Modelling fish spatial dynamics and local density-dependence relationships: detection of patterns at a global scale

Abstract

A model is used to explore whether local density-dependent recruitment relationships can be observed when considering a larger scale. A virtual population of spawners is tracked within an artificial environment composed of cells. Spawners can move from one cell to another on a spatial grid defined as a square lattice (lattice scale) made of 20 × 20 jointed hexagonal cells (local scale). Five spawner's behaviours are experimented successively: i) spawners stay in the same cell to spawn; ii) they move randomly towards one of the neighbouring cells; iii) they move towards the least populated neighbouring cell; iv) they move towards the most populated neighbouring cell; and v) they move randomly towards a neighbouring cell and then move towards the most populated neighbouring cell. When the migration of spawners is achieved, spawners reproduce only once, recruitment takes place and then they disappear. The recruitment is an event which occurs at a local scale: at the scale of the cell. Using Ricker's stock-recruitment relationship, in each cell the number of recruits is a function of the spawners. Random migrations and migrations towards the less populated cell allow a homogeneous distribution of the spawners throughout the lattice. Whereas in the three other cases, this distribution is not homogenised. The homogenisation of the lattice allows synchrony between local populations and then a stock-recruitment relationship is observable at the lattice scale. Simulations show that local density-dependence is not always detectable when considering large spatial scale. This result strengthens the idea that the choice of spatial scale is essential when studying stock-recruitment relationship.