Adjusting recruitment for yearly time step projections

[michellesculley]

Just thinking about how we need to adjust the recruitment of age 0 fish to account for the fact that they are born in July of the previous year, could we just use the number of age-1 fish in Jan of the following year? In SS3 all fish turn 1 at the start of the next calendar year which would make all the age one fish in Jan actually 6 months old. @fecor21 can correct me if I'm wrong, but in that case, we should be able to use those age-1 fish as the recruitment from the previous year and we won't have to correct for the half-year of mortality.

To clarify, I'm suggesting that we could use the numbers at age 1 in Jan-1 1990 for the recruitment that occurred in July 1989. What do you think @JonBrodziak? Those values can be easily pulled using the SS_to_agepro function we walked through yesterday.

[JonBrodziak]

I believe it would be useful to cross-check this idea.

We want to be able to use the estimated parameters of the Beverton-Holt stock-recruitment relationship. The SR curve produces numbers of age-0 recruits on July 1st of year Y based on spawning biomass in year Y and the recruitment deviation.

R(Y,0) = f( SB(Y), Recdev )

The value of predicted numbers at age-1 in year Y+1 (N) would be the same as the predicted recruitment (R) at age-0 in year Y if adjusted by one-half of the total annual mortality rate (Z) experienced at age-0 as

N(Y+1, 1) = R(Y, 0) * exp(-Z0/2)

If the fishing mortality rate on age-(1/4) and age-(2/4) fish is zero, then

N(Y+1, 1) = R(Y, 0) * exp(-M0/2)

should hold, given age-0 natural mortality rate M0. The question is how much mortality occurs due to fishery removals at age-0 (Q1 and Q2)? If F0 is very small then there will not be much difference between recruitment at age-0 adjusted for M0 on Jan 1st year Y+1 and the numbers at age-1 on Jan-1st of year Y+1, N(Y+1,1)

On Thu, Nov 30, 2023 at 9:49 AM Michelle Sculley @.***> wrote:

Just thinking about how we need to adjust the recruitment of age 0 fish to account for the fact that they are born in July of the previous year, could we just use the number of age-1 fish in Jan of the following year? In SS3 all fish turn 1 at the start of the next calendar year which would make all the age one fish in Jan actually 6 months old. @fecor21 https://github.com/fecor21 can correct me if I'm wrong, but in that case, we should be able to use those age-1 fish as the recruitment from the previous year and we won't have to correct for the half-year of mortality.

To clarify, I'm suggesting that we could use the numbers at age 1 in Jan-1 1990 for the recruitment that occurred in July 1989. What do you think @JonBrodziak https://github.com/JonBrodziak? Those values can be easily pulled using the SS_to_agepro function we walked through yesterday.

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[michellesculley]

In SS3 there is no Fishing mortality in Q1 and Q2 on age zero fish as there are no age-0 fish in the population, the model estimates an F for those quarters but they are all less than 0.8E-6, so essentially zero. All the age-0 fish born in Q3 then become the age 1 fish in Q1 of the following year, reduced by M/2 and F on age-0 fish in Q3 and Q4. The F on age-0 fish estimated from SS is also relatively small, between 0.02 and 0.8E-4 for all years/quarters in the model. I believe if you were to adjust the age-0 fish by just M/2 and compare it to the output of age-1 fish in the year following the recruitment, they should be almost identical, likely within rounding errors.

[JonBrodziak]

I agree.

And the question below was intended to refer to Q1 and Q2 of an age-0 fish's lifetime.

"The question is how much mortality occurs due to fishery removals at age-0 (Q1 and Q2)?"

The intended question was for the age-(1/4 year) in quarter 3 when they are one quarter of a year old, and for age-(2/4 year) fish in quarter 4 when they are two quarters of a year old. I denoted the ages of age-(1/4) fish by Q1 and age-(2/4) fish by Q2.

If the fishing mortality rate on age-(1/4) and age-(2/4) fish is nearly zero in quarters 3 and 4, then effectively one can say that the number of age-1 fish in year Y+1 is

N(Y+1, 1) = R(Y, 0) * exp(-M0/2)

which is what you point out in your reply.

Apologies for the confusing notation.

It would be informative to make the comparison as this would support adjusting the BH stock-recruitment model parameters to represent age-1 recruits.

Thanks, Jon

On Thu, Nov 30, 2023 at 2:01 PM Michelle Sculley @.***> wrote:

In SS3 there is no Fishing mortality in Q1 and Q2 on age zero fish as there are no age-0 fish in the population, the model estimates an F for those quarters but they are all less than 0.8E-6, so essentially zero. All the age-0 fish born in Q3 then become the age 1 fish in Q1 of the following year, reduced by M/2 and F on age-0 fish in Q3 and Q4. The F on age-0 fish estimated from SS is also relatively small, between 0.02 and 0.8E-4 for all years/quarters in the model. I believe if you were to adjust the age-0 fish by just M/2 and compare it to the output of age-1 fish in the year following the recruitment, they should be almost identical, likely within rounding errors.

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The views expressed in this message are my own and do not necessarily reflect any position of NOAA.

[JonBrodziak]

The age-0.5 adjustment has been added to the Build_Input_File code for recruitment models 2, 3, 5, and 14. It will be straightforward to add the adjustment for any other recruitment models that may be applied for MLS projections.