Efficient CPU-Optimized Parameter Estimation for Modeling Fish Schooling Behavior in Large Particle Systems

The schooling behavior of fish can be studied through simulations involving a large number of interacting particles. In such systems, each individual particle is guided by behavior rules, which include aggregation towards a centroid, collision avoidance, and direction alignment. The movement vector of each particle may be expressed as a linear combination of behaviors, with unknown parameters that define a trade-off among several behavioral constraints. A fitness function for collective schooling behavior encompasses all individual particle parameters. For a large number of interacting particles in a complex environment, heuristic methods, such as evolutionary algorithms, are used to optimize the fitness function, ensuring that the resulting decision rule preserves collective behavior. However, these algorithms exhibit slow convergence, making them inefficient in terms of CPU time cost. This paper proposes a CPU-efficient iterative (Cluster, Partition, Refine -- CPR) algorithm for estimating decision rule parameters for a large number of interacting particles. In the first step, we employ the K-Means (unsupervised learning) algorithm to cluster candidate solutions. Then, we partition the search space using Voronoi tessellation over the defined clusters. We assess the quality of each cluster based on the fitness function, with the centroid of their Voronoi cells representing the clusters. Subsequently, we refine the search space by introducing new cells into a number of identified well-fitting Voronoi cells. This process is repeated until convergence. A comparison of the performance of the CPR algorithm with a standard Genetic Algorithm reveals that the former converges faster than the latter. We also demonstrate that the application of the CPR algorithm results in a schooling behavior consistent with empirical observations.Comment: 10page

Population dynamic regulators in an empirical predator-prey system

Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, , in description of the predator dynamics. We derive theoretical conditions on , as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatory-prey system when exceeds a theoretically derived value . This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capelin.publishedVersio

Considerations for management strategy evaluation for small pelagic fishes

Management strategy evaluation (MSE) is the state-of-the-art approach for testing and comparing management strategies in a way that accounts for multiple sources of uncertainty (e.g. monitoring, estimation, and implementation). Management strategy evaluation can help identify management strategies that are robust to uncertainty about the life history of the target species and its relationship to other species in the food web. Small pelagic fish (e.g. anchovy, herring and sardine) fulfil an important ecological role in marine food webs and present challenges to the use of MSE and other simulation-based evaluation approaches. This is due to considerable stochastic variation in their ecology and life history, which leads to substantial observation and process uncertainty. Here, we summarize the current state of MSE for small pelagic fishes worldwide. We leverage expert input from ecologists and modellers to draw attention to sources of process and observation uncertainty for small pelagic species, providing examples from geographical regions where these species are ecologically, economically and culturally important. Temporal variation in recruitment and other life-history rates, spatial structure and movement, and species interactions are key considerations for small pelagic fishes. We discuss tools for building these into the MSE process, with examples from existing fisheries. We argue that model complexity should be informed by management priorities and whether ecosystem information will be used to generate dynamics or to inform reference points. We recommend that our list of considerations be used in the initial phases of the MSE process for small pelagic fishes or to build complexity on existing single-species models.publishedVersio

Population dynamic regulators in an empirical predator-prey system

Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, s, in description of the predator dynamics. We derive theoretical conditions on s, as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatoryprey system when s exceeds a theoretically derived value s > 0. This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capeli

Population dynamic regulators in an empirical predator-prey system

Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, , in description of the predator dynamics. We derive theoretical conditions on , as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatory-prey system when exceeds a theoretically derived value . This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capelin

Population dynamic regulators in an empirical predator-prey system

Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, T , in description of the predator dynamics. We derive theoretical conditions on T, as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatory-prey system when T exceeds a theoretically derived value T* > 0. This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capelin