Distribution of Sardine in US water used for current harvest guideline Nancy Lo (retiree from SWFSC)and Larry Jacobson (NWFCS) PACIFIC FISHERY MANAGEMENT COUNCIL WORKSHOP ON PACIFIC SARDINE DISTRIBUTION August 17-19, 2015

Outline Harvest guideline computation Model used to estimate relative biomass of Pacific sardine using spotter logbook data Verification of distribution: 87% Data sources to estimate the distribution of Pacific sardine (proportion of sardine population in US water) Conclusion and discussion

Outline Harvest guideline computation Model used to estimate relative biomass of Pacific sardine using spotter logbook data Data sources to verify the estimate of the distribution of Pacific sardine (proportion of sardine population in US water) Estimation of distribution: 87% Conclusion and discussion

Harvest guideline HG year = (BIOMASS year-1 - CUTOFF) FRACTION DISTRIBUTION where HG 2008 is the total USA (California, Oregon, and Washington) harvest guideline in 2008, as an example BIOMASS 2007 is the estimated July 1, 2007 stock biomass (ages 1+) from the 2007 assessment (832,706 mt), CUTOFF is the lowest level of estimated biomass at which harvest is allowed (150,000 mt), FRACTION is an environment-based percentage of biomass above the CUTOFF that can be harvested by the fisheries, and DISTRIBUTION (87%) is the percentage of BIOMASS 2007 assumed in U.S. waters for 2008 harvest guideline.

Outline Background: Harvest guideline computation Model used to estimate relative biomass of Pacific sardine using spotter logbook data Verification of distribution: 87% Data sources to estimate the distribution of Pacific sardine (proportion of sardine population in US water) Conclusion and discussion

6 Model: Delta-loglinear model I = D A = d P A [1] where I is the index of relative abundance for a given year (tons) D is density of Pacific sardine (tons/block) for all flights A is the area (no of blocks) covered by fish spotters where a block is an area of 10 ’ latitude by 10 ’ longitude (~ 80 miles 2 ) d measures Pacific sardine density (tons/block) for positive flights (flights during which P. sardine were seen) and P measures the proportion of blocks that were covered by positive flights (referred to as proportion positive)

The delta loglinear model for density is: Ln(d) = β 0 + Xβ + Zα +ϵ (2) And the model for proportion positive flights is: Ln(P+1) =  0 + X  + Zρ + τ (3) Where d is density (tons sighted per block searched) for positive flights, P is the proportion of positive blocks in which sardines were spotted for positive flights, X and β or  are data and parameters for years ( ), regions (1 and 3-5), seasons (spring, summer and fall), day/night and fish spotters (numbered 7-34). Z and α or ρ are data and parameters for interactions.

The estimate of d and P can be obtained with bias correction terms (equation 8, Lo et al. 1992) as d =exp[f(X,Z, β, α)]* ψ d and P+1=exp[g(X,Z, β, α)]* ψ P where ψ is the bias correction term which was not used in the original computation. Because E[ln(d)] not = ln[E (d)] exp(E[ln(d)] ) not =E(d)

9 Note: No variance was computed for the variance of relative abundance (I) (Lo et al. 1992)

Outline Background: Harvest guideline computation Model used to estimate relative biomass of Pacific sardine Verification of distribution: 87% Data sources to estimate the distribution of Pacific sardine (proportion of sardine population in US water) Conclusion and discussion

Verification of 87% based on data from and area information from because the document of the original computation based on data in was not located Estimate based on original procedure used to obtain 87% Estimate based on seasonal proportion

Verification of 87% based on from data and area information from Estimate based on original procedure used to obtain 87% Estimate based on seasonal proportion

Verification of 87% based on method used for 87% computation using current available data from and area information from

14 Study area, regions, and blocks covered By spotter pilots in 1989: (A r ) _________________________________

Model for density/block in positive flights (d) Model for proportion positive blocks (P) Density (dxP) Area (number unique blocks searched from Figure 2 in Lo et al. 1992) Schooling biomass Proportion by region Country Proportion by country Region effect (R ) Back- transformed (e R ) Region effect (R ) Back- transformed (e R ) US Mexico

Verification of 87% based on from data and area information from Estimate based on original procedure used to obtain 87% Estimates based on seasonal proportion

The relative abundance was computed for each season. Weighted means of the relative abundance were obtained where the weights are no of flights or positive flights occupied for each season Density (d sr ) and proportion of positives (P sr ) in region r for season S : d sr = exp(β 0 + β r + β s + α r,s ) ~ exp(β r + β s + α r,s ) with β 0 =β 0,p =0 P sr = exp(β 0,p + β r,p + β s,p + α p,s ) -1 ~ exp(β r,p + β s,p + α p,s ) ] Excluding both Intercepts. -1 was excluded to reduce the bias of P sr. Verification of 87% based on current available data from and Area information from Estimates stratified by season

Relative abundance in region r for season S: I sr =d sr P sr A r ~ exp (β r + β s + α r,s ) exp( β r,p + β s,p + α p,s ) A r I us,s = Σ I sr =Σ d sr P sr A r for r=1,2, and 3 in US water I total,s =Σ I sr =Σ d sr P sr A r for r=1 to 5 in US and Mx P s = I us,s / I total,s is proportion of sardine in US in season S P = Σ P s F s / Σ F s is the weighted average of proportion where F can be the no of positive flights or total flights in each season based on data. Proportion of sardine in US water (P) as weighted average of P s

Season Percent in US waters Ps N positive flights Fs Total flights Fs Winter (Jan-Mar) 87% Spring (Apr-May) 76% Summer (Jun-Sep) 88% Fall (Oct-Dec) 92%97210 Simple mean 86% Weighted mean 84%86% Weighted average of proportion of sardine in US with weighted by number of positive flights ) (84%), total number of flights (86%) from and simple average (86%)

Verification of 87% with four estimates of distribution Estimate based on original procedure used to obtain 87% 89% Estimate based on seasonal proportion 1.The seasonal proportion weighted by its positive flights from : 84% 2.The seasonal proportion weighted by its total number of flights: 86% 3.The simple average of seasonal estimates: 86%

Outline Harvest guideline computation Model used to estimate relative biomass of Pacific sardine Verification of distribution: 87% Data sources to estimate the distribution of Pacific sardine (proportion of sardine population in US water) Conclusion and discussion

Using spotter data of and not Calcofi larval data Population of sardine was low prior to 1985 Calcofi covers only US water starting 1985 Sardine population increased since mid-1980s Spotter surveys covered both US and Mexico water from

_____________________________________________ Starting 1985, Calcofi survey area has been in US water only Mex US ______________________________________________ 1985 US Mex

Using spotter data of and not Calcofi larval data Population of sardine was low prior to 1985 Calcofi covers only US water starting 1985 Sardine population increased since mid- 1980s Spotter surveys covered both US and Mexico water from , (best for summer and fall?)

Eggs/tow Larvae/0.05m2 By Calvet tows Larvae/0.05m2 By Bongo tows Catch of sardine Sardine DEPM survey in April-May 1994

Using spotter data of and not Calcofi larval data Population of sardine was low prior to 1985 Calcofi covers only US water starting 1985 Sardine population increased since mid-1980s Spotter surveys covered both US and Mexico water from

27 Distribution of aerial spotter effort from California to BC, (Kevin et al, 2007;Show) _________________________________________

Conclusions and discussions The estimates based on being 84-89% are close to 87% and should be more applicable to later years than 87% based on data As the ratio of relative abundances was used to compute the distribution, the bias due to the exclusion of interaction terms and the bias correction terms for anti-log are likely negligible. The analyses were performed close to 20 years ago. The dynamic of sardine population has changed since then. Analyses based on current data are needed to update the estimate of the distribution.

Questions?

Total flights by region and month for months summer fall US Mx Positive flights by region and month months US Mx Number of flights and positive flights for sardine by region and season from Region

32 Delta -Log linear model for tons/blocks for positive flights

33 dr = exp(β 0 + βr) used in original computation = exp( βr) used in verification

34

Number of blocks by year from

36

37

Using spotter data of and not Calcofi larval data Population of sardine was low prior to 1985 Calcofi covers only US water starting 1985 Sardine population increased since mid-1980s Calcofi larval data of winter and spring may not be optimal for estimating the biomass of Pacific sardine Spotter surveys covered both US and Mexico water from , (best for summer and fall?)

dr = exp(β 0 + βr) Pr = exp(β 0,p + βr,p) -1 For region r: I r =d r P r A r = exp(β 0 + βr) exp(β 0,p + βr,p) -1 ) A r I us = Σ I r =Σ d r P r A r = Σ e exp(β 0 + βr) exp(β 0,p + βr,p) -1 ) A r for r=1,2, and 3 I total = Σ I r =Σ d r P r A r = Σ exp(β 0 + βr) exp(β 0,p + βr,p) -1 ) A r for r=1 to 5 Distribution = I us / I total Where β 0 and β 0,p are intercepts. βr and βr,p are the coefficient for region r to estimate the density and proportion of positive flights. No interaction terms and bias correction terms were included. A r :Area size for region r Computation process of distribution of 87%

proportion by seasonNo of positive flights no of total flights winter (Jan- Mar) spring(April- May) summer(June- sept) fall(Oct-dec) ave unstratified by season0.89 Proportion of sardine in US by season with interaction terms of region and season and unstratified by season without interaction terms Weighted by Positive flights Total number of flights

dr = exp(β 0 + βr + βs+ αr,s) = exp( βr+ βs+ α r,s ) with β 0 =β 0,p =0 Pr = exp(β 0,p + βr,p + βs,p+ α r,p) -1 ~ exp( βr,p + α p,s) Excluding both Intercept and -1 reduced the bias of Pr. For season s, relative abundance was computed for each region r: I s,r =d s,r P s,r A r ~ exp (βr + βs+ α r,s) exp( βr,p + βs,p+ α p,s) A r I us,s = Σ I s,r =Σ d s,r P s,r A r = Σ exp (βr + βs+ α r,s) exp( βr,p + βs,p+ α r,s) A r for r=1,2, and 3 I total,s = Σ I s,r =Σ d s,r P s,r A r = Σ exp (βr + βs+ α r,s) exp( βr,p+ βsp + α p,s) A r for r=1 to 5 Distribution for season s = I us,s / I total,s where βr and βr,p are the coefficient for region r to estimate the density and proportion of positive flights. where βs and βs,p are the coefficient for season s to estimate the density and proportion of positive flights α r,s and α p,s are interaction terms for region and season and region and proportion of positive flights Area for each region in 1989 was used Verification of 87% based on current available data from and area information from based on stratified estimates stratified by season (S)

42 Delta-lognormal linear models (LLM) (Shimizu 1988) Excessive zero observations ----Delta The errors are not independent of the sightings ---- lognormal The sightings are affected by who, where, when and actual abundance of the fish in a multiplicative fashion ---- linear after log-transformation.

Hypothetical sardine distribution of the warm (light) and cold (dark) stock (Felis-Uraga et al. 2005) 0.87 in US 0.76 in US _________________________________________

Summer-fall season 0.88 in US 0.92 in US __________________________________________

Moratorium in 1967 Sardine population Declined starting In 1950s

I sr =d sr P sr A r ~ exp (β r + β s + α r,s ) exp[( β r,p + β s,p + α p,s )-1] A r I us,s = Σ I sr =Σ d sr P sr A r = Σ exp (β r + β s + α r,s ) [exp( β r,p + β s,p + α p,s )-1] A r for r=1,2, and 3 I total,s =Σ I sr =Σ d sr P sr A r = Σ exp (β r + β s + α r,s ) [exp( β r,p + β s,p + α p,s )- 1] for r=1 to 5 where β r and β r,p are the coefficient for region r to estimate the density and proportion of positive flights. where β s and β s,p are the coefficient for season s to estimate the density and proportion of positive flights α r,s and α p,s are interaction terms for region and season and region and proportion of positive flights Area (A r ) for each region in 1989 was used Relative abundance in US water (I us,s ) and total area (I total,s ) in region r for season S:

The estimate of d and P can be obtained with bias correction terms (equation 8, Lo et al. 1992) as d =exp[f(X,Z, β, α)]* ψ d and P+1=exp[g(X,Z, β, α)]* ψ P where ψ is the bias correction term which was not used in the original computation. In computing 87%, the relative abundance was first computed for each region (r). A weighted average was obtained with weights being no of blocks in each region. For the estimate in region ( r ), the following formulas were used for 87% dr = exp(β 0 + βr) Pr = exp(β 0,p + βr,p) -1 I r =d r P r A r For verification of 87%, the intercept estimates (β 0 and β 0,p ) and bias correction for anti-log transformation were not included based on data collected in Because E[ln(d)] not = ln[E (d)] exp(E[ln(d)] ) not =E(d)