) and found higher settlement rates for oriented larvae. Models of larval fish dispersal patterns within riverine ecosystems are rare (e.g., Wolter and Sukhodolov 2008;Korman et al 2004;Cowan et al 1993).…”