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Einar Hjörleifsson
2022-11-01
to view the slides press “w”. full view can be obtained pressing F11
the slides can be found on: https://heima.hafro.is/~einarhj/CFB
In this talk I want to highlight how some simple mathematical fisheries equations can provide an aid to clear thinking when it comes to:
The biomass of the fish at any one time is a product of:
So over time we have gains in form of growth and recuitment and loss because of natural causes and fishing.
Over time (here over one time step, from time t to t+1) we can expressed this in terms of a mass-balance equation:
Bt+1 = Bt + Gt + Rt - Mt - Ct
Expressing fish population dynamics in this form raises questions:
In some cases we try to apply this simplification:
Bt+1 = Bt + Gt + Rt - Mt - Ct
Bt+1 = Bt + f(Bt) - Ct
and then use some index (Survey index or catch-per-unit-effort):
CPUEt = q Bt
The f(Bt) is often refered to as production, its form being assumption driven
What data does one need to solve this riddle?
In its most simplistic term we can think of the catch over some very short time being a function of the mean biomass over that time:
Catch = Fishing pressure x Biomass, more succinctly
C = F B
Think here of the fishing pressure as the proportion of the biomass that is removed by fishing:
F = C / B
often termed harvest rate or fishing pressure.
We have here three variables. If we only have measures of one, we know from our school mathematics that one can not derive the other two terms.
Imagine we have a total catch (data) of some 200 t over a month. This catch could have arisen from different scenarios, e.g.:
Scenario 1: Fishing pressure = 0.2, Biomass = 1000 t C = FB Catch = 0.2 x 1000 t = 200 t Scenario 2: Fishing pressure = 0.4, Biomass = 500 t C = FB Catch = 0.4 x 500 t = 200 t
So a certain catch can come from a high stock size using a low fishing pressure or from a low stock size using high fishing pressure.
Ergo, catch alone does not inform us about biomass nor fishing pressure.
Most national fisheries policies refer to MSY. So
C = F B
becomes specifically:
MSY = FMSY BMSY
So in order to achieve MSY we need to know FMSY and/or BMSY
The fishing pressure can be split into two components:
F = qE, where:
q = F/E
Scenario 1: 10 small vessels go out for 1 day Total effort: 10 fishing days Catchability: 0.01 F = q E: 0.01 x 10 = 0.1 Scenario 2: 1 large vessels go out fishing for 1 day. Total effort: 1 fishing days. Catchability: 0.10 F = qE = 0.10 x 1 = 0.1
Ergo we can exert the same fishing pressure (a)nd hence obtain the same catch) by having high effort and low catchability or low effort and high catchability.
More importantly, we have a societal choise to make (q vs E, i.e. how vs how much)
We have C = FB and F = qE
hence
C = qEB
and when expressed in the form of the illusive goal:
MSY = qMSY EMSY BMSY
We can regulate directly or indirectly using any of these components
Going from: q -> E -> C -> B means ever more management cost data needs
We often have within the national management system:
The net effect may be that the fishing pressure may not be reduced
The MPA’s panacea:
The direct effect is often just a displacement of effort and increase in the cost of fishing
We know that catches as well as fish stock are composed of different sizes of fish.
Higher effort Lower effort
The steepness of the size spectrum is an indirect measure of the fishing pressure, i.e.
F=f(sizespectrum)
If we can solve this we have two estimates of the fundamental catch equation:
C=FB
and we can thus solve the riddle:
B=C/F
Adding measurements on the size composition of the catch hence reduces the assumption one needs to make in order to solve the riddle in the fundamental fisheries equation.
Solving the fundamental catch equation is not simple, achieved only by indirect means and requires data time series (fleet and gear composition, effort, catch, cpue, size composition, survey data, …)
In this context older data are of extreme value.
To facilitate solving the riddle