DOI: 10.7291/d10q2m
title: Data for: An integrated population model and population viability assessment for the southern population of a data-poor species

description: We use Monte Carlo methods which draw parameters from Bayesian posterior
 distributions to generate a distribution of population size estimates and
 trajectories, thus giving managers a fuller accounting of the uncertainty
 in the population status. We then propagate this population estimate and
 its associated uncertainty into a model using Monte Carlo methods to
 assess the impact of fishing bycatch on the species. We show that the
 population is below the recovery goal of 3,000 adults. The current total
 population estimate (including juveniles) is approximately 10,000 fish.
 Our model finds that fishing bycatch pressure reduces an otherwise assumed
 stable population by a median value of 0.4% per year, which could impede
 the recovery of the species. Fisheries bycatch is only one of many threats
 this population faces, and future work is needed to assess how other
 threats, such as spawning habitat alteration through dams and water
 diversions, may affect this population’s trajectory. The framework
 presented here is suitable for further data integration or modular
 expansion to incorporate the cumulative effects of challenges facing green
 sturgeon recovery.
description: We assessed the number of spawning green sturgeon adults in
 annual surveys of the Sacramento River, CA, USA from the Irvine Finch Boat
 Ramp (river kilometer 320, just west of Chico) up to Redding (river
 kilometer 480) (Fig. 1). Acoustic tag data and egg mat studies have
 confirmed that this is the extent of the spawning grounds (Poytress et al.
 2013; Thomas et al. 2014). We surveyed any site along that section of the
 river with depths greater than 5 m (Erickson et al. 2002). Generally, we
 see green sturgeon in approximately 40 sites. This section of the river
 provides the vast majority (effectively all) of the southern DPS green
 sturgeon spawning locations.  <strong>2.3 Spawner
 survey</strong> A detailed description of the
 methods is published by Mora et al. (2015) and is only briefly described
 here. The survey has taken place continuously since 2010. There are three
 phases of the survey conducted over three weeks in mid-June. In phase one,
 a survey crew drifts downstream over the deepest parts of the channel with
 a depth sounder. The crew contour maps areas of the river with depths
 greater than 5 m using a sonar system. The survey generally finds
 approximately 70 areas with a depth over 5 m within the study area (Fig.
 1). The crew marks locations with spawner observations in the last 5 years
 for an automatic revisit in phase three. In phase two, the crew uses a
 Dual frequency IDentification SONar (DIDSON; Sound Metrics, Bellevue,
 Washington) video camera to scan for green sturgeon during 3 passes at
 sites without spawners in the previous 5 years. In phase three, the crew
 visits all sites where sturgeon have been seen in the past 5 years as well
 as any new ones added during phase two. At each site, the crew makes 7
 passes recording DIDSON footage. The DIDSON footage from phase three is
 reviewed in random order three times and counts are combined into an
 estimate of the number of sturgeon at each site location. The sum of
 counts from all sites is the total number of spawners observed.
 <strong>2.4 Life table, IPM, and sensitivity
 analysis</strong> <strong>2.4.1 Literature
 parameters</strong> Both the IPM and life table
 models need some parameters describing demographics, behavior, and
 physiology. We took a subset of these parameters directly from the
 literature (Appendix S1). All these parameters are for the northern DPS
 green sturgeon as similar data is unavailable for the southern
 population. <strong>3.4.2 Length vs. age
 relationship</strong> We used the age vs length
 data for southern DPS green sturgeon on the Sacramento River from
 supplement 1 of Ulaski and Quist (2021). We fit these data with Bayesian
 regression in R using JAGS (packages used rjags, purr, ggplot, dplyr,
 patchwork, viridis, minpack.lm, ggextra, mcmcplots, and furrr) (Plummer
 2003; R Core Team 2015; RStudio Team 2015; Wickham 2016b; Elzhov et al.
 2016; Wickham 2016a; Curtis 2018; Wickham et al. 2018; Garnier 2018;
 Attali & Baker 2019; Pedersen 2019; Vaughan & Dancho
 2021). The model and priors are as follows:  
 L ~ normal(Μ_L, Τ)
 Μ_L = L_∞ (1-e^((-k(A-t_0)))) L_(∞ ) ~
 normal(μ = 190 cm, τ = 0.05 (1/cm)) k ~ gamma(ϕ = 1, θ
 = 0.2 (1/yrs)) t_0 ~ normal(μ = -3 yrs, τ = 0.001
 (1/yrs)) Τ ~ gamma(ϕ = 0.001, θ = 0.001
 (1/cm)) Eq. 1
 where L is
 the length, M<sub>L</sub> is the mean of the length
 distribution, T is the precision of the length distribution,
 L<sub>∞</sub> is the asymptotic length, k is the growth
 coefficient, A is age in years, and t<sub>0</sub> is agee at
 zero length. Priors are loosely informed by data from northern green
 sturgeon (Adair et al. 1983; Farr et al. 2002). We ran three MCMC chains
 with 1000 adaptation steps and 20000 burn-in steps and saved 10000 samples
 per chain at 90% thinning. Each chain had random starting values based on
 draws from the prior distributions. All chains converged based on visual
 inspection or running means. We compared these results to fits for the
 northern DPS of green sturgeon as previous population estimates used that
 data (Beamesderfer et al. 2007; Mora et al. 2018).
 <strong>3.4.3 Annual survival</strong>
 Appendix S1 presents an estimate of mortality based on a catch
 curve analysis from a fishery in the Columbia Estuary. We used the
 telemetry data from the sturgeon on our system to calculate annual
 mortality. We then used these two values to bookend the estimate of annual
 mortality in the life table model and IPM. We used data from the BARD for
 all green sturgeon tags from 2007-2018. We only used data where length was
 labeled as either total length or fork length. We converted all lengths to
 fork lengths and all lengths reported in this manuscript are fork lengths.
 We used the mean parameters from Eq. 1 to convert the lengths to ages. We
 grouped the data in 5-year bins to reduce noise. Instantaneous mortality
 is equal to the slope of the change in counts with age after natural-log
 transformation. We calculated the slope of the descending arm and
 converted it from instantaneous mortality to annual survival using (annual
 survival) = exp(-instantaneous mortality) (Ricker 1975). Subsequent
 calculations involving survival drew mortality from a uniform distribution
 over the range between the Columbia River and this estimate.
 <strong>3.4.4 Probability of being an
 adult</strong> Rather than using published ages
 of maturity or the maturity curve implied by the Beamesderfert al. (2007)
 cohort model, we based the timing of maturity on data specific to the
 southern population. We calculated the probability that fish of a certain
 length are adults (i.e. potential spawners) using the same raw data set
 from the BARD. We flagged fish as adults if they were marked as “mature”,
 “adult,” or “eggs” (meaning they were caught with eggs) or if detections
 were above river kilometer 320 (the bottom of the spawning ground) (note
 the BARD uses a different river kilometer 0, thus river kilometer 320
 equates to 410 in the BARD). Only tagging-year records were used so that
 length and maturity data were contemporaneous. We grouped individuals by
 sex into females and others (males and unknown). We obtained two separate
 estimates of the probability of maturation with length using Bayesian
 logistic regression. The first estimate was a sex-specific hierarchical
 model fit divided between females and others in which the sexes shared a
 common slope but had separate intercepts. We used the female parameters
 from this model in the sensitivity analysis calculation because that
 analysis needed fecundity. The second estimate was a fit with all the data
 for use in the population estimate, which needed the total number of
 spawners. The models are as follows: 
 P ~ Bernoulli(Μ_A) Μ_A =
 (1+e^(-(b_0+b_1 L)))^(-1) b_(1 ) ~ normal(μ = 0 (1/cm),
 τ = 10^(-12) cm) b_0 ~ normal(μ = 0, τ =
 10^(-12)) Eq. 2
 where P is
 the probability of being an adult, M<sub>A</sub> is the mean
 of the probability distribution, L is the length,
 b<sub>0</sub> is the intercept and b<sub>1</sub>
 is the slope. Thus, in the hierarchical model, females and others share
 the b<sub>1</sub> term but have separate
 b<sub>0</sub> terms. We used broad normal priors (Eq. 2). We
 ran three chains with 1000 adaptation steps and 20000 burn-in steps and
 saved 10000 samples at 90% thinning per chain. Each chain had random
 starting values based on draws from the prior distributions. All chains
 converged. We compared these results to fits for the northern population
 of green sturgeon as previous population estimates used that data
 (Beamesderfer et al. 2007; Mora et al. 2018).
 <strong>3.4.5 Spawning interval
 distribution</strong> The population estimate
 portion of the IPM needs the distribution of spawning intervals for all
 adults and the sensitivity analysis requires the average spawning interval
 of females. To calculate these data, we took all detections from the BARD
 above river kilometer 320 for months during the spawning season (March -
 September). We removed any detections from the same year the fish was
 tagged as well as any detections for fish without a detected outmigration
 between upstream records. For each fish, we then found both the interval
 between tagging and the first return and, if available, the interval
 between the first and second return. We divided these into two groups (all
 fish and females). We then constructed a distribution showing the fraction
 of fish that have a return interval greater than each interval and
 calculated the average return interval. We compared these results to fits
 for the northern population of green sturgeon as previous population
 estimates used that data (Beamesderfer et al. 2007; Mora et al.
 2018). <strong>3.4.6 Calculate the fraction of
 the population that is adults and spawners</strong>
 We then sampled from the estimated distributions of survival,
 maturation, and spawning interval described above to make 10,000 life
 tables (the average parameter values converged at approximately 8,000
 samples) from which we calculated the fraction of the population that is
 adults. We selected a random set of parameters from the posterior
 distribution of the Bayesian fit of the length vs. age data, a slope
 parameter for the length-to-weight equation using a normal distribution
 and confidence interval from Appendix S1, a mortality value from a uniform
 distribution between the two annual mortality values, and a random set of
 parameters from the posterior distribution of the Bayesian fit of the
 probability of being an adult vs. length data. We used the length age
 relationship to calculate the length at each age from a life table
 starting at age 1. Each year we calculated the number surviving using the
 mortality estimate. We calculated the probability of being an adult given
 length and thus the total number of adults each year. Using the average
 spawning interval, we then calculated the number of adults that spawn each
 year.  <strong>3.4.7 IPM
 </strong> To calculate 10,000 different rolling
 population estimates, we first selected values for the number of spawners
 seen each year. We get these values by drawing a random number for each
 year of the survey. These random draws are from normal distributions with
 mean and confidence intervals for the number of spawners observed each
 year in the survey. We then calculated a rolling estimate of the number of
 adults using the following equation: 
            (I_max-1)<br>N_A = ∑
 [N_(s,j)  S^j  P(I&gt;j)]<br>           (j=0)
 Eq. 3 
 Here N<sub>A</sub> is
 the number of adults in the population, I is the return interval,
 I<sub>max</sub> is the maximum return interval,
 N<sub>s,i</sub> is the number of spawners seen in year j, S is
 the annual survival rate drawn from a uniform distribution over the
 estimated range of survival, and P(I &gt; j) is the probability of a
 return interval greater than j. Years before the first year of the survey
 (2010) are assumed to have the same values as the first year for
 calculation purposes. To estimate the distribution of the total population
 size across years while reflecting parameter uncertainty, we divided each
 of the estimates of the adult population by the fraction of the population
 that is adults (mature). We took this fraction from a randomly selected
 life table drawn from the set of life tables with equal values of annual
 survival as used in Eq. 3. <strong>3.4.8
 sensitivity analysis</strong> To look at the
 potential effect of fishing bycatch pressure on the population, we first
 built a set of life tables with a stable population, then applied fishing
 pressure and calculated the effect on the population growth rate. We took
 500 samples from the set of population estimates. Each sample was the
 population estimate of the most recent year (2018) and the full set of
 parameters used to calculate that estimate. We then made a life table with
 the 2018 population estimate and those parameters. We solved for the
 annual recruitment (egg to first-year survival) to make the life table
 stable in time.  To perturb this life table with
 fishing pressure we used the fleet-wide bycatch estimate for the numbers
 of southern DPS green sturgeon caught in the open access California
 halibut fisheries (79% of captures are in this fishery), limited entry
 California halibut fisheries, and the limited entry and individual fishing
 quota bottom trawl (Richerson et al. 2019), at-sea hake fishery, and the
 total population estimate to calculate the possible fractions of the
 population which are caught. This method allows the number caught to
 decrease as the population decreases, i.e., we assumed that the bycatch
 would represent a consistent fraction of the population caught and not
 simply a consistent number of fish caught regardless of population level.
 There were only 16 annual bycatch numbers available and so the calculation
 randomly selected one value each year rather than sampling a fitted
 distribution. From the bycatch reports we knew the size distribution of
 bycatch, which we used to distribute the bycatch risk over appropriate
 length classes. We then simulated each of the 500 sample sets out over 100
 years. For each year we drew a random fraction caught from the data set.
 Then we used that fraction and that year’s current population level to
 calculate the number caught. We distributed these catches over the lengths
 in the life table based on the bycatch length data. Each length class got
 several random draws equal to the total number of fish caught that year.
 This value was multiplied by the probability of a bycatch incident being
 in that length class times the probability of the fish dying. The
 probability of a fish dying is 25% based on the probability of a fish
 dying in the net (25/508) (Lee et al. 2020 see Figure 2-12 raw data in
 Appendix S2 of this manuscript) and the probability of a fish dying
 post-release (11/51) (Doukakis et al. 2020) (1-[1-25/508]*[1-11/51] =
 0.25). After the program removed the number of sturgeon bycaught from the
 population, it advanced all age classes by one year and calculated a new
 age-1 population. We repeated this process 100 times to project the
 population over 100 years.
description: # Data for: An integrated population model and population viability
 assessment for the southern population of a data-poor species
 [https://doi.org/10.7291/D10Q2M](https://doi.org/10.7291/D10Q2M) ##
 Description of the data and file structure Variables: * estimatedCount:
 The estimated average number of green sturgeon * variationCount: the
 variation in the count * error: the standard error of the count *
 squareError: error squared * SDCount: the standard deviation of the count
 * lowerCI: the lower confidence interval * upperCI: the upper confidence
 interval * year: the survey year * fractionMissed: the fraction that were
 traveling between spawning holes during the survey according to telemetry
 data * total: the total number of tagged fish in the spawning ground that
 year * outTotal: the total that were on the spawning ground sometime that
 year but not when we surveyed according to telemetry data * fractionOut:
 that fraction that we missed in the survey ## Sharing/Access information
 NA ## Code/Software NA