Changes between Version 8 and Version 9 of EwEugForagingTimeAndPredationRisk


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Timestamp:
2010-11-21 23:36:51 (9 years ago)
Author:
shermanl
Comment:

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  • EwEugForagingTimeAndPredationRisk

    v8 v9  
    11== 3.6 Foraging time and predation risk == 
    2 The food consumption prediction relationship in Eq. 52 (see [[Predicting consumption.htm|Predicting consumption]]) contains two parameters that directly influence the time spent feeding and the predation risk that feeding may entail: ''a'',,''ij'',, and ''v’'',,''ij'',,. To model possible linked changes in these parameters with changes in food availability as measured by per biomass food intake rate ''c'',,''it'',,'' = Q'',,''it'',,'' / B''^''it''^ (''i''=juvenile index ''J'' or adult index ''A''), we need to specify how changes in ''c'',,''it'',, will influence at least relative time spent foraging. 
     2The food consumption prediction relationship in Eq. 52 (see [EwEugPredictingConsumption Predicting consumption]) contains two parameters that directly influence the time spent feeding and the predation risk that feeding may entail: ''a'',,''ij'',, and ''v' '',,''ij'',,. To model possible linked changes in these parameters with changes in food availability as measured by per biomass food intake rate ''c'',,''it'',,'' = Q'',,''it'',,'' / B''^''it''^ (''i''=juvenile index ''J'' or adult index ''A''), we need to specify how changes in ''c'',,''it'',, will influence at least relative time spent foraging. 
    33 
    4 Denoting the relative time spent foraging as ''T'',,''it'',,, measured such that the rate of effective search during any model time step can be predicted as ''a'',,''jit'',, = ''T'',,''it'',,'' a'',,''ji'',, for each prey type'' j'' that ''i'' eats. Further, we assume that time spent vulnerable to predation, as measured by'' v’'',,''ij'',, for all predators j on i, is inversely related to ''T'it'', i.e., v’,,ij,,t = v’,,ij,, / T,,it,,. An alternative structure that gives similar results is to leave the ''a'',,''ij'',, constant, while varying the ''v'',,''ij'',, by setting ''v'',,''ijt'',,'' = T'',,''jt'',,'' · v'',,''ij'',,' in the numerator of Eq. 52 in [wiki:EwEugPredictingConsumption Predicting Consumption] and ''v'',,''ijt'',,'' = T'',,''it'',,'' · v'',,''ij'',, in the denominator. 
     4Denoting the relative time spent foraging as ''T'',,''it'',,, measured such that the rate of effective search during any model time step can be predicted as ''a'',,''jit'',, = ''T'',,''it'',,'' a'',,''ji'',, for each prey type'' j'' that ''i'' eats. Further, we assume that time spent vulnerable to predation, as measured by'' v' '',,''ij'',, for all predators j on i, is inversely related to ''T'it'', i.e., v',,ij,,t = v',,ij,, / T,,it,,. An alternative structure that gives similar results is to leave the ''a'',,''ij'',, constant, while varying the ''v'',,''ij'',, by setting ''v'',,''ijt'',,'' = T'',,''jt'',,'' · v'',,''ij'',,' in the numerator of Eq. 52 in [wiki:EwEugPredictingConsumption Predicting Consumption] and ''v'',,''ijt'',,'' = T'',,''it'',,'' · v'',,''ij'',, in the denominator. 
    55 
    6 For convenience in estimating the ''a'',,''ij'',, and ''v’'',,''ij'',, parameters, we scale ''T'',,''it'',, so that ''T'',,''i0'',, = 1, and ''v’,,I j,,''= ''v'',,''ij'',,. Using these scaling conventions, the key issue then becomes how to functionally relate T,,it,, to food intake rate ''c'',,''it'',, so as to represent the hypothesis that animals with lots of food available will simply spend less time foraging, rather than increase food intake rates. 
     6For convenience in estimating the ''a'',,''ij'',, and ''v' '',,''ij'',, parameters, we scale ''T'',,''it'',, so that ''T'',,''i0'',, = 1, and ''v',,I j,,''= ''v'',,''ij'',,. Using these scaling conventions, the key issue then becomes how to functionally relate T,,it,, to food intake rate ''c'',,''it'',, so as to represent the hypothesis that animals with lots of food available will simply spend less time foraging, rather than increase food intake rates. 
    77 
    88In Ecosim a simple functional form for ''T'it'' is implemented that will result in near constant feeding rates, but changing time at risk to predation, in situations where rate of effective search ''a'',,''ji'',, is the main factor limiting food consumption rather than prey behaviour as measured by ''v'',,''ji'',,. This is implemented in form of the relationship: 
     
    1010[[Image(wiki:EwEugImages:0800002A.png)]] ''' Eq. 65''' 
    1111 
    12 where, a is a user-defined Feeding time adjustment rate [0, 1] on the Ecosim [[Group info.htm#_Read_time_series|Group info]] form; ''c,,i,opt,,'' is the (internally computed) feeding rate that optimizes feeding rate versus mortality risk for ''i''; ''c,,i,t-1,,'' is the consumption/biomass ratio in the previous time step for the group. The time spent feeding is constrained by a user-defined value (Maximum relative feeding time on the ''Group info'' form with default of two times the feeding rate in the Ecopath base model). 
     12where, a is a user-defined Feeding time adjustment rate [0, 1] on the Ecosim [EwEugGroupInfo Group info] form; ''c,,i,opt,,'' is the (internally computed) feeding rate that optimizes feeding rate versus mortality risk for ''i''; ''c,,i,t-1,,'' is the consumption/biomass ratio in the previous time step for the group. The time spent feeding is constrained by a user-defined value (Maximum relative feeding time on the ''Group info'' form with default of two times the feeding rate in the Ecopath base model). 
    1313 
    1414The relationship between foraging time, consumption and predator biomass is illustrated in Figure 3.4.