A life-table model estimation of the parr capacity of a late 19th century Puget Sound steelhead population

The Stillaguamish River basin is located in the north-central region of Puget Sound in Washington, USA, discharging to Admiralty Inlet approximately 25 miles north of the city of Everett, Washington (Fig. 1). Puget Sound is a fjord system of flooded glacial valleys that acts as a large inland sea in Washington, USA. It is bounded by the Olympic Mountains to the west and the Cascade Mountains to the east covering 648 000 hectares with approximately 4023 km of shoreline. Numerous large (sixth-order and larger) and medium-sized (fourth- and fifth-order) rivers drain to Puget Sound and currently support 32 independent steelhead populations (Myers et al. 2015). The Stillaguamish River basin contains two major branches, the North and South Forks, which both arise on the west slopes of the North Cascade mountain range. Both forks contain spawning and rearing habitat for steelhead and Pacific salmon species over the majority of their lengths. The river basin has a drainage area of 1230 km² (Myers et al. 2015, Table D-1), which is the size of an average Puget Sound river basin (Roni et al. 2010). The river is typical of most northern Puget Sound rivers in spanning a mixture of hydrologic regimes from lowland rain-dominated regions with historically forested floodplains to transitional rain/snow mixed piedmont, to snow-dominated forested headwaters (Myers et al. 2015). All hydrologic and climatic regions, except for small first- and second-order headwater tributaries provided historical spawning and (or) rearing habitat for steelhead.

We modeled a steelhead population consisting of a total of six age-classes, with four adult ages (3–6). We modeled females only and assumed a 1:1 sex ratio (Withler 1966; Ward and Slaney 1988; Seamons et al. 2004). The model includes repeat spawning at ages four, five, and six because repeat spawning is believed to have been an important characteristic of steelhead life history prior to the major reductions in winter-run steelhead population sizes during the past 40 years (Hard et al. 2015). The model consists of 19 stages. This results in a square population projection matrix, 19 rows by 19 columns, with fecundity values in the first row and transition rates or zero entries in all other rows. Life stages, transition rates, and fecundities used in the projection matrix and their abbreviations are listed in Supplementary Material 1, Tables S1 and S2. Figure 2 shows a schematic of the life-cycle model starting with parr (age 1) and terminating at each adult age (3–6) and life stage or fate (maiden or repeat spawner, surviving to spawn or harvested).

Fecundity (# eggs·female⁻¹) is treated as age- and type-specific (maiden or repeat spawner) based on weight-at-age (Supplementary Material 1, Table S2; Supplementary Material 2). The model includes a single smolt age-class (age 2), which is the most common smolt age for most coastal and Puget Sound steelhead populations (Withler 1966; Quinn 2005; Hard et al. 2015). Population projections of the model were conducted at annual time steps.

Density dependence is incorporated during the period of freshwater residence prior to smolting in the transition from emergent fry-to-age-1 (parr). Accordingly, the model includes two sub-age-1 life stages: eggs and fry. Fry-to-parr survival (fp) is modeled as a type II (Beverton–Holt) function with fixed parameters α and β:where α is the inherent maximum fry-to-parr survival rate at low density under optimal conditions, β is the inverse of the number of fry at which fry-to-adult survival = α/2, and n _fry is the number of fry. The number of fry is:where n _eggs is the total egg deposition, sr is the sex ratio, ef is the deterministic egg-to-fry survival rate. Consequently, fp will vary nonlinearly with the number of fry produced by each year’s total spawner abundance as will the number of parr produced the following year by each age and type spawner. All other life-stage transitions are considered deterministic and density independent. The model tracks all life stages from egg deposition to adult return by age and stage class, so that production by each spawner type (age and repeat-spawning status) could be accounted separately.

For modeling convenience, we assume that repeat spawners attempt to repeat spawn the year after their maiden spawning and that there are no third-time spawners. Repeat spawning the year after maiden spawning was found to be the most common pattern in steelhead in Kamchatka as determined by scale analysis of several hundred samples collected by a joint US-Russian conservation research program between 1996 and 2005 (Pavlov et al. 2001; N. Gayeski, personal observation, 2015). Repeat spawning was modeled for each maiden spawner in age-classes three to five by simply assigning an age-specific probability of surviving spawning to re-enter the ocean. We assumed that there was no difference in reproductive effort between maiden spawners in a given age-class that succeeded in repeat spawning and those that did not. The maximum adult age was set at six and the maturation rate of six-year old fish was set implicitly to 1. Modeling was conducted in MATLAB 7.10.

Puget Sound steelhead in the late 19th century were harvested exclusively in terminal areas (river mouths and associated estuary or nearshore) and in-river fisheries (Wilcox 1898). Thus, only mature fish, both maiden and potential repeat spawners, were harvested. Gayeski et al. (2011) argued that given that the peak commercial harvest of steelhead in Puget Sound occurred in 1895, six years after statehood and the initiation of large-scale commercial fishing for steelhead, the total adult return (harvest plus spawning escapement) was likely recruited from a population at or very near its unfished equilibrium abundance, as determined by the average conditions in freshwater and the marine environment that existed in the final quarter of the century. Gayeski et al. (2011) employed a Bayesian approach to estimate the posterior distribution of the 1895 adult return to the Stillaguamish from the reported commercial steelhead catch for the Stillaguamish augmented by estimates of unreported, non-commercial in-river harvest of steelhead by settlers and others based on historical records and reports. The commercial harvest data were reported in pounds, which Gayeski et al. converted to estimates of total numbers landed using a distribution of average steelhead weights estimated for the period. The total return was then estimated from the estimated total numbers landed and an estimate of the distribution of the total harvest rate assuming a binomial distribution for the harvest process. The posterior mode (single most probable value) of the estimated total adult return in 1895 was 69 200 corresponding to an estimate of 34 600 adult females assuming a sex ratio of 1:1.

Gayeski et al. (2011) estimated that this return was most likely harvested at a rate of nearly 55%, yielding a total harvest of females of nearly 18 900 and a spawning escapement of approximately 15 700. We assumed that this was the case and employed the life-cycle model to estimate the number of age-1 individuals that must have been produced in order to recruit a female population of 34 600. We did this by running the model for 25 time steps (years) starting with 10 years of no harvest and adding harvest at time step 11 that built up steadily to a maximum rate of 0.545 at time step 16 equal to the harvest rate on the 1895 population estimated by Gayeski et al. (2011). The model was run for an additional 9 time steps to verify that the year 16 total catch was a maximum, reflecting the historical harvest record (Fig. 3). The density-dependence capacity parameter was adjusted to achieve the estimated 1895 total catch and total spawner abundance, as described below. The model was then run with the harvest rate set to zero to determine the total unfished equilibrium abundance of all ages at the stable age distribution. We refer to this henceforth as the 1895 equilibrium.

We tracked the annual abundance of harvested and unharvested maiden and repeat spawners separately in order to evaluate the impact of harvest on age-classes and on maiden and repeat spawners. The model has 19 stages, including 17 stages for the four oldest age-classes, of which 14 stages are matures. These enable the model to keep track of all spawner life histories and the life histories of all harvested matures (Fig. 2, Table S2).

Fertilities, also referred to as “effective fecundities,” are measured as the number of age-1 progeny (parr) produced by each spawner of a particular age and type, x; that is, the number of offspring surviving to year t + 1 produced by each age-x spawner in year t. These numbers occupy the first row of the square population projection matrix. Thus, the model assumes a prebreeding census, whereby parents are counted each year prior to spawning and their offspring are counted prior to spawning the following year. Fertilities are, therefore, matrix elements generated by underlying vital rates. The vital rates are fecundity (eggs/age and type female), sex ratio, egg-to-emergent fry survival, and density-dependent fry-to-parr survival (Supplementary Material 1, Table S2). Fecundity was treated as age- and size- (weight)-specific for both maiden and repeat spawners in each mature age-class. Since repeat spawners must recover body condition upon re-entering marine waters before they invest energy in gonad production and because they have less time to feed in marine waters before returning to freshwater to spawn than maiden fish of the same age, we assigned repeat spawners a fecundity value slightly greater than maiden spawners in the previous age-class (to account for some body size increase) but less than the value assigned to maiden spawners in the same age-class.

Age-specific weights and fecundities are based on length, weight, and fecundity data collected from steelhead in western Kamchatka on the Russian North Pacific Rim in 2001–2004 (N. Gayeski, personal observation, 2015), and scale analyses of the same individuals made by Dr. Kiril Kuzhichin at the Department of Ichthyology, Moscow (Russia) State University. We used data from Kamchatka because we had fecundity (egg number) and length, weight, and age data for each of approximately 80 individual females. We selected representative lengths-at-age for 3-, 4-, 5-, and 6-year-old maiden and repeat-spawning females that provided representative weights for given lengths and ages. We compared both measured and estimated fecundity-at-length from the Kamchatka data to length-fecundity data for several British Columbia steelhead populations provided to the lead author by Dr. Bruce Ward to evaluate how representative of North American steelhead Kamchatka steelhead are. Kamchatka steelhead had slightly greater fecundity at a given length and weight than the majority of British Columbia winter-run populations. We then adjusted the expected fecundity-at-length downward by adjusting the intercept of the natural log–log regression of fecundity on length of the Kamchatka samples to obtain an average fecundity approximately equal to the mean value reported by Quinn (2005, Table 15-1) that was based on a survey of available published and unpublished data, including the British Columbia data that we examined. We expected that the average fecundity value reported in Quinn (2005) was more likely than the unadjusted Kamchatka data to be representative of Puget Sound steelhead in the late 19th century, as indicated by the range of average steelhead weights reported by Gayeski et al. (2011). The resulting parameterization of the model was corroborated by the model’s achieving the target average adult weight of Puget Sound winter-run steelhead of 8.25 lbs. estimated by Gayeski et al. (2011). Length-weight and length-fecundity equations are provided in Supplementary Material 2. Age-specific fecundities are listed in Supplementary Material 1, Table S2.

Estimating the number of parr produced at the 1895 equilibrium requires that we appropriately partition the recruitment process between the freshwater and marine (post-smolt) periods. Because there are scant empirical data for annual survival rates of smolts and post-smolt age-classes of Pacific salmon and steelhead, we chose two marine survival scenarios, one low and one high, that we believe bracket the likely true values of age-specific post-smolt marine survival of steelhead during the late 1800s.

The production of parr of both sexes from the eight models ranged from 826 000 to 1 926 000 and averaged 1 320 000 (Table 1; Supplementary Material 1, Table S3). Gayeski et al. (2011) estimated that 668 linear kilometers of mainstem and tributary stream habitat was accessible to winter-run steelhead in the Stillaguamish River in 1895. We updated this estimate using data for historical mainstem and tributary rearing habitat in the Stillaguamish (Pess et al. 1999; Pollock et al. 2004). We estimate that there were a total of 706 km of tributary habitat available for juvenile steelhead rearing and 160 km of mainstem. For tributaries, we estimated the average channel width available to steelhead rearing during near baseflow conditions during the summer and fall growing season to be 3 m based on the two sources cited above, Roni et al. (2010), and unpublished field survey data by two of us (Pess and Beechie). This resulted in an estimated total tributary rearing area of 2 118 000 m². For mainstem rearing habitats, we used a range of estimates of the average width (each bank) over the total length of mainstem shallow shoreline available for juvenile steelhead rearing during the summer and fall growing season of 2, 3, and 4 m (4, 6, and 8 m both banks combined). The shallow shoreline is defined as the area of mainstem river channel adjacent to the bank where channel depth is no greater than 0.5 m and surface current velocity is not greater than 0.5 m·s⁻¹ (Stanford et al. 2005). This is the area of river main channels where we expect the majority of O. mykiss parr to rear during baseflow and near-baseflow conditions during the summer/fall growing season. This results in a range of total mainstem rearing habitat area of 640 000–1 280 000 m². Added to the estimate of tributary rearing area, these estimates yield an estimate of total historically available juvenile parr rearing area of 2 780 000, 3 078 000, and 3 398 000 m² (Table 2).

Dividing each of the eight estimates of 1895 equilibrium parr production by the three estimates of total rearing area yields estimates of parr densities in juvenile rearing habitats of 0.24–0.70 parr·m⁻². For the average total parr production of 1 320 000 (averaged across all eight model runs), rearing densities range from 0.39 to 0.48 parr·m⁻². The average across the four low marine survival scenarios is 0.49–0.61 parr·m⁻². The average across the four high marine survival scenarios is 0.29–0.35 parr·m⁻² (Table 3).

Figure 5 shows box plots of parr densities for all eight modeled scenarios for each of the three estimates of total rearing area.

Roni et al. (2010) estimated steelhead parr production in a modeled Puget Sound watershed the size of the Stillaguamish before restoration, which is to say, under current conditions. They estimated the lengths of three types of stream habitats, small, medium, and large, and the current number of parr produced by each. Small and medium streams correspond to tributaries in our analysis: large streams to mainstems. The total length of large streams is 117 751 m (118 km). Steelhead parr production in large streams was estimated to be 99 238. Using our estimates of mainstem rearing habitat area as equal to stream length × 4, 6, and 8 m, the estimated rearing areas of large streams are 471 000, 707 000, and 942 000 m² (Table 4). This yields parr densities of 0.21, 0.14, and 0.11 parr·m⁻², respectively. These densities are lower than the mean values of our historic estimates of 0.48, 0.43, and 0.39 parr·m⁻², respectively (Table 3).

Marine (smolt-to-adult return) survival rates are known to have declined during the past quarter of a century and have undoubtedly contributed to recent declines and listing of several steelhead populations under the Endangered Species Act, including Puget Sound steelhead (Smith et al. 2000; Ward 2000; Welch et al. 2000; Friedland et al. 2014). Friedland et al. (2014), for example, estimated changes in smolt-to-adult survival rates for steelhead between 1977 and 2005 from the well-studied Keogh River population on the East Coast of Vancouver Island, British Columbia. They estimated that average survival rates decline threefold from 14% during the first half of the period to 5% during the second half. Survival rates of Puget Sound populations over the past decade may have been even lower (Moore et al. 2015).

It may be thought that such changes in marine survival render our estimates of the parr capacity of the Stillaguamish River in 1895 of little relevance for the conservation of Stillaguamish steelhead under current conditions. We do not believe that this is the case. First, our estimates of first year post-smolt survival and age-3-to-age-6 survival to adult return for low and high marine survival scenarios resulted in cohort smolt-to-adult return survival rates of 0.105–0.172 (Table 1). This is comparable to mean survival rates estimated for the Keogh River during the mid-1980s of 0.14–0.16, with survival rates for individual cohorts as high as 0.26 (Ward and Slaney 1988; Friedland et al. 2014). Hence, our modeled marine survival rates are likely conservative with respect to conditions that existed in the late 19th century. Second, the effect of employing conservative estimates of marine survival on our estimates of parr capacity would be to inflate those estimates relative to the number of parr at equilibrium required under more favorable marine survival rates (Table 1; Supplementary Material 1, Table S3). That is, the greater the marine survival, the fewer number of parr and smolts required in order to recruit a given number of spawning adults.

For similar reasons, our acceptance of the best estimate of the 1895 equilibrium of the Stillaguamish River of 69 200 estimated by Gayeski et al. (2011) for the purpose of estimating parr capacity in 1895 is conservative. If the adult estimate is inflated, then our estimate of parr capacity in 1895 will be similarly inflated. If anything, therefore, our estimates of parr capacity and densities in the Stillaguamish in 1895 would push the bounds of realistic parr densities that we estimate were required to sustain the adult equilibrium abundance estimated by Gayeski et al. (2011). As we show in the following section, this does not appear to be the case. This result has the indirect effect of providing independent evidence that the estimate of Gayeski et al. (2011) is biologically realistic.

Gayeski et al. (2011) estimated a 100-fold decline in the abundance of adult Stillaguamish River steelhead between 1895 and the first decade of the 21st century. This decline far exceeds what might be expected in response to the estimated loss of only 33% of stream habitat accessible to adult steelhead since 1895. When potential juvenile rearing habitat is considered, the loss is greater than estimated in Gayeski et al. (2011). Depending on the estimate of main channel shallow shoreline rearing area, the loss has been between 56% and 63% (Tables 2 and 4). In either case, this implies that the productivity of the freshwater rearing environment has experienced a decline since 1895 that is considerably out of proportion to the loss of accessible stream habitat area. Consistent with the estimate of adult steelhead abundance at the end of the 19th century, our results show that parr abundance and densities were significantly greater than estimates for typical tributary and mainstem river juvenile rearing habitats under current conditions. Our results suggest that currently reduced steelhead abundance is the product of both loss of quantity of suitable juvenile rearing habitat and loss of quality of extant rearing habitats expressed as a reduction in the densities of parr that habitat of a given area can support. We believe that this is the case even after accounting for recent reductions in marine survival of steelhead.

Our model estimates of parr densities are averages over all stream types, tributary and mainstem. These estimates were made by assuming that all tributary and mainstem rearing habitats were equal in quality. We, therefore, simply assigned the total numbers of parr to mainstem and tributary habitat in direct proportion to the respective estimated total rearing area of each stream type (Table 2). We did this for lack of any historical or current information on the distribution of total steelhead parr across stream types, which is largely a result of the absence of parr estimates at the whole basin scale. This probably results in somewhat underestimating the rearing capacity of tributaries and overestimating that of the mainstem river. However, we minimized this potential bias by estimating rearing habitat area for each stream type by assuming a maximum width of stream, corresponding to the shallow shoreline (sensu Stanford et al. 2005), within which most rearing during the summer-fall growing season occurred. This approach treats mainstem river rearing habitats more like that in tributaries with respect to the key features of depth and velocity. Consequently, we expect that our densities should be reasonably accurate as average values for both tributary and mainstem rearing habitats combined.

Our estimates of the numbers of steelhead parr produced under the conditions of the 1895 equilibrium are considerably larger than any credible estimate of annual numbers of parr under current conditions for larger river basins in Puget Sound (e.g., Roni et al. 2010), which is what we expected given the estimated 1895 equilibrium adult population (Table 1 and Fig. 4). Nonetheless, our estimates of the per-unit-area capacity of tributary and mainstem rearing habitats in the Stillaguamish River in the late 19th century are comparable in magnitude to or smaller than several recent estimates of densities of rearing juvenile steelhead in small tributary streams. McCarthy et al. (2009) reported rearing densities of ages 0–2 rainbow/steelhead for nine small (approximately third order) tributary streams of the South Fork of the Trinity River in northern California. Harvey et al. (2005) reported densities for steelhead/rainbow parr (less than 130 mm fork length) in 59 small habitat units in a small coastal stream in northern California (average width 4 m). Harston and Kennedy (2015) reported densities of rearing steelhead yearlings (parr) in several small tributaries to the Clearwater River in Idaho. Mean densities of parr-sized fish from all three studies ranged from 0.16 to 0.9 m⁻².

There are few published estimates of rearing densities of larger mainstem rivers, fifth order or higher. The best available recent information on the density of steelhead parr in Puget Sound and coastal Washington rivers that lie to the west of Puget Sound under presumed fully seeded conditions is that provided by Gibbons et al. (1985) (see also, Hard et al. 2015, Appendix C). Gibbons et al. measured parr density by dividing the total parr counts from each surveyed mainstem river reach by the total cross-sectional area of each reach (reach length × mean reach width), rather than scaling total counts to shallow shoreline rearing area as we do. To facilitate a comparison to Gibbons et al. (1985), we rescaled the Gibbons et al. (1985) data for mainstem river reaches to our shallow shoreline rearing area-based estimates using the lengths of mainstem reaches reported in Table 3 of Gibbons et al. (1985). Details are provided in Supplementary Material 3. Results are shown in Fig. 6 where they are compared to our model results and to the results from Roni et al. (2010).

The rearing densities from Gibbons et al. (1985) rescaled to our three estimates of main channel rearing widths average 0.086 parr·m⁻² (width = 8 m) to 0.173 parr·m⁻² (width = 4 m). Our adjusted parr density estimates range from 0.243 parr·m⁻² for the most productive high marine survival scenario and maximum rearing channel width of 8 m (model H4, Table 3) to 0.698 parr·m⁻² for the least productive low marine survival scenario and minimum rearing channel width of 4 m (model L1, Table 3). The mean of the four low marine survival scenarios across the three rearing channel widths ranges from 0.492 to 0.606 parr·m⁻², and for the four high marine survival scenarios ranges from 0.285 to 0.351 parr·m⁻² (Table 3). The average density over all eight models ranges from 0.388 to 0.478 parr·m⁻². Thus, our model-based estimates of mainstem parr rearing densities circa 1895 are 2.8–4.5 times the rescaled densities estimated by Gibbons et al. (1985) for main channel rearing habitats. It is worth noting, however, that the parr count for one of Gibbons et al.’s main channel sites (Sol Duc 2, Supplementary Material 3, Table S4) rescaled to our shallow shoreline rearing widths results in densities ranging from 0.279 to 0.557 parr·m⁻², which spans the range of densities estimated by most of our eight models. So, this site at the time that it was surveyed in the early 1980s shows that densities in main channel rearing habitats are capable of achieving the densities estimated by our model. We conclude that our model-based estimates of total parr production required to produce the Stillaguamish River 1895 equilibrium are not unrealistically high.

Although there are data showing that declines in the productivity of the marine environment in recent decades have impaired the recruitment of steelhead on a regional basis (Ward and Slaney 1988; Smith et al. 2000; Ward 2000; Friedland et al. 2014; Moore et al. 2015), considerably less is known about how alterations of freshwater habitats have affected juvenile production. In general, little is known about where in the freshwater life cycle from egg deposition to smolt emigration key bottlenecks are located. Nonetheless, the majority of remedial actions directed at recovering Puget Sound steelhead are most likely to be directed at freshwater habitat conditions (NMFS 2013). Partitioning the life history between the freshwater and marine phases of the life cycle in our model facilitates the identification of conditions that can result in positive population growth (λ > 1). In particular, it should facilitate the identification of minimum spawner-to-smolt survival rates necessary to achieve positive population growth under varying marine survival scenarios. This is well-illustrated by the contrast in equilibrium fry-to-parr survival rates between our low and high marine survival scenarios (Table 1; Supplementary Material 1, Table S3), where lower marine survival requires higher fry-to-parr survival rates (weaker density dependent fry mortality, greater total fry capacity) than when marine survival rates are higher.

The results from our modeling effort suggest that measuring and monitoring the parr capacity of rearing habitats by measuring parr density provides an integrative metric of population performance within the entire freshwater life cycle. It can provide the most direct link between remedial actions aimed to improve the quantity and quality of rearing habitats and improvements in survival to a critical early juvenile life stage, age-1 parr. Consequently, quantifying parr capacities and parr-to-smolt survival rates are key information needs for recovery planning. In addition, estimates of spawner age composition and size-specific fecundity can provide estimates of potential egg deposition that when combined with estimates of parr production can provide estimates of egg-to-parr survival. Developing credible estimates of egg-to-parr and parr-to-smolt survival rates should help to focus scarce recovery resources on the most appropriate habitat actions to undertake in order to improve survival across the total life cycle, particularly given limited ability (in the near term at least) to affect improvements in marine survival.

Our model-based estimates of parr densities in 1895 provide a credible baseline from which all these issues can be addressed. To illustrate the value of achieving the higher parr densities estimated from our model, Table 5 shows the adult returns expected from achieving mean parr densities from the lower range of our model estimates given the amount of rearing habitat in the Stillaguamish River estimated to be currently available. We assumed parr-to-smolt survival of 0.3 (Hard et al. 2015), and smolt-to-adult return survival of 0.03, which is below the recent average for the Keogh estimated by Friedland et al. (2014) and likely near values achieved by wild steelhead in northern Puget Sound rivers within the past decade.

Depending on the width of shallow shoreline rearing habitat, average rearing densities of 0.24 parr·m⁻² in tributaries and mainstem combined could recruit 2200–3200 adults at a smolt-to-adult survival rate of 0.03. Average rearing densities of 0.4 parr·m⁻² would recruit 3700–5400. Clearly, achieving such modest mean parr rearing densities would achieve significant improvements in wild steelhead recruitment in the Stillaguamish River, and elsewhere in Puget Sound, relative to current levels of abundance (Ford 2011; Hard et al. 2015).

Our model of the 1895 steelhead population assumed a more complex age-structure than exists today in the Stillaguamish River, particularly with respect to the degree of repeat spawning. The model also assumed four mature ages, 3–6, with the proportions at equilibrium dominated by the two older age classes, which combined accounted for 70% of annual returns at equilibrium. These assumptions resulted in an average fecundity (eggs/female) of the modeled populations of 4800 and 4900 for the two marine survival scenarios (Table 1; Supplementary Material 1, Table S3), which are essentially identical to the average value for steelhead generally noted by Quinn (2005). The contemporary population has a much lower, perhaps negligible, percentage of repeat spawners (Hard et al. 2015), and is dominated by age-3- and age-4-year-old individuals (Hard et al. 2007). This undoubtedly has reduced the average fecundity of the population and thus the total potential egg deposition.

These changes in the age- and life-history structure of the contemporary population, however, do not affect the validity of our results as the purpose of the modeling is to provide estimates of the abundance of parr and the associated rearing densities that were most likely responsible for the level of adult equilibrium abundance in 1895 estimated by Gayeski et al. (2011). These estimates are directly relevant to conservation planning for Stillaguamish and other Puget Sound steelhead populations. As illustrated in the preceding subsection and Table 5, attaining higher rearing densities in the Stillaguamish River is directly relevant to the recovery of the steelhead population. So also is recovering the historic proportion of repeat spawners. Repeat spawning is likely to be especially important for recovery of Puget Sound steelhead given current depressed levels of marine survival, which primarily affects steelhead smolts early during the first year in the marine environment (Friedland et al. 2014; Moore et al. 2015). Post-spawning adults are likely to be much less susceptible to marine mortality upon re-entering the marine environment than much smaller bodied smolts and their return to spawn a second time achieves a functional increase in the effective cohort smolt-to-adult survival rate, as shown in Table 1 and Supplementary Material 1, Table S3. A significant increase in the proportion of repeat spawners to levels in the neighborhood of 20% of total annual spawners could be critical to achieving the increase in parr densities that our modeling results show to be realistic. It is worth noting in this regard that according to recent run reconstruction data provided to the lead author by Washington Department of Fish and Wildlife staff, repeat spawning rates of winter-run steelhead in the Queets River in Olympic National Park to the west of Puget Sound have ranged between 20% and 30% since the early 1980s. So such repeat spawning rates are still achievable today at least by some populations.

Regardless of the recovery of greater rates of repeat spawning, increasing the mean densities of steelhead parr in the Stillaguamish River can be expected to return significant dividends for rebuilding depressed levels of adult abundance of this population. Even modest increases to densities above 0.2 parr·m⁻² should yield meaningful sustained increases in the abundance of returning adults. Achieving such increases will require both improvements to habitat quality and quantity (physical structure and complexity, and food web) and synergistic increases in the numbers of returning adult spawners. The results of our modeling of the parr capacity of the Stillaguamish River in 1895 show that such historic levels of parr density were not extreme by comparison with many studied populations today and that it is not unreasonable to expect to attain such densities in rivers today if appropriate recovery actions are undertaken.