FMSP stock assessment tools Training workshop

Yield Software Theory

Yield Software Theory 1Contents

• What is Yield Software used for?

• What are Yield and Yield per Recruit Analyses?

• What are Biological Reference Points?

• Using Biological Reference Points

• What are the Yield Software data requirements?

• What is Simulating under uncertainty?

• Summary

What is Yield Software used for? (1/3)

• ‘Yield’ is a mathematical model that simulates a fish population in both equilibrium and transient states. It is a single species model.

• It is a predictive tool for fisheries managers to be used in conjunction with other fisheries stock assessment tools

• It will simulate a fish population with given uncertainty in input biological and fishery parameters. This enables fisheries managers to evaluate the degree of uncertainty in management advice.

What is Yield Software used for? (2/3)

EQUILIBRIUM STATE: The model may be used to:

• Simulate the state (YPR/Yield) of a fishery under different levels of fishing effort (F=qE)

• Calculate reference values for F that leave the fish population in a specified state (Biological Reference Points)

• Additionally the model may be used to examine the effect of varying length at first capture; and the effect of changing the fishing season or closed seasons.

What is Yield Software used for? (3/3)

TRANSIENT STATE (Non-equilibrium): The model may be used to:

• Examine the effects of inter-annual variation in recruitment on the fish population

• Predict the effects of changing fishing effort (F=qE) on the fish population, and thus assist in defining appropriate management strategies

• Simulate one particular transient BRP, the transient SSB

Yield and Yield per Recruit Analyses (1/3)

• Yield Per Recruit analyses (models) calculate the equilibrium yield per recruit for a given value of fishing mortality (F) and a given length (Lc) or age (Tc) at first capture.

• F and Tc or Lc are parameters over which, in principle, a fishery manager has control.

• Such models are thus commonly employed to examine the question of optimising yield to prevent over-fishing through management controls on effort and length or age at first capture.

D. Total biomass at age (= B x C)

C. Numbers at age

B. Weight at age

A. Length at age

Growth parameters K, Linfinity, t0, (estimated by LFDA or other method)

Wt / L parameters, a, b

Natural mortality rate, M

E. Fish maturity at age

F. Mature biomass (SSB) (= D x E)

Area under curve = spawning stock biomass (SSB) in unexploited stock

50% mature

100% mature

Steps in estimating spawning stock biomass for an unfished stock

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Fishing mortality rate, F

G. Fishing mortality rate at ageC. Numbers at age

B. Weight at age

A. Length at age

Growth parameters K, Linfinity, t0

Wt / L parameters, a, b

Natural mortality rate, M + Fishing mortality rate, F

E. Fish maturity at age

D. Total biomass at age (= B x C)

F. Mature biomass (SSB) (= D x E)

Fishery selectivity (gear mesh sizes, fishing locations etc) and fishing intensity

H. Catch at age (= D x G)

SSBPR reference points, e.g. F20%SPR, where SSBPR is 20% of its unfished level

YPR reference points, e.g. F0.1, where slope of YPR curve is 10% of that at the origin

‘Yield’ estimates relative indicators - spawning stock biomass (area under line in graph F) and catch (area under line in graph H) - at different levels of the fishing mortality rate, F, and thereby finds the values of different F-based reference points, e.g. F0.1, F%SPR

Note reduced spawning stock biomass in fished stock

Total catch = area under curve

Note lower biomass of older fish in

fished stock

Steps in estimating reference points for an exploited fish stock

Yield and Yield per Recruit Analyses (2/3)

Yield and Yield per Recruit Analyses (3/3)

Biological Reference Points (1/9)

• Biological Reference Points (BRPs) are known values of the fishing mortality rate (F), acting on a known biomass of fish (B), that will leave the population in specified state, for example, with a particular yield (Y or YPR).

• In many fisheries, such as those managed by ICES it has become customary to use selected reference points for F either as:– target reference points, or as – limit reference points (i.e. levels of F which, if

exceeded, will leave the population in an undesirable state).

(i.e. parameters that a manager can estimate for a fishery, and then take an appropriate course of action to manage that fishery)

Biological Reference Points (2/9)

Biological Reference Points (3/9)

• The reference points that ‘Yield’ looks at are values of F that result in particular states in the fishery. These are Yield, Biomass and Effort:

YIELD

• Maximum Sustainable Yield (MSY) – Yield: FMSY;

– YPR: FMaxYPR

BRPs – MSY / FMSY & FMaxYPR (4/9)

• For many fisheries, a primary management objective is to take an annual catch equal or less than the maximum sustainable yield (MSY) or Maximum Yield per Recruit. Thus, a commonly calculated reference point, a target reference point in this case, is the value of F (=qE) that in an equilibrium population will result in taking the MSY. This value is normally called FMSY.

Biological Reference Points (5/9)

BIOMASS

• Spawning Stock Biomass (SSB)– Yield: FSSB20

– YPR: FSSB20 per recruit

• % Fishable Biomasse.g. MSY achieved when at 50% fishable biomass / fishable Biomass per recruit

• % Total BiomassLess clear what a target value should be (65%? Of total biomass / total Biomass per recruit)

BRPs – FSSB20 & FSSB20 per recruit (6/9)

• Fishery management objectives may require conservation of the stock, For example, a management aim could be to maintain the SSB at a certain proportion of its unexploited level or not let it fall below a threshold level.

• Thus another commonly calculated reference point for F, is the value of F that in an equilibrium population will result in the SSB being left at or above a percentage (e.g.20%) of its unexploited level (or 20% of unexploited biomass per recruit).

Biological Reference Points (7/9)

EFFORT

• F0.x (for both Yield and YPR vs. F curves)

(And recall that Yield can also examine the effects of changing Lc50 upon FMSY; and FMaxYPR)

Biological Reference Points - F0.x (8/9)

• Another such reference point is F0.1.

• For many species the relationship between yield and F is not clear and a proposed conservative target reference point was proposed by Gulland and Boerema (1973).

• Here the level of F0.1 is described as the level of F where the slope of the yield per recruit curve is 10% of its initial value.

Biological Reference Points – F0.x (9/9)

From Caddy and Mahon (1995)

Using BRPs (1/2)

• We have previously shown that it is possible to get estimates of the total mortality rate “Z” and the natural mortality rate “M” (LFDA), and the catchability coefficient “q” (CEDA).

• If we assume there is no movement of individuals into or out of a stock then;

F = Z – M And this can be related to the effort in the fishery;

F = qE

Using BRPs (2/2)

• If we have an estimate of “F” for a fishery, we can then use this in a Yield and/or Yield-per-Recruit Analysis to see how the current level of fishing mortality compares to our various biological reference points. Some examples are:

F > FMSY Over-fishing

F > F0.1 Potential over-fishing

F < F2/3 MSY Exploited and sustainable

This will indicate a particular course of management action related to the target or limit reference point(s) selected as the basis of any management strategy.

Yield Software Data Requirements (1/5)

What data are required to do Yield / YPR analysis?

• Yield and yield pre recruit analyses are data hungry. Biometric and fishery data are needed – i.e. parameters that describe the life history of the stock, and those describing fishing on it.

• This is not a great deal of data in terms of number of individual data parameters, but to derive each of these requires a significant sampling programme.

• These data come from a wide range of all parts of fisheries stock assessment.

Yield Software Data Requirements (2/5)

• Growth Parameters L, K, T0 [… from LFDA]

• Length-Weight ,

• Natural Mortality M (Temperature)

• Maturity and Capture Lengths (or ages) at first maturity and capture

• Seasonality Spawning and fishing seasons

• Stock Recruitment Relationship and parameters

Yield Software Data Requirements-SRR(3/5)

Yield Software Data Requirements (4/5)

• Possible data sources i.e. Where to get this data?

• Through LFDA you will have seen that a number of these parameters can be obtained from your own biological sampling programmes or catch monitoring programmes.

• Others derive from direct biological sampling

• VPA can provide a number of the parameters and particularly SRR

• Other sources of data can be found from the literature or the Internet (e.g. the very useful www.fishbase.org).

Yield Software Data Requirements (5/5)• ‘Yield’ can use single or point estimates of each of the

above parameters, but it is designed to use a range of parameters

• Few analytical methods provide parameter estimates in which we have total confidence (as seen in LFDA). Also uncertainty in one parameter, e.g. K leads to uncertainty in the estimates of other parameters dependant upon it, e.g. M.

• It is best therefore to derive a range of parameters (or see what the range of estimates is in FISHBASE) and to calculate mean values with standard deviation and coefficient of variation. This describes the probability of a parameter being a particular value. Yield uses these probabilities to explore uncertainty.

Simulating under uncertainty (1/2)

• Two types of uncertainty are dealt with in ‘Yield’:– statistical uncertainty about the values of biological &

fishery parameters used in calculations– uncertainty in the annual numbers of recruits arising

from stochastic variability about the SRR.

• A primary purpose of ‘Yield’ is to quantify that uncertainty as it has implications for uncertainty in any management actions applied to the fishery

• ‘Yield’ does this by sampling from the probability distributions for input biological parameters and repeating the calculations a user set number of times (e.g 100)

Simulating under uncertainty (2/2)

Summary - Use of Yield Software• ‘Yield’ simulates a user specified fish population. • Yield and YPR analyses simulate the effect of fishing on

yield (catch) and enable mangers to see what the current status of fishing effort is compared to predicted outcomes of fishing.

• Desirable equilibrium target or limiting reference points may be calculated to guide any fisheries management strategy.

• The model may be used to explore potential management actions in equilibrium: Changing fishing mortality, F, Length at first capture, closed or different fishing seasons; or in the transient state: the effect of changing fishing mortality over time including fishing bans for a number of years

• A transient SSB reference point may be derived

Go to practical presentation

Yield Software Theory Session 2: Equilibrium analyses

FMSP stock assessment tools Training workshop

Equilibrium Analyses (1/7)

The model may be used to:

• Simulate the state (YPR/Yield) of a fishery under different levels of fishing effort (F=qE)

• Calculate reference values for F that leave the fish population in a specified state (BRPs)

• Additionally the model may be used to examine the effect of varying length at first capture; and the effect of changing the fishing season or closed seasons.

Equilibrium Analyses – YPR (2/7)

• In addition to equilibrium Yield Per Recruit we can calculate equilibrium biomass per recruit. Three are of interest:

– Equilibrium SSB per recruit– Equilibrium fishable biomass per recruit– Equilibrium total biomass per recruit

• Like the Equilibrium YPR the Eq. biomass is a function of two parameters over which the manager has control, F and Tc. ‘Yield’ allows the user to vary these parameters

Equilibrium Analyses – YPR (3/7)

Equilibrium Analyses – Yield (4/7)

• In addition to equilibrium Yield we can calculate equilibrium biomass

– Equilibrium SSB – Equilibrium fishable biomass – Equilibrium total biomass

• Because we have a stock recruitment relationship we can also calculate the equilibrium number of recruits at different levels of fishing mortality.

Equilibrium Analyses – Yield (5/7)

Eq. Analyses –YPR Reference Points (6/7)

F0.1Fmax

Showing the relationship between Yield’s Indicator graphs (Equilibrium YPR and Equilibrium Yield)

and the Reference Points graphs

Eq. Analyses-Yield Reference Points (7/7)

Yield Software Theory Session 3: Transient Projections

FMSP stock assessment tools Training workshop

Transient Projections (1/5)

The model may be used to:

• Examine the effects of inter-annual variation in recruitment on the fish population

• Predict the effects of changing fishing effort (F=qE) on the fish population, and thus assist in defining appropriate management strategies

• Simulate a transient ‘risk-based’ BRP, the transient SSB

Transient projections (2/5)

• Unlike the equilibrium projections which assume constant (deterministic) recruitment, Transient projections take account of stochastic variability in recruitment.

• Transient projections look at the fishery over time for specified levels of fishing mortality, F.

Transient projections-Variation in SRR (3/5)

Transient projections–Yearly projection (4/5)

Transient Projections – SSB ref. Point (5/5)

• This reference point calculates the value of FSSB that will result in the SSB falling below a given value, say 20% of the initial SSB, with a given probability (say 0.1) in a specified number of years (say 20).

• That is, Yield will calculate the value of FSSB that will result in the SSB falling below 20% of its initial value only twice in 20 years.

Summary - Managing under uncertainty

• Managers base their decisions on certain reference points that indicate a particular course of action. Yield derives these. However we have seen that statistical uncertainty in the biological data estimated for a fishery, and inter-annual variation in the SRR can lead to considerable uncertainty the values of the reference points and thus in management decisions.

• Yield quantifies this uncertainty and enables managers to make more informed decisions about how best to manage.

• Yield can be a powerful tool when used properly and in conjunction with other stock assessment tools.