{"id":2240,"date":"2023-12-04T16:11:12","date_gmt":"2023-12-04T21:11:12","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/?post_type=chapter&p=2240"},"modified":"2025-10-31T05:17:56","modified_gmt":"2025-10-31T09:17:56","slug":"predicting-spatial-effort","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/chapter\/predicting-spatial-effort\/","title":{"raw":"Predicting spatial effort","rendered":"Predicting spatial effort"},"content":{"raw":"

EwE works with multiple fishing fleets, with fishing mortality rates (F<\/em>) initially distributed between fleets based on the distribution in the underlying Ecopath base model. In Ecospace the F<\/em>\u2019s are distributed using a simple logit-choice or \"gravity model\" where the proportion of the total effort allocated to each cell is assumed proportional to the sum over groups of the product of the biomass, the catchability, and the profitability of fishing the target groups, divided by relative cost of fishing the cell [footnote]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\u20131328. https:\/\/doi.org\/10.1139\/f75-15<\/a>[\/footnote] [footnote]Hilborn, R., and Walters, C. J. 1987. A general model for simulation of stock and fleet dynamics in spatially heterogeneous fisheries. Canadian Journal Of Fisheries And Aquatic Sciences, 44(7):1366-1369 https:\/\/doi.org\/10.1139\/f87-163<\/a>[\/footnote]. This profitability of fishing includes factors such as the cell-specific cost of fishing.<\/p>\r\n

Assuming that there are N <\/em>cells representing water areas, each fleet k<\/em> can cause a total fishing mortality rate N \u00b7 F<\/em>k<\/sub>. For each step in the simulation this rate is distributed among cells, c<\/em>, in proportion to the relative utility weights G<\/em>kc<\/sub> calculated as<\/a><\/p>\r\n[latex]G_{kc}=O_{kc} U_{kc} \\frac{\\sum\\limits_{i} p_{ki} q_{ki} B_{ic}} {C_{kc}} \\tag{1}[\/latex]\r\n\r\nwhere O<\/i>kc<\/em><\/sub> is 1 if cell c <\/i>is open to fishing by fleet k, and 0 if not; U<\/i><\/span>kc <\/span><\/sub>is 1 if the user has allowed fleet k <\/i>to work in the habitat type to which cell c <\/i>belongs, and 0 if not; p<\/i><\/span>ki <\/span><\/sub>is the relative price fleet k<\/em> receives for group i <\/i>fish, q<\/i><\/span>ki <\/span><\/sub>is the catchability of group i<\/em> by fleet k<\/em> (equal to the F<\/i><\/span>ki <\/span><\/sub>in the Ecopath model); B<\/i><\/span>ic<\/sub> \u00a0<\/span>is the biomass of group i<\/em> in cell c<\/em>; and C<\/i><\/span>kc<\/sub>\u00a0<\/span>is the cost for fleet k <\/i>to operate in cell c<\/i>. Based on the weights in Eq. 1<\/a><\/span>\u00a0the total mortality rate is distributed over cells according to<\/span>\r\n\r\n[latex]F_{kc}=N \\ F_k \\ G_{kc}^p \/ \\sum\\limits_{c} G_{kc}^p\\tag{2}[\/latex]\r\n

\r\n

while each group in the cell is subject to the total fishing mortality<\/p>\r\n[latex]F_{ic}= \\sum\\limits_{k}F_{kc} \\ q_{ki}\\tag{3}[\/latex]\r\n\r\nThe p parameter here represents variation among fishers in perception of the best place to fish, and is set to 1.0 by default.\u00a0 Setting p to higher values results in effort being more concentrated in the most profitable cells, and lower values cause effort to be more spread out (due to either wide variation among fishers in their actual best locations to fish, or lack of information that causes them to just try fishing everywhere).\u00a0 Readers familiar with logit choice theory may recognize the G weights as exp(utility) values, with utility assumed to be proportional to the logarithmic difference ln(income)-ln(cost) in income and cost components of decision choices.\r\n

\r\n

Attribution <\/strong>This chapter is in part adapted from the unpublished EwE User Guide: Christensen V, C Walters, D Pauly, R Forrest. 2008. Ecopath with Ecosim User Guide.\u00a0<\/span><\/p>\r\n\r\n<\/header><\/div>\r\n<\/div>","rendered":"

EwE works with multiple fishing fleets, with fishing mortality rates (F<\/em>) initially distributed between fleets based on the distribution in the underlying Ecopath base model. In Ecospace the F<\/em>\u2019s are distributed using a simple logit-choice or “gravity model” where the proportion of the total effort allocated to each cell is assumed proportional to the sum over groups of the product of the biomass, the catchability, and the profitability of fishing the target groups, divided by relative cost of fishing the cell [1]<\/sup><\/a> [2]<\/sup><\/a>. This profitability of fishing includes factors such as the cell-specific cost of fishing.<\/p>\n

Assuming that there are N <\/em>cells representing water areas, each fleet k<\/em> can cause a total fishing mortality rate N \u00b7 F<\/em>k<\/sub>. For each step in the simulation this rate is distributed among cells, c<\/em>, in proportion to the relative utility weights G<\/em>kc<\/sub> calculated as<\/a><\/p>\n

[latex]G_{kc}=O_{kc} U_{kc} \\frac{\\sum\\limits_{i} p_{ki} q_{ki} B_{ic}} {C_{kc}} \\tag{1}[\/latex]<\/p>\n

where O<\/i>kc<\/em><\/sub> is 1 if cell c <\/i>is open to fishing by fleet k, and 0 if not; U<\/i><\/span>kc <\/span><\/sub>is 1 if the user has allowed fleet k <\/i>to work in the habitat type to which cell c <\/i>belongs, and 0 if not; p<\/i><\/span>ki <\/span><\/sub>is the relative price fleet k<\/em> receives for group i <\/i>fish, q<\/i><\/span>ki <\/span><\/sub>is the catchability of group i<\/em> by fleet k<\/em> (equal to the F<\/i><\/span>ki <\/span><\/sub>in the Ecopath model); B<\/i><\/span>ic<\/sub> \u00a0<\/span>is the biomass of group i<\/em> in cell c<\/em>; and C<\/i><\/span>kc<\/sub>\u00a0<\/span>is the cost for fleet k <\/i>to operate in cell c<\/i>. Based on the weights in Eq. 1<\/a><\/span>\u00a0the total mortality rate is distributed over cells according to<\/span><\/p>\n

[latex]F_{kc}=N \\ F_k \\ G_{kc}^p \/ \\sum\\limits_{c} G_{kc}^p\\tag{2}[\/latex]<\/p>\n

\n

while each group in the cell is subject to the total fishing mortality<\/p>\n

[latex]F_{ic}= \\sum\\limits_{k}F_{kc} \\ q_{ki}\\tag{3}[\/latex]<\/p>\n

The p parameter here represents variation among fishers in perception of the best place to fish, and is set to 1.0 by default.\u00a0 Setting p to higher values results in effort being more concentrated in the most profitable cells, and lower values cause effort to be more spread out (due to either wide variation among fishers in their actual best locations to fish, or lack of information that causes them to just try fishing everywhere).\u00a0 Readers familiar with logit choice theory may recognize the G weights as exp(utility) values, with utility assumed to be proportional to the logarithmic difference ln(income)-ln(cost) in income and cost components of decision choices.<\/p>\n

\n
\n

Attribution <\/strong>This chapter is in part adapted from the unpublished EwE User Guide: Christensen V, C Walters, D Pauly, R Forrest. 2008. Ecopath with Ecosim User Guide.\u00a0<\/span><\/p>\n<\/header>\n<\/div>\n<\/div>\n

  1. 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\u20131328. https:\/\/doi.org\/10.1139\/f75-15<\/a> ↵<\/a><\/li>
  2. Hilborn, R., and Walters, C. J. 1987. A general model for simulation of stock and fleet dynamics in spatially heterogeneous fisheries. Canadian Journal Of Fisheries And Aquatic Sciences, 44(7):1366-1369 https:\/\/doi.org\/10.1139\/f87-163<\/a> ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":1909,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2240","chapter","type-chapter","status-publish","hentry"],"part":418,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/2240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/users\/1909"}],"version-history":[{"count":17,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/2240\/revisions"}],"predecessor-version":[{"id":3721,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/2240\/revisions\/3721"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/parts\/418"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapters\/2240\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/media?parent=2240"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/pressbooks\/v2\/chapter-type?post=2240"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/contributor?post=2240"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ewemodel\/wp-json\/wp\/v2\/license?post=2240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}