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Complex hydraulic and substrate variables limit freshwater mussel speciesrichness and abundanceAuthor(s): Daniel C. Allen and Caryn C. VaughnSource: Journal of the North American Benthological Society, 29(2):383-394. 2010.Published By: North American Benthological SocietyDOI: 10.1899/09-024.1URL: http://www.bioone.org/doi/full/10.1899/09-024.1

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Complex hydraulic and substrate variables limit freshwater musselspecies richness and abundance

Daniel C. Allen1AND Caryn C. Vaughn2

Oklahoma Biological Survey, Ecology and Evolutionary Biology Graduate Program, andDepartment of Zoology, University of Oklahoma, Norman, Oklahoma 73019 USA

Abstract. We examined how substrate and complex hydraulic variables limit the distribution offreshwater mussels. We sampled mussels and measured substrate and hydraulic variables (at low andhigh flows) at 6 sites in the Little River, Oklahoma. To test which variables were most limiting to musselspecies richness and abundance, we evaluated univariate and multiple 95th-, 90th-, and 85th-quantileregression models using a model selection approach. Across all 3 quantiles analyzed, hydraulic variablesrelated to substrate stability (relative shear stress ratio [RSS] and shear stress) at high flows most limitedmussel species richness and abundance. High-flow substrate stability models performed the best, butmodels that used substrate variables (substrate size and heterogeneity) also performed relatively well.Models that used complex hydraulic variables estimated at low flows performed poorly compared to thoseusing the same variables estimated at high flows, a result suggesting that hydraulic conditions at low flowsdo not limit mussel habitat in our system. Our results demonstrate that substrate stability at high flows isan important factor governing mussel distributions. Last, our quantile regression approach successfullyquantified the limiting-factor relationships of substrate and hydraulic characteristics on mussel habitat,and this approach could be used in other studies investigating habitat requirements of aquatic organisms.

Key words: Unionidae habitat, quantile regression, model selection, limiting-factor, constraintrelationships.

Recent catastrophic declines in the abundance anddiversity of freshwater mussel populations (Bival-via:Unionoida) have led conservationists to recognizethese animals as North America’s most imperiledfauna (Strayer et al. 2004). Only ¼ of the ,300 NorthAmerican species are considered to have stablepopulations (Williams et al. 1993). Mussel populationdeclines have multiple causes, including invasivespecies, water-quality degradation, and habitat alter-ation by impoundments (Lydeard et al. 2004, Strayeret al. 2004). Alteration of flow regimes by impound-ments, channelization, and other man-made modifi-cations has led to biodiversity losses in many riverinefaunal groups (Poff et al. 2007), but freshwater musselcommunities seem particularly sensitive to changes inhydrologic conditions (Watters 2000, Strayer et al.2004).

Freshwater mussels often occur in dense multispe-cies aggregations (mussel beds) that are patchilydistributed within streams and rivers. Locations ofthese aggregations and mussel abundance at smaller

scales have been predicted successfully with complexhydraulic variables (Gangloff and Feminella 2007,Steuer et al. 2008, Zigler et al. 2008). Complexhydraulic variables related to near-bed flow charac-teristics, such as shear stress, are thought to beimportant factors for mussel habitat. Excessive shearstresses (hydraulic forces parallel to the substratesurface) at high flows can initiate substrate move-ment, so mussel aggregations are most likely topersist in areas where shear stresses remain lowduring spates, i.e., where substrates are stable (Strayer1999, 2008, Strayer et al. 2004). Excessive shearstresses can also prevent juvenile mussels fromsettling into streambed substrates (Layzer and Madi-son 1995, Hardison and Layzer 2001), and musselabundances are low in areas of high shear stressesduring high flows (Hardison and Layzer 2001,Howard and Cuffey 2003, Gangloff and Feminella2007).

However, several issues prevent mollusk ecologistsfrom reaching a consensus on the importance ofsubstrate stability for freshwater mussel distributions.First, shear stress is not the only factor that influencessubstrate stability. Armoring and substrate size also

1 E-mail addresses: [email protected] [email protected]

J. N. Am. Benthol. Soc., 2010, 29(2):383–394’ 2010 by The North American Benthological SocietyDOI: 10.1899/09-024.1Published online: 16 February 2010

383

are important factors determining whether substrateswill become entrained during high flows (Gordon etal. 2004), so substrate characteristics also must bequantified. Studies that have used substrate charac-teristics and hydraulic variables have had somesuccess predicting mussel abundance (Steuer et al.2008). Second, very few studies have estimatedhydraulic variables with data collected at both lowand high flows (but see Hardison and Layzer 2001).Several authors have suggested that hydraulic vari-ables should be more important at high than at lowflows (Hardison and Layzer 2001, Howard andCuffey 2003, Gangloff and Feminella 2007), butvariables at high flows often are estimated frommeasurements of channel geomorphology rather thanmeasured directly. Last, studies that have foundsubstrate stability to be important for mussel habitathave primarily used computer simulations that havenot been adequately ground-truthed. For example, themussel dynamics model developed by Morales et al.(2006a) simulated mussel colonization using substratestability to determine suitable habitats. However, thismodel has yet to be rigorously tested in the field andrelies on many untested assumptions and parametervalues (Morales et al. 2006b). Shear stress andsubstrate stability successfully predicted musselabundance in a computer simulation by Zigler et al.(2008), but interpretation of these results was limitedbecause of a significant time lag between the dates ofcollection of mussel and hydrologic data. The mostrigorous support for substrate stability being animportant factor for freshwater mussel habitat is froma field study in which mussels were most abundant inareas where marked stones moved the least during aspate (Strayer 1999). However, an alternative expla-nation for this result is that mussels themselves werestabilizing substrates, such that the marked stonesmoved the least in areas where mussel abundanceswere highest. It has been suggested that freshwatermussels might stabilize substrates (Johnson andBrown 2000, Vaughn and Spooner 2006, Strayer2008), although the results of a recent laboratoryinvestigation were inconclusive (Zimmerman and deSzalay 2007).

Use of mussel abundance as the sole indicator ofmussel habitat quality has limited our ability tointerpret the results of studies on the relationshipsbetween freshwater mussel distributions and complexhydraulic variables (but see Gangloff and Feminella2007). A positive relationship between substratestability and mussel abundance is expected becausewhen substrates are more stable over time, adultmussels should be less likely to be washed out duringfloods and the number of colonizing juvenile mussels

surviving into adulthood should increase (Strayer1999, Hardison and Layzer 2001, Hastie et al. 2001).However, different freshwater mussel species mightprefer different hydraulic conditions or differentlevels of substrate stability. It seems likely that ifsubstrate stability is associated with lower adultmussel mortality and greater juvenile mussel coloni-zation more mussel species would also be present, butstudies investigating relationships between substratestability and mussel species richness are lacking.Given that declines in mussel species richness are ofas much concern as declines in mussel abundance(Lydeard et al. 2004, Strayer et al. 2004), a great needexists for studies that investigate habitat requirementsfor species-rich mussel beds.

Most previous studies have used predictive statis-tical models to analyze relationships between com-plex hydraulic variables and mussel habitat quality(Gangloff and Feminella 2007, Steuer et al. 2008,Zigler et al. 2008). Strayer (2008) argued that manyfactors in addition to hydraulic and substrate charac-teristics influence freshwater mussel distributions.These other factors include fish host distributions,food quality and quantity, water quality, and tem-perature. Therefore, even if substrate and hydraulicconditions were optimal, overall mussel habitatquality could be quite poor if these other require-ments were not met (e.g., fish hosts not abundant orfood quality low). Consequently, substrate andhydraulic variables should be analyzed as constraintsor limiting factors rather than predictive variablesbecause, at best, they can only partially explainmussel distributions.

We investigated how substrate stability (assessedwith substrate and complex hydraulic variables)limits mussel habitat. We measured mussel speciesrichness and abundance, substrate characteristics, andhydraulic variables in situ, and we evaluated quantileregression models to determine whether and howthese factors constrained mussel distributions.

Methods

Study area and variables

We conducted our study in the Little River insoutheastern Oklahoma, USA (Fig. 1). The Little Riveris a major tributary of the Red River that drains10,720 km2 in Oklahoma and Arkansas (Matthews etal. 2005). This river has high biodiversity andsupports 110 fish and .36 mussel species (Matthewset al. 2005). Mussel communities in this river havebeen studied (Vaughn and Taylor 1999, Galbraith etal. 2008), so we selected a priori 6 sites known to haveabundant, diverse, and reproducing mussel commu-

384 D. C. ALLEN AND C. C. VAUGHN [Volume 29

nities (Fig. 1). Some mussel assemblages in the LittleRiver are influenced by 1 mainstem and 1 tributaryimpoundment on the Mountain Fork River (Fig. 1;Vaughn and Taylor 1999, Matthews et al. 2005). Thetributary impoundment affects mussel communitiesprimarily through cold water releases and hydroelec-tric peaking, but all of our study sites were upstreamof this influence. The mainstem impoundment (PineCreek Reservoir) is used for flood control andrecreation, but the influence of this reservoir isnegligible downstream of the confluence with atributary, the Glover River, which enters the LittleRiver and modulates flows (Vaughn and Taylor 1999).Our 6 sites were all downstream of the confluence ofthe Glover with the Little River and were onlyminimally affected by Pine Creek Reservoir, asevidenced by low summer flows (mean 6 SEdischarge during low-flow sampling = 0.63 6

0.08 m3/s), warm summer temperatures (mean =

30.6uC), and diverse and abundant mussel assem-blages with juvenile recruitment. Seasonal mediandischarges calculated from monthly averages during1977 to 2007 at a US Geological Survey (USGS)gauging station (07338500) immediately downstreamof site 4 (Fig. 1) were 63.7 m3/s in spring (March–May), 7.9 m3/s in summer (June–August), 11.9 m3/sin autumn (September–November), and 60.3 m3/s inwinter (December–February).

During July 2006, a period of low flows, weestablished 6 equidistant transects across the river ateach site. Transects were 10 to 20 m apart dependingon the size of the mussel bed (mean width of ourtransects across the river = 21.9 6 0.94 m) andcovered both riffles and pools. We measured water

depth and current velocity at the centers of 1-m cellsalong 1 transect at each site for discharge calculations.We placed four 0.25-m2 quadrats, evenly spacedacross the river cross-section, along each transect.This stratified-block design and distance markersalong the riverbank allowed us to locate each quadrateasily by boat at higher flows (see below).

At each quadrat, we measured water depth with ameter stick and current velocity at 0.6 3 depth with aMarsh–McBirneyTM Flo-Mate flowmeter (Marsh–McBirney, Frederick, Maryland). We chose a randompoint in each quadrat and used a trowel to collectsuperficial substrates until we filled a 0.72-L plasticbag (,20% of the superficial substrate in the quadrat).Larger rocks (,§63.5 mm) were kept in separate bagsso that we had at least a 0.72 L sample to process aftersubstrates .63.5 mm were excluded from the sample(to remove the bias of larger particles on substratevariables; Church et al. 1987). We sampled formussels in each quadrat as the last step of the fieldprotocol. We excavated each quadrat to a depth of15 cm, removed all mussels from the quadrat,identified them, measured their shell length, andreturned them to the quadrat (Vaughn and Spooner2006, Galbraith et al. 2008). We took the substratesamples to the laboratory, dried them for 48 h at100uC, passed the samples through a series of 12geological sieves (63.5, 38.1, 19, 8, 3.962, 1.981, 0.991,0.495, 0.246, 0.175, 0.088, and 0.061 mm), and weighedeach fraction.

We returned to each site during periods of highflow between autumn 2006 and spring 2007 (meandischarge during high-flow sampling = 53.07 6

7.92 m3/s). We measured water depth and currentvelocity at the centers of 1-m cells along 1 transect ateach site for discharge calculations, and we measureddepth and current velocity at each quadrat on all 6transects. We made all measurements from a boatsecured to a cable stretched across the transect. Wemeasured depth with a HondexTM digital depthsounder (Honda Electronics Co. Ltd., Toyohashi City,Japan), and we measured current velocity by sus-pending a Marsh–McBirneyTM Flo-Mate flowmeterfixed to a 13.6-kg Columbus-type sounding weight(Scientific Instruments, Milwaukee, Wisconsin) on amarked cable at 0.6 3 depth in the center of thequadrat.

We calculated substrate and hydraulic variablesfrom formulae in Table 1. We refer to hydraulicvariables estimated at low and high flows with LFand HF, respectively. We chose 0.065 as the value forShield’s parameter (hc) because substrates at our sitesconsisted of normally packed gravel with fairlyrandom grain arrangements (Gordon et al. 2004). We

FIG. 1. Sampling sites on the Little River in southeasternOklahoma.

2010] HYDRAULICS, SUBSTRATE, AND MUSSEL HABITAT 385

calculated exceedance levels of our calculated dis-charge relative to historical data (1946–2007) from USGeological Survey (USGS) gauging station 07338500 toquantify the relative flow levels represented by ourdata.

Data analysis

Multicollinearity among estimated hydraulic vari-ables has been observed in other studies (Hardisonand Layzer 2001). We wanted to reduce redundancyand multicollinearity bias (r . 0.8) in our statisticalmodels because it can interfere with interpretation ofresults even though it would not violate the assump-tions of our model selection approach describedbelow (Burnham and Anderson 2002). We calculatedPearson correlation coefficients between all substrateand estimated hydraulic variables. Shear velocity (U*)and shear stress (t) were strongly correlated at lowand high flows (r = 0.87 and 0.97, respectively),Froude number (Fr) and t were strongly correlated atlow and high flows (0.81 and 0.92), and HF boundaryReynolds number (Re*) was strongly correlated with

mean substrate particle size (D) (r = 0.83). Therefore,we dropped U*, Fr, and Re* from all subsequentanalyses. We chose to keep t and drop Fr and U*because previous studies have shown relationshipsbetween t and mussel distributions (Hardison andLayzer 2001, Howard and Cuffey 2003, Gangloff andFeminella 2007) and because t is important forsubstrate stability (Gordon et al. 2004). We chose toretain D instead of Re* because substrate stabilityshould be inversely related to substrate size givenequal shear stresses (Gordon et al. 2004), and becauseSteuer et al. (2008) found that substrate size was apredictor of mussel abundance.

Quantile regression models have been used inecological studies to estimate functions along or nearthe upper boundary of the response distribution tomeasure limiting factors (Cade and Noon 2003).Quantile regression is based on least absolute devia-tion regression, which models the conditional median(50th quantile), but the approach can be extended toany quantile (Cade et al. 1999, Cade and Noon 2003,Koenker 2005). Quantile regression estimates aresemiparametric; no parametric distributional form is

TABLE 1. Summary of substrate variables and hydraulic variables estimated at low and high flows. Dx = substrate particle size(cm) at which x% of the sample by mass is finer, d = water depth (cm), w = unit of substrate size (w = –log2D [mm]), wx =

substrate particle size (w) at which x% of the sample by mass is finer, U = mean current velocity (cm/s), g = acceleration ofgravity (980 cm/s), v = kinematic viscosity of water (0.01 cm2/s), r = density of water (0.998 g/cm3), rs = density of substrate(2.65 g/cm3), hc = Shield’s parameter (0.065) (Gordon et al. 2004).

Variable (symbol, unit) Formula Description Source

Substrate variables

D (cm) (D16zD50zD84)

3

Mean particle size of sample Folk 1965

Sorting index (D S.D.; w converted to cm) w84{w16ð Þ2

Substrate heterogeneity Gordon et al. 2004

Bed roughness (ks, cm) 3:5|D84 Topographical variation of stream bed Gordon et al. 2004

Hydraulic variables

Froude number (Fr, dimensionless)ffiffiffiffiffiffiU2

gd

sRatio of inertial to gravitational forces Statzner et al. 1988

Reynolds number (Re, dimensionless) Ud

v

Ratio of inertial to viscous forces Statzner et al. 1988

Boundary Reynolds number (Re*,dimensionless)

U�ks

v

Roughness of flow near substrate Statzner et al. 1988

Shear velocity (U*, cm/s) U

5:75log10

12d

ks

� � Friction velocity Statzner et al. 1988

Shear stress (t, dynes/cm2) r U�2� �

Force of friction on substrate Statzner et al. 1988

Critical shear stress (tc, dynes/cm2) hcgD50 rs{rð Þ Shear stress required to initiate substratemotion for a typical sample substratesize (D50)

Gordon et al. 2004

Relative shear stress (RSS, dimensionless) t

tc

Ratio of observed to critical shear stress(values . 1 represent substratemovement for a typical samplesubstrate size [D50])

Morales et al. 2006a


assumed for random errors but is assumed for thedeterministic portion of the model (Cade and Noon2003). Therefore, unlike traditional least-squares re-gression, quantile regression relaxes the assumptionsof normally distributed data and homoscedacity (Haoand Naiman 2007). In ecological studies, 95th-quantileregressions have been used to estimate limiting-factorrelationships; i.e. ,95% of the observations are belowthe fitted line (Schooley and Wiens 2005).

One limitation of focusing on the 95th quantile isthat a large sample size is required for the analysis tobe robust because a small fraction of the data (in thiscase, ,5%) is heavily weighted when parameterestimates are generated for regression functions andmodel fit is calculated. Our sample size was relativelysmall (n = 144), so we modeled 3 extreme quantiles(95th, 90th, 85th) for a more robust analysis. We

ffiffiffiffiffiffiffiffiffiffixz1p

-transformed mussel abundance data before analysis(Zar 1999). We fit linear, quadratic, or Ricker curves tothe data (with and without y-intercepts), and chosethe best-fitting model based on Akaike informationcriterion (AIC) provided it had non-0 parameterestimates for model coefficients. We used the samefunctions to fit multivariate quantile regression mod-els. We conducted quantile regression analyses usingthe quantreg package (version 4.24 developed by R.Koenker) for R software (version 2.8.1; R Foundationfor Statistical Computing, Vienna, Austria).

We evaluated quantile regression models with AIC.We followed Schooley and Wiens (2005) and calcu-lated AIC for quantile regression models asAIC=n( logs2)z2K (Hurvich and Tsai 1990), whereK is the number of estimated variables + 2 (interceptand residual variance) and substituted the weightedabsolute deviations (the absolute deviation of valuespredicted by the model from observed values,weighted by p for the pth quantile if the predictedvalue . observed value and [1 – p] if the predictedvalue , observed value; Hao and Naiman 2007) for s.We converted AIC to small-sample AIC (AICc;Burnham and Anderson 2002), and calculated thecoefficient of determination (R) as 1 – (sum of theweighted absolute deviations of the model of interestdivided by sum of the weighted absolute deviationsof the intercept-only model) (Schooley and Wiens2005, Hao and Naiman 2007). We report a pseudo-R2

for quantile regression models as 1 – (1 – R)2 toprovide a unit of measure comparable to R2 (McKeanand Sievers 1987, Schooley and Wiens 2005).

We generated 15 models (7 multivariate modelsand 8 univariate models) a priori to avoid data-dredging and to ease interpretation of results (John-son and Omland 2004). We chose the 7 multivariatemodels to represent different hypotheses that might

explain mussel distributions: 1) substrate model (D +substrate heterogeneity [D S.D.]), 2 and 3) LF and HFhydraulics models (LF or HF Re + t + RSS), 4 and 5)LF and HF hydraulics and substrate models (LF or HFRe + t + RSS + D + D S.D.), 6) HF substrate stabilitymodel (HF t + RSS), and 7) a global model (allsubstrate and flow variables, an overparameterizedmodel used for comparison). For each quantile, wereport AICc differences (Di) and Akaike weights (wi,the relative likelihood of a model given a data set andset of models) for the 5 best models and the pseudo-R2

of an averaged model based on predicted values fromthe best-performing models (Di , 2) weighted by wi

(Burnham and Anderson 2002). Last, we determinedthe 5 best models across the 95th, 90th, and 85th

quantiles by averaging wi for each model from all 3quantile model selection analyses.

Results

Mussel communities were diverse and abundant atall 6 sites. Mean mussel species richness at our siteswas 18.33 6 0.76 (SE), and mean mussel abundance(no./m2) was 44.95 6 4.80. Juvenile mussels (individ-uals , 30 mm in length) were recorded at all sites. Formore detailed descriptions of the mussel communitiesin the Little River, see Vaughn and Taylor (1999) andGalbraith et al. (2008). Low and high flow levelscorresponded to exceedances of 95.15 6 0.99 and27.02 6 2.06, respectively. Safety concerns preventedus from recording depth and flow measurements atpeak flow levels (311.49 m3/s was the highestrecorded discharge at the USGS gauging station nearour sites between 2006–2007).

Substrate and hydraulic variables estimated at lowand high flows showed limiting-factor relationshipswith mussel species richness and abundance (Figs2A–H, 3A–H). The limiting-factor relationships be-tween D and mussel species richness and abundancewere unimodal and best described by the Rickerfunction for all extreme quantiles (Figs 2A, 3A). Incontrast, the shape of the limiting-factor relationshipsbetween D S.D. and species richness and abundancediffered depending on the quantile (Figs 2B, 3B). Thelimiting-factor relationships between Re and t andspecies richness and abundance were unimodal anddescribed by Ricker and quadratic functions at bothlow and high flows (Figs 2C–F, 3C–F). However, theshape of the limiting-factor relationships between RSSand species richness and abundance depended onflow level. The limiting-factor relationships betweenLF RSS and species richness and abundance wereunimodal and described by the Ricker function(Figs 2G, 3G), whereas the limiting-factor relation-


FIG. 2. Quantile regression models for mussel species richness/0.25-m2 quadrat for substrate (A, B) and hydraulic (C–H)variables. Solid, dashed, and dotted lines represent 95th, 90th, and 85th quantile regression lines, respectively. LF and HF designatethat the variable was estimated at low or high flows. Abbreviations for variables are given in Table 1.


FIG. 3. Quantile regression models forffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimusselabundancez1p

/m2 for substrate (A, B) and hydraulic variables (C–H). Solid,dashed, and dotted lines represent 95th, 90th, and 85th quantile regression lines, respectively. LF and HF designate that the variablewas estimated at low or high flows. Abbreviations for variables are given in Table 1.


ships between HF RSS and species richness andabundance were decreasing functions. For speciesrichness, the negative constraint was described by alinear function (Fig. 2H), whereas for abundance, itwas described by the decreasing portion of a concavequadratic function (Fig. 3H).

Models with substrate variables performed best forthe 95th quantile, whereas models with hydraulicvariables related to substrate stability performed bestfor the 90th and 85th quantiles (AICc selection;Tables 2, 3). When Akaike weights (wi) were averagedfrom our 3 quantile model selection analyses, modelsusing hydraulic variables estimated at high flowsperformed better than models using substrate vari-ables (Table 4). Summed average wi for models withHF hydraulic variables were 0.79 and 0.61 for speciesrichness and abundance, respectively, whereassummed average wi for models with substratevariables for were 0.23 and 0.33 for species richnessand abundance, respectively. HF RSS appeared to bethe most important HF hydraulic variable because itwas included in all of the best-performing modelswith HF variables for both species richness andabundance. HF t was important only in models thatalso included HF RSS for both species richness andabundance. HF Re was important only in models thatincluded both HF RSS and HF t, and only for speciesrichness. Among models with substrate variables,summed average wi for models with D were 0.23 and0.17 for species richness and abundance, whereassummed average wi for models with D S.D. were 0.18and 0.31 for species richness and abundance, respec-tively. Models with LF hydraulic variables performedpoorly (summed average wi = 0.002 and 0.09 forspecies richness and abundance, respectively).

Discussion

The most important result of our study was thatacross all 3 extreme quantiles analyzed, hydraulicvariables related to substrate stability at high flowswere most limiting for mussel species richness andabundance. Substrate models also performed well inour AICc selection analysis, but only at more extremequantiles (95th for species richness and abundance,and 90th for abundance). Second, models withhydraulic variables estimated at high flows per-formed much better than models with the samevariables estimated at low flows. Last, quantileregression is a useful analytical tool for investigatingthe ability of any single group of habitat factors toexplain mussel distributions.

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abundance and species richness. HF RSS alone or inconjunction with HF t performed very well for bothspecies richness and abundance. HF Re appeared tobe less important, and only performed well inconjunction with HF RSS and HF t. These resultssupport those of other studies suggesting thatsubstrate stability during high flows restricts musselabundance (Strayer 1999, Morales et al. 2006a, Gangl-off and Feminella 2007). Moreover, our analysis is thefirst to show that substrate stability during high flowsalso restricts mussel species richness. Therefore,substrate stability during spates is likely to limit thedistribution of dense and speciose mussel beds. Ouranalysis also suggests that t might not always be auseful surrogate measure for substrate stability, evenwhen estimated at high flows. By itself, HF tperformed poorly in our analysis, and HF t per-formed well only in the presence of HF RSS. Thisresult shows the importance of quantifying bothsubstrate characteristics and hydraulic variables toestimate substrate movement when assessing suit-ability of mussel habitat.

Our estimates of substrate stability at high flowssuggest that mussels might be able to tolerate somesubstrate movement. Mussel abundance and musselspecies richness were high when HF RSS was .1, butdropped sharply when HF RSS was .2 (RSS . 1indicates substrate movement; Figs 2H, 3H). Howev-er, our estimates of RSS used a typical sized particle(D50) to estimate substrate movement. Therefore, RSS. 1 does not necessarily mean that the entire streambed is in motion because D50 could represent just asmall fraction of the larger materials sampled fromthe bed surface (Gordon et al. 2004). Thus, musselsmight be able to tolerate movement of smallersubstrate particles during high flows, but not move-ment of larger particles or the entire stream bed.

TABLE 4. Akaike weights (wi) averaged from small-sample Akaike information criterion (AICc) selection ofunivariate and multiple 95th, 90th, and 85th quantileregression models for mussel species richness andabundance. LF and HF designate that the model usedhydraulic variables estimated at low or high flows. Modelswith 5 highest average Akaike weights (wi) are shown,abbreviations for variables are given in Table 1.

Species richness Abundance

Model Average wi Model Average wi

HF RSS 0.299 HF t + RSS 0.290HF t + RSS 0.236 HF RSS 0.195HF Re + t + RSS 0.229 D S.D. 0.151D + D S.D. 0.174 D + D S.D. 0.146D 0.034 HF Re + t + RSS 0.078

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Furthermore, we omitted substrate particles .

63.5 mm from our substrate analysis to reduce thebias larger particles can have on substrate variables(Church et al. 1987). Omitting the largest substrateparticles reduces D50 values and could have causedoverestimation of substrate movement. Alternatively,if mussels themselves stabilize substrates as otherauthors have suggested (Johnson and Brown 2000,Vaughn and Spooner 2006, Strayer 2008), all sub-strates might have remained stable at RSS . 1.Mussels increase sediment compaction and cohesion(Zimmerman and de Szalay 2007), which shoulddecrease the ability of substrate particles to becomeentrained (Gordon et al. 2004). Estimates of substratestability based on RSS use substrate and hydraulicvariables, so biological influences on substrate stabil-ity are not taken into account. We think in-depthstudy of the influence of mussels on substrate stabilityis warranted.

Models with the substrate variables D and D S.D.performed the best in 95th quantile regressions forboth mussel species richness and abundance, but didnot perform as well for any other quantile. This resultmight indicate that model performance was stronglyinfluenced by data points at the boundary of theresponse distribution. Further evidence of this possi-bility is given by the differences among the best-fitting functions of the quantile regressions for D S.D.across the 95th, 90th, and 85th quantiles. For bothspecies richness and abundance, the best-fittingquantile regressions for D S.D. did not have consistentmathematical functions. Instead the functions werelinear, concave, or convex depending on the quantile(Figs 2B, 3B). However, substrate variables were notentirely absent from models that performed well forquantiles other than the 95th because the D S.D. modelhad wi = 0.163 for the 90th quantile of musselabundance. Therefore, substrate model performancemight be somewhat spurious for the 95th quantile, butwe think that substrate variables probably have asmall limiting effect that is overwhelmed by HFhydraulic variables related to substrate stability in oursystem. This disparity in the size of the effects mightexplain why substrate variables were importantfactors for mussel habitat in some studies (Steuer etal. 2008) but not in others (Strayer 1999).

Hydraulic variables estimated at high flows out-performed the same variables estimated at low flows.This result supports our hypothesis that hydrauliccharacteristics are more important to mussel habitat athigh than at low flows, a conclusion that has beensuggested by other authors (Hardison and Layzer2001, Howard and Cuffey 2003, Gangloff and Femin-ella 2007). However, our results contrast with those of

Steuer et al. (2008), who found that hydraulicvariables estimated at low flows were better predic-tors of mussel abundance in the Upper MississippiRiver than hydraulic variables estimated at highflows. Steuer et al. (2008) suggested that minimumRe* and Fr might be required during low flows todeliver food or transport waste products. Thus,hydraulic variables estimated at low flows might notlimit mussel distributions in smaller rivers, such asour system, but might be important in larger rivers,such as the Upper Mississippi River.

Quantile regression was a useful tool for studyingthe limiting effect of substrate and complex hydraulicvariables on mussel species richness and abundance.The prevailing view in freshwater mussel ecology isthat many factors in addition to hydraulic andsubstrate variables influence freshwater mussel dis-tributions, including fish host distributions, foodquantity and quality, and water quality (Strayer2008). Thus, we should not expect any single groupof variables to predict mussel habitat quality ade-quately. Rather, these variables should have limiting-factor relationships that constrain mussel distribu-tions. For example, in our study the highest musselabundances and species richness occurred in quadratswith low HF RSS, but mussel abundance and speciesrichness in other quadrats were low when HF RSSvalues were low (Figs 2H, 3H). Presumably, someunmeasured factor was limiting in quadrats weestimated to be stable at high flows but with lowmussel abundances or species richness.

We were able to quantify limiting-factor relation-ships with quantile regression models, in cases wherepredictive models would have had very low power.For example, the predictive power of substrate size,water depth, and water velocity on mussel abundancewas very low (r2 , 0.05) in a study by Strayer (1999),but a reanalysis with quantile regression of the datashown in fig. 4 in Strayer (1999) would be interestingand might show unimodal limiting-factor relation-ships. Quantile regression has the additional benefitthat it relaxes the assumptions of normally distributedand homoscedastic data (Hao and Naiman 2007), andtherefore, is very useful for analysis of ecological data(Cade and Noon 2003). Future studies investigatingany single group of factors on mussel distributionsshould also use analyses that focus on quantifyinglimiting-factor relationships.

Acknowledgements

We thank Dane Morris, Nate Franssen, andWhitney Allen for field assistance, Jim Barker foraccess to 2 of our field sites, and the Little River


Wildlife Refuge for cooperation in establishing sam-pling sites on their managed lands. Carl Sondergeld(Oklahoma University Department of Geology) al-lowed us to use his substrate processing equipment.Michael Patten and John Van Sickle provided statis-tical advice, and David Strayer, Jeff Kelly, IngoSchlupp, and 2 anonymous referees provided com-ments that improved this manuscript. Funding wasprovided by the Oklahoma Department of WildlifeConservation (SWG T-38) and the National ScienceFoundation (DEB 0211010). This work is submitted inpartial fulfillment of the degree requirements for aPhD, Department of Zoology, University of Okla-homa, and is a contribution to the program of theOklahoma Biological Survey.

Literature Cited

BURNHAM, K. P., AND D. R. ANDERSON. 2002. Model selectionand multimodel inference. 2nd edition. Springer, NewYork.

CADE, B. S., AND B. R. NOON. 2003. A gentle introduction toquantile regression for ecologists. Frontiers in Ecologyand the Environment 1:412–420.

CADE, B. S., J. W. TERRELL, AND R. L. SCHROEDER. 1999.Estimating effects of limiting factors with regressionquantiles. Ecology 80:311–323.

CHURCH, M., D. G. MCLEAN, AND J. F. WOLCOTT. 1987. Riverbed gravels: sampling and analysis. Pages 43–88 in C. R.Thorne and R. D. Hey (editors). Sediment transport ingravel-bed rivers. John Wiley and Sons, New York.

FOLK, R. L. 1965. Petrology of sedimentary rocks. HemphillPublishing, Austin, Texas.

GALBRAITH, H. S., D. E. SPOONER, AND C. C. VAUGHN. 2008.Status of rare and endangered freshwater mussels inSoutheastern Oklahoma. Southwestern Naturalist 53:45–50.

GANGLOFF, M. M., AND J. W. FEMINELLA. 2007. Stream channelgeomorphology influences mussel abundance in south-ern Appalachian streams, USA. Freshwater Biology 52:64–74.

GORDON, N. D., T. A. MCMAHON, B. L. FINLAYSON, C. J. GIPPEL,AND R. J. NATHAN. 2004. Stream hydrology: an introduc-tion for ecologists. 2nd edition. John Wiley and Sons,West Sussex, UK.

HAO, L., AND D. Q. NAIMAN. 2007. Quantile regression. SagePublications, Thousand Oaks, California.

HARDISON, B. S., AND J. B. LAYZER. 2001. Relations betweencomplex hydraulics and the localized distribution ofmussels in three regulated rivers. Regulated Rivers:Research and Management 17:77–88.

HASTIE, L. C., P. J. BOON, M. R. YOUNG, AND S. WAY. 2001. Theeffects of a major flood on an endangered freshwatermussel population. Biological Conservation 98:107–115.

HOWARD, J. K., AND K. M. CUFFEY. 2003. Freshwater musselsin a California North Coast Range river: occurrence,distribution, and controls. Journal of the North Amer-ican Benthological Society 22:63–77.

HURVICH, C. M., AND C. L. TSAI. 1990. Model selection forleast absolute deviations regression in small samples.Statistics and Probability Letters 9:259–265.

JOHNSON, J. B., AND K. S. OMLAND. 2004. Model selection inecology and evolution. Trends in Ecology and Evolution19:101–108.

JOHNSON, P. D., AND K. M. BROWN. 2000. The importance ofmicrohabitat factors and habitat stability to the threat-ened Louisiana pearl shell, Margaritifera hembeli (Con-rad). Canadian Journal of Zoology 78:271–277.

KOENKER, R. 2005. Quantile regression. Cambridge Univer-sity Press, New York.

LAYZER, J. B., AND L. M. MADISON. 1995. Microhabitat use byfreshwater mussels and recommendations for determin-ing their instream flow needs. Regulated Rivers:Research and Management 10:329–345.

LYDEARD, C., R. H. COWIE, W. F. PONDER, A. E. BOGAN, P.BOUCHET, S. A. CLARK, K. S. CUMMINGS, T. J. FREST, O.GARGOMINY, D. G. HERBERT, R. HERSHLER, K. E. PEREZ, B.ROTH, M. SEDDON, E. E. STRONG, AND F. G. THOMPSON. 2004.The global decline of nonmarine mollusks. BioScience54:321–330.

MATTHEWS, W. J., C. C. VAUGHN, K. B. GIDO, AND E. MARSH-MATTHEWS. 2005. Southern Plains rivers. Pages 283–325in A. C. Benke and C. E. Cushing (editors). Rivers ofNorth America. Elsevier, Boston, Massachusetts.

MCKEAN, J. W., AND G. L. SIEVERS. 1987. Coefficients ofdetermination for least absolute deviation analysis.Statistics and Probability Letters 5:49–54.

MORALES, Y., L. J. WEBER, A. E. MYNETT, AND T. J. NEWTON.2006a. Effects of substrate and hydrodynamic condi-tions on the formation of mussel beds in a large river.Journal of the North American Benthological Society 25:664–676.

MORALES, Y., L. J. WEBER, A. E. MYNETT, AND T. J. NEWTON.2006b. Mussel dynamics model: a hydroinformatics toolfor analyzing the effects of different stressors on thedynamics of freshwater mussel communities. EcologicalModelling 197:448–460.

POFF, N. L., J. D. OLDEN, D. M. MERRITT, AND D. M. PEPIN. 2007.Homogenization of regional river dynamics by damsand global biodiversity implications. Proceedings of theNational Academy of Sciences of the United States ofAmerica 104:5732–5737.

SCHOOLEY, R. L., AND J. A. WIENS. 2005. Spatial ecology ofcactus bugs: area constraints and patch connectivity.Ecology 86:1627–1639.

STATZNER, B., J. A. GORE, AND V. H. RESH. 1988. Hydraulicstream ecology: observed patterns and potential appli-cations. Journal of the North American BenthologicalSociety 7:307–360.

STEUER, J. J., T. J. NEWTON, AND S. J. ZIGLER. 2008. Use ofcomplex hydraulic variables to predict the distributionand density of unionids in a side channel of the UpperMississippi River. Hydrobiologia 610:67–82.

STRAYER, D. L. 1999. Use of flow refuges by unionid musselsin rivers. Journal of the North American BenthologicalSociety 18:468–476.


STRAYER, D. L. 2008. Freshwater mussel ecology: a multifactorapproach to distribution and abundance. University ofCalifornia Press, Berkeley, California.

STRAYER, D. L., J. A. DOWNING, W. R. HAAG, T. L. KING, J. B.LAYZER, T. J. NEWTON, AND S. J. NICHOLS. 2004. Changingperspectives on pearly mussels, North America’s mostimperiled animals. BioScience 54:429–439.

VAUGHN, C. C., AND D. E. SPOONER. 2006. Unionid musselsinfluence macroinvertebrate assemblage structure instreams. Journal of the North American BenthologicalSociety 25:691–700.

VAUGHN, C. C., AND C. M. TAYLOR. 1999. Impoundments andthe decline of freshwater mussels: a case study of anextinction gradient. Conservation Biology 13:912–920.

WATTERS, G. T. 2000. Freshwater mussels and water quality:a review of the effects of hydrologic and instreamhabitat alterations. Pages 261–274 in R. A. Tankersley, D.I. Warmolts, G. T. Watters, B. J. Armitage, P. D. Johnson,and R. S. Butler (editors). Freshwater Mollusk Sympo-

sium Proceedings. Ohio Biological Survey, Columbus,Ohio.

WILLIAMS, J. D., M. L. WARREN, K. S. CUMMINGS, H. L. HARRIS,AND R. J. NEVES. 1993. Conservation status of thefreshwater mussels of the United States and Canada.Fisheries 18(9):6–22.

ZAR, J. H. 1999. Biostatistical analysis. 4th edition. PrenticeHall, Upper Saddle River, New Jersey.

ZIGLER, S. J., T. J. NEWTON, J. J. STEUER, M. R. BARTSCH, AND J. S.SAUER. 2008. Importance of physical and hydrauliccharacteristics to unionid mussels: a retrospectiveanalysis in a reach of large river. Hydrobiologia 598:343–360.

ZIMMERMAN, G. F., AND F. A. DE SZALAY. 2007. Influence ofunionid mussels (Mollusca: Unionidae) on sedimentstability: an artificial stream study. Archiv fur Hydro-biologie 168:299–306.

Received: 12 February 2009Accepted: 14 October 2009


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