Information about Age-Structured Models: Yield-Per-Recruit

A little summary of Age-structured models for fisheries in particular yield-per-recruit. The slides were developed from part 2 of Chapter 2 in the fantastic book "Modeling and Quantitative Methods in Fisheries" by Malcolm Haddon.

Authors: Daniele Baker and Derek Crane

Authors: Daniele Baker and Derek Crane

Objectives Why develop age-structured models? Mortality rates (H vs. F) How to determine mortality or fishing rate? Yield-per-recruit Determining optimums Model assumptions Equations and definitions Targets and conclusions

Logistic Model Brief stop… ��+1 = �� + ��� ൬1 − �� � ൰− ��

Use of age-structured Why do you think it’s better to use age- structured vs. whole-population models? Growth rate, size, egg-production http://afrf.org/primer3/ + http://www.fao.org/docrep/W5449E/w5449e06.htm (VERY USEFUL SITES)

0 200 400 600 800 1000 0 4 8 12 16 20 24 28 32 36 40 44 PopulationSize Time Bt, Z=.25 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 0 4 8 12 16 20 24 28 32 36 40 44 Biomass(kg) PopulationSize Time Bt, Z=.25 Biomass Age-structure example Length, weight, fecundity increase with time Population decreases with time At some pt. biomass peaks 0 2000 4000 6000 8000 10000 12000 0 50 100 150 200 250 300 0 4 8 12 16 20 24 28 32 36 40 44 Fecundity(#ofeggs) Weight+Length Age (yrs) Length (in) Weight(lbs) Fecundity

Age-structure in Forestry “From a biological standpoint, trees and shrubs should not be cut until they have at least grown to the minimum size required for production utilization… Trees and shrubs usually should not be allowed to grow beyond the point of maximum average annual growth, which is the age of maximum productivity; foresters call this the "rotation" age of the forest plantation.” http://www.fao.org/docrep/T0122E/t0122e09.htm

Age-structured Why not apply the same fishing mortality to all fish? Short lived <1 year Must pin point the time within the year in order to catch more and allow for reproduction

Age-structure btw. species Species vary in growth rate, fecundity, age of maturity Makes some species very vulnerable (sturgeon). WHY? 0 5 10 15 20 American Shad Bluefish Striped bass Winter flounder Shortnose sturgeon Age(years) FishSpecies First maturity 50% EPR 0 500 1000 1500 2000 2500 American Shad Bluefish Striped bass Winter flounder Shortnose sturgeon Fecundity(eggsinthousands) FishSpecies Data from Boreman and Friedland 2003

Annual vs. Instantaneous Compound interest- continuous vs. annual Which collects more interest ($)? Positive interest � = � ቀ1 + � � ቀ ��

Annual vs. Instantaneous Which has greater annual mortality? Negative Exponential decay = draining bathtub Larger decrease between .1 + .35 then .5 + .75 0 200 400 600 800 1000 0 4 8 12 16 20 PopulationSize Time Bt, Z=.1 Bt, Z=.25 Bt, Z=.5 Bt, Z = 1 � = −��ቀ1 − �ቀ��+1 = ���−� 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 AnnualPercentMortality Instantaneous Fishing Mortality F H F

Age-structured model Assumptions ○ Age-structure of fish population has attained equilibrium with respect to mortality (recruitment is constant or one cohort represents all) ○ r individuals at tr are recruited (tr = minimum age targeted) ○ Once recruited submitted to constant mortality ○ Fish older than tmax are no longer available ○ Minimal immigration/ emigration ○ Fishery reached equilibrium with fishing mortality ○ Natural mortality and growth characteristics are constant with stock size ○ Use of selective-size actually separates out all fish > Tc ○ Have an accurate estimate of population size and good records of total commercial catch

Age-structured model Equations Expected outcomes Target fishing mortality (F)- determines constant fishing rate harvest strategy Target age at first capture (Tc)- determines gear type ��+1 = ���−(�+��) �� = �� − ��+1 �� = ��൫1 − �−ቀ�+� ቀ ൯

Conclusions Limitations Don’t address sustainability of optimal F. Why? Fo.1 instead of Fmax Overfishing Growth-overfishing Recruitment overfishing Other options. Which is best? Egg-per-recruit Dollar-per-recruit

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 AnnualPercentMortality Instantaneous Fishing Mortality F H F Slight correction to this graph: The red line plots the relationship of Annual Mortality (as a FRACTION, not a percent) to values of F, the Instantaneous Mortality rate. The dotted line is a 1:1 line (in other words, on this line, the value of Y is the same as that of X). What Haddon is showing in this diagram is that at low values of F, the corresponding annual mortalities are about the same value – a value of F = 0.1 produces an annual mortality of 0.1 (i.e., 10% of the population dies that year). At higher levels of F, the red line diverges from the 1:1 line – thus, at F = 1, the annual mortality is around 0.63 (63%). Etc.

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