Oecologia DOI 10.1007/s00442-012-2402-0

POPULATION ECOLOGY - ORIGINAL RESEARCH

Inter- and intra-specific patterns of density dependence and population size variability in Salmoniformes Ned A. Dochtermann • Mary M. Peacock

Received: 28 November 2011 / Accepted: 15 June 2012 Ó Springer-Verlag 2012

Abstract Population dynamics are typically affected by a combination of density-independent and density-dependent factors, the latter of which have been conceptually and theoretically linked with how variable population sizes are over time—which in turn has been tied to how prone populations are to extinction. To address evidence for the occurrence of density dependence and its relationship with population size variability (pv), we quantified each of these for 126 populations of 8 species of Salmoniformes. Using random-effects models, we partitioned variation in the strength of density dependence and the magnitude of pv between and within species and estimated the correlation of density dependence and population size variability at both the between- and within-species levels. We found that variation in the strength of density dependence was predominately within species (I2 = 0.47). In contrast, variation in population size variability was distributed both between and within species (I2 = 0.40). Contrary to theoretical and conceptual expectations, the strength of density dependence and the magnitude of population size variability were positively correlated at the between species level (r = 0.90), although this estimate had 95 %

Communicated by Marc Mangel.

Electronic supplementary material The online version of this article (doi:10.1007/s00442-012-2402-0) contains supplementary material, which is available to authorized users. N. A. Dochtermann (&)  M. M. Peacock Department of Biology, University of Nevada, Reno, USA e-mail: [email protected] Present Address: N. A. Dochtermann Department of Biological Sciences, North Dakota State University, Fargo, USA

credibility intervals (Bayesian analogues to confidence intervals) that overlapped zero. The within-species correlation between density dependence and population size variability was not distinguishable from zero. Given that density dependence for Salmoniformes was highly variable within species, we next determined the joint effects of intrinsic (density-dependent) and extrinsic (densityindependent) factors on the population dynamics of a threatened salmonid, the Lahontan cutthroat trout (Oncorhynchus clarkii henshawi). We found that densitydependent and -independent factors additively contributed to population dynamics. This finding suggests that the observed within-species variability in density dependence might be attributable to local differences in the strength of density-independent factors. Keywords Population dynamics  Lahontan cutthroat trout  Salmoniformes  Ecological stability  State–space models

Introduction The relative influences of intrinsic versus extrinsic factors on population dynamics is a persistent and often contentious topic in ecology (Nicholson 1933; Davidson and Andrewartha 1948; White 2008). The presence of densitydependent (intrinsic) versus -independent (extrinsic) regulation is also strongly tied to arguments regarding the role of competition in structuring populations and communities. Indeed, the signal of density dependence in population growth is often considered indicative of competition (Connell and Sousa 1983; White 2008). However, because density-dependent and density-independent factors interact (Sibly and Hone 2002), characterizing the dynamics of any

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one population or species as either density-dependent or density-independent is inappropriate. Nonetheless, attempts continue to differentiate taxa based on whether they exhibit density dependence. From a theoretical perspective, density dependence is also tied to variability in population sizes over time (Holling 1973; May et al. 1974; Connell and Sousa 1983; Hanski 1990), and broad taxonomic patterns in population size variability have been dismissed (Connell and Sousa 1983), suggested (Schoener 1985), refuted (Inchausti and Halley 2001, 2002), and suggested again (Reed and Hobbs 2004). Generally, populations experiencing strong densitydependent effects are expected to exhibit relatively less population size variability and vice versa. Besides being a putative indicator of the action of density-dependent factors, population size variability is also considered indicative of the extinction risk facing a population and is thus of conservation interest (Pimm et al. 1988; Bengtsson and Milbrink 1995; Vucetich et al. 2000; Fagan et al. 2001; Inchausti and Halley 2003). Ultimately, there do not seem to be clear patterns among taxa in population size variability (Inchausti and Halley 2001, 2002), and densitydependent effects are generally weak (Knape and de Valpine 2012). Thus, whether density dependence and population size variability covary—as would be expected—remains an unresolved question within the ecological literature. Salmoniformes as an order present considerable opportunities for asking general questions about population dynamics (Dochtermann and Peacock 2010). Members of this order have been of considerable economic and conservation concern, and as a result sampling records for periods greater than 100 years are available for some populations (Dochtermann and Peacock 2010), with data for well over 100 populations being available in the publicly accessible global population dynamics database (GPDD; NERC Centre for Population Biology I.C 1999). This makes the taxonomic group ideal for questions about the prevalence of density dependence and its relationship with population size variability. Further, despite the historical focus on density dependence versus independence at broad taxonomic levels, a potentially more informative question is the relative degree to which density dependent versus -independent factors influence population dynamics at the level of specific populations (Sæther et al. 2000). Evidence across taxa has demonstrated that density-dependent and -independent factors vary or interact to shape the dynamics of populations. For example, population regulation in black-throated warblers (Dendroica caerulescens) is related to multiple mechanisms that vary locally (Rodenhouse et al. 2003). Likewise, there is increasing awareness that long-studied population dynamics of desert rodents thought to be

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dominated by density dependence (Brown 1989; Brown et al. 2000, 2002) are in actuality profoundly affected by density-independent factors (Lima et al. 2008). Determining the relative contribution of density dependence and independence is also vital to understanding the population dynamics of species vulnerable to stochastic events and the potential effect of climate change (Sæther et al. 2000). The Lahontan cutthroat trout (Oncorhynchus clarkii henshawi), a threatened subspecies of cutthroat trout (O. clarkii) endemic to western North America and a member of the order salmoniformes, (Electronic Supporting Material), is one such species where many populations face local extirpation. While Lahontan cutthroat trout historically lived in large multiple-order stream networks, their range is currently heavily fragmented due to water diversions, unsuitable water temperatures, and non-native competitors, and most extant populations are restricted to small isolated headwater reaches (Coffin and Cowan 1995; Dunham and Vinyard 1997; Dunham et al. 1999; Peacock and Kirchoff 2004). This fragmentation among subpopulations has important implications, as the historical life history variation (resident or migratory life histories) and metapopulation dynamics inherent in such systems were likely key components of the species’ long-term persistence (Neville et al. 2006). Given the imperiled status of this subspecies and its restriction to less than 10 % of its historical range (Coffin and Cowan 1995), a better understanding of the determinants of population growth rate will advance our basic understanding of population dynamics and inform recovery strategies for this and perhaps ecologically similar salmonid species. To address these topics, we used data extracted from the GPDD to test for the presence and magnitude of density dependence and how density dependence relates to population size variability across the order Salmoniformes. We extended previous meta-analytical discussions (Turchin 1990; Sibly and Hone 2002; Sibly et al. 2005; Brook and Bradshaw 2006; Dochtermann and Peacock 2010; Knape and de Valpine 2012) by (1) explicitly partitioning variation in density dependence and population size variability to between and within-species levels, and (2) explicitly examining the relationship between density dependence and population size variability and how this relationship is manifested between and within species. While the ecological literature is replete with the assertion that the strength of density dependence and population size variability should be negatively associated (Holling 1973; May et al. 1974; Connell and Sousa 1983; Hanski 1990), this relationship has received little empirical attention. Further, because Salmoniformes exhibit considerable within-species variation in the strength of density dependence, we sought to disentangle the effects of density-dependent and density-independent factors on the population dynamics of

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Lahontan cutthroat trout. To do so, we estimated the relative contribution of both density dependence and density independence on abundances.

Materials and methods Inter-specific patterns of density dependence and population size variability We tested for the presence of density dependence between and within species of the order Salmoniformes based on the availability of records in the GPDD. Following Dochtermann and Peacock (2010), all populations for which population estimates based on individual counts were determined yearly without apparent extinction and without sampling gaps of more than 1 year were included. This resulted in a database of 126 populations, representing 8 species, with sampling periods ranging from 6 to 111 years (Table 1). Data analysis To estimate the strength of density dependence, we fit Salmoniformes population records to Gompertz models under which abundances are generally modeled as (Eq. 1): Nt ¼ Nt1 expða þ b ln Nt1 þ et Þ

ð1Þ

where a and b are constants, Nt and Nt - 1 are population abundances at times t and t - 1, respectively, and et is residual error (incorporating both measurement error and stochastic fluctuation in population sizes). Negative estimates of b correspond to negative density-dependent population dynamics with the strength of this dependence decreasing as b approaches 0 (density independence). We selected the Gompertz model as it generally conforms to the observed shape of population growth across a wide range of taxa (Sibly et al. 2005; Dennis et al. 2010),

performs well for ecological research (Dennis et al. 2010), has been extensively used in the ecological literature both historically (e.g., Holyoak and Lawton 1992) and recently (Brook and Bradshaw 2006; Knape and de Valpine 2012), and is not sensitive to differences in population sizes. Importantly, because et incorporates both measurement error and stochastic fluctuations in population sizes (also called process error), simply fitting population abundances to Eq. 1 can result in overestimates of b, the strength of density dependence (Dennis et al. 2006; Knape 2008; Knape and de Valpine 2012). Thus, we used ‘‘state–space’’ models to estimate b. State–space models explicitly estimate measurement error and stochastic variation in population sizes. State–space models have been developed for a variety of population models (Dennis et al. 2006, 2010; Knape et al. 2011; Knape and de Valpine 2012), including the Gompertz model, and substantially reduce bias in the estimation of b (Knape 2008). State–space estimation of b was conducted using the R statistical language with programing code modified from Dennis et al. (2010), and we multiplied all estimates of b by -1 to give an estimate of the strength of density dependence (dd) (Knape and de Valpine 2012). Thus, as values of dd increase so too does the estimated strength of density dependence. From these Gompertz state–space models, we also estimated the ratio of process error to total error for each population (henceforth er). Next, for each population, we calculated how variable population sizes were over time using Heath’s measure of population variability (Heath 2006). Heath’s population size variability (pv) is highly correlated with other measures of population size variability, but is less sensitive to large random population fluctuations (Heath 2006; Dochtermann and Peacock 2010). Higher values of pv correspond to greater population size variability and, thus, given proposed connections with density dependence, a negative relationship was expected between pv and dd (i.e. between pv and -1 9 b).

Table 1 Salmoniformes species used to detect inter-specific patterns of density dependence and population size variability Years of sampling

b (SD)

Heath’s pva (SD)

9

10–111

-0.62 (0.47)

0.45 (0.10)

7

6–7

-0.56 (0.31)

0.41 (0.08)

Oncorhynchus tshawytscha

1

26

-0.34 (NA)

0.20 (NA)

Chum salmon

Oncorhynchus keta

8

14–38

-0.53 (0.36)

0.40 (0.11)

Coho salmon

Oncorhynchus kisutch

10

-0.41 (NA)

0.53 (NA)

Pink salmon

Oncorhynchus gorbuscha

57

7–44

-0.72 (0.51)

0.57 (0.11)

Sockeye salmon

Oncorhynchus nerka

42

10–67

-0.31 (0.33)

0.52 (0.11)

Steelhead trout

Oncorhynchus mykiss

1

7

-0.71 (NA)

0.51 (NA)

Common name

Species

Atlantic salmon

Salmo salar

Brook trout

Salvelinus fontinalis

Chinook salmon

Number of populations

1

a

Values reported for estimates of Heath’s pv differ slightly from those reported by Dochtermann and Peacock (2010) in which jackknifing was used for both point and range estimates

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Finally, to determine the relative contribution of between versus within-species differences to both the strength of density dependence and population size variability as well as to estimate the correlation between these two population parameters, we used a multiresponse mixed-effects model. Mixed-effects models allow variation at different hierarchical levels to be partitioned and explicitly estimated (Zuur et al. 2009; Hox 2010). For density dependence and population size variability we fit the following model (Eq. 2a):
yij ¼ b0y þ b1y er þ species0yj þ e0yij
zij ¼ b0z þ b1z er þ species0zj þ e0zij ð2aÞ where yij and zij correspond, respectively, to the strength of density dependence (dd) and population size variability (pv) of population i of species j. species0yj and species0zj are estimated as random intercepts and can be thought of as average species deviations for y and z from the overall means of y and z (i.e. b0y and b0z) and e0yij and e0zij can be thought of as the population specific deviations. Error ratio (er) was included for both density dependence and population size variability as a fixed effect specifically because it was thought to possibly effect the observed magnitude of population size variability for a population (i.e. zij). b0y, b0z, b1y, and b1z were modeled as independent of each other (Matsuyama and Ohashi 1997) and correspond, respectively, to estimates of density dependence, population size variability, the effect of er on density dependence, and the effect of er on population size variability across Salmoniformes. The species-specific (species0j) and population contributions (e0j) to density dependence and population variability were modeled based on a multivariate normal distribution with a variance–covariance structure (Xspecies) specifying the between-species variances ðVspecies0y and Vspecies0z Þ and the between-species covariance between density dependence and population size variability (COVspecies0y ;species0z ; Eq. 2b). The population-specific deviations (e0ij), which include both population effects and residual error, were likewise assumed to be drawn from a multivariate normal distribution and
having within-species variances Ve0y and Ve0z , and withinspecies covariances (COVe0y ;e0z ; Eq. 2b):   species0yj  MVNð0; Xspecies Þ; species0zj   Vspecies0y COVspecies0y ;species0z Xspecies ¼ COVspecies0y ;species0z Vspecies0z     COVe0y ;e0z Ve0y e0yj  MVNð0; Xe Þ; Xe ¼ COVe0y ;e0z Ve0z e0zj ð2bÞ This model was fit using a Bayesian approach with the MCMCglmm library in R 2.14.1 (Hadfield 2010) with a

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total of 1.3 9 106 iterations with a 3.0 9 105 burn-in, a sampling interval of 1,000, and a prior that was flat (i.e. uniform) for variances and set as uninformative for both variances and covariances. This number of iterations and length of burn-in maintained low levels of autocorrelation and high levels of mixing. Effects were evaluated based on the mode of Bayesian posterior distributions of fixedeffects, and between- and within-species variances and covariances were then used to calculate the between- and within-species correlations between the strength of density dependence and population size variability along with 95 % credibility intervals, Bayesian analogues to confidence intervals. Similarly, from Bayesian posterior distributions, we determined the modal estimates and corresponding credibility intervals for density dependence (dd) and population size variability (pv) across all Salmoniformes (i.e. b0y and b0z) as well as the effect size estimate and credibility intervals for the effect of error ratio on either density dependence or population size variability. We also calculated the relative contribution (and credibility intervals) of between-species variation to the total variation in either the strength of density dependence or population size variability. These relative contributions were calculated as I2 (Eq. 3; Nakagawa and Santos 2012): I2 ¼

Vspecies0 Vspecies0 þ Ve0

ð3Þ

where Vspecies0 and Ve0 correspond to between- and withinspecies variances for either density dependence or population size variability (as in Eq. 2b). This approach to partitioning variation allowed us to determine the levels at which Salmoniformes exhibit variation in density dependence and population size variability, and to distinguish how these population parameters are correlated. Because there is not a well-resolved phylogeny spanning the entire Salmoniformes order, we assumed a star phylogeny (Garland et al. 2005) throughout.

Intra-specific patterns in Lahontan cutthroat trout We tested for correlative relationships among abiotic factors and population abundances of Lahontan cutthroat trout as well as for density dependence in these same population parameters. These tests were based on longterm population monitoring of Lahontan cutthroat trout in Gance Creek, a tributary to the North Fork Humboldt River in the North Fork Humboldt River subbasin within the greater Lahontan hydrographic basin, which spans much of northern Nevada, USA (Electronic Supporting Material).

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Population sampling and population size estimation The population of Lahontan cutthroat trout in Gance Creek was sampled and population size estimated during two time periods. The first period of sampling was from 1978 to 1985 (Platts and Nelson 1988) and the second from 1993 to 2002 (Ray et al. 2007). Sampling during both periods was conducted according to standard depletion sampling methods for the species (Platts and Nelson 1988; Dunham et al. 1999; Dochtermann and Peacock 2010). Multiple sampling transects were established within Gance Creek, although sampling transects differed between sampling periods, and the population size estimated with a multi-pass depletion method using backpack electro-fishing units. Prior to sampling, block-nets were established at both the down- and upstream ends of the sampling transect. Sites were then sampled using an electro-fishing unit moving to upstream between block-nets. Movement from the downto upstream block-net constituted a single pass and passes continued until no more fish were caught. The standardlength of individuals (mm) was determined at capture and all individuals were returned to point of capture at the completion of the final pass. Because young-of-year (individuals who hatched during the year of sampling) cannot be reliably sampled due to variable emergence times from spawning gravels, they were excluded from all analyses. From the number of individuals captured during each pass—and the resulting depletion curve—the number of Lahontan cutthroat trout was estimated using maximumlikelihood in the program Microfish (Van Deventer and Platts 1989). The overall population size for each year was then estimated by extrapolating the average number of individuals captured within transects of known length across the occupied length of the creek (Dunham et al. 1999; Dochtermann and Peacock 2010). Flow rate We focused on the flow rate of Gance Creek as a key density-independent determinant of Lahontan cutthroat trout population dynamics because we had an a priori expectation that magnitude of spring flows would be related to population dynamics, as spawning occurs between April and June. In particular, the recruitment of trout is related to the timing and magnitude of discharge (Seegrist and Gard 1972; Erman et al. 1988; Strange et al. 1992; Latterell et al. 1998). For example, recruitment of youngof-year trout is often inversely related to spring discharge because higher spring stream discharges may scour spawning gravels and can dislodge incubating eggs (Seegrist and Gard 1972; Erman et al. 1988; Strange et al. 1992; Montgomery et al. 1999).

We determined the average maximum daily spring discharge (i.e. March 1 through June 30) directly for the water years of 1979/1980 to 1986/1987 from a US Geological Survey stream gauge at Gance Creek (USGS Station 10317450). Unfortunately, discharge data were not available for this station after 1987. To determine maximum monthly spring discharge for Gance Creek for the remaining years, we used data from a nearby station in Mary’s River (USGS Station 10315500). We first fit a quadratic regression of Gance Creek discharge over the discharge from Mary’s River (MRD) from 1979 to 1987. Discharges of each creek were log10-transformed prior to analyses to achieve linearity. The relationship between creeks was estimated as: Gance Creek discharge ¼ 0:564  0:478  MRD þ 0:301  MRD2 This properly characterized variation in Gance Creek’s discharge (r2 = 0.87; p \ 0.001) and so we used the regression equation to estimate Gance Creek’s discharge. Data analysis To determine the relative contributions of density dependence and density-independent factors to Lahontan cutthroat population growth rates, we used least squares estimation to fit the total population size observed (N) in a particular year (t) to five Gompertz model variants. Gompertz models were used to allow for comparison with inter-specific patterns (above) and because they generally conform to the observed shape of population growth (Sibly et al. 2005; Dennis et al. 2010). Unfortunately, to our knowledge, state–space Gompertz models incorporating extrinsic factors have not yet been developed. Following the approach to modifying Ricker population models used by Holyoak and Lawton (1992) and Turchin (1990), we modified Gompertz equations to incorporate extrinsic effects on population growth: Model 1: Nt ¼ Nt1 expða þ et Þ Model 2: Nt ¼ Nt1 expða þ b1 logNt1 þ et Þ Model 3: Nt ¼ Nt1 expða þ b1 Flowt1 þ b2 Flowt þ et Þ Model 4: Nt ¼ Nt1 expða þ b1 log Nt1 þ b2 Flowt1 þ b3 Flowt þ et Þ Model 5: Nt ¼ Nt1 expða þ b1 log Nt1  b2 Flowt1 b3 Flowt þ et Þ where r is the population growth rate, Flow corresponds to Gance creek’s discharge in years t - 1 and t, and other model terms are as above (b1 in models 2 and 4 corresponds to b in Eq. 1). Model 5 included main effects and two-way interactions. The log of each model was simplified and then fit using least-squares estimation and the

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log-likelihood of each model estimated. For example, for Model 1, we fit the corresponding statistical model as: log

Nt ¼ a þ et : Nt1

From the log-likelihood, we then calculated Akaike’s information criterion (AIC), AIC differences (DAIC), and model weights. We used AIC differences and model weights to assess relative support for each model (Burnham and Anderson 2002). We did not use AICc because it does not generally reduce bias (Richards 2005) but does lead to a conflation of sample size with the values on which inferences are drawn, leading to biases analogous to concerns about power and Type II errors. Support for model 1 would suggest that none of the factors we included in the model set adequately explain the data and it is a general density-independent model of population growth. Support for models 2 and 3 would suggest support for strictly density dependence or density independence, respectively. Support for model 4 would suggest that density dependence and density independence additively contribute to observed population dynamics, while support for model 5 would suggest interactions amongst density-dependent and density-independent factors. For the best fit model, we also conducted hierarchical partitioning (Chevan and Sutherland 1991) to determine the proportion of explained variation that could be attributed to either density dependence or the density-independent effects of flow rate. We also calculated how variable population size was in Gance Creek (Heath 2006; Dochtermann and Peacock 2010). All inter- and intra-specific analyses were conducted using R 2.14.1.

Results Inter-specific patterns of density dependence and population size variability The strength of density dependence across Salmoniformes was 0.51 (0.24–0.91; Fig. 1a). Variation in the strength of density dependence was primarily within species (Table 2). Salmoniformes also exhibited considerable variation in population size variability which, for all Salmoniformes, was estimated as 0.47 (0.34–0.61). However, variation in pv was split more equally between and within species (Table 2). Error ratio did not substantively contribute to estimates of either density dependence (b1y = 0.065; CI 0.190 to 0.31) or population size variability (b1z = 0.123; CI -0.166 to 0.353). Multiresponse random-effects analysis suggested that the strength of density dependence was strongly and positively correlated with Heath’s pv at the between-species

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Fig. 1 a Estimates of the strength of density dependence (dd) in 125 populations of 8 Salmoniforme species (average strength = 0.51, indicated by dashed vertical line). b Between-species estimates of the magnitude of population size variability among eight Salmoniformes as estimated by Heath’s pv versus the strength of density dependence (r = 0.90). Data from the global population dynamics database, GPDD

level (r = 0.90; Fig. 1b), although this estimate had broad credibility intervals that overlapped zero (Table 2). At the within-species levels, density dependence and Heath’s pv were effectively uncorrelated (r = -0.03; Table 2). Intra-specific patterns in Lahontan cutthroat trout Population growth of the Gance Creek population was most strongly attributable to the additive contributions of density-dependent (Fig. 2) and density-independent factors (model 4; Table 3). These model comparisons provide support for additive effects of density dependence and independence, although there was also some support for either density-independent factors alone or interacting with density dependence (Table 3). The observed strength of density dependence in this population (dd = 0.45) was slightly weaker than that observed for Salmoniformes in general (0.56). Overall, the additive contribution of density-dependent and -independent factors explained 46 % of

Oecologia Table 2 Between- and within-species variation in and correlations between density dependence and population size variability Estimate

95 % credibility interval

Density dependence

0.118

(0.020 to 0.692)

Population size variability

0.398

(0.145 to 0.926)

I2

Correlation between density dependence and population size variability Between species

0.899

(-0.869 to 0.989)

Within species

0.027

(-0.175 to 0.199)

Ratio of total variation in either the strength of density dependence or population size variability attributable to between-species differences rather than within-species differences (I2; Nakagawa and Santos 2012). All parameter estimates are Bayesian posterior modes with 95 % credibility intervals in parentheses

the total variation in population growth. Hierarchical partitioning suggests that this explained variation was less strongly attributable to density dependence, which contributed 33 % of the explained variation, relative to density independence which contributed a total of 67 % of the explained variation (Flowt - 1 = 53 %; Flowt = 14 %). The Gance Creek population of Lahontan cutthroat trout also exhibited moderately high population size variability (Heath’s pv = 0.48).

Discussion Our meta-analysis of density dependence in Salmoniformes identified several interesting results. First, consistent with other taxonomic surveys (e.g., Knape and de Valpine 2012), our results suggest that the occurrence of density dependence was generally moderate (Fig. 1a). However, because many of the species examined are anadromous, density dependence may be manifested within cohorts rather than across cohorts as examined in the current analysis. Such an influence of life history on how density dependence is manifested is also important to consider in interpreting the inferences drawn by other broad population dynamics meta-analyses (e.g., Inchausti and Halley 2001, 2003; Sibly et al. 2005; Brook and Bradshaw 2006; Dochtermann and Peacock 2010; Knape and de Valpine 2012). Second, the strength of density dependence was highly variable within species, with between-species differences only accounting for 12 % of the variation in density dependence (Table 2). This result is particularly important because it demonstrates that inferences about population dynamics might not be reliable across populations of the same species. Third, population size variability was also quite variable within species: between-species differences accounted for 40 % of the observed variation (Table 2), thus the remaining 60 % of observed variation was within species. We previously demonstrated that within-species differences in population size variability (Dochtermann and Peacock 2010) accounted for

approximately 68 % of the observed variation in this population parameter, and that these random-effect model results support this finding. Fourth, and perhaps most interesting, despite historical discussions in the ecological literature about population size variability and density dependence (Holling 1973; May et al. 1974; Connell and Sousa 1983; Schoener 1985; Hanski 1990), we found that the strength of density dependence and population size variability were positively related (Table 2; Fig. 1b). Since regulation via density dependence is expected to dampen population size fluctuations (Holling 1973; May et al. 1974), this result is surprising and raises serious questions that have heretofore not been addressed within the ecological literature. Possible explanations for this surprising relationship between density dependence and population size variability are not immediately clear. Leveraging effects of outliers

Fig. 2 Density dependence in Lahontan cutthroat trout (Oncorhynchus clarkii henshawi) as illustrated by a negative relationship between the size of the population in  one year  (lnNt - 1) versus the population growth rate to the next

ln NNt1t . 46 % of the observed

variation in Lahontan cutthroat trout population sizes was attributable to either direct density dependence or flow rates. However, of this total, only 33 % was attributable to the population size in the previous year, i.e. to density dependence

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Oecologia Table 3 Model comparison results for the relationship between population growth and density-dependent (b1logNt (b2Flowt - 1 ? b3Flowt) effects Model 1

Nt = Nt

- 1exp(a

? et)

2

Nt = Nt

- 1exp(a

? b1logNt

3 4

Nt = Nt Nt = Nt

5

Nt = Nt

-

- 1

? et)

1exp(a ? b1Flowt - 1 ? b2Flowt ? et) 1exp(a ? b1logNt - 1 ? b2Flowt - 1 ? b3Flowt ? et)

- 1exp(a

? b1logNt

- 1

9 b2Flowt

- 1

9 b3Flowt ? et)a

- 1)

or density-independent

Loglikelihood

k

AIC

DAIC

Model weight

-12.86

2

29.72

3.44

0.08

-11.68

3

29.36

3.08

0.09

-9.80 -8.14

4 5

27.60 26.28

1.32 0

0.23 0.44

-5.1

9

28.20

1.92

0.17

Based on differences in Akaike’s information criterion (DAIC) and model weights, a model incorporating both density-dependent and -independent factors was most well supported a

Also includes main effects and 2-way interactions

can unduly change inferences; however, that does not seem to be the case here. The only apparent outlier of the eight species examined were sockeye salmon (O. nerka), and this species did not influence the direction of the estimated correlation between density dependence and population size variability (r without sockeye: 0.99). Sockeye may exhibit differences from other Salmoniformes due to natural history differences as they migrate into large-volume lakes. Importantly, the relationship between density dependence and population size variability is complicated by the fact that measures of population size variability combine both the stochastic variation of interest and possible measurement error. While our inclusion of the ratio of stochastic variation to measurement error as a fixed-effect should help ameliorate this concern, it may not have done so if instead the effects of combining these sources of error operated at the level of the correlation between density dependence and population size variability. To address this possibility, we extended the bivariate mixed-effects model and its components (Eqs. 2a, 2b) to a trivariate randomeffects model including the ratio of process error (stochastic variation) to total error as a response variable (and omitting it as a fixed-effect). We then estimated the partial correlations between the three values. After controlling for the relationships amongst all three variables, density dependence and population size variability remained highly correlated (r = 0.88)—although the credibility interval for this correlation remained broad—suggesting that the relationship is robust to varying levels of measurement error in the GDPP. While our demonstration of this counterintuitive relationship between density dependence and population size variability is novel, because it was based on only eight species (three of which were only represented by single populations), it also warrants further study and verification in other systems. The strong differences between populations of the same species in the strength of density dependence (Table 2) are likely attributable to the local conditions populations

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experience. For example, we demonstrated that the population dynamics of Lahontan cutthroat trout are jointly affected by density dependence and local density-independent factors, the latter of which being more influential. The biological basis of density dependence in Lahontan cutthroat trout likely arises from a combination of intraand inter-age class interactions. Larger, older, age classes (3?) defend pool habitat (Dunham et al. 2002) which is associated with temperature, with pools typically being cooler than other components of a stream. Temperature is negatively associated with both recruitment and survival (Dickerson and Vinyard 1999; Dunham et al. 2003; Meeuwig et al. 2004), so class competition for cooler habitats may thus affect recruitment at higher densities. Young and adult trout both consume insect larvae, crustaceans, and meiofauna (Dunham et al. 2000; Keeley and Grant 2001), suggesting that food may be limiting and that intraspecific competition between adults and smaller size classes may be high (Dunham et al. 2000), leading to spatial segregation among age classes which would contribute to the signal of density dependence we detected here. Likewise, competition for habitats and resources within age classes may also affect the probability of successful recruitment and survival. The density-independent effect of spring stream flow in previous years on population dynamics also has a clear connection with the biology of Lahontan cutthroat trout. High spring discharge tends to clear debris (sedimentation and any submerged macrophytes) which decreases salmonid egg survival from redds (Henson et al. 2007). Removal of debris increases both water flow through redds and dissolved oxygen exchange with eggs, leading to increased hatching success. While we were not able to reliably sample fry and other early-stage individuals hatched in a particular year, this increased hatching success is indicated by the positive relationship between spring flow rates and population growth. An additional and non-mutually exclusive explanation is that higher spring flows may lead to greater summer base flows due to increased groundwater

Oecologia

recharge, affecting metabolic demands of thermal regulation and, potentially, changing resource availability. In contrast, low spring discharge can result in increased survivorship among the younger age classes (i.e. 1? and 2?) by reducing the chance of being displaced from the stream channel and stranded in the riparian flood zones during high flow events. Our demonstration that density-dependent and densityindependent factors additively contribute to population dynamics in Lahontan cutthroat trout reinforces recent calls to recognize the relative contribution of each (e.g., Sæther et al. 2000). Similarly, our results suggest generality for demonstrations that systems historically characterized as driven by density dependence are actually affected by a variety of factors, including stochastic perturbations (Lima et al. 2008). Particularly for populations of conservation concern, this generalization necessitates a greater understanding of all the factors that influence how the sizes of population change with time. Combined, our inter- and intra-specific results generate several new and interesting questions. First, is the observed relationship between density dependence and population size variability general across taxa? If so, how does this affect our understanding of density dependence and population dynamics as a whole? Second, why is variation at the between- and within-species level partitioned differently for density dependence and population size variability? If this is due to local differences in densityindependent factors, which our intra-specific results suggest is possible, how then can we interpret recent taxonomically broad evaluations of density dependence and population size variability (e.g., Inchausti and Halley 2001; Brook and Bradshaw 2006; Knape and de Valpine 2012)? Future work with public repositories of data like the GPDD should allow these questions to be addressed. Acknowledgments We would like to thank Lisa Heki, Project Leader, Lahontan National Fish Hatchery Complex, United States Fish and Wildlife Service for funding and Robbie Bear, Jason Dunham, Joel Hoffman, Jessica Kenzie, Anita Lahey, Michael Meeuwig, Helen Neville, Matt Rahn, Chris Rosamond, Robert Schroeder, and Gary Vinyard for indispensable help in the field. Marc Mangel, Sean Hayes, and an anonymous reviewer provided important critical feedback that greatly helped this paper.

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