Introduction

Across taxa, body size is a key characteristic which determines individual life history decisions and lifetime fitness (Quinn and Peterson 1996; Fujiwara et al. 2004; Begon et al. 2006; Satterthwaite et al. 2010). A large body size relative to conspecifics can confer advantages in the competition for food and space, aid in the endurance of adverse conditions and periodic food shortages, and help attract and safeguard mates (Abbott and Dill 1989; Nakano 1995; Rose et al. 2001; Fujiwara et al. 2004). In the face of limited resources, size disparities within an age class typically arise when individual demands increase and the competition intensifies (Begon et al. 2006). While variations in size distributions are fairly well documented (Rubenstein 1981; DeAngelis et al. 1993; Crozier et al. 2010; Parra et al. 2012; Ohlberger et al. 2013), it is less well understood how size distributions are created and maintained in wild populations (Lomnicki 1999; Pfister and Stevens 2002; Peacor and Pfister 2006; Peacor et al. 2007a).

When the timing of birth is fairly synchronized, and where individuals experience similar conditions as their conspecifics, size variation within a cohort is ultimately generated by individual differences in their ability to acquire resources and grow under the prevailing conditions (Ricker 1958; Uchmański 1999; Pfister and Stevens 2002; Pfister 2003). The origin of this size variation arise from the advantages (or disadvantages) conferred by a certain size at a given point in time (Ricker 1958), or from persistent individual traits that have a genetic or learned basis such as physiology and foraging behavior (Pfister and Stevens 2002; Pfister 2003; Fujiwara et al. 2004; Peacor et al. 2007a, b). The two categories are not mutually exclusive, and may be difficult to disentangle in wild populations (Pfister and Stevens 2002). Ecologically, both generate asymmetric competition, which result in a range of individual sizes within a population in response to the dynamic selection pressures (Ebenman and Persson 1988; Pfister and Stevens 2002; Fujiwara et al. 2004; Peacor et al. 2007a).

In variable environments and over varying degrees of competition for food and space, it is thus likely that size disparities among individuals manifest unequally between local populations (Rubenstein 1981; Parra et al. 2012; Ohlberger et al. 2013). For example, do initially larger individuals always grow faster, hence perpetuating the size inequality in a population, or do conditions exist where a relatively smaller body size is more beneficial in terms of growth? Individual differences can be particularly evident in fishes because they exhibit relatively flexible and indeterminate growth within a life stage (Rose et al. 2001; Pfister and Stevens 2002) and because phenotypic plasticity can generate multiple life history expressions (Satterthwaite et al. 2010; Benjamin et al. 2013; Phillis et al. 2016). Further, because they are poikilothermic, with a sensitive relationship between temperature and energy use, fishes represent a tractable system with which to study the interacting effects of demographic density dependence and abiotic factors on individual size and growth (Diana 2003; Myrvold and Kennedy 2015a).

Due to their plastic potential and sensitivity to abiotic conditions, a number of studies have investigated the effects of water temperature and population density on the size-at-age and growth rates of stream salmonids. A vast range of results have been reported, which is not surprising given the wide variety of environments that salmonids inhabit and the fact that limiting factors rarely operate in isolation (Crozier et al. 2010; Sloat and Reeves 2014; Myrvold and Kennedy 2015a; Thompson and Beauchamp 2016). Environmental conditions, population density, food availability, and interspecific interactions can greatly influence average demographic responses in local populations, but there is increasing interest in the characteristics of the individuals that make up those populations (Nakano et al. 1991; Nakano 1995; Satterthwaite et al. 2010; Bærum et al. 2013). Individuals in the same stream reach compete for access to food and space, which makes an individual’s ability to compete not only dependent on itself but also on the abilities of its competitors (Nakano et al. 1991; Nakano 1995). In stream salmonids, an individual’s rank in the dominance hierarchy (as evidenced by aggressive displays, quality of feeding territory, and growth performance) has often been attributed to its size (Abbott and Dill 1989; Nicieza and Metcalfe 1999), but the relationships between size and growth are complex and depend on environmental context and individual traits (Höjesjö et al. 2004; Reid et al. 2011). An interesting question, then, is to identify the conditions which may govern size-dependent growth performance.

In the present study we were interested in understanding the circumstances under which an individual’s size relative to conspecifics within a stream reach conferred a growth advantage (Fig. 1). The factors we tested for were population density and water temperature, as both have been shown to influence individual growth rates in stream salmonids (e.g., Crozier et al. 2010; Parra et al. 2012; Bærum et al. 2013; Myrvold and Kennedy 2015a). We use detailed data on individual growth from discrete study sites, which cover a range of densities and temperatures. While we expect that larger individuals are generally better competitors (i.e. when there is sufficient food relative to the water temperature), we hypothesize that high water temperatures can slow down this advantage due to the relationship between metabolic demands and temperature (Myrvold and Kennedy 2015b). We therefore expect a negative effect of the interaction between temperature and relative body mass on individual growth rates. Finally, because body size may confer a dominance advantage, we do not expect density to substantially impede growth in relatively larger individuals.

Fig. 1
figure 1

Schematic showing three processes of size-dependent growth. In the top panel the initially larger individual grows faster than the smaller individuals, whereas the bottom panel shows a situation where the initially smaller individual grows faster than the larger individuals. This study aimed at identifying the circumstances when this was occurring

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Methods

Study area

This study took place in the Lapwai Creek watershed in Idaho, United States. The 694 km2 watershed is located at the transition between the Columbia River Plateau and the Northern Rockies ecoregions (McGrath et al. 2002), and spans a gradient of land cover and land use from its headwaters on Craig Mountain (elevation 1530 m) to its confluence with the Clearwater River (elevation 237 m). Lapwai Creek is designated as critical habitat for a threatened population of wild Snake River steelhead (NMFS 2010). Summer water temperatures in lower reaches approach the tolerance level for steelhead (Myrvold and Kennedy 2015b), whereas winter air temperatures are at or below freezing from December through February. The steelhead population in this watershed has been reported on previously (Myrvold and Kennedy 2015a, b, c, d). As part of this work, we established an array of study sites representative of the physiographic variation in the watershed (Fig. 2). The study sites were approximately 100 m long, and key characteristics have been provided in Myrvold and Kennedy (2015c).

Fig. 2
figure 2

Study sites in the Lapwai Creek watershed, Idaho, United States (inset)

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Juvenile steelhead data

We captured fish via three-pass depletion electrofishing using a Smith-Root LR-24 backpack electrofisher (Smith-Root Inc., Vancouver, Washington, USA). We visited each study site monthly from June to October in 2010–2012. Prior to any handling we anesthetized the fish with tricaine methanesulfonate (MS-222), and measured fork length in millimeters and mass to the nearest decigram. Individuals were classified as subyearling (hatched in May the same year) or overyearling (hatched in a previous year) based on size frequency histograms at the sampling visit. We tagged individuals 65 mm and longer with Passive Integrated Transponder (PIT) tags (Biomark HPT 12 mm full duplex tags, Biomark Inc., Boise, Idaho, USA). Following handling, fish were first allowed to recover in buckets with aerated water, and then released back into the stream. We estimated the size of each age class using Carle and Strub’s (1978) maximum weighted likelihood estimator for removal data, and calculated density by dividing the population estimate by the area sampled. The density estimate was expressed as the number of juvenile steelhead per 100 m2 and natural log-transformed.

We were interested in measuring the growth of subyearling steelhead compared to the other subyearlings in the respective stream reaches. We therefore considered periods in each site (from visit t to t + 1) for which we obtained growth measurements from four or more individuals. We calculated specific individual growth rate as the percent change in body mass per day between capture and recapture. Relative size was calculated as the difference between the mass of a fish and the average mass of fish in the same site at the sampling visit, and expressed in grams.

Temperature data

Streamwater temperatures were recorded every 30 min in each study site for the duration of the study using HOBO TidbiT v2 temperature loggers (Onset Computer Corporation, Pocasset, Massachusetts, USA). In the modeling we used the average temperature (°C) during the 4 week period between capture and recapture. The distribution of water temperatures among the study sites are given in Appendix 1.

Statistical methods

In order to quantify how much of the variation in the juvenile steelhead growth rates that could be attributed to the different levels in the data (individual and sampling visit to a study site) we performed a one-way analysis of variance (Raudenbush and Bryk 2002). The model for the variance components for the individual- and visit levels (also known as the empty or unconditional model) can be written as

$$ {growth}_{ij}={\gamma}_{00}+{u}_{0j}+{r}_{ij} $$
(1)

Here, γ 00 is the grand mean growth rate of all individuals across all sampling visits; u 0j is the random visit effect, i.e. the deviation of visit j from the grand mean; and r ij is the residual individual effect, i.e. the deviation of individual ij from the sampling visit mean. Because individual steelhead and sampling visits to a study site were randomly sampled from a larger statistical population of potential fish and visits we can assume that u 0j ~ N(0, τ 00) and r ij  ~ N(0,σ 2) (Raudenbush and Bryk 2002). We found substantial clustering by sampling visit, which means that observations made within a sampling visit were more similar than when compared with observations from all sampling visits. We hence modeled the growth rate variation under a hierarchical framework, that is, with both individual- and visit-level effects (Raudenbush and Bryk 2002).

We investigated the effects of individual mass, mass relative to conspecifics (relative mass), population density, and temperature on individual growth rate (Table 1). The complete derivation of the models are given in Appendix 2. Individual mass and relative mass are at the same hierarchical level as the response variable growth. However, to introduce population density and temperature we had to account for the multilevel structure in the data as these variables are not independent among the individuals in a site (Raudenbush and Bryk 2002). This means that the effects of individual mass and relative mass on its growth rate also depend on characteristics of the sampling visit to a study site. A hierarchical linear model with cross-level interactions between characteristics at the sampling visit level (here: temperature) and the individual level can be expressed as

$$ \begin{array}{l}{growth}_{ij}={\gamma}_{00}+{\gamma}_{01}{temp}_j+{\gamma}_{10}{mass}_{ij}+{\gamma}_{20}{relative}_{ij}+{\gamma}_{11}{mass}_{ij}\times {temp}_j+\hfill \\ {}{\gamma}_{21}{relative}_{ij}\times {temp}_j+{u}_{0j}+{u}_{2j}{relative}_{ij}+{r}_{ij}\hfill \end{array} $$
(2)
Table 1 Candidate models to explain the variation in growth rates (% body mass per day) in subyearling steelhead (Oncorhynchus mykiss) in Idaho, United States. Each model contains the absolute and relative mass of individuals (g), and they vary in the inclusion and combination of temperature (°C; monthly average over a 4 week period between capture and recapture) and density (natural log-transformed, per 100m2). Model 0, the empty model, contains only variance components and was used to partition the levels of variance
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This model tests the effects of individual mass, its mass relative to PIT-tagged conspecifics, and the effects of temperature alone and in interaction with individual specific mass, on an individual’s growth rate. We performed the same analysis with population density as the visit-level predictor variable (see Table 1 for a list of the models considered).

We used SAS 9.2 Proc MIXED (SAS Institute, Cary, North Carolina, USA) specified with the Kenward and Roger (1997) approximation of denominator degrees of freedom, and maximum likelihood as the estimator in all the analyses. Models were ranked using Akaike’s Information Criterion (Akaike 1973); the model with the lowest AIC value is the best approximating model of the data (Burnham and Anderson 2002). Variance inflation factors were less than 2 among the independent variables, and there were hence no problems with multicollinearity. Finally, we visually inspected the residual plots using the ods graphics option in SAS to ensure that statistical assumptions were met (i.e. that the variance components had means of zero and constant variances).

Results

Subyearling steelhead growth rates in the Lapwai Creek watershed averaged 0.91% body mass per day (SE = 0.046) among the 1228 individuals in this study. The variance could be attributed almost equally to individual-level (48% of the variance) and visit-level factors (52%), which suggest that both levels of effects contributed substantially towards the overall variation in subyearling steelhead growth rates.

Model 6 was the best approximating model of growth rate variation, receiving 61% of the support, and model 2 received 22% of the support among the models (Table 1). Because model 6 received more support than model 2, and because model 2 is a subset of model 6, we focus our treatment primarily on model 6. In addition to controlling for mass and relative mass (as with all other candidate models), model 6 included interaction terms with temperature (Table 2). Importantly, the cross-level interaction between relative size and temperature was negative (estimate = −0.0236, SE = 0.0097, t = −2.45, P(|t|) = 0.017). Cross-level interactions show how much the effect of the individual-level variable changes depending on the value of a visit-level variable. This shows that, controlling for an individual’s absolute and relative size, the effect of relative size on its growth rate decreased as temperatures were increasing (Fig. 3). The interaction between absolute mass and temperature was positive. This means that the effect of an individual’s mass on its growth rate increased with increasing temperatures. This owes to the larger average body sizes of steelhead rearing in sites with relatively warmer temperatures and lower densities.

Table 2 Parameter estimates for the unconditional model (empty model) and the best approximating models (models 2 and 6 in the candidate set) for growth rate variation in subyearling steelhead. The variance partitioning for the empty model showed similar contribution from the individual- and visit levels. The variance explained at each level, ρconditional, is equivalent to the coefficient of determination in ordinary least squares regression, and is partitioned between the visit- and individual levels following inclusion of the variables
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Fig. 3
figure 3

Predicted growth rates (from the best approximating model) for three sizes of steelhead (6 g, 10 g, and 14 g) and three relative sizes (average, 4 g smaller than average, and 4 g larger than average)

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Overall, the best model explained 11% of the variation in the growth data (Table 2). The covariates mass and relative mass explained 4% of the variation on the individual level, and inclusion of temperature in interaction with mass and relative mass explained 19% of the visit-level variation. Because the visit-level covariate temperature explained more of the variation in our data, there is reason to believe that the environmental context (i.e. variation in temperature between sites) largely affected the growth dynamics within our study reaches.

Compared to the effects of temperature, we found no substantial effects of density on individual growth rates (Table 1). This suggests that the impacts of temperature were stronger than those of competition when considering an individual’s size relative to its conspecifics; however, this does not imply that density is unimportant.

Discussion

Using data on individual steelhead growth in relation to other known individuals we found that relatively larger fish grew faster, but that their growth advantage depended upon the context. Specifically, there was a negative interaction between an individual’s relative mass and the water temperature. This shows that, controlling for an individual’s absolute size, the positive effects of an individual’s relative mass on its growth rate decreased as temperatures were increasing.

Body size influences most aspects of the relations between an organism and its environment (Ebenman and Persson 1988; Lomnicki 1999; DeRoos et al. 2003; Peacor et al. 2007a). At the level of species, size can determine trophic interactions, and at the level of individuals, larger size often confers advantages in the competition over limited resources and survival (Werner and Gilliam 1984; Ebenman and Persson 1988; Pfister and Stevens 2002). Because body size is closely tied to fitness, individual size variation can affect population density and dynamics (DeAngelis et al. 1993; DeAngelis and Mooij 2005). Some of the variation in size might reflect heritable traits, which underlie natural selection (Gårdmark et al. 2003). As Peacor et al. (2007a) noted the factors that affect size variation within a cohort are hence implicated in exposing different traits to natural selection or masking this variation from selection by preventing expression of trait characters. However, we still have limited understanding of the processes that ultimately generate size variation within a cohort, and the circumstances under which size disparities persist in a dynamic environment (Pfister and Stevens 2002; Peacor and Pfister 2006; Peacor et al. 2007a). Studying individual growth performance within a cohort over relatively short time intervals can help unravel the relationships between individual size, growth, and the environment.

In stream salmonids, growth performance has been linked to an individual’s rank in a local dominance hierarchy. Dominant fish typically acquire better microhabitats and food resources, and as a result, they often grow faster than subordinate conspecifics (Abbott and Dill 1989; Nicieza and Metcalfe 1999; Keeley 2001). Nakano et al. (1991) found that within pools in a Japanese mountain stream, relatively larger red spotted masu salmon (O. masou) grew faster than smaller individuals inhabiting the same pool, despite there being no relationship between initial size and growth when considering the stream as a whole. Subsequently, Nakano (1995) investigated the role of dominance status in explaining this variation in growth rates. Dominant individuals occupied better feeding stations, chose larger prey, and consequently grew faster. Further, dominant individuals were also larger, which is common in stream salmonids when food is abundant. For example, Abbott and Dill (1989) found that dominant juvenile steelhead grew faster than their subordinate counterparts because the appetite and conversion efficiency in subordinates were greatly reduced in the presence of dominant individuals. In experimental channels, Keeley (2001) found that large, aggressive juvenile steelhead consumed a disproportionate amount of the food. Consequently, size inequality within the juvenile stage increased with stocking density and decreased with increases in food availability (Keeley 2001).

There are, however, conditions under which dominance and/or large body size are not beneficial in the sense that they do not confer a growth advantage. Martin-Smith and Armstrong (2002) studied juvenile Atlantic salmon (Salmo salar) in a flow-regulated channel with fluctuating food supply. They found support for the hypothesis that individual growth correlates with movement but not with the ability to dominate good feeding locations. Further, aggressiveness (which can confer social status) has also been linked to physiology and behavior. Reid et al. (2011) found that standard metabolic rate was a strong predictor of social rank, which in turn was related to resource acquisition. However, standard metabolic rate did not predict growth performance, presumably due to the higher associated metabolic costs (Reid et al. 2011). In another study, Vøllestad and Quinn (2003) found that aggressive coho salmon (O. kisutch) grew slower than individuals exhibiting lesser levels of aggression, likely due to the same reason.

The influence of behavior and genotype on growth performance may therefore depend on the environmental context. Höjesjö et al. (2002) studied brown trout (S. trutta) in Sweden and found that although dominant individuals outgrew subordinates, nonaggressive individuals (those not partaking in territorial disputes) grew as fast as the aggressive, dominant individuals. Reid et al. (2012) found that resting metabolic rate in juvenile Atlantic salmon was related to dominance, but that when the food supply was less predictable and the habitat more visually complex, this social dominance was not advantageous in terms of growth. Höjesjö et al. (2004) found a similar pattern in brown trout, where the growth advantage of aggressive and dominant individuals diminished with increasing habitat complexity. In a study of juvenile steelhead in experimental streams, Sloat and Reeves (2014) found a positive directional selection on standard metabolic rate when the distribution of food was predictable. However, when the delivery of food resources was spatially unpredictable there was a negative selection for this trait (Sloat and Reeves 2014). This shows that the local environment may exert an important selection pressure because of physical heterogeneity and dynamic food supply.

Which biotic or environmental factors are limiting to growth depend on the conditions relative to the needs of the organism (Diana 2003; Begon et al. 2006). In previous studies in the Lapwai Creek watershed we have documented the various influences of water temperature on the density variation, cohort regulation, and individual energetics in juvenile steelhead (Myrvold and Kennedy 2015a, b, d). The Lapwai Creek population is located within the range of steelhead and redband rainbow trout, but at a relatively low elevation (250–700 m). The area has a dry summer (June–October), and in lower reaches the water temperatures can approach and temporarily exceed the thermal tolerance of rearing steelhead (Myrvold and Kennedy 2015b). Water temperature thus exerts an important control over individual performance and population dynamics in this system, and may hence be an important driver of growth compensation (i.e. a reduction in the size variability over time).

The discussion has focused on the role of physiological and behavioral underpinnings that may generate size differences in cohorts at different densities and temperatures. Our analysis concerned the subyearling cohort (i.e. individuals hatched in the same year as the sampling took place) to avoid the confounding factor of ontogenetic changes such as those associated with smoltification and migration (Diana 2003). Steelhead in the Lapwai Creek watershed outmigrate primarily at age two, and as yearlings at the earliest (Hartson and Kennedy 2015). However, can we completely discount the role of ontogenetic changes on the size and growth of individuals in such a diverse and plastic species? For the subyearling cohorts studied here we most likely could. Physiological changes occur after the decision to migrate has been made, which is usually months prior to the initiation of movement (Sloat et al. 2014). These physiological changes affect the partitioning of energy to various functions in the body, including somatic growth (Metcalfe 1998; Nicieza and Metcalfe 1999; Sloat et al. 2014; Kendall et al. 2015). However, due to the timing of our sampling (June to October) being 5–6 months prior to the primary outmigration period in this watershed (March–April) we expect the potential for such changes to be very limited in this study.

Ecologists are increasingly viewing a population as a set of individuals rather than as an entity with a mean and some deviation (Rubenstein 1981; Nakano 1995; Lomnicki 1999; DeAngelis and Mooij 2005). Body size influences most aspects of how an organism interacts with its environment directly, its fitness, and how it contributes to the dynamics of its population (Ebenman and Persson 1988; DeAngelis et al. 1993; Lomnicki 1999; Uchmański 1999). Understanding the intrinsic processes that generate size variation in a population (Pfister and Stevens 2002; Peacor et al. 2007a) in concert with abiotic constraints (Reid et al. 2012) can therefore provide great insights into the regulation of populations of mobile organisms and the selection on individual traits (Peacor et al. 2007a). Although natural settings provide the most realistic context to study these processes, they also prove challenging in disentangling the mechanisms generating size variation. More empirical studies from a variety of taxa and ecosystems are thus needed to address the causes and consequences of body size variation in natural populations.