Abstract

Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams of the United States occur at the southernmost portion of their native range, and occupy small, isolated, and low-productivity headwater streams. The existing standard weight (Ws) equation is applicable only to Brook Trout > 120 mm total length (TL), but many individuals in the region are smaller than this minimum size threshold due to their habitat characteristics. Here, we developed a new Ws equation for Brook Trout in southern Appalachian Mountains streams using length–weight data on 72,502 individuals. The weighted quadratic empirical-percentile method minimized length-related bias in relative weight compared to the regression-line-percentile and weighted linear empirical-percentile methods. The proposed Ws equation was: log10W = −3.364 + 1.378 × log10L + 0.397 × (log10L)2, where W was weight (g) and L was TL (mm). The new equation characterized body condition of Brook Trout in southern Appalachian Mountains streams more accurately than the existing equation.

Introduction

Weight–length relationships are a key index in fisheries management as they provide a rapid, noninvasive means of evaluating the physiological condition of fish (Neumann et al. 2012). Of several methods to assess fish condition, managers often rely on relative weight (Wr), where an individual fish's weight is compared to that of a fish with the same length based on a standard weight (Ws) equation developed for that species (Blackwell et al. 2000). Researchers have developed standard weight equations for a number of North American freshwater fishes (Murphy et al. 1990), with different equations for a single species by sex (Brown and Murphy 1993; Neumann and Willis 1994), habitat type (Milewski and Brown 1994; Simpkins and Hubert 1996), and body size (Flammang et al. 1999). Given their ability to exploit a variety of lotic and lentic habitat types, this practice is common for fishes in family Salmonidae, including Brown Trout Salmo trutta (Milewski and Brown 1994; Hyatt and Hubert 2001a), Rainbow Trout Oncorhynchus mykiss (Simpkins and Hubert 1996), and Cutthroat Trout Oncorhynchus clarkii (Kruse and Hubert 1997).

Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams occur at the southernmost limit of their native range in eastern North America (Figure 1) and are a Species of Greatest Conservation Need in North Carolina, South Carolina, and Tennessee (North Carolina Wildlife Resources Commission 2015; South Carolina Department of Natural Resources 2015; Tennessee Wildlife Resources Agency 2015). These populations have declined greatly due to habitat loss and fragmentation and introductions of nonnative Brown Trout and Rainbow Trout (Moore et al. 1986; Hudy et al. 2008; Kanno et al. 2016a). Small, isolated Brook Trout populations in southern Appalachian Mountains streams show signs of genetic drift including decreased genetic diversity, low effective population size, and increased extinction risk (Pregler et al. 2018; Weathers et al. 2019). Remaining populations occur in low-productivity, high-elevation headwater streams (i.e., suboptimal habitat), where limited food availability and habitat space lead to small adult size (Konopacky and Estes 1986; Ensign et al. 1990; Kulp and Moore 2005; Knoepp et al. 2016). The existing Ws equation for Brook Trout (Hyatt and Hubert 2001b) is applicable to fish 120–620 mm in total length (TL), but those in southern Appalachian Mountains streams attain a much smaller maximum body size (≤ 270 mm TL; see below) with many fish below the 120-mm TL minimum threshold for the existing equation. Importantly, researchers developed the existing Ws equation based on a data set comprised of 113 sites (68 lotic and 45 lentic sites) across 15 U.S. states and two Canadian provinces, with only two lotic sites in the southern Appalachian Mountains region (North Carolina) included in the analysis (Hyatt and Hubert 2001b). Fisheries biologists should not apply standard weight equations for individuals outside the target body size range (Flammang et al. 1999), highlighting the need for a separate Ws equation for Brook Trout populations in the southern Appalachian Mountains streams. To achieve an unbiased assessment of body condition of Brook Trout in southern Appalachian Mountains streams, we developed a new Ws equation using length–weight data on 72,502 individuals from 153 populations.

Figure 1.

Locations of 153 populations from which we developed the standard weight (Ws) equation for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams using data from 1980 to 2019. States shown are Georgia (GA), North Carolina (NC), South Carolina (SC), Tennessee (TN), and Virginia (VA). The shaded region of the inset map indicates the native range of Brook Trout in the eastern United States.

Figure 1.

Locations of 153 populations from which we developed the standard weight (Ws) equation for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams using data from 1980 to 2019. States shown are Georgia (GA), North Carolina (NC), South Carolina (SC), Tennessee (TN), and Virginia (VA). The shaded region of the inset map indicates the native range of Brook Trout in the eastern United States.

Methods

To develop a Ws equation for Brook Trout in southern Appalachian Mountains streams, we compiled a length (mm) and wet weight (g) data set of self-reproducing Brook Trout (i.e., no stocked fish) collected by backpack electrofishing surveys in wadeable streams (mean stream width = 5.9 m; SD = 3.0 m) from four states (Georgia, North Carolina, South Carolina, and Tennessee; Figure 1; Data S1, Supplemental Material). We measured length as TL for all records. We defined a population as a collection of individuals from the same stream. We filtered sampling dates to range from June through September (mean = July 22) by following the approach of Hyatt and Hubert (2001b) for developing the North American range-wide equation for Brook Trout. Additionally, we removed populations with < 20 individuals (Bonvechio et al. 2010) and individuals with weight > 2 SD from the mean for each 10-mm length category. Finally, we limited the body length range to 80–266 mm TL. We chose the minimum body length following the variance-to-mean ratio method (Murphy et al. 1990), and this threshold approximately removed young-of-the-year fish. Individuals larger than the maximum limit were not common in our small headwater streams (≤ 10 individuals per 10-mm length category). After the screening process, the data set included 72,502 individuals from 153 populations collected between 1980 and 2019 (Table 1). Forty-one percent of the individuals in our data set were below the 120-mm TL minimum size threshold for the existing equation (Hyatt and Hubert 2001b).

Table 1.

Geographic distribution, date range, number of populations, and number of individuals used to develop a new standard weight (Ws) equation for southern Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams.

Geographic distribution, date range, number of populations, and number of individuals used to develop a new standard weight (Ws) equation for southern Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams.
Geographic distribution, date range, number of populations, and number of individuals used to develop a new standard weight (Ws) equation for southern Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams.

We developed and compared three Ws equations using the regression-line-percentile (RLP) method (Murphy et al. 1990) and weighted linear and quadratic empirical-percentile (EmP) methods (Gerow et al. 2005; Bonvechio et al. 2010). The RLP method characterizes weight–length relationships by giving an equal weight to each population, and its derivation included three steps: 1) fit a linear regression between log10 length and log10 weight for each population, 2) identify the 75th percentile predicted weights in each 10-mm length category across populations, and 3) log10 transform the 75th percentile predicted weights and regress them against the log10 transformed midpoint of each 10-mm length category. The EmP method is similar to the RLP method, except that the 75th percentile weights in each 10-mm length category are based on means from measured body weights across populations (Gerow et al. 2005). For the EmP method, we used weighted linear regression (EmP–L) and quadratic regression (EmP–Q), the latter of which is effective in reducing length-related bias by allowing the log10(length)–log10(weight) relationship to be curvilinear (Gerow et al. 2005). We used the number of populations represented in each 10-mm length category as regression weights. Thus, fish of commonly observed body length ranges influenced the function of length–weight relationship. All three methods resulted in similar weight–length functional forms (i.e., an exponential increase in weight with length). We chose one equation by quantifying bias as the 75th percentile of mean measured weights across populations for each 10-mm length category divided by predicted weights, and visually confirming lack of length-related bias in predicted weights. Finally, we predicted and compared weights using the new equation and the existing equation (Hyatt and Hubert 2001b) and characterized percent differences in predicted weights between the two methods for each 10-mm length category. We performed all analyses in R v. 4.0.2 (R Core Team 2020).

Results

Both the RLP and EmP-L approaches resulted in length-related bias, but we did not observe this in the EmP-Q method (Figure 2). The 75th percentile of mean measured weights across populations exceeded predicted weights at the smallest and largest individuals in the RLP and EmP-L methods, and the bias was particularly evident at 230–269 mm TL (3–6%). The EmP-Q method quantified the length–weight relationships most accurately across the body length range considered here (80–266 mm); Equation 1 is our proposed Ws equation for Brook Trout in southern Appalachian Mountains streams:
formula
where W is weight (g) and L is TL (mm).
Figure 2.

Length-related bias plots of the regression-line-percentile (RLP; left panel), linear empirical-line percentile (EmP-L; middle panel), and quadratic empirical-line percentile (EmP-Q; right panel) standard weight (Ws) equations developed for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams using data from 1980 to 2019. Length categories are in 10-mm increments (e.g., 105 = 100–109.99 mm TL), and % of Ws represents the 75th percentile of mean measured weights across populations for each 10-mm length category divided by the predicted weights and expressed as a percentage. The dashed line at 100 represents the point at which the predicted and measured weights are equal.

Figure 2.

Length-related bias plots of the regression-line-percentile (RLP; left panel), linear empirical-line percentile (EmP-L; middle panel), and quadratic empirical-line percentile (EmP-Q; right panel) standard weight (Ws) equations developed for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams using data from 1980 to 2019. Length categories are in 10-mm increments (e.g., 105 = 100–109.99 mm TL), and % of Ws represents the 75th percentile of mean measured weights across populations for each 10-mm length category divided by the predicted weights and expressed as a percentage. The dashed line at 100 represents the point at which the predicted and measured weights are equal.

Find equations derived from the RLP and EmP-L methods in Figure S1, Supplemental Material. Predicted weights based on the new equation were lower than those predicted by the existing Ws equation across all length categories (Figure 3).

Figure 3.

(A) Comparison of the existing standard weight (Ws) equation (Hyatt and Hubert 2001b; dashed line: log10W = −5.186 + 3.103 log10L) and the new Ws equation for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams (solid line: log10W = −3.364 + 1.378 × log10L + 0.397 × [log10L]2). (B) Percent difference between predicted weight values of the existing Ws equation and new southern Appalachian Ws equation. Length categories are in 10-mm increments (e.g., 105 = 100–109.99 mm TL).

Figure 3.

(A) Comparison of the existing standard weight (Ws) equation (Hyatt and Hubert 2001b; dashed line: log10W = −5.186 + 3.103 log10L) and the new Ws equation for Brook Trout Salvelinus fontinalis in southern Appalachian Mountains streams (solid line: log10W = −3.364 + 1.378 × log10L + 0.397 × [log10L]2). (B) Percent difference between predicted weight values of the existing Ws equation and new southern Appalachian Ws equation. Length categories are in 10-mm increments (e.g., 105 = 100–109.99 mm TL).

Discussion

The small body length of Brook Trout in southern Appalachian Mountains streams, for which the existing Ws equation for the species (Hyatt and Hubert 2001b) cannot apply, necessitated the development of a separate Ws equation. Our study highlighted additional insights on the importance of this new equation for characterizing and managing these populations at the southern periphery of the native range. Predicted weights based on the new equation were consistently lower than those predicted by Hyatt and Hubert (2001b) across the body length range considered in this study. Lower weights at given body lengths are likely due to the low-productivity, high-elevation headwater streams (i.e., suboptimal habitat) in which Brook Trout currently persist (Konopacky and Estes 1986; Ensign et al. 1990; Kulp and Moore 2005; Knoepp et al. 2016). Historically, Brook Trout occurred in larger streams which are currently predominated by nonnative Brown Trout and Rainbow Trout (Moore et al. 1986; Hudy et al. 2008; Kanno et al. 2016a). The new equation is applicable to fish ≥ age 1 from 80 to 266 mm TL in the isolated headwaters of the southern Appalachian region. In addition, the new equation was derived using the EmP-Q method, whereas the existing equation was derived using the RLP method (Hyatt and Hubert 2001b). The EmP-Q method minimized length-related bias in this study and provides a more accurate tool to evaluate body condition of Brook Trout across a range of body lengths. The superior performance of the EmP-Q method is due to its ability to accommodate a curvilinear relationship between body length and weight, which persists even after both variables are log10 transformed (Gerow et al. 2005).

Evaluation of trout condition is critical in the face of emerging and continued threats to southern Appalachian Brook Trout, such as disease (Ruiz et al. 2017a, 2017b) and climate change (Kanno et al. 2016b). Southern Appalachian Mountains Brook Trout not only occupy unique habitat, but are also genetically distinct from the northern populations within the native range (Danzmann et al. 1998; Fausch 2008). Fisheries managers tasked with the conservation of Brook Trout, such as those in southern Appalacian Mountains streams, may put forth management goals and actions based on biased inferences when comparing their resources to those in other portions of the species range using a universal Ws equation. However, the new Ws equation allows managers to make unbiased inferences regarding fish condition among populations within their jurisdictional waters and monitor the same populations over time in response to management actions and environmental change. The new Ws equation provides fisheries managers with a tool to characterize body condition more accurately than the existing equation.

Supplemental Material

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.

Data S1. Excel spreadsheet containing the compiled Brook Trout Salvelinus fontinalis length and weight data from Georgia, North Carolina, South Carolina, and Tennessee. Compiled data include observations from 1980 to 2019. Table includes the following fields: total length in millimeters (Length_mm), weight in grams (Weight_g), and 10-mm length category (Length_Cat).

Found at DOI: https://doi.org/10.3996/JFWM-20-026.S1 (1.02 MB XLSX).

Figure S1. Comparison of the existing equation (Hyatt and Hubert 2001b; dashed line: log10W = −5.186 + 3.103 log10L), new regression-line-percentile equation (RLP; dotted line: log10W = −5.164 + 3.072 × log10L), new linear empirical-line percentile equation (EmP-L; dot-dashed line: log10W = −5.187 + 3.082 × log10L), and new quadratic empirical-line percentile equation (EmP-Q; solid line: log10W = −3.364 + 1.378 × log10L + 0.397 × [log10L])2. The new equations were developed for Brook Trout Salvenius fontinalis in southern Appalachian Mountains streams using data from 1980 to 2019.

Found at DOI: https://doi.org/10.3996/JFWM-20-026.S2 (98 KB DOCX).

Acknowledgments

This study was financially supported by the North Carolina Wildlife Resources Commission via funds provided by the U.S. Fish and Wildlife Service's Federal Aid in Sport Fish Restoration Program. We thank Matt Kulp (Great Smoky Mountains National Park), Anthony Rabern (Georgia Department of Natural Resources), and Dan Rankin (South Carolina Department of Natural Resources) for their assistance with the access and acquisition of trout data. We thank Jim Habera, Matt Kulp, Anthony Rabern, three anonymous reviewers, and the editors at Journal of Fish and Wildlife Management for their constructive reviews of an earlier version of this manuscript.

Any use of trade, product, website, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

References

Blackwell
BG,
Brown
ML,
Willis
DW.
2000
.
Relative weight (Wr) status and current use in fisheries assessment and management
.
Reviews in Fisheries Science
8
:
1
44
.
Bonvechio
TF,
Bonvechio
KI,
Cailteux
RL.
2010
.
Proposed standard weight (Ws) equation and standard length categories for Suwannee Bass
.
North American Journal of Fisheries Management
30
:
983
988
.
Brown
ML,
Murphy
BR.
1993
.
Management evaluation of body condition and population size structure for Paddlefish: a unique case
.
Prairie Naturalist
25
:
93
108
.
Danzmann
RG,
Morgan
RP
II,
Jones
MW,
Bernatchez
L,
Ihssen
PE.
1998
.
A major sextet of mitochondrial DNA phylogenetic assemblages extant in eastern North American Brook Trout (Salvelinus fontinalis): distribution and postglacial dispersal patterns
.
Canadian Journal of Zoology
76
:
1300
1318
.
Ensign
WE,
Strange
RJ,
Moore
SE.
1990
.
Summer food limitation reduces Brook and Rainbow Trout biomass in a southern Appalachian stream
.
Transactions of the American Fisheries Society
119
:
894
901
.
Fausch
KD.
2008
.
A paradox of trout invasions in North America
.
Biological Invasions
10
:
685
701
.
Flammang
MK,
Olson
JA,
Willis
DW.
1999
.
Application of the relative weight index to juvenile Walleyes
.
North American Journal of Aquaculture
61
:
310
314
.
Gerow
KG,
Anderson-Sprecher
RC,
Hubert
WA.
2005
.
A new method to compute standard-weight equations that reduces length-related bias
.
North American Journal of Fisheries Management
25
:
1288
1300
.
Hudy
M,
Thieling
TM,
Gillespie
N,
Smith
EP.
2008
.
Distribution, status, and land use characteristics of subwatersheds within the native range of Brook Trout in the eastern United States
.
North American Journal of Fisheries Management
28
:
1069
1085
.
Hyatt
MW,
Hubert
WA.
2001
a.
Proposed standard-weight (Ws) equation and length-categorization standards for Brown Trout (Salmo trutta) in lentic habitats
.
Journal of Freshwater Ecology
16
:
53
56
.
Hyatt
MW,
Hubert
WA.
2001
b.
Proposed standard-weight equations for Brook Trout
.
North American Journal of Fisheries Management
21
:
253
254
.
Kanno
Y,
Kulp
MA,
Moore
SE.
2016
a.
Recovery of native Brook Trout populations following the eradication of nonnative Rainbow Trout in southern Appalachian Mountains streams
.
North American Journal of Fisheries Management
36
:
1325
1335
.
Kanno
Y,
Pregler
KC,
Hitt
NP,
Letcher
BH,
Hocking
DJ,
Wofford
JEB.
2016
b.
Seasonal temperature and precipitation regulate Brook Trout young-of-the-year abundance and population dynamics
.
Freshwater Biology
61
:
88
99
.
Knoepp
JD,
Vose
JM,
Jackson
WA,
Elliott
KJ,
Zarnoch
S.
2016
.
High elevation watersheds in the southern Appalachians: indicators of sensitivity to acidic deposition and the potential for restoration through liming
.
Forest Ecology and Management
377
:
101
117
.
Konopacky
RC,
Estes
DR.
1986
.
Age and growth of Brook Trout in Southern Appalachian streams
.
Proceedings of the Annual Conference of the Southeastern Association of Fish and Wildlife Agencies
40
(1986)
:
227
236
.
Kruse
CG,
Hubert
WA.
1997
.
Proposed standard weight (Ws) equations for interior Cutthroat Trout
.
North American Journal of Fisheries Management
17
:
784
790
.
Kulp
MA,
Moore
SE.
2005
.
A case history in fishing regulations in Great Smoky Mountains National Park: 1934–2004
.
North American Journal of Fisheries Management
25
:
510
524
.
Milewski
CL,
Brown
ML.
1994
.
Proposed standard weight (Ws) equation and length-categorization standards for stream-dwelling Brown Trout (Salmo trutta)
.
Journal of Freshwater Ecology
9
:
111
117
.
Moore
SE,
Larson
GL,
Ridley
B.
1986
.
Population control of exotic Rainbow Trout in streams of a natural area park
.
Environmental Management
10
:
215
219
.
Murphy
BR,
Brown
ML,
Springer
TA.
1990
.
Evaluation of the relative weight (Wr) index, with new applications to Walleye
.
North American Journal of Fisheries Management
10
:
85
97
.
Neumann
RM,
Guy
CS,
Willis
DW.
2012
.
Length, weight, and associated indices
.
Pages
637
670
in
Zale
AV,
Parrish
DL,
Sutton
TM,
editors.
Fisheries techniques. 3rd edition
.
Bethesda, Maryland
:
American Fisheries Society
.
Neumann
RM,
Willis
DW.
1994
.
Relative weight as a condition index for Muskellunge
.
Journal of Freshwater Ecology
9
:
13
18
.
North Carolina Wildlife Resources Commission.
2015
.
North Carolina State Wildlife Action Plan
.
Pregler
KC,
Kanno
Y,
Rankin
D,
Coombs
JA,
Whiteley
AR.
2018
.
Characterizing genetic integrity of rear-edge trout populations in the southern Appalachians
.
Conservation Genetics
19
:
1487
1503
.
R Core Team.
2020
.
R: a language and environment for statistical computing. Vienna, Austria
.
Available: https://www.R-project.org/ (March 2021).
Ruiz
CF,
Rash
JM,
Arias
CR,
Besler
DA,
Orélis-Ribeiro
R,
Womble
MR,
Roberts
JR,
Warren
MB,
Ray
CL,
Lafrentz
S,
Bullard
SA.
2017
.
Morphological and molecular confirmation of Myxobolus cerebralis myxospores infecting wild-caught and cultured trout in North Carolina (SE USA)
.
Diseases of Aquatic Organisms
126
:
185
198
.
Ruiz
CF,
Rash
JM,
Besler
DA,
Roberts
JR,
Warren
MB,
Arias
CR,
Bullard
SA.
2017
b.
Exotic “gill lice” species (Copepoda: Lernaeopodidae: Salmincola spp.) infect Rainbow Trout (Oncorhynchus mykiss) and Brook Trout (Salvelinus fontinalis) in the southeastern United States
.
Journal of Parasitology
103
:
377
389
.
Simpkins
DG,
Hubert
WA.
1996
.
Proposed revision of the standard-weight equation for Rainbow Trout
.
Journal of Freshwater Ecology
11
:
319
325
.
South Carolina Department of Natural Resources.
2015
.
South Carolina's State Wildlife Action Plan
.
Tennessee Wildlife Resources Agency.
2015
.
Tennessee State Wildlife Action Plan
.
Weathers
TC,
Kazyak
DC,
Stauffer
JR,
Kulp
MA,
Moore
SE,
King
TL,
Carlson
JE.
2019
.
Neutral genetic and phenotypic variation within and among isolated headwater populations of Brook Trout
.
Transactions of the American Fisheries Society
148
:
58
72
.

The findings and conclusions in this article are those of the author(s) and do not necessarily represent the views of the U.S. Fish and Wildlife Service.

Author notes

Citation: Harris AC, Hanks RD, Rash JM, Goodfred DW, Kanno Y. 2021. Standard weight equation for Brook Trout in southern Appalachian Mountains streams. Journal of Fish and Wildlife Management 12(1):183–189; e1944-687X. https://doi.org/10.3996/JFWM-20-026

Supplementary data