# Setting Base Effort

Carl J. Walters

Ecospace attempts to predict the spatial distribution of fishing effort in relation to changes in profitability of fishing in different cells and policy changes such as marine protected areas and seasonal closures. It predicts the fishing effort Eijg by gear g in spatial cell i,j at each time step by using a gravity ^{[1]} or logit choice model, which apportions total effort Eg for the gear using proportions by cell pgij

[latex]E_{gij}=E_g p_{gij} = E_g \frac{A_{gij}}{\sum \limits_{ij}A_{gij}} \tag{1} \label{eq1}[/latex]

Here, Agij is an attraction weight for cell i,j that depends on the relative profitability of fishing in that cell. Profitability for cell i,j is predicted from prices and abundances of species taken by the gear, spatial cost factors, whether the gear can operate in the habitat type set for the cell, and whether or not the cell is open to fishing by gear type g. Note that the proportions [latex]p_{gij}=A_{gij}/ \sum \limits_{ij}A_{gij}\tag{2} \label{eq2}[/latex] must sum to 1.0. Note also that total efforts Eg can be made to vary over time by supplying relative effort multipliers over time for each gear type in Ecosim, where a multiplier value of 1.0 represents the Ecopath base fishing impact.

When moving from Ecopath and Ecosim to Ecospace, it is important to set a base total effort value for Eg such that the Ecospace effort allocation calculation (eq. 1) results in overall (over all grid cells) fishing mortality rates that are as close as possible to the Ecopath base values Fgk=Cgk/Bk for each fishing gear and Ecopath biomass group k, where Cgk is the Ecopath base catch of group k by gear g and Bk is the Ecopath base biomass for group k. Note that replication of the Ecopath/Ecosim model over the nw active (water) cells in a spatial grid results in total biomasses over the grid of nwBk, so base effort needs to be set so as to give total catches over the grid that are as close as possible to nwCgk, otherwise Ecospace will predict total fishing mortality rates that differ widely from Fgk. For gears that fish spatially concentrated species (pgij high for only a few cells i,j), we cannot simply set total base effort to nw (number of water cells times base effort of unity per cell), since allocation of such a high total effort to just a few cells with high pgij can result in gross overestimation of by-cell fishing rates Fkij for those few cells. We also need to guard against such over-prediction of fishing mortality rates for groups that use the whole spatial grid, but are modelled to have migratory behaviour so as to be spatially concentrated in varying parts of the grid in different months of each simulation year.

Given the complex profitability calculations used to predict pgij from attractivenesses Agij (1), it is not in general possible to choose base efforts Eg so as to exactly predict Ecopath base fishing rates Fgk for all gears and species. For most models, about the best that we can do is to choose Eg so that it at least predicts the total Ecopath base catch nwCg, where [latex]C_g = \sum \limits_k C_{gk}\tag{3} \label{eq3}[/latex] is the total catch by gear g summed over biomass groups that it catches (landings and discards). To achieve this prediction, we need to set Eg so that it satisfies the total catch condition,

[latex]n_w C_g=E_g \sum \limits_{i,j} p_{gij} \sum \limits_k q_{gk} \cdot B_{ijk}\tag{4} \label{eq4}[/latex]

Here, Egpgij is the effort allocated to cell i,j, qgk is the catchability coefficient (Ecopath base fishing rate per unit of effort) for gear g on group k, and [latex]\sum \limits_k q_{gk} B_{ijk}\tag{5}\label{eq5}[/latex] is the total catch per effort summed over groups k for gear g in cell i,j. Simply solving (2) for Eg results in the desired base effort:

[latex]E_g = n_w C_g / ( \sum \limits_{i,j} p_{gij} \sum \limits_k q_{gk} \cdot B_{ijk}) \tag{6} \label{6}[/latex]

Note that if all gravity weights are the same, i.e. biomasses and costs are uniform over the spatial grid, each pgij is just 1/nw and each grid cell’s catch is Cgij=Cg, then (6) just predicts Eg=nw. At the opposite extreme, if all fishing by gear g occurs in just one grid cell such that pgij for that cell is 1.0, and all biomass available to gear g is also in that one cell (Bijk=nwBk for every k), then Eg will be set to 1.0. For intermediate cases in terms of spatial concentration of attractivenesses and biomasses, (6) generally predicts Eg values between 1.0 and nw.

Application of (6) requires an initial assessment of the biomass distributions Bijk, and of the attractivenesses Agij that depend at least partly on the biomass distributions. Particularly for models that include migratory species, reasonable values for these distributions and attractivenesses are not available until at least a few time steps into each simulation, after enough time to allow for some spatial mixing and oriented movement. So the convention used in Ecospace is to initially set the Eg for each group to the number of spatial cells that the gear is physically able to fish, then simulate a few time steps and reset Eg to the value implied by the spatial biomass distribution after those steps. In some cases, it may still be necessary to adopt an iterative approach and to use total effort multipliers (Ecospace > Input > Ecospace fishery > Fleet dynamics > Tot. eff. multiplier) to increase or decrease efforts for some gears after initial simulation trials indicate persistent over- or under-prediction of fishing mortality rates.

- Caddy, J.F. 1975. Spatial model for an exploited shellfish population, and its application to the Georges Bank scallop fishery. J. Fish. Res. Board Can. 32: 1305–1328. https://doi.org/10.1139/f75-152 ↵