incorporating environmental variation into models …incorporating environmental variation into...

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American Fisheries Society Symposium 73:407–426, 2010© 2010 by the American Fisheries Society

Incorporating Environmental Variation into Models of Community Stability: Examples from Stream Fish

Gary D. Grossman*D. B. Warnell School of Forestry & Natural Resources, University of Georgia

Athens, Georgia 30602, USA

John L. SaboSchool of Life Sciences, Arizona State University

Post Office Box 874501, Tempe, Arizona 8528, USA

Abstract.—Stochastic dynamics are central to theory, data analysis, and un-derstanding in the fields of hydrology and population ecology. More importantly, hydrologic variability has been identified as a key process affecting biodiversity and coexistence in stream fish assemblages. Until recently, however, we have lacked tools by which hydrologic variability can be directly linked to measures of com-munity stability. Herein, we show how a modification of Fourier analysis of daily average discharge data can be used to quantify aspects of hydrologic variability for three reference streams and then linked to measures of fish assemblage stability in Coweeta Creek, North Carolina; Sagehen Creek, California; and Otter Creek, In-diana) via multivariate autoregressive (MAR) models. Specifically, we define the magnitude of catastrophic variability as the standard deviation of residual flows ref-erenced to a long-term annual trend, and individual catastrophic events as flows greater than (floods) or less than (droughts) two times this magnitude (i.e., 2s). We then directly link the magnitude of annual residual flows with MAR models that quantify the relationship between flows and the stability of fish assemblages from the same or nearby streams. Our results confirm that these streams represent a gradient in the stability properties of fish assemblages; Sagehen Creek is the most stable, whereas Otter Creek is the least stable. The timing of catastrophic high and low flows is most predictable in Sagehen Creek and least predictable in Big Raccon Creek (reference stream for Otter Creek), whereas the magnitude and frequency of catastrophic events varied in a manner less consistent with the gradient in fish community stability. Nevertheless, the stability of fish communities covaried signif-icantly with both residual flow magnitudes (high- and low-flow events). Although this technique is not without limitations (e.g., it is most relevant to resident spe-cies), it appears to be a promising new tool for linking hydrologic variability directly to fish assemblage stability and, more broadly, for quantifying links between flow regulation and the viability of native aquatic faunas.

* Corresponding author: [email protected]

408 grossman and sabo

Introduction

In the past 30 years, ecological theory has be-come pluralistic. Prior to this time, the majority of ecological theory was based on the assump-tion that interspecific competition was the main factor determining the diversity and abundance of species in ecosystems (McIntosh 1985). In the ensuing years, multiple researchers have shown that environmental variation (including disturbance) may be as important in determin-ing biodiversity as competition and predation (Sousa 1979, 1984; Grossman et al. 1998 and 2010, this volume): a finding based to no small extent on studies of stream fish assemblages. Certainly, streams are excellent systems for the study of environmental variation because of the frequency of both floods and droughts in these habitats (Horwitz 1978; Grossman et al 1982, 1995, 1998; Poff et al. 2007). From a histori-cal perspective, it is worthwhile to note that the assemblage-level effects of flow-related distur-bance on stream fishes was recognized as early as the 1950s by scientists such as William Starrett (1951) and R. Weldon Larimore (1954, 1959). These scientists reported substantial effects of flow variation on the abundance and composi-tion of stream fish assemblages. Nonetheless, it took until the late 1970s and early 1980s until the consequences of this phenomenon for eco-logical theory were recognized (Grossman et al. 1982).

Variation in flow may have profound ef-fects on stream fishes and these impacts depend upon the magnitude, timing, frequency, and du-ration of hydrologic variation, as well as its rela-tionship to the life history characteristics of the species within the assemblage (Grossman et al. 1982, 1998). Specifically, does the magnitude of high- or low-flow events exceed the tolerances of assemblage members?, do high- and low-flow events occur during critical life history events such as reproduction, early development, or

migration of assemblage members?, and does the duration of high/low flow events exceed a significant portion of the life spans of assem-blage members? Previous research has shown that all of these aspects of hydrologic variation may influence both the structure of stream fish assemblages and the dynamics of populations composing these assemblages (Grossman et al. 1998; Matthews 1998). For example, extreme high- or low-flow events may cause shifts in stream fish assemblage structure in streams lo-cated across the United States (Grossman et al. 1998; Matthews 1998; Jackson et al. 2001) and Australia (Kennard et al. 2007), and the same is true for general variability in flow (e.g., streams with low versus high frequencies of disturbance, Pusey et al. 1993; Poff and Allan 1995; Taylor et al. 2005). The timing of extreme events also determines their biological impacts, and a bank-full flood may have a much greater impact if it occurs during a period of seasonally low flows or during a critical life history stage (egg deposi-tion, fry emergence, etc.) than if it occurs during seasonally high flows or periods when vulner-able life history stages are not present (Gross-man et al. 1982: Harvey 1987). Both local and landscape conditions also affect the impacts of variability in flow (Bunn and Arthington 2002). Erman et al. (1988) provide an example of local landscape effects where the impacts of winter floods on sculpin in a Sierra Nevada stream dif-fered depending on the presence or absence of snow on the streambanks. Finally, the duration of high/low flows obviously will have different biological impacts depending upon the longev-ity and reproductive frequency of assemblage members (Matthews 1998).

One of the first measures used to quan-tify hydrologic variation (i.e., high-flow distur-bance) was the recurrence interval (Gordon et al. 2004). Recurrence intervals are calculated from long-term time series of annual maximum flows and Log-III Pearson distributions (Riggs

409flow variation and stream fish assemblages

1972; Kottegoda 1980) and provide quantita-tive relationships between the frequency and magnitude of high-flow events. Hence, a high-flow event of a given magnitude has a quantifi-able recurrence interval (e.g., 1-year flood, 10-year flood, 100-year flood). Recurrence intervals have attractive properties as measures of vari-ability in streamflow because high flows drive geomorphological processes such as pool and bar formation, sediment transport, and habitat scouring (Gordon et al. 2004). Bank-full flows maintain channel form and represent a thresh-old for bed movement. Flows of this magnitude occur with sufficient regularity (~every 1.6 years in gravel bed streams, Kennard et al. 2007) such that we can expect most fishes to have evolved in their presence. Although recurrence intervals have long been used in hydrology, ecology, and fisheries, they lack reference to the seasonal oc-currence (i.e., annual timing) of an event. More-over, low-flow recurrence intervals estimated using the same technique (i.e., Log Pearson III methods) do not have the same geomorphic relevance as bank-full (high) flows. Quantifying hydrologic variation only in terms of high flows may be appropriate for sessile organisms or those with low mobility such as benthic inver-tebrates. Nonetheless, motile organisms such as fishes can move off-channel to refugia during high flows. In addition, traditional hydrologic methods assign equal significance to a given flow magnitude regardless of the timing of that flow or the difference between the magnitude and expected flows for that day. This is unfortunate because we know that the biological impacts of high flows may vary tremendously depending on base flows or local conditions (Erman et al. 1988; Bunn and Arthington 2002).

Since the 1980s, a bewildering variety of more complex indices have been developed to measure hydrologic variation in lotic systems, and Olden and Poff (2003) performed a thor-ough statistical analysis of 171 of these indices.

Their analysis indicated that a desirable index would measure the timing, magnitude, and frequency of various flow events and that this could be summarized via the use of two to four hydrologic indices. Olden and Poff (2003) con-cluded that (1) many of the indices have high levels of redundant inputs (i.e., correlated vari-ables are treated as independent), and (2) hy-drologic data frequently show significant levels of skewness, and indices must be able to deal with nonnormally distributed data. Although many hydrologic indices exist, it remains quan-titatively difficult to link these values directly to important assemblage-level properties. For example, relationships between composite properties such as diversity, species richness, biomass, or population characteristics can be plotted or regressed against various univariate measures such as number of high-flow events or mean peak flow or even hydrologic index values. Nonetheless, it is difficult to capture the multi-variate properties of flow variation typically present in the hydrographs of unaltered streams with univariate analyses, recurrence values, or even hydrologic indices (Olden and Poff 2003). For example, in Coweeta Creek (North Caro-lina) during the drought of 1985–1988, all flow measures were low in 1985, 1987, and 1988, but 1986 yielded low flows combined with a higher frequency of high-flow events atypical of drought (Grossman et al. 1998, 2006). Even using multivariate techniques such as principal component analysis on flow measures that in-clude means, variance measures, and frequen-cies of high-flow events (Grossman et al. 2006), it is difficult to identify and represent significant hydrologic variation and subsequently link it to biological properties, especially because some of these relationships are nonlinear (Figure 1). In addition, there is evidence that extreme or unusually timed events may be the flows that have the greatest effect on assemblage dy-namics, and these also may prove difficult to


Figure 1. The differential effects of flow on recruitment of mottled sculpin in drought versus normal and high-flow years (Coweeta Creek, North Carolina). The solid square represents two annual data points. After Grossman et al. (2006).

quantify via composite indices (Grossman et al. 1982, 1998; Bunn and Arthington 2002). Consequently, it would be useful to have a measure of hydrologic variability that could be directly coupled to quantitative measures of assemblage structure and stability and esti-mate its effects on these properties.

In this paper, we link two relatively new techniques—modified Fourier analysis for measurement of catastrophic variation in daily flows (Sabo and Post 2008) to multivariate autoregressive models MAR-1 that measure assemblage stability (i.e., stability, resilience, and return time), and estimate coefficients of interaction strength both within and among species (Ives et al. 2003). The stochastic prop-erties measured for assemblage stability: am-plification, return time, and reactivity—all represent meaningful properties for stream fish assemblages (Ives et al. 2003) and all are likely affected by hydrologic variation. Conse-

quently, we used Fourier analysis on ~20-year time series of daily average discharge measure-ments to compare the magnitude, frequency, and timing of catastrophic high- and low-flow events in three small streams with disparate hydrology. Fourier analysis also allowed us to identify a time series of maximum/minimum annual residual flows (referenced to the long-term Fourier trend). We then linked hydrology and fish community stability in a single analy-sis by including these maximum and minimum residual annual flow time series as covariates in a stability analysis of the three fish assemblages using MAR-1 (Ives et al. 2003).

Methods

Data Sources and Site Descriptions

We used published time series of fish abundance and hydrologic data for Sagehen Creek, Califor-nia, USA (1951–1961, Gard and Flittner 1974),


Otter Creek, Indiana, USA (1962–1974, Gross-man et al. 1982), and Coweeta Creek, North Carolina, USA (1984–1995, Grossman et al. 2006 and unpublished). Detailed descriptions of the sites and collecting methods have been published in the aforementioned articles. In brief, Sagehen Creek is a tributary to the Truc-kee River, which drains into Lake Tahoe on the eastern side of the Sierra Nevada Mountains. Ot-ter Creek is located in Vigo County, Indiana and a tributary of the Wabash River. Coweeta Creek is a tributary of the Little Tennessee River in the southern Blue Ridge Mountains in western North Carolina. To characterize the hydrology of these three stream systems, we used average daily discharges from the U.S. Geological Survey (USGS) National Water Information System for Sagehen Creek (USGS Station 10343500) and for Big Raccoon Creek, near Coxville, Indi-ana (USGS Station 03341300) for Otter Creek. For Coweeta Creek we used average daily dis-charge data from Weir 8 (Shope Fork Creek) obtained from USDA Forest Service Coweeta Hydrologic Laboratory. Weir 8 is at the base of Shope Fork just before its confluence with Ball Creek that forms Coweeta Creek. The weir is less than 400 m from the fish collection site. Our analysis is limited by the fact that it was not pos-sible to completely match hydrologic and fish abundance records for either Sagehen or Otter Creek. Hydrologic data for Sagehen Creek exist only for the past 6 years of the fish data set, and the closest gauge for a similarly sized stream to Otter Creek (Big Raccoon Creek) is in a nearby county. Otter, Sagehen, and Coweeta creeks dif-fer in geography, fish diversity, and hydrology, although their choice was dictated mainly by the presence of long-term fish abundance data sets. Consequently, the three streams represent systems in which hydrologic variation differs substantially, and these differences may differ-entially affect the properties of their respective fish assemblages.

Hydrologic Variation

We quantified seasonal and extreme hydrolog-ic events using Fourier analysis and extreme event statistics. A complete description of the primary method is provided in Sabo and Post (2008). Here we provide a brief overview of methods and a detailed description of a meth-odological extension used to characterize three key aspects of the disturbance regime in the three stream systems—the magnitude, frequency, and timing of catastrophic low- and high-flow events. We used Fourier analysis because it better enables us to define the char-acteristic “signals” (frequencies, phases, and amplitudes) of seasonal hydrologic variation (Sabo and Post 2008) and, thus, more appro-priately quantify the magnitude, frequency, and timing of potentially catastrophic events. We defined catastrophic events as those ei-ther higher (floods) or lower (droughts) than two standard deviations of the distribution of residual variation around the long-term seasonal trend estimated by Fourier analysis (2s, Sabo and Post 2008). We used 2s as our cutoff for catastrophic events because 2s is a standard upward limit for significance testing assuming a type I error rate of 5% for regres-sion parameters.

We used the fast Fourier transform imple-mented in Matlab v. 7.1 (R14) Service Pack 3 with statistics toolbox to obtain the power spectrum (in the frequency domain of the time series data) of the three 20-year data sets. Spe-cifically, the average amplitude of the seasonal trend and the interannual variability around this seasonal trend (“noise”) were measured by Arms and Nrms, respectively. We calculated signal to noise ratios (S/N) = 20 × ln(Arms/Nrms) to compare seasonality relative to inter-annual variability in stream hydrographs. Most importantly, we define stochastic variation in stream discharge using several descriptive sta-


tistics. The first, Nrms is a simple measure of en-vironmental stochasticity. The second (ud), is a composite measure of the temporal autocorre-lation structure of variation in the hydrograph. This is known as “noise color” and is a measure of the flashiness of the hydrograph. Noise col-or ranges from 0 (white noise with no autocor-relation—highly flashy hydrographs) to values over 2 (reddened, streams with strong autocor-relation in which high- or low-flow events per-sist over the short term). The third and most important measure is the standard deviation of residual flow magnitudes and gives a composite measure of the degree of catastrophic variation, akin to disturbance. We relied on the statisti-cal distribution of “residual events” to quantify the magnitude, frequency, and timing of cata-strophic events experienced by a stream fauna. Residual events were flow magnitudes above

or below the long-term seasonal average (from Arms, Figure 2). We removed dependence (tem-poral autocorrelation in these residual values) by using only maximum or minimum values in strings of related residuals, daily data equal to or of the opposite sign of the string bound in time. We fit these “whitened” residual events to the appropriate side of a normal distribution and es-timate the standard deviation of the magnitude of these events (right-hand side: shf; left hand side: slf). These standard deviations yielded a composite measure of the magnitude of residual or catastrophic high- and low-flow variation in the hydrograph and were directly comparable because they are defined in equal units. Values for shf and slf are an indication of the long-term magnitude of residual flow variation (over 20-year record) but did not provide much informa-tion about the significance of individual events

Figure 2. Cartoon illustrating concept of residual and absolute or extreme events in ecohydrology. Ex-treme events are the highest (for floods) flows of the year (arrow connecting zero flow to open circle). Annual maxima across a long-term record are then fitted to a Log-III Pearson function to estimate the recurrence interval of events of various magnitudes. Residual high flows are those measured above the seasonal trend (arrows connecting long-term seasonal trend to triangles). Residual events carry infor-mation about the timing of high flows; absolute or extreme events do not. As a result, the small residual flow (filled triangle) is equal in magnitude to the residual flow of the absolute high flow (open circle).


(e.g., within years in a single hydrograph). We adapted these methods to look at individual events and quantify the magnitude, frequency, and timing of these events across years brack-eting our records of fish sampling.

Adapting Seasonally Referenced Events to Quantify Disturbance Regimes

After calculation of long-term seasonal trend and shf and slf, we identified the frequency, magnitude and timing of all events in which high- or low-flow events were greater than 2 × shf or greater than 2× slf, respectively. We term these catastrophic events to differentiate them from extreme events defined by more tradi-tional (Log Pearson III or other exceedence methods). We identify predictability relative to the seasonal trend by Julian day (i.e., the av-erage event for a day on the hydrograph). Thus, we also quantified the temporal distribution of catastrophic events. For example, this method allowed us to quantify the distribution of cata-strophic events across months. Consequently, we were able to quantify three key aspects of the disturbance regime—the maximum or av-erage magnitude, the frequency, and the tim-ing of catastrophic discharge events.

Fish Assemblage Stability

Although there is a variety of methods for quan-tifying fish assemblage structure (Grossman et al. 1990), we used first order multivariate au-toregressive models (MAR-1; Ives et al. 2003) to quantify stability properties of fish assemblages. This method is advantageous because it can (1) fully utilize time series structure of the data, (2) provide quantitative estimates of species inter-action strengths and the stability properties of the fish assemblage, (3) provide estimates of uncertainty for interaction strengths and stabili-ty properties, and (4) directly enable us to insert hydrologic variability into the stability analysis

via vectors of appropriate covariates. Stabil-ity properties identified via MAR-1 stability are numerous and different from standard de-terministic definitions of stability (Ives et al. 2003). First and foremost, because we are em-bracing the stochastic nature of communities, we acknowledge that the term “equilibrium” is relevant to a range of abundance values, not a single value. Hence, we quantified this range in three ways: (1) variance stability—a measure of the degree to which environmental fluctua-tions (e.g., Nrms, or shf, slf) augment intrinsic fluctuations in relative abundance driven by bi-otic processes, (2) return time—a measure of the time required for the abundance patterns to return to a characteristic range of values follow-ing a perturbation, and (3) reactivity—a mea-sure of the degree to which abundance patterns change following a perturbation. The methods for estimating various parameters for MAR-1, stability properties, and their confidence in-tervals are outlined in Ives et al. (2003). We employed the freeware program Lambda (S. V. Viscido and E. E. Holmes, Northwest Fisher-ies Science Center, unpublished manuscript) to estimate these parameters and summary statistics. Specifically, for Coweeta and Sage-hen creeks, we used all fish species present. For Otter Creek, we observed 22 species over the 13-year record, but many of these species were uncommon and almost all were missing from at least one annual sample. We assumed that the 13-year record was too short to reliably estimate parameters for a 22 species assemblage; thus, to narrow the fish assemblage objectively, we only included the four species observed in every an-nual sample (spotfin shiner Cyprinella spiloptera (also known as Notropis spilopterus), greenside darter Etheostoma blennioides, central stoner-oller Campostoma anomalum, and silverjaw minnow Ericymba buccata). These four species are the second, fifth, sixth, and seventh most abundant species in the assemblage, respective-


ly, and display many of the patterns observed in the larger data set—reversals in relative abun-dance from year to year and strong interannual variation in individual abundances. We trans-formed abundance data (log10 + 1) in Lambda and then determined which interactions to use in the interaction matrix (B) to include in the MAR-1 analysis via conditional least squares (500 replications). After identifying the most appropriate community matrix (B), we then estimated MAR-1 parameters using this matrix of coefficients. This analysis produced estimates of the coefficients in the B matrix (interaction strengths), as well as estimates of stability prop-erties for the assemblage. We assessed goodness of fit for each species in the analysis via coeffi-cients of determination and nonzero species in-teraction coefficients and stability properties via 95% confidence intervals that did not include zero. These confidence intervals were obtained numerically via 2,000 bootstrap samples.

We incorporated flow variation in the MAR-1 analysis by including the maximum an-nual flow and minimum annual residual flow (Figure 2) from the hydrologic data as covari-ates in the analysis. Significance of covariates was assessed via 95% confidence intervals as above.

Results

Hydrologic Variation among Streams

The three streams had strikingly different hy-drographs, with both Shope Fork (henceforth Coweeta Creek) and Sagehen Creek showing substantial seasonality in average daily flow and Big Raccoon Creek (reference stream for Otter Creek) showing little evidence of seasonality (Figure 3; Table 1). Seasonality in average dai-ly flow at Sagehen Creek was likely due to late spring and summer snowmelt, whereas season-ality at Coweeta Creek was due to greater rain-fall in spring than in other seasons. Noise color

for all three streams was pink with Coweeta Creek being closest to white noise (low tran-sient storage—flashiest) and Sagehen pinkest (highest transient storage—least flashy, Table 1). Signal to noise ratios for the hydrographs of the three streams were fairly similar, with Sagehen having the highest S/N and the Ot-ter Creek reference stream having the lowest S/N (Table 1; Figure 3). Compared to other North American streams, the S/N of the three streams examined all fell within the inner quartile portion of the distribution, indicating that these streams were not outliers with respect to S/N properties (Figure 4). The magnitude of the average 2-year flood was highest for Sage-hen Creek and lowest for the Otter Creek ref-erence stream, whereas 2-year low-flow magni-tudes were highest in the Otter Creek reference stream and lowest at Coweeta Creek (Figure 3). Finally, both the standard deviations of residual high (shf) and low (slf) flow values were high-est at Coweeta Creek and lowest at the Otter Creek reference stream, respectively (Table 1), suggesting that composite measures of the mag-nitude of high and low residual flows were high-est at Coweeta Creek and lowest at the Otter Creek reference stream.

Magnitude, Frequency, and Timing of Disturbance Regime

In contrast to results from composite measures of catastrophic flows (shf and slf), our exten-sion of Fourier methods to quantify the mag-nitude, frequency, and timing of catastrophic events identified several differences among streams. Catastrophic events—those 2shf or 2slf above or below the seasonal trend for a given Julian day—were observed in all three streams (Figures 5 and 6), although cata-strophic low flows were not observed in Sage-hen Creek during the period of fish sampling. In general, catastrophic high and low flows were observed in a majority of the years during


Figure 3. Hydrographs for Sagehen Creek and gauges on streams near Coweeta and Otter creeks. The black dots are normalized daily mean dis-charge values. Normalized discharge is the log10 mean daily discharge divided by the average of log10 daily mean values over the 20-year record shown. The thick gray line is the 20-year seasonal trend from Fourier analysis, and the black line is the magnitude of discharge with a 2-year recur-rence interval. Values for the root mean squared amplitude (“signal” or Arms) and noise (Nrms) are given for comparison.

Table 1. Hydrologic analysis and quantification of environmental variability. See text for definitions of terms.

Sagehen Creek Coweeta Creek Otter Creek Hydrologic measure California North Carolina Indiana

Gage location Sagehen Creeka Upstream from fish Adjacent stream in sampling locationb same catchmentc

Period of record 1957–1976 1984–2001 1960–1979ARMS (seasonality, “signal”) 0.2809 0.40 0.0919NRMS (stochasticity, “noise”) 0.0065 0.014 0.0039S/N (signal to noise ratio) 75.32 66.65 63.22ud (noise color, daily) 1.77 1.12 1.55shf (standard deviation in residual high flows) 0.67 1.94 0.28slf (standard deviation in residual low flows) 0.31 0.4 0.17

a U.S. Geological Survey 10343500, Sagehen Creek near Truckee, California.b Shope Fork, Weir 8 at USDA Forest Service Coweeta Hydrologic Laboratory. c U.S. Geological Survey 03341300, Big Raccoon Creek at Coxville, Indiana.

fish sampling for both Coweeta and the Otter Creek reference stream. Thus, there were not strong differences between these two streams in terms of the number of years in which cata-strophic events were observed. We did find differences between these two streams in both the frequency and timing of catastrophic events among streams (Figures 5 and 6). Coweeta Creek displayed higher frequencies of cata-strophic high flows than either Sagehen or the Otter Creek reference stream (Figure 7). When both high- and low-flow events were combined, both Coweeta Creek and the Otter Creek reference stream had higher frequen-cies of catastrophic events than Sagehen Creek (Figure 7). The Otter Creek reference stream displayed distinct 4–5-year cycles between years with many catastrophic high (1962, 1967, and 1973) and low flows (1966 and 1971) and years with high frequencies of catastrophic high flows (Figure 7). Finally, the timing of large residual events differed considerably among streams (Figure 8). Specifically, catastrophic events (mostly high-flow events) coincided with sea-sonal high flows in Sagehen Creek but not in the other two streams. In addition, catastrophic


Figure 4. A comparison of signal/noise (S/N) ratios for the three streams examined versus the distri-bution of S/N values calculated for 91 streams in North America (Sabo and Post 2008). S/N ratios are Sagehen Creek, California (diamond) and for Shope Fork, North Carolina (Watershed 8, star) and Otter Creek, Indiana (Big Raccoon Creek, triangle). All three S/N values are plotted arbitrarily at the same level on the ordinate (y = 10).

Figure 5. Magnitude of maximum residual high (circles) and low (triangles) flow events (|residual| for comparison) for all years in the record of fish abundance (gauge locations as in Figure 3 and Tables 1 and 2). Lines mark the magnitude corresponding to two standard deviations of the distribution of all residual flows across the 20-year record (solid = shf for high flows, and dashed = slf for low flows). Circles above the solid line and triangles above the dashed line indicate events with catastrophic magnitudes.


Figure 6. Magnitude of all residual high (circles) and low (triangles) flow events (|residual| for compari-son) for all years in the record of fish abundance (gauge locations as in Figure 3 and Tables 1 and 2). Lines mark the magnitude corresponding to two standard deviations of the distribution of all residual flows across the 20-year record (solid = shf for high flows, and dashed = slf for low flows). Circles above the solid line and triangles above the dashed line indicate events with catastrophic magnitudes.

events in Coweeta Creek and the Otter Creek reference stream were observed across a wider range of calendar days than in Sagehen Creek. Most importantly, catastrophic events were ob-served in almost all months of the year in the Otter Creek reference stream. Timing of cata-strophic flows is thus predictable in Sagehen, less predictable in Coweeta Creek, and almost completely unpredictable in an Indiana stream with putatively similar flows as Otter Creek.

Fish Assemblage Structure

Time series of fish abundance for the three systems were strikingly different (Figure 9). Sagehen Creek displayed fairly stable trajec-tories for the four species examined, whereas Otter Creek showed erratic variation in which more than half the species dominated the as-semblage during one or more years. In Cowee-

ta Creek, the most abundant species, mottled sculpin Cottus bairdii was highly stable over time, whereas the five less abundant species varied substantially (Figure 9). Comparison of the different assemblages demonstrates that the most abundant taxon is the same spe-cies for all years in both Sagehen Creek and Coweeta Creeks but varies from year to year in Otter Creek. In addition, all species in Sage-hen Creek displayed generally similar patterns of variation over time, whereas those for every species but mottled sculpin in Coweeta Creek varied substantially (Figure 9).

The MAR-1 analyses produced reason-ably high conditional R2 values (i.e., >0.45) for fishes in both Coweeta and Otter creeks but less so for fishes from Sagehen Creek (Ta-ble 2). The stability analysis generally yielded parameter estimates that did not overlap zero


(10 of 12, Table 2), and Sagehen Creek gen-erally displayed the highest level of stability, regardless of the metric. Although we allowed MAR-1 to solve for interaction coefficients, results for Coweeta Creek generally matched empirical results from this system with three exceptions. It is highly unlikely that rosyside dace Clinostomus funduloides compete with either mottled sculpin or longnose dace Rhin-ichthys cataractae, nor is it likely that longnose dace and greenside darter have a mutualistic relationship (indicated by a positive interac-tion strength value in Table 3). These results probably are produced by negative and posi-tive covariation, respectively, to common en-vironmental variation in the site. In addition, conditional least squares did not detect den-sity-dependence in mottled sculpin, although

this has been shown previously in this popu-lation (Table 3). Patterns for Otter Creek fishes ran the gamut of density-dependence, interspecific competition, and mutualism (Table 4), although we have scant empirical information to validate these results. Finally, MAR-1 analysis for Sagehen Creek fishes in-dicated little evidence of interspecific com-petition or density-dependence, but some evidence of facilitation (Table 5). These inter-action strength values should be treated with caution given our observation of differences between MAR-1 and empirical estimates of some pairwise interactions.

We incorporated flow variation into our stability analysis by using maximum and mini-mum residual annual flows as covariates in the MAR-1 analysis. Specifically, we extracted an-

Figure 7. The frequency of catastrophic flows based on annual counts of events of magnitude greater than shf for high flows or slf for low flows for all years in the record of fish abundance (gauge locations as in Figure 3 and Tables 1 and 2). Circles are annual counts of high flow and triangles are counts of low flows. Solid and dashed lines mark the frequency corresponding to 2 standard deviations of the distribution of annual counts across the 20-year record (i.e., N = 20). Circles above the solid line and triangles above the dashed line indicate years with extremely high frequencies of catastrophic events compared to the long-term record.


Figure 8. Timing of residual high (circles) and low (triangles) flow events in terms of calendar, or Ju-lian days (|residual| for comparison) for all years in the record of fish abundance (gauge locations as in Figure 3 and Tables 1 and 2). Lines mark the magnitude corresponding to 2 standard deviations of the distribution of all residual flows across the 20-year record (solid = shf for high flows, and dashed = slf for low flows). Circles above the solid line and triangles above the dashed line indicate days with catastrophic event magnitudes and when plotted against Julian day, illustrate the timing of these events across the biological record of interest.

nual maximum and minimum residual flows across the period of record for fish data to gen-erate two time series or vectors of values de-scribing flow covariates. MAR-1 then assesses the relationship between these high- and low-flow covariates and the stability properties of the fish assemblage. Note that in this analysis we use residual (maximum or minimum of any event above or below trend in a year) instead of catastrophic (events 2s above or below the trend in a year) flows. Thus, vectors of high flows may include catastrophic high flows in some years but not all, and this fingerprint of high- or low-flow variation is then matched to variation in the fish assemblage time series. Our results from this analysis indicate that minimum flow magnitude in a given year af-fected mottled sculpin, longnose dace, and ro-

syside dace in Coweeta Creek, although these effects varied among species (Table 3). Both minimum and maximum flows affected mul-tiple species in Otter Creek (Table 4). These results are consistent with the fact that Otter Creek was the least stable assemblage in the MAR-1 analysis and with the observation of oscillations between years with high frequen-cies of catastrophic high and low flows.

Discussion

It is likely that various attributes of hydrologic variation (e.g., frequency, timing, magnitude, and duration of extreme events) may strong-ly affect stream fish assemblage stability and structure (Grossman et al. 1998, 2010). We have proposed a method that directly links


Figure 9. Log10 abundance of fishes in Sagehen, Coweeta, and Otter creeks. S is the species richness.Bold lines are time series for species included in MAR-1 models. Species key: 1. speckled dace Rhin-ichthys osculus, 2. Piaute sculpin Cottus beldingii, 3 Lahontan redside Richardsonius egregious, 4. mountain whitefish Prosopium williamsoni, 5. mottled sculpin C. bairdii, 6. longnose dace, 7. rainbow trout Oncorhynchus mykiss, 8. rosyside dace, 9. greenside darter, 10. central stoneroller Campostoma anomalum, 11. spotfin shiner, 12. greenside darter, 13. central stoneroller, and 14. silverjaw minnow Ericymba bucccata.

hydrologic variation to measures of stream fish assemblage stability using Fourier analy-sis and MAR-1 stability analysis. Flow varia-tion manifests itself in a variety of forms, and aquatic ecologists recognize that statistics based on magnitude alone may not incorpo-rate all biologically relevant aspects of flow variation (Bunn and Arthington 2002; Olden and Poff 2003; Arthington et al. 2006). In rec-ognition of the complexities of the relation-ships between flow and stream processes, we have provided a new approach that facilitates identification of catastrophic events (i.e., re-sidual events outside 2s of the distribution of these events across a long-term record) and quantifies both their frequency and timing. This should aid researchers in identifying re-lationships between flow events, their timing,

and characteristics of both stream fish popu-lations and assemblages.

Although our paper demonstrates how Fourier analysis and MAR models can be used in stream fish ecology, we were hampered by several requirements of these techniques. For example, we know that drought affects biodi-versity and assemblage structure in Coweeta Creek (Grossman et al. 1998, 2010); however, these effects mainly are manifested via an in-crease in species richness rather than large de-creases in population size of residents or local extinctions (Grossman et al. 1998, 2010). This increase in species richness during drought periods is produced by immigration into the site by new species from downstream, whereas they return downstream after the cessation of low flows (Grossman et al. 1998, 2010). Be-


Table 2. Stability analysis of fish assemblages via MAR-1 coupled to Fourier based flow covariates. Stabil-ity is a measure of the degree to which environmental fluctuations (e.g., Nrms, shf, or slf) augment intrinsic fluctuations in relative abundance. Return time is a measure of the time required for the abundance pat-terns to return to a characteristic range of values following a perturbation, and reactivity is a measure of the degree to which abundance patterns change following a perturbation. We provide two alternate ways to measure reactivity (see Ives et al. 1998 for details). For all four measures of stability, increasing values indicate decreasing stability. Species abbreviations follow: CA = central stoneroller, CB = mottled sculpin, CF = rosyside dace, CO = Piute sculpin Cottus beldingii, EB = greenside darter, ER = silverjaw minnow, NS = spotfin shiner, OM = rainbow trout Oncorhynchus mykiss, PW = mountain whitefish Prosopium williamsoni, RC = long-nose dace, RE = Lahontan redside Richardsonius egregious, and RH = speckled dace Rhinichthys osculus.

Measure Sagehen Creek Coweeta Creek Otter Creek

Year of record 1951–1961 1984–1995 1962–1974Number of years 11 12 13Number of times sampled 11 24 13Number of species 4 6a 22Number species analyzed (% abundance) 5 (100) 6 (100) 4 (29.6 )b

Hydrograph U.S. Geological Surveyc Long Term Ecological Researchd U.S. Geological Surveye

Number of non-zero species interactions 2 of 16 4 of 36 11 of 16Significant high flow covariates – 0 of 6 3 of 4Significant low flow covariates – 3 of 6 2 of 4Model fitConditional R2f CB: 0.3992 CB: 0.4649 NS: 0.8745 RO: 0.4105 RC: 0.8496 EB: 0.7814 RE: 0.1613 CF: 0.9361 CA: 0.9602 PW: 0.1431 OM: 0.6188 ER: 0.9094 EB: 0.5956 CA: 0.6945 det(B)2/p, Stability (CI) 0.14(0.029–0.34) 0.23(0.08–0.43) 0.38(0.09–0.67)max(lBVB), Return time (CI) 0.51(0.23–0.87) 0.61(0.34–0.95) 0.78(0.37–1.27)–tr(^)/tr(V

`), Trace

reactivity (CI) 0.45(–0.72––0.17) –0.45(–0.51––0.28) –0.16(–0.44––0.14)g

max(lBVB) – 1, Worst-case reactivity 0.51 (–0.33–3.09)g 4.3 (2.28–9.06) 10.69 (6.76–18.17)Relative environmental variation Most stable Intermediate Least stable

2 30-m reach at Coweeta Creek Station 1 using biannual sampling of all fish (juveniles and adults; see Grossman et al (2006) for details.b We used four numerically dominant fish species in this species rich assemblage: Ns, Eb, Ca and Erb. These fishes were used because they were the four most abundant species that had non-zero abundances across the entire record. See Grossman et al 1982 for details on assemblage.c U.S. Geological Survey 10343500, Sagehen Creek near Truckee, California.d Shope Fork, Weir 8 at USDA Forest Service Coweeta Hydrologic Laboratory e U.S. Geological Survey 03341300, Big Raccoon Creek at Coxville, Indiana; closest gauged stream of similar size to Otter Creek (Vigo County, Indiana) the origin of fish data. Gage located in county neighboring county to south.

cause it is computationally difficult for MAR-1 to handle population time series with multiple zeros, these species necessarily were excluded from our analysis. The same problem occurred with the Otter Creek data set, where most of the species had multiple zeros in the time se-ries and, hence, were excluded from the analy-

sis. Consequently, our analysis must be viewed as providing information on the structure and dynamics of resident species in the assemblage rather than on all species even those that may dominate an assemblage for one or more years but then disappear (Grossman et al. 1982). It also is likely that this bias (i.e., the exclusion


Table 3. Coweeta Creek B and C matrices from MAR-1 analysis. Max. high represents the maximum re-sidual value for a given year and Min. low, represents the minimum low flows for a given year. Species abbreviations follow: CB = mottled sculpin, RC = longnose dace, CF = rosyside dace, OM = rainbow trout, EB = greenside darter, and CA = central stoneroller. Negative values represent competitive re-lationships or density-dependence and positive values represent facilitative relationships. Intraspecific relationships are in bold.

B-matrix (VARIATES)

Species CB RC CF OM EB CA

CB 0 0 0 0 0 0RC 0 –0.57 –0.32 0 0.53 [–0.89, –0.15] [–0.54, –0.10] 0 [0.12 , 0.96] 0CF –1.97 0 0 0 0 0 [–2.49, –1.42] OM 0 0 0 0 0 0EB 0 0 0 0 0 0CA 0 0 0 0 0 0

C-matrix (COVARIATES)

Max. annual Min. annualSpecies high flow low flow

CB 0 0.56 [0.10, 1.02]RC 0 –0.56 [–1.10, –0.01]CF 0 –0.48 [–0.90 , –0.07]OM 0 0EB 0 0CA 0 0

of species with multiple zeros) has limited our ability to link hydrologic variation to assemblage structure and stability, especially with respect to low-flow events that produce local extinctions. Consequently, we are continuing to examine the robustness of MAR-1 with respect to the inclu-sion of species with multiple zeros in their time series because this is important to any analysis of assemblage structure and stability.

We estimated species interaction coeffi-cients using conditional least squares rather than prior knowledge because investigators may not have prior information on the assemblage they are studying. In essence, this is a test of the abil-ity of MAR-1 to identify interactions, and the technique generally performed in accordance with what is previously known about both Coweeta and Otter creeks. In addition, the in-

clusion of the magnitude of catastrophic events as a covariate in the analysis indicated that this measure was correlated with assemblage stabil-ity. Sagehen Creek was the most stable with re-spect to both hydrologic and assemblage struc-ture data, and Otter Creek was the least stable in both sets of characteristics. Nonetheless, both prior knowledge and information theoretic ap-proaches also can be used to estimate interac-tion strengths (Ives et al. 2003), and the choice should be based on maximizing realism in the analysis. One final limitation of our interpreta-tion of MAR-1 results is our simplification of the Otter Creek community (including only those species with time series without zeroes). We simplified the community from 22 to 4 species in an attempt to increase the precision of MAR-1 estimation of stability and interac-


Table 4. Otter Creek B and C matrices from MAR-1 analysis. Max. High represents the maximum re-sidual value for a given year and Min. Low, represents the minimum low flows for a given year. Species abbreviations are as follows: NS = spotfin shiner, EB = greenside darter, CA = central stoneroller, and ER = silverjaw minnow. Negative values represent competitive relationships or density-dependence and positive values represent facilitative relationships. Intraspecific relationships are in bold.

B-matrix (VARIATES)

Species NS EB CA ER

NS –0.32 0 2.19 –1.87 [–0.58, –0.00] [1.59, 2.83] [–2.81, –0.92]EB 0 0 0 0CA –0.56 0.71 0.61 –1.07 [–0.68, –0.43] [0.41, 1.10] [0.33, 0.87] [–1.48, –0.71]ER –0.49 0.51 0.62 –0.61 [–0.66, –0.31] [0.05, 1.03] [0.24, 1.00] [–1.22, –0.12]

C-matrix (COVARIATES)

Max annual Min annualSpecies high flow low flow

NS 0 4.87 [2.10, 7.90]EB 2.05 0 [ 0.57, 3.71] 0CA 1.11 –3.12 [0.10, 1.93] [–4.30, –1.77]ER 3.38 0 [1.98, 4.66]

Table 5. Sagehen Creek B matrix values from MAR-1 analysis. Species abbreviations follow: CO = Piute sculpin, RH = speckled dace, RE = Lahontan redside, and PW = mountain whitefish. There was no C matrix for this analysis because the hydrograph did not completely overlap the years of fish data. Nega-tive values represent competitive relationships or density-dependence and positive values represent facilitative relationships. Intraspecific relationships are in bold.

B-matrix (VARIATES)

Species CO RO RE PW

CO 0 0 0 0RO 0 0 0 0.48 [0.10, 0.91]RE 0 0 0 0PW 0 0 0 0.60 [0.10, 0.97]

tion strength parameters. In doing so, we likely overestimate the stability of the fish assemblage and may also miss some important correlations between high- and low-flow variation and fish stability. The fact that we may overestimate

fish stability is at least a conservative bias with respect to our comparison of fish assemblage properties in these three stream systems; Ot-ter Creek has the lowest stability of all three in spite of our omission of the most variable spe-


cies. Nonetheless, longer time series are needed to more effectively link whole communities to hydrologic data.

Fourier analysis of extreme events also de-lineated a variety of differences among the three streams, including differences in the frequency, magnitude, and timing of these events. These differences also corresponded to differences in assemblage stability, with Sagehen Creek being most predictable (highest S/N) with a differ-ent pattern in seasonality of extreme events (re-stricted to seasons with high flows) than the less stable Coweeta and Otter Creek assemblages. In addition, the timing of extreme events in the Ot-ter Creek reference stream had little predictabil-ity, and flow appeared to alternate between years with strings of alternating high- and low-flow events. The latter pattern is suggestive of the in-fluence of larger scale climatic factors, such as jet stream- or Gulf Stream-related weather events.

One clear limitation of our proposed link-age of hydrologic and biological data is the avail-ability of data. In our analysis of Otter Creek fish stability, we were limited by the lack of appro-priate flow data on the same stream and thus used data from a nearby stream with similar catchment area. Surrogate flow data for Otter Creek clearly limit our ability to make strong conclusions about the links between flows and fish community stability in this system. If storm frequency and intensity is spatially heteroge-neous, maximum and minimum residual flow values (used as covariates) could differ within years among streams separated by even short distances. This could produce false detection or prevent detection of relationships between residual flows and fish stability from the same stream system. Future research should examine how much bias surrogate flow data introduces to such analyses.

Research over the past decade has shown that the maintenance of natural flow regimes may be integrally linked with the health of river-

ine communities (Olden and Poff 2003; Rich-ter et al. 2003; Arthington et al. 2006). This was formalized in the natural flow paradigm (Poff et al. 1997), which has served as a useful guid-ing precept for management and restoration of lotic systems. Nonetheless, although hydrologic variation clearly plays an important role in the maintenance of stream fish assemblage struc-ture (Grossman et al. 1982, 1998; Pusey et al. 1993; Taylor et al. 2005), it also is clear that re-storing natural flows in disturbed systems may not be sufficient for their biological restoration (Arthington et al. 2006; Stewart-Koster et al. 2007). This is particularly true where invasive species have become established and are able to withstand the natural hydrologic variation pres-ent in the system (Propst et al. 2008). However, there is substantial support for the proposition that restoration of natural variation in flow re-gimes is an excellent starting point for stream restoration (Arthington et al. 2006). We hope that Fourier analysis and MAR-1 will aid inves-tigators in both the identification of variabil-ity in stream hydrographs and establishment of linkages between this variability and ecological patterns in stream assemblages.

Acknowledgments

GDG appreciates the aid and support of Cowee-ta Hydrologic Laboratory, D. Elkins, B., R., and A. Grossman, P. Hazelton, and R. Ratajczak. Portions of this project were funded by the N. S. F. Coweta Long-Term Ecological Research Pro-gram (DEB-9632854 and DEB-2018001) and USDA Forest Service McIntire-Stennis Grant GEO-0086-MS and GEOZ-0144-MS to the senior author. Additional support for GDG was provided by the D. B. Warnell School of Forest-ry and Natural Resources. JLS thanks Jan Hod-der and the Oregon Institute of Marine Biology for providing a peaceful place to work on the ideas in this manuscript and Ryan Sponseller


for many hours of creative thinking and discus-sion of the application of hydrological analysis to community assembly. We are deeply indebt-ed to Angela Arthington and an anonymous reviewer whose comments greatly improved the manuscript. This work was funded by NSF grants DEB-0317137 and DEB-0635088 to the junior author.

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