A biostatistician with 30 years of experience



Because the Gompertz model, like the Ricker model, may be fit using linear least squares, we analyzed its properties as a multistage stock-recruitment model. We found that if a life cycle model is a sequence of Gompertz stock and recruitment curves at each life stage, then the entire life cycle is also a Gompertz stock-recruitment model. This is similar to the well-known result for the Beverton-Holt stock-recruitment model. The Gompertz model is guaranteed to yield least squares estimates and therefore, can offer a distinct advantage over the Beverton-Holt model, which cannot be fit using linear regression and may not yield valid maximum likelihood estimates. We illustrate the use of this modeling framework by applying it to Snake River Spring/Summer Chinook Salmon. Past work by others on these populations has usually assumed that parr-to-adult survival is density-independent. However, we found that this assumption is incorrect: when we applied a two-stage Gompertz model to these populations, we found that density dependence also occurs at the parr-to-adult stage. This suggests that previous life cycle modeling has been overly optimistic about the benefits of survival rate increases in the hydrosystem and elsewhere to improve the viability of salmon populations threatened with high extinction risk.

For salmon populations in the Columbia River basin, estimates of the proportion of hatchery-origin adults in spawning areas (p) are needed to assess population status and potential for interbreeding between hatchery- and wild-origin adults. To identify hatchery-origin fish on spawning grounds, some hatchery releases are given visible marks, some are tagged with coded-wire tags (CWTs) or parentage-based tags (PBTs), or all three. The PBT approach uses genotypes of hatchery broodstock and parentage assignments to identify the origin and brood year of their progeny. We derived a maximum likelihood estimator (MLE) of p and applied it to the 2012 and 2013 carcass survey data for Spring Chinook salmon Oncorhynchus tshawytscha in the South Fork Salmon River, USA. Precision of p from MLE increased with the expected number of tag recoveries, whether CWT or PBT. In the South Fork Salmon River application, there were 340% more parentage-based tag recoveries than CWT recoveries, leading to greater precision in release-specific ps from MLE. To design a program for estimating p, we recommend selecting a target level of precision and then choose a tagging fraction and sampling rate that delivers that precision in the most cost-effective way.

Using the optimality paradigm of movement ecology, behavior of river-dwelling juvenile salmonids is modeled in terms of the trade-offs among feeding, predator avoidance, and migration. The model predicts seven possible optimal behaviors that fall into two broad categories: feeding and predator avoidance or rapid migration. Optimal behavior is determined by the marginal fitness of displacement relative to marginal predation risk of displacement, the current velocity, and bioenergetics. If the absolute value of marginal fitness of displacement exceeds the marginal predation risk of displacement, rapid migration is favored over feeding and predator avoidance. Downstream migration is characterized as active or passive, depending on the bioenergetic cost of swimming. The optimal foraging behavior is either station holding or appetitive movement, depending critically upon the maximum current velocity. If maximum current velocity falls below the optimal growth speed, appetitive movement may be favored over station holding. This suggests an experiment to test the influence of current velocity on foraging and migration behavior. The model is compared to observed movement patterns of juvenile ocean-type chinook salmon in streams.
On the Columbia River, at the Bradford Island Visitor’s Center of Bonneville Dam, visitors peer through windows into a fish ladder to witness the pageant of native Pacific salmons. In early summer, however, visitors instead see large schools of non-indigenous American shad, an anadromous clupeid fish native to East Coast rivers that first invaded the Columbia River in the 1870s. Tallies of adult shad on the Columbia River have been available since the U.S. Army Corp of Engineers began counting them in the fish ladders of Bonneville Dam (river km 235) in 1938. The ladder counts show that after The Dalles Dam (river km 309) was built in 1957, the adult shad population passing through Bonneville Dam increased dramatically. By 1977, adult shad at Bonneville Dam outnumbered adult fish of all native salmon species combined. Since it was known from pioneering work by William Leggett in the early 1970s that the timing of the spawning migration of shad corresponds closely to temperature, we hypothesized that the successful upriver colonization of the Columbia River was in part dependent on temperature. To test this hypothesis, we regressed the percentage of adult shad population that migrates beyond McNary Dam (river km 471) against temperature measured at Bonneville Dam. Statistical regressions showed that the upriver distribution of shad was significantly related to temperature averaged over the months of May-August. In warmer years, larger proportions of adult American shad migrate to spawning areas upstream of McNary Dam. When average temperature rose by 1 degree C, the regression model predicted that roughly 8% more of the shad population counted at Bonneville dam migrated to points upstream of McNary Dam. This suggests that the gradual conversion of the Columbia River into a series of reservoirs has altered temperatures regimes in favor of a wider shad distribution, possibly increasing shad reproductive success, and partially explaining trends in abundance observed for this invasive species
Wherever they are sympatric, Chinook salmon populations spawning in interior locations typically return earlier than populations spawning in downstream locations. We hypothesized that since Chinook spawning downstream require a shorter upriver migration on average, they delay river entry to take advantage of a slightly longer ocean feeding period. Furthermore, in contrast, interior Chinook populations migrating through upriver streams which are sometimes impassable during the migration season, begin migrating earlier to avoid missing the best spawning opportunities. To test this hypothesis, we described the selective pressures on migration timing in a stochastic optimality model, and then used the model to predict the upstream migration timing of interior populations compared to downstream populations. We found that optimal run timing depended critically upon the distribution and duration of passage opportunity time wlndows in the stream. All else being equal, individuals experiencing rarer passage opportunities optimally begin upstream migration before those experiencing more frequent passage opportunities. Since downstream spawning populations not only experience more frequent, if not continuous, passage opportunities, but require less time to travel to their spawning grounds, they optimally begin migrating later than interior populations.