We performed two modeling exercises to estimate the relative fitness of the yearling and subyearling migration tactics. The modeling exercises were based primarily on detailed demographic data for adult Snake River fall Chinook salmon that had been intercepted at the adult trap at Lower Granite Dam between 1999 and 2006, before being transported to Lyons Ferry Hatchery (Fig. 1). At the hatchery, the gender and length of each fish were determined, and scales were sampled. Based on subsequent scale reading, natural fish were distinguished from hatchery fish, total age was identified and age at ocean entry (subyearling versus yearling) was determined (see Connor et al. 2005 for methods). The combined population of wild spawners sampled at Lyons Ferry Hatchery consisted of approximately 70% spawners destined for the Snake River and 30% to the Clearwater River. Based on scale samples taken from adults on the Clearwater spawning grounds, the ageclass distribution for adults that came from subyearling or yearling juvenile migrants was the same as for the combined population sampled at Lyons Ferry Hatchery; however, 76% came from yearling juveniles. We, therefore, weighted the overall adult returns by the Clearwater River proportions to estimate the expected proportion of Snake River adults that came from subyearling and yearling migrants. We estimated fecundity of females from their length and an egg–length relationship derived by Galbreath and Ridenour (1964).
The analyses are based on the Euler–Lotka equation (Lotka 1959) for individuals maturing at ages 3–6:
 (1)
where x refers to the age at maturity, r is the fitness, l_{x,y} the survival through age x for migration tactic type y and m the corresponding fecundity (see Stearns 1992 for examples of applications of this equation to populations). Based on agespecific survival and fecundity estimates, we solved for fitness, r_{y}, for each migration tactic type.
The first analysis examined how relative fitness of yearling migrants to subyearling migrants varied in response to ranges in lifestagespecific survival that characterize the uncertainty in these parameters. We varied survival across two juvenile life stages and early ocean survival. In this analysis, we estimated a separate fitness for each ageatmaturity and migration tactic and determined relative fitness for fish of the same ageatmaturity.
The goal of the second analysis was to estimate the relative fitness (for all age classes combined) of individuals adopting the yearling versus subyearling migration tactic. We related relative fitness to a key, but unknown parameter – the proportion of juveniles adopting each migration tactic. After we specified this parameter, we could determine the relative survival (and consequently relative fitness) of each lifehistory type based on the proportion of returning adults known to have adopted each lifehistory type as juveniles.
Method 1
The primary purpose of this analysis was to identify the range of survival probabilities that would differentially favor individuals that adopt the yearling and subyearling smoltmigration tactics. Life tables delineate the agespecific survival probabilities and fecundity for individuals adopting either the subyearling or yearling tactic and returning to spawn after 1, 2 or 3 years at sea (Tables 1, 2). Irrespective of the tactic adopted, individuals are assumed to have the same survival probabilities from the egg stage to the time they emigrate from the Snake River (S_{emigrant} = 0.10) and in the ocean as subadults (S_{sea} = 0.80 per annum). There are two key differences in the life tables. The first is the term S_{river} that represents the probability that a smolt survives the period (approximately 1 year) during which it resides in freshwater. This parameter was allowed to vary between 0.2 and 0.8. The second difference in the life tables is the survival probability experienced during the migration of smolts through the Columbia River to the sea. This parameter, S_{migration}, ranged between 0.05 and 0.25 for subyearling smolts [based on unpublished passive integrated transponder (PIT)tag and acoustictag data]. Among yearling smolts, for which a larger size may be associated with higher survival immediately prior to and/or shortly after entry to the ocean, S_{migration} was increased by a factor τ ranging between 1 (same survival as subyearlings) and 3 (three times the survival of subyearlings; Faulkner et al. 2007 estimated 61% for yearlings in 2006) (Table 2).
Table 1. Life table for subyearling smolts returning after 2–4 years at sea (x = 3–5, respectively). Life stage  Time period (month_{year})  Stagespecific survival, S_{x}  Age at maturity (x)  Agespecific fecundity (m_{x}) 

Egg to emigration from Snake River  Nov_{0}–Apr_{1}  S_{emigrant} = 0.1   0 
Smolt migration  May_{1}–Oct_{1}  S_{migration} = 0.05–0.25   0 
Subadult  Nov_{1}–Oct_{2}  0.80   0 
Subadult  Nov_{2}–Oct_{3}  0.80  3  3868 
Subadult  Nov_{3}–Oct_{4}  0.80  4  5132 
Subadult  Nov_{4}–Oct_{5}  0.80  5  5741 
Table 2. Life table for yearling smolts returning after 1–3 years at sea (x = 3–5, respectively). Life stage  Time period (month_{year})  Stagespecific survival (S_{x})  Age at maturity (x)  Agespecific fecundity (m_{x}) 

Egg to emigration from Snake River  Nov_{0}–Apr_{1}  S_{emigrant} = 0.1   0 
River residence  May_{1}–Apr_{2}  S_{river} = 0.2–0.8   0 
Smolt migration  May_{2}–Oct_{2}  S_{migration} = 0.05–0.25   0 
Subadult  Nov_{2}–Oct_{3}  0.80  3  3209 
Subadult  Nov_{3}–Oct_{4}  0.80  4  4671 
Subadult  Nov_{4}–Oct_{5}  0.80  5  5474 
To bound the range of survival probabilities, we used estimated smolttoadult return ratios (SARs) developed from fall Chinook salmon tagged with PITs (Prentice et al. 1990) and released between 1995–2000 for a study to evaluate juvenile migration, survival and timing (Smith et al. 2003). The juvenile fish were automatically detected at dams during the downstream migration; likewise, automatic detection of adults occurred as they passed through detectors at Lower Granite Dam. We also used data (unpublished NMFS studies) from fish PITtagged in 2001 and released similarly to the earlier Smith et al. (2003) studies. We grouped juvenile detections at Lower Snake River dams into three categories: (i) fish detected between June and August, (ii) fish detected in September and October (most detection facilities at dams ceased operation by the end of October) and (iii) fish detected the following spring. We assigned adult PITtagged fish detected at Lower Granite Dam to their respective juvenile outmigration years, by category, then divided the totals for each outmigration year, by category, by the number of juveniles detected in the outmigration associated with each category. We then took the geometric mean of these annual PITtag estimates to develop relative rates of return for fish migrating as juveniles during the three different time periods.
Method 2
Based on the demographic data for returning adults, we derived the following terms: P_{x,y} is the proportion of returning adults of life history type y (y = 0 denotes subyearling migrant and y = 1 denotes yearling migrant) returning at age x. These terms sum to 1.0 within lifehistory types. P_{y} is the proportion of returning adults of migration tactic type y. is the mean length (cm) of individuals of migration tactic type y and return age x is the mean fecundity of individuals of migration tactic type y and return age x.
Estimating model terms for the Euler–Lotka equation required several steps. First, we developed a simple model based on the key lifehistory terms (Fig. 2), where P refers to the adult probabilities and p the juvenile probabilities. We assumed a common survival, S_{J} = 0.1, during the early juvenile period, corresponding to egg deposition to shortly after emergence. Next, we specified a juvenile to adult survival for the entire population, S_{T} = 0.01, based roughly on PIT tag data. We note that the values of S_{T} and S_{J} are not critical for the overall conclusions of the analysis. We defined the proportion of juveniles destined to adopt each lifehistory tactic as p_{0} for the proportion of individuals destined to adopt the subyearling migration tactic and p_{1} for the proportion of individuals destined to adopt the yearling migration tactic. We then define a juvenile to adult survival rate (S_{y}) for each lifehistory type. This period encompasses juvenile rearing, downstream migration, ocean residence and return migration.
Although we estimated p_{0} below, this estimation required several assumptions. Thus, we developed our model such that the relative fitness of the two tactics is expressed as a function of p_{0}. In this way, we could examine the response of relative fitness to varying values of p_{0}. Once we specified p_{0}, we could calculate adult survival rate (S_{y}) for each lifehistory type based on the proportion of adults that adopted each migration tactic (P_{0} and P_{1}) and the overall adult survival rate for the entire population, S_{T}, as follows.
First we note that overall adult survival is
 (2)
Next, we express the proportion of adults returning with the subyearling migration tactic as
 (3)
Rearranging terms in equation (3), we obtain:
 (4)
We calculated S_{1} in a similar manner.
As noted above, Snake River fall Chinook salmon are semelparous and mature at several ages. Therefore, to implement the Euler–Lotka equation, we needed to estimate survival through each ageatmaturity by migration tactic, S_{x,y} (equivalent to l_{x,y} in the Euler–Lotka equation), and the proportion of fish breeding by age, b_{x,y}. To do this, we first assumed that survival of adults in the ocean (S_{O}) was 0.8, an assumption commonly made in Chinook salmon lifecycle models (e.g. Kareiva et al. 2000; Zabel et al. 2006). We then expressed juvenile to adult survival (for individuals maturing at ages 3–5) as:
 (5)
Note that all individuals of each tactic have a common survival through the third year, and survival in subsequent years was determined by proportioning remaining to breed and ocean survival.
Based on equation (5), S_{y} [calculated from equations (2) and (3)], and age at return data, we estimated S_{3,y} and the b_{x,y} terms. We then used these terms to determine survival through all age classes. Finally, we modified the Euler–Lotka equation to reflect that only a proportion of the adults (ages 3–6) breed at a given age:
 (6)
We then calculated the relative fitness (of the yearling migration tactic to the subyearling migration tactic) as r_{REL} = r_{1}/r_{0}. We note again that this relative fitness is a function of the (unobserved) proportion of juveniles adopting each lifehistory type. Therefore, we calculated r_{REL} as a function of p_{0}.
To simplify the presentation of the results, we calculated the ratio of the fitness associated with the yearling tactic relative to that associated with the subyearling tactic, for individuals maturing at ages 3–5 years. When this ratio exceeds 1, individuals adopting the yearling smoltmigration tactic have higher fitness than those with the subyearling tactic.
Estimation of migrant proportions
Method 2 required an estimate of the proportion of smolts in the outmigration destined to enter the ocean as subyearlings and yearlings. We based this estimate on juvenile fall Chinook salmon collected and PIT tagged in their rearing areas on the Snake River across the migration season (Connor and Burge 2003). PITtagged individuals were detected in juvenile fish bypass systems at three downstream sites: Lower Granite Dam (site 1), Little Goose Dam (site 2) and Lower Monumental Dam (site 3, see Fig. 3). We used these data to account for the fates of all fish.
We first separated annual releases (1998–2004) into four sequential release groups per year with an equal number of fish in each group (28 release groups with between 302 and 1369 individuals per group). We then used standard methods (Cormack 1964; Jolly 1965; Seber 1965; Smith et al. 2003) to calculate the detection probability (d_{i}) at each site i and the joint probability of active migration and survival (m_{i}) to each site for each release cohort (note that ‘loss’ of fish can occur by either mortality or by yearling migrants ceasing migration). During 1998–2004, the management strategy was to collect all fish in bypass systems and load them onto barges or trucks for transport to a release site downstream of Bonneville Dam (the last dam in the Columbia River Basin hydropower system). Therefore, d_{i} represents the proportion of individuals in the population that passed each dam and was subsequently transported. We also estimated m_{i} for each of the releases from point of release to the tailrace of Lower Granite Dam (m_{1}), from the tailrace of Lower Granite Dam to the tailrace of Little Goose Dam (m_{2}) and from the tailrace of Little Goose Dam to the tailrace of Lower Monumental Dam (m_{3}). For each dam, we calculated a mean d_{i} and m_{i} across years (Table 3). We assumed that the members of the first cohort were actively migrating juveniles destined for a subyearling migration based on the observation that nearly all PITtagged fish detected early the migration season and later observed as an adult are subyearling migrants (W. Connor, unpublished data). We thus equated the m_{i} for each year’s first cohort to survival of actively migrating subyearlings and termed this S_{0,i}. We estimated the mean proportion of yearlings ceasing migration in each river segment i that overwintered as:
 (7)
We then used these probabilities to estimate the fate of all fish. For instance, for a fish to overwinter in Lower Granite reservoir, it had to migrate to Lower Granite Dam (m_{1}), not pass via the bypass system (1 − d_{1}), and then cease to migrate (p_{1,1}). Thus, multiplying these terms together yields the proportion of fish overwintering in Lower Granite Pool.
Table 3. Data (top three rows) used to generate estimated proportions of juveniles destined for yearling and subyearling migration (bottom two rows).  River segment number  Migrant below Lower Monumental  Transported  Total 

To Lower Granite  Lower Granite to Little Goose  Little Goose to Lower Monumental 


Joint probability of migrating and surviving (m_{i})  0.473  0.793  0.741    
Subyearling survival (S_{0,i})  0.598  0.856  0.846    
Detection probability (d_{i})  0.560  0.629  0.490    
Proportion of subyearlings in each category (p_{0,i})  0.318*  0.0278*  0.0083*  0.0231†  0.360‡  0.737 
Proportion of yearlings in each category (p_{1,i})  0.209¶  0.0153¶  0.0076¶   0.0313‡  0.263 
We made the following assumptions :
 1
All members of the wild subyearling population that had actively migrated and survived to the tailrace of Lower Monumental became subyearling ocean entrants. This assumption is based on observations from acoustically tagged fish (unpublished NMFS data), where nearly all fish tagged above Lower Monumental Dam as subyearlings and subsequently detected, appear to have an active downstream migration to Bonneville Dam.
 2
Based on the reading of adult scales, approximately 0.08 of the transported subyearlings survived to over winter in freshwater or the estuary downstream of Bonneville Dam and entered saltwater the following spring as yearlings (unpublished NMFS data).
Our above analyses entailed some assumptions and thus may have some limitations. We estimated that conservatively, at most about 26% of juveniles had a yearling migration tactic. We have no direct measures for this value, but it considerably exceeds the <5% proportion of fish with a yearling migration from the total population of PITtagged fish observed. However, the observed fish represent only the survivors of the population with the yearling migration tactic. Based on PITtagged fish, the adult return rates of fish that migrate as subyearlings in the fall were similar to that for fish that migrated the following spring, suggesting that overwintering survival was high. We recognize that most of the subyearling migrants were collected at dams on the Snake River and transported to below Bonneville Dam. However, analyses of data on fall Chinook salmon transported from the Snake River indicate that transported fish do not return at rates different from migrant fish (Williams et al. 2005). Therefore, removing fish from the river should not bias our two modeling analyses.