Bayesian Analysis of Extinction Risk in Atlantic Salmon

A.J.F. Gibson1, P.G. Amiro1 and R.A. Myers2

1Department of Fisheries and Oceans, Dartmouth, NS 2Dalhousie University, Halifax, NS

Overview • Endangered Species • Approach to Assessment • Questions - Needs • Inner Salmon • Index-based model of population size and trajectory • Summary: • Bayesian considerations for endangered species • Future work

Species-at-Risk vs. Fisheries Modeling

• The range of actions or activities to be evaluated are typically wider • habitat protection, creation or restoration, supportive rearing, bycatch reduction

• Abundance is at levels where dynamics are less certain • potential Allee effects, demographic vs. environmental stochasticity

• Populations are often data poor

• Higher level of precision is sometimes required • unachievable

• Dynamics have likely changed • implications for selection of priors Endangered Species: Challenges for Modelling • Challenges: • often data poor • life history often not well understood

• Recovery planning has very specific requirements: • assessment of recovery potential, critical habitat designation, recovery targets • may require greater knowledge and model resolution than for exploited species • What is the role of Bayesian methods in this process?

Species at Risk: Three Key Questions

1. What is the population’s current size and trajectory? • Risk, timeline for recovery

2. What are the differences in the past and the present population dynamics? • Which life history parameters changed, when and by how much? • Are there correlates that may explain the pattern?

3. Is the population tracking a declining carrying capacity? • importance of density dependence • key question for recovery planning Inner Bay of Fundy Atlantic Salmon

• Designated as endangered by COSEWIC and listed by GoC on Schedule 1 (SARA prohibitions in effect) • IBoF Salmon are different and distinct from other salmon populations • life history: • very high incidence of fish that mature after 1 winter at sea • high incidence of repeat spawning • genetic: • unique mitochrondrial DNA haplotype that has not been found in salmon outside the inner Bay of Fundy IBoF Atlantic Salmon: Area of Occupancy

Big Salmon River

E

E

Stewiacke River

0 25 50 kilometers River, NS: Salmon Data

Year 1960 1970 1980 1990 2000 Rec. Catch (adults) Adult Counts (fence) Adult Counts (boat electrofishing) Adult M-R estimates Adult Age Comp. Electrofishing Big Salmon River, NB: Salmon Data

Year 1960 1970 1980 1990 2000 Rec. Catch (adults) Adult Counts (fence) Adult Counts (snorkel) Adult Age Comp. Redd Counts Electrofishing Smolt Counts (Fence) Smolt Counts (M-R ests.) Smolt Age Comp. The Problem

• We want to estimate the population size and trajectory from the available data • when did the decline occur? • is the population still declining? • when is extinction expected to occur?

• From a Bayesian perspective can we avoid subjectivity (prior belief) when building the model? Two Model Components: 1. Annual abundance estimated by modeling catch-effort data and any auxiliary data that can be interpreted as an abundance index (Rago 2001) • Parameter estimates are obtained using ML • Parameter uncertainty is assessed using MCMC to derive posteriors 2. Forward projections (PVA) using Monte Carlo simulations using the estimated change in population size from one year to the next (Dennis et al. 1991) • Projections using the posteriors for abundance, and the mean and variance of log(lambda) • Advantages: uncertainty in parameter estimates is included in the PVA; parameter covariance is preserved

The Model (catch equations)

• We begin with the standard catch equation for a Type I fishery:

−Ft ,s Ct,s = Nt,s (1− e )

• We assume Ft,s is proportional to the fishing effort in year t: F = q E t,s s t The Model (harvesting)

• Calculated the proportion of the catch that was harvested • 0.824 for small salmon (1983 to 1990) • 0.758 for large salmon in 1983. • used as constants in analysis • could lead to overestimate of escapement in early years

Esct,s = Nt,s − Ht,s The Model (fence counts)

• Counts assumed complete in 1994 and 1995, but not in 1992 and 1993. • The 1992 and 1993 counts were adjusted upwards using the mark and recapture estimates. • The fence counts then equal to the number of fish returning to the river in each size category and each year:

Fencet,s = Nt,s The Model (adult electrofishing)

• electrofishing occurs after fishing and is an index of escapement • reported for size categories combined • modeled use the catch equation:

qboat Eboat ,t Cboat,t = (1− e )∑ Esct,s s The Model (egg deposition)

• mean fecundity of salmon was calculated using data of Amiro (1990) • weighted by number at age and sex ratio • 2,364 eggs per small salmon • 7,545 eggs per large salmon • used as constants in this analysis

Eggst = ∑ Esct,s fecs s The Model (juvenile electrofishing)

• we use Beverton-Holt model to describe the relationship between juvenile abundance and egg deposition in the previous years: • age-0 density in year t is a index of egg deposition in year t-1 • age-1 density in year t is a index of egg deposition in year t-2 • age-2 density in year t is a index of egg deposition in year t-3 • two parameters estimated for each size class α Eggs P = a t−a−1 t,a α Eggs 1+ a t−a−1 R0a The Model: estimated parameters

• We set up the model to estimate: • the log of the total escapement in each year (37 parameters) • the average proportion of the population that are small salmon (1 parameter) • the catchability coefficients for the recreational fisheries and boat electrofishing (3 parameters) • the slope at the origin and asymptotic level for the 3 ages of fish in the electrofishing data (6 parameters) • Total of 47 parameters Model Fitting:

• Parameter estimates were obtained using maximum likelihood • Lognormal errors were assumed for all data except the adult mark-recapture experiments (hyper-geometric structure assumed) • σ could not be estimated for all data sets simultaneously • fixed σ at 0.33 for the electrofishing data and estimated σ for the other model components • Parameter estimates were obtained by minimizing the value of an objective function (O.B.V.) that is the sum of the negative log likelihoods (no weights):

O.F.V. = −( fence +  catch +  electrofishing +  boat +  mr ) The Model (Bayesian component)

• We assumed uniform bounded priors for all model parameters • Bounds were wide enough not to influence the fit. • We used 2,000,000 iterations after a burn in of 200,000 iterations. • We sampled every 2,000th iteration to derive the posterior distribution. • This level of thinning was sufficient to ensure that autocorrelation in the chain was not problematic.

The Model (diagnostics)

• We ran many iterations of the model using several starting values to ensure convergence to a global maximum • model is robust in this respect • Convergence of the Markov chain was inferred informally • by comparison of the posterior densities based on the first 1,000,000 iterations with those from the second 1,000,000 iterations • by comparison of the posterior densities from several chains

Results (recreational fishing)

Recreational Fishing Effort

10000 • effort increased through 8000

6000 4000 the '70's and early 80's Days Rod 2000 and then decreased 0 1970 1980 1990 2000 • catches are variable but Year increase in the 1980's Large Salmon Catch 600

400 • fitted catch tracks the

200

observed catch of Fish Number 0 reasonably well 1970 1980 1990 2000 • a near perfect fit is Year Salmon Salmon Catch obtained if the 2000 1500

proportion in each size 1000

500 category is estimated of Fish Number 0 for each year 1970 1980 1990 2000 Year Results (recreational fishing)

• MLE's for the log of catchability coefficients are: - 9.522 (small) and –10.214 (large) • smaller fish are easier to catch Given an effort of 3000 rod days: the MLE and 80% B.C.I. for the catch 1.0 0.8 rates are: Small Salmon Large Salmon 0.8 0.6 Large salmon: 10.4% 0.6 0.4 (6.5 to 20.1%) 0.4 0.2 0.2 Probability Density Probability Small salmon: 19.7% Density Probability 0.0 0.0 (13.0 to 34.1%) -14 -12 -10 -9 -8 -14 -12 -10 -9 -8 log(q) log(q)

Results (recreational harvest rates) • Shown MLE's and 95 % CI's for the annual harvest rates Recreational Fishery Exploitation Rate: Small Salmon 0.8 MLE's for harvest rates 0.6 increased to a maximum of 0.4 0.2 40.5 % (small salmon) and Rate Exploitation 0.0 21.8 % (large salmon) in 1970 1980 1990 2000 1983 and decreased Year thereafter Recreational Fishery Exploitation Rate: Large Salmon 0.8 Rates would be 0.6 underestimated if catch and 0.4 0.2 release increased during Rate Exploitation 0.0 time 1970 1980 1990 2000 Year

Results (boat electrofishing)

• Catches with the electrofishing boat ranged between 58 salmon (1991) and 0 (1997) • Effort ranged between 31.8 and 123 km • At an effort of 40 km, the expected catch is 1.4% Electrofishing of the population 0.6 Boat

0.4 Boat El ect r of ishi ng: l ar ge and small sal mon combi ned

60 0.2

40 Probability Density Probability

20 0.0

Number of Fish 0 -9 -8 -7 -6 1985 1990 1995 2000 log(q) Year Results (juvenile electrofishing)

200

• Between 27 and 44 150 age-0 sites electrofished 100 annually since 1984 50 0 • Consistent downward 1985 1990 1995 2000 trends are evident for 200 150 age-1

all three age classes 100

50

• no wild fry captured 0 1985 1990 1995 2000

since 1999 Density (number/100m^2) • slight increase in age-1 30 age-2 20

density in 2002 10

probably due to LGB 0 1985 1990 1995 2000 releases Year Results (juvenile electrofishing)

Age-0 Density 120 100 80 60 • Fitted densities capture 40 20 the pattern in the m^2 Fish 100 per 0 1970 1980 1990 2000 observed data Year Age-1 Density reasonably 40 30 • Exceptions are: 20 10

• age-0 fish in the late m^2 Fish 100 per 0 1970 1980 1990 2000 1960's Year Age-2 Density • age-1 parr in the mid 10 8 1980's (two years only) 6

4 • age-2 parr in the mid- 2

Fish per 100 m^2 Fish 100 per 0 1980's 1970 1980 1990 2000 Year Results (juvenile electrofishing)

Age-0 120 100 80 • Relationships between egg 60 40 deposition and juvenile 20 Fish per100 m^2 0 densities are shown 0 10^7 2*10^7 3*10^7 4*10^7 Number of Eggs Age-1 • Density dependent effects 40 appear stronger in the 30 20 older age classes 10

Fish per100 m^2 0 0 10^7 2*10^7 3*10^7 4*10^7 • Estimated carrying Number of Eggs Age-2 capacities are: 10 2 8 • age-0 = 59.1 fish/100 m 6

2 4 • age-1 = 20.8 fish/100 m 2 2 Fish per100 m^2 0 • age-2 = 6.1 fish/100 m 0 10^7 2*10^7 3*10^7 4*10^7 Number of Eggs Results (juvenile electrofishing)

0.006 0.8 Age 0 0.005 Age 0 0.6 0.004 • Posterior probability densities 0.003 0.4 0.002 are shown 0.2 0.001 0.0 0.0 • high uncertainty in age-0 R0 -14 -12 -10 -8 0 200 600 1000 log(alpha) R0 • pattern in alpha is inconsistent 0.8 0.06 • can't produce less age-0 fish 0.6 Age 1 Age 1 0.04 • than age-1 fish in a cohort 0.4 0.02 • overdispersion or size-selective 0.2 0.0 0.0 sampling are 2 possible -14 -12 -10 -8 0 20 40 60 explanations ProbabilityProbabilityProbabilityProbabilityProbabilityProbability Density Density Density Density Density Density log(alpha) R0

• not problematic if the 0.12 0.6 Age 2 0.10 Age 2 relationship is stationary since 0.08 0.4 the densities are being used as a 0.06 0.2 0.04 0.02 index 0.0 0.0 -14 -12 -10 -8 0 20 40 60 log(alpha) R0 Results (abundance time series)

• Estimated abundance shows Small Salmon Returns 8 annual variability but a 6

4 decreasing trend since the mid- 2 Thousands of Fish 1970's 0 1970 1980 1990 2000 • Estimated returns were highest Year Large Salmon Returns

in 1974 at 10,800 salmon 4 3

(80% BCI = 5,100 to 24,800) 2 1

• Estimated returns have not Thousands of Fish 0 exceeded 50 since 1997 1970 1980 1990 2000 Year

• Based on the model, there is a MR Estimates and Total Returns 30 90% probability that less than 25 20 2, 10 and 8 fish returned to the 15 10 5 Stewiacke River in 1999, 2000 Thousands of Fish 0 and 2001 respectively 1970 1980 1990 2000 Year Percent Decline

• Calculated the 5 year mean number f fish returning to the river annually for the periods: • 1997 – 2001 • 1991 – 1996 (5-year comparison) • 1987 – 1991 (10-year comparison) • 1977 – 1981 (20 year comparison) • 1967 – 1971 (30 year comparison) • Percent decline calculated using the ratios of the 5 year means

Trends in Adult Abundance

• Stewiacke R: 20 Stewiacke River, NS 15 10

5

0 • Big Salmon R. 1970 1980 1990 2000 8 Big Salmon River, NB 6 Thousands of Fish of Thousands 4

2

0 1970 1980 1990 2000

Year Posteriors for Percent Decline in 5-Year Mean Population Size

Stewiacke River, NS Big Salmon River, NB

0.25 0.03 0.20 5 Year 5 Year

0.15 0.02

0.10 0.01 0.05

0.0 0.0

75 80 85 90 95 100 40 60 80 100

4 0.25

3 30 Year 0.20 30 Year

Probability Density Probability 0.15 2 0.10 1 0.05

0 0.0

95 96 97 98 99 100 80 85 90 95 100

Percent Decline Results (declines)

• calculated the ratio Nt/Nt-1 to evaluate patterns in changes in abundance overall trend in abundance was downward since the mid 1970's, but prior to 1990, the population increased as often as it deceased (decreases were greater than increases) • since 1990, the abundance has decreased in 9 of l ambda the 12 years 4

3

2 lambda 1

0 1970 1980 1990 2000 Year Posteriors for Log-Normal Distribution for λ

Stewiacke River, NS Big Salmon River, NB

15 5 median 4 median 10 3

2 5 1

0 0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

3.0 1.0 2.5 sigma 0.8 sigma 2.0 Probability Density 0.6 1.5 0.4 1.0 0.5 0.2 0.0 0.0

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

Lambda Monte Carlo Population Projections

• One simulation per step in Stewiacke River, NS the Markov Chain (1000 15 simulations in total) 10

• Starting N and mean and 5 std. dev. of λ from each 0 step 2000 2005 2010 2015 2020 150 Big Salmon River, NB Number of FishNumber • Random variability added 100 by sampling from a 50 lognormal distribution for 0 λ for each time step in the 2000 2005 2010 2015 2020 projection Year

Summary

• Application: • Index-based approach useful when insufficient data available for full age-structured population model

• Bayesian methods allow uncertainty in all parameters to be carried forward into the PVA while preserving parameter covariance

• Limitations: • Observation error not separated from process error • Confounding effects: e.g. aquaculture escapes

• Next Steps: • Risk analysis by evaluating relationship between λ and explanatory variables

Potential Biases:

• By not including the commercial fishery we are underestimating spawning run size in the 1970's and 1980's and therefore percent decline • Timing of 5-year periods selected to reflect decades and do not include the highest abundance estimates in the mid-1970's • The assumption that catch-release practices did not change would lead to an overestimation of egg deposition in the earlier years (effect on percent decline is unknown) • The assumption that fishing mortality is a linear function of effort. If catchability increases as population size decreases the effect would be to underestimate the percent decline • relationship estimated at low abundance Results (commercial fishing) • The commercial harvest is reported in SFD's 42 and 43 which include other rivers • Not included in the model due to uncertainty in the proportion of the landings that are native to the Stewiacke R. • if all were native, Commercial Catch (Districts 42 and 43)

exploitation rates 2500

would have ranged 2000

between 7 and 46 %. 1500

1000 Number of Fish of Number 500

0

1970 1980 1990 2000 Year Distribution and Abundance

2000 2002 2003 •Electrofishing in 49 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 N N N iBoF rivers since Mispec River [ ] 2 1 0 Black River [] 1 [ ] 3 [ ] 3 Emerson Creek 2 0 0 Gardner Creek [ ] 2 1 0 2000 Bains Brook [ ] 3 [] 1 0 Mosher River 1 0 0 Irish River [] 2 [ ] 3 0 Big Salmon River [ ] 5 [ ] 7 [ 12 Little Salmon River [ ] 2 [] 1 0 Quiddy River 2 0 0 Goose Creek 2 0 0 Goose River 0 3 0 Point Wolfe River 0 [ ] 24 [ ] 6 •Evidence of river 0 [] 32 [] 6 Shepody River 0 1 0 Crooked Creek [] 1 1 0 Demoiselle Creek 1 [] 1 [ ] 3 specific extirpations [] 8 [ ] 8 [ ] 14 2 9 8 Carters Brook 0 3 1 Tantramar River 1 0 0 during this time Maccan River 4 [] 9 0 [] 3 4 0 Apple River 3 4 0 Ramshead River 0 1 0 Diligent River 2 1 0 period Parrsboro River [] 2 [ ] 3 0 Moose River 0 1 0 Harrington River 2 [ ] 7 0 North River 0 1 0 Economy River [] 2 3 3 Bass River 3 4 0 Portapique River [ ] 2 7 2 Great Village River [ ] 2 [] 6 [] 2 •LGB supported Folly River [] 1 [ ] 4 1 Debert River 0 [ ] 3 0 Chiganois River 2 [ ] 2 0 North River (Truro) [] 4 [] 7 [] 2 rivers provide Salmon River (Truro) 2 6 12 Stewiacke River [ ] 33 [ ] 40 [ 34 [ ] 2 [] 7 0 3 [] 7 0 0 3 0 evidence that rivers St. Croix River [ ] 4 0 0 Halfway River 0 2 0 [] 1 [ ] 8 [ ] LGB supported 3 [ ] 3 5 0 are capable of Habitant River 0 2 not LGB supported 0 Pereaux River 0 1 0 supporting juvenile salmon populations 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Density (number/100 m²) Equilibrium analysis of the effect of changing habitat quality and quantity

Past ( 1964 - 1989) Pr esent ( 1990 - 2003) 40 40

30 30

20 20

10 10 Smolt (thousands) Smolt 0 (thousands) Smolt 0

0 10 20 30 40 0 10 20 30 40 Eggs ( mil l i ons) Eggs ( mil l i ons)