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.

The present study presents a method of assessing and fitting a stock-recruitment relationship. The method is based on a combination of an equilibrium production model and a yield per recruit model. It does not use recruitment data which are, in general, highly dispersed, but production data. Thus, the relationship obtained is not of the parametric form of classical stock-recruitment relationship such as those of the Beverton and Holt (1957) and Ricker (1954), however, in some cases, the resulting stock-recruitment curve resembles models currently used in fisheries science. It is interpreted as an expectation of the recruitment conditionally to stock spawning biomass and stock demographic structure. However, for some realistic values of the parameters, the curve thus obtained describes a loop which suggests that two different recruitment levels may be expected from the same stock spawning biomass level. This theoretical property is illustrated with simulations. As an illustrative example, the method is applied to North-West Atlantic gadoid stocks. The significance of the method, its originality, the validity of the underlying assumptions and their conceptual consequences are discussed.