Computing Relative Weights in FSA
2026-01-09
Source:vignettes/articles/Computing_Relative_Weights.qmd
Introduction
Condition is a measure of the physical condition of a population of fish based on the relative heaviness or plumpness of the fish as compared to a standard. One measure is called relative weight and is simply 100 times the observed weight of a fish divided by a standard weight derived from an accepted model for that species and the individual’s observed length; i.e.,
where is the relative weight, is the observed weight, and is the standard weight for the th fish. Individual relative weights are summarized to provide an overall measure of condition for the population. Relative weight and condition are explained in a variety of sources, including Ogle (2016). The goal of this vignette is to demonstrate how to calculate relative weights using functions inFSA.
The following packages are used herein. Note that the FSA functions described here were modified after version 0.9.6 and are thus specific to FSA >v0.9.6.
Looking Up Standard Weight Equations
Equations for computing the standard weight (i.e., ) from an individual fish’s observed length (i.e., ) have been derived for a number of freshwater game fish in the United States, as well as several non-game fish in the United States and some other fish from outside of the United States. The specifics of these equations have been collated into the WSlit data.frame1 distributed with FSA and are most easily accessed with wsVal(). For example, the specifics of the standard weight equation for Bluegill are retrieved below.
wsVal("Bluegill")
#> species measure units ref method min.TL int slope source
#> 34 Bluegill TL metric 75 Other 80 -5.374 3.316 Hillman (1982)The results returned from wsVal() are:
-
species: species of fish asked for. -
group: the sub-group for the species. Some species have separate standard weight equations for sub-groups (e.g,.maleorfemale, orlenticandlotic). Ifgroupdoes not appear in the output then there is no sub-group for that species (as illustrated here). The sub-group can be chosen withgroup=inwsVal()as demonstrated later.2 -
measure: the length measure used (will generally beTLfor total length, but depending on the species could beFLfor fork length,BLfor body length, orCLfor caudal length). -
units: the units for which the equation was developed. The default ismetricwhich has length in mm and weight in grams. However,Englishcan also be used which has lengths in inches and weight in pounds.3 These are the only two “units” for which the equation can be returned; thus, if you recorded lengths and weights in different units you will need to adjust your data accordingly (or adjust the standard weights computed from the equations (see below) accordingly). -
ref: the quantile used when developing the standard weight equation. The 75th percentile is used for most species, but some species have alternatives (50th or 25th percentile).4 -
method: the method used to develop the standard weight equation. This will usually beRLP(regression-line-percentile) orEmP(empirical percentile) but isOtheronly for Bluegill, as shown here. Some (very few) species have equations for both methods.5 -
min.TL: the minimum length for which the standard weight equation is appropriate.6 -
max.TL: the maximum length for which the standard weight equation is appropriate. Maximum lengths have not been specified for all species and, thus, may not appear in all outputs (e.g., for Bluegill here). -
int: the intercept, on the common logarithm (i.e., log10) scale, for the standard weight equation. -
slope: the slope, on the log10 scale, for the standard weight equation. -
quad: the coefficient for the quadratic term, on the log10 scale, of the standard weight equation. Most species will not have a quadratic term and, thus, this may not appear in many outputs. -
source: the literature source for the standard weight equation. -
comments: comments about the standard weight equation. Not all species have comments, thus, this may not appear in many outputs.
A simpler output of only the equation coefficients and the lengths for which it applies may be returned by including simplify=TRUE in wsVal().7
wsVal("Bluegill",simplify=TRUE)
#> species min.TL int slope
#> 34 Bluegill 80 -5.374 3.316Blue Sucker is an example where some of the “optional” values are returned (e.g., max.TL and quad). The example below further illustrates that the results can be returned in “English” units for many species.
wsVal("Blue Sucker",units="English")
#> species measure units ref method min.TL max.TL int slope quad
#> 31 Blue Sucker TL English 75 EmP 9.5 31.75 -3.354 2.273 0.461
#> source
#> 31 Neely et al. (2008)Use of wsVal() requires spelling (and capitalizing) the species name as it appears in WSlit. One can see all species names available in WSlit with wsVal() without any arguments.
wsVal()
#>
#> Species name must be one of following. Be careful of spelling and capitalization.
#> [1] "Aegean Chub" "African Sharptooth Catfish"
#> [3] "Alabama Bass" "Alabama Bass (original)"
#> [5] "Ankara Nase" "Arctic Grayling"
#> [7] "Bighead Carp" "Bigmouth Buffalo"
#> [9] "Bigmouth Sleepers" "Bigmouth Sleepers (lotic)"
#> [11] "Bigmouth Sleepers (overall)" "Black Bullhead"
#> [13] "Black Crappie" "Blacktail Redhorse"
#> [15] "Blue Catfish" "Blue Sucker"
#> [17] "Bluegill" "Bridgelip Sucker"
#> [19] "Brook Chub" "Brook Trout"
#> [21] "Brook Trout (Appalachia)" "Brook Trout (lentic)"
#> [23] "Brook Trout (lotic)" "Brook Trout (overall)"
#> [25] "Brown Bullhead" "Brown Trout"
#> [27] "Brown Trout (lentic)" "Brown Trout (lotic)"
#> [29] "Bull Trout" "Burbot"
#> [31] "Cavedano Chub" "Chain Pickerel"
#> [33] "Channel Catfish" "Chinook Salmon"
#> [35] "Chinook Salmon (landlocked)" "Cisco"
#> [37] "Common Carp" "Cutthroat Trout"
#> [39] "Cutthroat Trout (lentic)" "Cutthroat Trout (lotic)"
#> [41] "European Chub" "European Perch"
#> [43] "Flannelmouth Sucker" "Flathead Catfish"
#> [45] "Flier" "Fourbarbel Scraper"
#> [47] "Freshwater Drum" "Gizzard Shad"
#> [49] "Golden Shiner" "Golden Trout"
#> [51] "Goldeye" "Green Sunfish"
#> [53] "Horse Barbel" "Humpback Chub"
#> [55] "Kokanee" "Lake Chubsucker"
#> [57] "Lake Herring" "Lake Trout"
#> [59] "Largemouth Bass" "Largescale Sucker"
#> [61] "Longear Sunfish" "Longnose Gar"
#> [63] "Marble Trout" "Mountain Mullet"
#> [65] "Mountain Whitefish" "Muskellunge"
#> [67] "Muskellunge (female)" "Muskellunge (male)"
#> [69] "Muskellunge (overall)" "Nile Tilapia"
#> [71] "Nipple-Lip Scraper" "Northern Pike"
#> [73] "Northern Pikeminnow" "Northern Pikeminnow (original)"
#> [75] "Northern Snakehead" "Paddlefish"
#> [77] "Paddlefish (female)" "Paddlefish (male)"
#> [79] "Paddlefish (overall)" "Palmetto Bass"
#> [81] "Pejerrey" "Pumpkinseed"
#> [83] "Pursak Chub" "Rainbow Trout"
#> [85] "Rainbow Trout (lentic)" "Rainbow Trout (lotic)"
#> [87] "Razorback Sucker" "Redbreast Sunfish"
#> [89] "Redear Sunfish" "Riffle Dace"
#> [91] "River Carpsucker" "River Goby"
#> [93] "Rock Bass" "Roundtail Chub"
#> [95] "Ruffe" "Sardine"
#> [97] "Sauger" "Saugeye"
#> [99] "Shoal Bass" "Shorthead Redhorse"
#> [101] "Shovelnose Sturgeon" "Silver Carp"
#> [103] "Smallmouth Bass" "Smallmouth Buffalo"
#> [105] "South European Roach" "Spotted Bass"
#> [107] "Spotted Bass (original)" "Spotted Gar"
#> [109] "Spotted Sunfish" "Striped Bass"
#> [111] "Striped Bass (landlocked)" "Striped Bass X White Bass"
#> [113] "Suwannee Bass" "Tiger Muskellunge"
#> [115] "Utah Chub" "Walleye"
#> [117] "Walleye (30-149 mm)" "Walleye (overall)"
#> [119] "Warmouth" "White Bass"
#> [121] "White Catfish" "White Crappie"
#> [123] "White Perch" "White Sturgeon"
#> [125] "White Sucker" "Yellow Bass"
#> [127] "Yellow Bullhead" "Yellow Perch"All parts of the species names in WSlit are capitalized (e.g., “Blue Sucker” and not “blue sucker” or “Blue sucker”). wsVal() will return an informative error message if your capitalization is not correct but the message will be less informative if your spelling is off.
wsVal("Blue sucker")
#> Error:
#> ! There is no Ws equation in 'WSlit' for "Blue sucker". However, there is
#> an entry for "Blue Sucker" (note spelling, including capitalization).
wsVal("Blue suckr")
#> Error:
#> ! There is no Ws equation in 'WSlit' for "Blue suckr". Type 'wsVal()' to
#> see a list of available species.It is also not always obvious whether a species has equations for sub-groups or not. One way to deal with this is to just ask for the equation for your species of interest without using group=. If sub-groups exist then you will get an error message asking you to choose which sub-group to use.
wsVal("Brown Trout")
#> Error:
#> ! "Brown Trout" has Ws equations for these sub-groups: "lentic" and
#> "lotic". Please use 'group=' to select the equation for one of these
#> groups.Then try again by choosing the sub-group with group=.
wsVal("Brown Trout",group="lentic")
#> species group measure units ref method min.TL int slope
#> 51 Brown Trout lentic TL metric 75 RLP 140 -5.422 3.194
#> source
#> 51 Hyatt and Hubert (2001b)These same species and sub-group combinations can be also accessed by combining the species name and sub-group name (in parenthesis) into the first argument (and then not using group=).
wsVal("Brown Trout (lotic)")
#> species measure units ref method min.TL int slope
#> 57 Brown Trout (lotic) TL metric 75 RLP 140 -4.867 2.96
#> source
#> 57 Milewski and Brown (1994)The same general process can be used for species that have equations developed from multiple methods; though, only the sub-group identifiers can be combined (with parentheses) in the species name and used in the first argument.
wsVal("Arctic Grayling")
#> Error:
#> ! Ws equations exist for both the RLP and EmP 'method's for "Arctic
#> Grayling". Please select one or the other with 'method='.
wsVal("Arctic Grayling",method="EmP")
#> species measure units ref method min.TL int slope
#> 8 Arctic Grayling TL metric 75 EmP 150 -5.279 3.096
#> source comment
#> 8 Gilham et al. (2021) authors note that either RLP or EmP method may be usedOr for multiple reference groups.
wsVal("Ruffe")
#> Error:
#> ! Ws equations exist for more than one 'ref'erence value for "Ruffe".
#> Please select one of the following values with 'ref=': 50 or 75.
wsVal("Ruffe",ref=50)
#> species measure units ref method min.TL max.TL int slope quad
#> 190 Ruffe TL metric 50 EmP 55 205 -3.3524 1.3969 0.4054
#> source
#> 190 Ogle and Winfield (2009)There are two species (Chinook Salmon and Striped Bass) that appear to have sub-groups (i.e., “landlocked”) but only that one specific sub-group appears in WSlit. The standard weight literature for these species did not identify the equation as only being for “landlocked” populations. However, these entries were added to facilitate use when calculating proportional size distribution (PSD) metrics,8 which were defined just for “landlocked” populations, and relative weight metrics with the same data.frame.9 The standard weight equations for these species can be accessed by either just the species name or the species name with the group in parentheses. However, note that they are the exact same information.
wsVal("Striped Bass")
#> species measure units ref method min.TL int slope
#> 220 Striped Bass TL metric 75 RLP 150 -4.924 3.007
#> source
#> 220 Brown and Murphy (1991b)
wsVal("Striped Bass (landlocked)")
#> species measure units ref method min.TL int slope
#> 222 Striped Bass (landlocked) TL metric 75 RLP 150 -4.924 3.007
#> source
#> 222 Brown and Murphy (1991b)
#> comment
#> 222 Not clear just landlocked; added to simplify use with PSDlitThere are also a few species where an original standard weight equation has been revised in the literature. The original and revised equations are available in WSlit with the revised equations accessed by just using the species name and the original equations accessed by appending “(original)” to the species name.
wsVal("Spotted Bass") # revised definitions
#> species measure units ref method min.TL max.TL int slope
#> 211 Spotted Bass TL metric 75 EmP 150 490 -5.3467 3.197
#> source comment
#> 211 Sammons et al. (2025) also used RLP and EmP-quadratic but did not recommend
wsVal("Spotted Bass (original)")
#> species measure units ref method min.TL int slope
#> 214 Spotted Bass (original) TL metric 75 RLP 100 -5.392 3.215
#> source comment
#> 214 Wiens et al. (1996) HAS BEEN REVISEDWe strongly urge you to have a good understanding of the standard weight literature for your species’ of interest and make sure that wsVal() is returning the values that you expect.
Calculate Individual Relative Weight
For Typical Linear Equation
The specifics of the standard weight equation returned by wsVal() can be used to compute the standard weight for a fish given its observed length. As an example, suppose that the relative weight of a Largemouth Bass with an observed length of 350 mm and weight of 650 g is desired.
Begin by assigning the specifics of the standard weight equation for Largemouth Bass returned by wsVal() to an object (e.g., wsLMB here).
( wsLMB <- wsVal("Largemouth Bass") )
#> species measure units ref method min.TL int slope source
#> 114 Largemouth Bass TL metric 75 RLP 150 -5.528 3.273 Henson (1991)The intercept and slope for the standard weight equation on the log10-log10 scale can be extracted from this object.10
wsLMB[["int"]]
#> [1] -5.528
wsLMB[["slope"]]
#> [1] 3.273The standard weight is then computed from these results and the log10-transformed observed length as follows (with the result saved to an object, called ex1 here). Make sure to note the use of 10^ to back-transform the log10-transformed standard weight to a standard weight on the raw scale.
( ex1 <- 10^(wsLMB[["int"]]+wsLMB[["slope"]]*log10(350)) )
#> [1] 629.1218This calculation suggests that the standard weight for a 350 mm Largemouth Bass is 629.1 g. With this and Equation 1, the relative weight for this individual is computed (recalling that the observed weight was 650 g).
100*650/ex1
#> [1] 103.3186This indicates that the individual is (slightly) heavier than a “standard fish” of the same length as this values is greater than 100.
For Quadratic Equation
A similar process can be followed for a species where the standard weight equation includes a quadratic term. The only “trick” here is to include the quadratic term multiplied by the square of the log10-transformed observed length when computing the standard weight. This calculation is illustrated below with a 500 mm and 1010 g Blue Sucker.
Cautions
A few things to consider when calculating relative weights for individuals.
- Make sure the individual is longer than the minimum and shorter than the maximum (if given) length returned by
wsVal(). - Make sure to log10-transform the observed length when computing the standard weight. Note that all standard weight equations use log10 so never use the natural log with standard weight calculations.
- Make sure to back-transform (i.e., raise to the power of 10) the value so that the standard weight is on the raw rather than log10-transformed scale.
- Relative weights have traditionally been reported on a scale where the fraction is multiplied by 100 (i.e., so 100 means that the observed weight equals the standard weight). Thus, don’t forget to multiply by 100 when computing the relative weight.
Calculate Relative Weights for All of One Species
It is not common to compute the standard and relative weights for a single individual as was done in the previous section. Rather, it is more useful to calculate these values for all individuals in a sample, and then summarize those values for an overall assessment of the condition of those individuals.
Consider the CiscoTL data.frame distributed with the FSAdata package that contains the lengths (mm) and weights (g) of Cisco (Coregonus artedii) sampled from Trout Lake, WI, USA over a 25 year period. Note that there are many missing weights in this data.frame.
data("CiscoTL",package="FSAdata") # retrieve the data.frame
peek(CiscoTL,n=10)
#> lakeid year4 sampledate gearid spname length weight sex
#> 1 TR 1981 8/11/1981 VGN032 CISCO 140 21.4 F
#> 955 TR 1983 7/29/1983 VGN032 CISCO 196 NA <NA>
#> 1910 TR 1984 7/24/1984 VGN038 CISCO 213 NA <NA>
#> 2865 TR 1987 7/28/1987 VGN038 CISCO 208 NA <NA>
#> 3820 TR 1991 7/30/1991 VGN025 CISCO 139 NA <NA>
#> 4774 TR 1993 7/27/1993 VGN038 CISCO 213 NA <NA>
#> 5729 TR 1997 7/28/1997 VGN032 CISCO 174 NA <NA>
#> 6684 TR 1999 7/26/1999 VGN025 CISCO 137 NA <NA>
#> 7639 TR 2002 7/23/2002 VGN025 CISCO 144 NA <NA>
#> 8594 TR 2006 7/20/2006 VGN038 CISCO 216 NA <NA>“Manual” Calculations
The relative weight calculation begins by finding the specifics of the standard weight equation for Cisco and assigning them to an object (here, wsC).
( wsC <- wsVal("Cisco") )
#> species measure units ref method min.TL int slope
#> 72 Cisco TL metric 75 RLP 100 -5.517 3.224
#> source comment
#> 72 Fisher and Fielder (1998) same as for Lake HerringTwo new variables – Ws for standard weight and Wr for relative weight – are added to the data.frame in three steps below. First, Ws is calculated using the coefficients from the standard weight equation and the log-transformed length variable as shown above (but within mutate() from dplyr). Second, if the observed length is less than the minimum length for which the standard weight equation should be applied, then the previously calculated Ws is replaced with an NA (for missing value).11 Finally, the relative weight is computed from the observed weight and standard weight variables using Equation 1.
CiscoTL <- CiscoTL |>
mutate(Ws=10^(wsC[["int"]]+wsC[["slope"]]*log10(length)),
Ws=ifelse(length<wsC$min.TL,NA,Ws),
Wr=100*weight/Ws)
peek(CiscoTL,n=10)
#> lakeid year4 sampledate gearid spname length weight sex Ws Wr
#> 1 TR 1981 8/11/1981 VGN032 CISCO 140 21.4 F 25.24159 84.7807
#> 955 TR 1983 7/29/1983 VGN032 CISCO 196 NA <NA> 74.68503 NA
#> 1910 TR 1984 7/24/1984 VGN038 CISCO 213 NA <NA> 97.65531 NA
#> 2865 TR 1987 7/28/1987 VGN038 CISCO 208 NA <NA> 90.45575 NA
#> 3820 TR 1991 7/30/1991 VGN025 CISCO 139 NA <NA> 24.66492 NA
#> 4774 TR 1993 7/27/1993 VGN038 CISCO 213 NA <NA> 97.65531 NA
#> 5729 TR 1997 7/28/1997 VGN032 CISCO 174 NA <NA> 50.87809 NA
#> 6684 TR 1999 7/26/1999 VGN025 CISCO 137 NA <NA> 23.53895 NA
#> 7639 TR 2002 7/23/2002 VGN025 CISCO 144 NA <NA> 27.64144 NA
#> 8594 TR 2006 7/20/2006 VGN038 CISCO 216 NA <NA> 102.15953 NAUsing the WrAdd() Convenience Function
wrAdd() can be used to add a relative weight variable to a data.frame for all species in the data.frame for which a standard weight equation exists.12 The main argument to wrAdd() is a formula of the form weight~length+species where weight is the name of the observed weight variable, length is the name of the observed length variable, and species is the name of the species variable. One constraint here is that the species names in the species variable must be spelled (and capitalized) exactly as in WSlit. In these data, the species name is in spname but is in all capital letters as “CISCO”, rather than the required “Cisco”. capFirst()13 may be used to convert a word to a form where just the first letter is capitalized, and is used below.14
data("CiscoTL",package="FSAdata")
CiscoTL <- CiscoTL |>
mutate(Wr=wrAdd(weight~length+capFirst(spname)))
peek(CiscoTL,n=10)
#> lakeid year4 sampledate gearid spname length weight sex Wr
#> 1 TR 1981 8/11/1981 VGN032 CISCO 140 21.4 F 84.7807
#> 955 TR 1983 7/29/1983 VGN032 CISCO 196 NA <NA> NA
#> 1910 TR 1984 7/24/1984 VGN038 CISCO 213 NA <NA> NA
#> 2865 TR 1987 7/28/1987 VGN038 CISCO 208 NA <NA> NA
#> 3820 TR 1991 7/30/1991 VGN025 CISCO 139 NA <NA> NA
#> 4774 TR 1993 7/27/1993 VGN038 CISCO 213 NA <NA> NA
#> 5729 TR 1997 7/28/1997 VGN032 CISCO 174 NA <NA> NA
#> 6684 TR 1999 7/26/1999 VGN025 CISCO 137 NA <NA> NA
#> 7639 TR 2002 7/23/2002 VGN025 CISCO 144 NA <NA> NA
#> 8594 TR 2006 7/20/2006 VGN038 CISCO 216 NA <NA> NAA more general approach to deal with species that are spelled differently than expected in WSlit is to provide a named list or vector that defines how the original species names (i.e., the items in the vector to the right of the =) relate to the species names required by WSlit (i.e., the names in the vector to the left of the =) to thesaurus=. wrAdd() will match the two names appropriately while creating the relative weight variable.
CiscoTL <- CiscoTL |>
mutate(Wr2=wrAdd(weight~length+spname,thesaurus=c("Cisco"="CISCO")))
peek(CiscoTL,n=10)
#> lakeid year4 sampledate gearid spname length weight sex Wr Wr2
#> 1 TR 1981 8/11/1981 VGN032 CISCO 140 21.4 F 84.7807 84.7807
#> 955 TR 1983 7/29/1983 VGN032 CISCO 196 NA <NA> NA NA
#> 1910 TR 1984 7/24/1984 VGN038 CISCO 213 NA <NA> NA NA
#> 2865 TR 1987 7/28/1987 VGN038 CISCO 208 NA <NA> NA NA
#> 3820 TR 1991 7/30/1991 VGN025 CISCO 139 NA <NA> NA NA
#> 4774 TR 1993 7/27/1993 VGN038 CISCO 213 NA <NA> NA NA
#> 5729 TR 1997 7/28/1997 VGN032 CISCO 174 NA <NA> NA NA
#> 6684 TR 1999 7/26/1999 VGN025 CISCO 137 NA <NA> NA NA
#> 7639 TR 2002 7/23/2002 VGN025 CISCO 144 NA <NA> NA NA
#> 8594 TR 2006 7/20/2006 VGN038 CISCO 216 NA <NA> NA NAthesaurus= can be used even if only some of the species names are non-“standard.” Additionally, the named list/vector in thesaurus= can contain names that don’t exist in the original data.frame. Thus, a global thesaurus containing all species that could be encountered could be created, for example as an agency-wide definition, and used with a variety of specific data.frames.
wrAdd() handles species that have more than one standard weight equation15 with WsOpts=. For example, consider adding a relative weight variable to the RuffeSLRH92 data.frame distributed with FSAdata. Note that there is no species variable, which is needed by wrAdd(), so one was added with mutate().16 Additionally, for simplicity of presentation, I removed several other variables (with select()) that are not needed for this example.
data("RuffeSLRH92",package="FSAdata") # retrieve the data.frame
RuffeSLRH92 <- RuffeSLRH92 |>
mutate(species="Ruffe") |>
select(species,length,weight,sex)
peek(RuffeSLRH92,n=10)
#> species length weight sex
#> 1 Ruffe 90 9.3 male
#> 82 Ruffe 120 24.0 male
#> 164 Ruffe 142 33.1 female
#> 246 Ruffe 84 7.4 female
#> 328 Ruffe 100 12.6 male
#> 410 Ruffe 25 0.2 unknown
#> 492 Ruffe 94 13.0 male
#> 574 Ruffe 85 7.9 male
#> 656 Ruffe 145 39.1 male
#> 738 Ruffe 160 52.9 femaleCode similar to that used above for Cisco returns an error because there are standard weight equations for Ruffe for both 50th and 75th percentile references (see snippet below with the error message).
RuffeSLRH92 <- RuffeSLRH92 |>
mutate(Wr=wrAdd(weight~length+species))
#> species group ref method
#> 190 Ruffe <NA> 50 EmP
#> 191 Ruffe <NA> 75 EmP
#> Error in `mutate()`:
#> ℹ In argument: `Wr = wrAdd(weight ~ length + species)`.
#> Caused by error:
#> ! More than one Ws equation exists for "Ruffe". Please use a named list
#> in 'WsOpts=' to select one equation for "Ruffe" by specifing 'group',
#> 'ref', or 'method' as appropriate. See details in documentation and
#> above (for reference).To continue, wrAdd() must be instructed as to which of these two equations should be used to calculate the standard weight and, thus, relative weight. This is handled with a list in WsOpts= which will include the species name set equal to a list which identifies the specific equation to use (i.e., ref=50 in this example).
RuffeSLRH92 <- RuffeSLRH92 |>
mutate(Wr=wrAdd(weight~length+species,WsOpts=list(Ruffe=list(ref=50))))
peek(RuffeSLRH92,n=10)
#> species length weight sex Wr
#> 1 Ruffe 90 9.3 male 110.34512
#> 82 Ruffe 120 24.0 male 119.03123
#> 164 Ruffe 142 33.1 female 97.21733
#> 246 Ruffe 84 7.4 female 107.76315
#> 328 Ruffe 100 12.6 male 108.98596
#> 410 Ruffe 25 0.2 unknown NA
#> 492 Ruffe 94 13.0 male 135.44538
#> 574 Ruffe 85 7.9 male 111.08527
#> 656 Ruffe 145 39.1 male 107.53033
#> 738 Ruffe 160 52.9 female 106.51935Calculate Relative Weights for All of Multiple Species
The real value of wrAdd() is that it can be used to efficiently add a relative weight variable for multiple species in a single data.frame. This is illustrated below for a variety of scenarios.
“Good” Names and No Groups
InchLake2 distributed with FSAdata contains lengths and weights for several species captured from Inch Lake. These data provide a simple example for using wrAdd() because all species names are spelled as required and none of the species have sub-groups.17
data("InchLake2",package="FSAdata") # retrieve the data.frame
peek(InchLake2,n=10)
#> netID fishID species length weight year
#> 1 206 501 Bluegill 1.5 0.7 2008
#> 57 16 208 Black Crappie 11.6 380.0 2007
#> 115 101 583 Bluegill 5.5 48.0 2008
#> 172 102 642 Bluntnose Minnow 2.1 1.3 2008
#> 229 116 760 Largemouth Bass 2.8 2.0 2008
#> 287 109 843 Largemouth Bass 13.1 460.0 2008
#> 344 130 902 Largemouth Bass 10.1 173.0 2008
#> 401 6 178 Bluegill 6.2 62.0 2007
#> 459 12 45 Bluntnose Minnow 2.7 6.0 2007
#> 516 4 127 Bluegill 6.6 90.0 2007A complication here is that length and weight are in “mixed” units; i.e., inches for length and grams for weight. One or the other must be converted to the same unit type. Below length is converted to mm before wrAdd() is used to add a relative weight variable.
InchLake2 <- InchLake2 |>
mutate(length=length*25.4,
Wr=wrAdd(weight~length+species))
peek(InchLake2,n=10)
#> netID fishID species length weight year Wr
#> 1 206 501 Bluegill 38.10 0.7 2008 NA
#> 57 16 208 Black Crappie 294.64 380.0 2007 86.69675
#> 115 101 583 Bluegill 139.70 48.0 2008 87.45204
#> 172 102 642 Bluntnose Minnow 53.34 1.3 2008 NA
#> 229 116 760 Largemouth Bass 71.12 2.0 2008 NA
#> 287 109 843 Largemouth Bass 332.74 460.0 2008 86.27960
#> 344 130 902 Largemouth Bass 256.54 173.0 2008 76.01188
#> 401 6 178 Bluegill 157.48 62.0 2007 75.92630
#> 459 12 45 Bluntnose Minnow 68.58 6.0 2007 NA
#> 516 4 127 Bluegill 167.64 90.0 2007 89.57900Note that species without known standard weight equations in WSlit (e.g., Bluntnose Minnow) will have NA for the relative weight variable, as will individuals with lengths outside the range of lengths for which the standard weight equation should be applied.
“Bad” Names and No Groups
Now consider the BGHRfish data.frame (distributed with the FSAdata package) that has the lengths (mm) and weights (g) of three species – Smallmouth Bass, Largemouth Bass, and Bluegill – from Big Hill Reservoir, KS. These three species do not have sub-groups defined in WSlit, but upon observing the data below18 it is seen that the species variable (specCode) contains codes for the species names rather than the names required by PSDlit.
data(BGHRfish,package="FSAdata") # retrieve the data.frame
peek(BGHRfish,n=10)
#> UID fishID specCode length weight count
#> 1 1 1 116 100 NA 1
#> 30 2 7 118 317 390 1
#> 59 4 9 122 151 90 1
#> 89 6 NA 122 180 NA 2
#> 118 10 2 116 356 520 1
#> 148 12 3 122 152 80 1
#> 177 15 4 118 311 370 1
#> 207 19 4 118 304 350 1
#> 236 20 NA 118 80 NA 1
#> 266 20 21 122 171 120 1One way to deal with the issue of “bad” species names is to use a named list or vector that defines how the names from WSlit should be matched to the names in the data.frame. For this purpose, the species names in WSlit are the names in the vector (i.e., before the =) and the species names in the data.frame are the items in the vector (i.e., after the =).19
thes <- c("Smallmouth Bass"="116","Largemouth Bass"="118","Bluegill"="122")This list/vector is then given to thesaurus= in wrAdd() which will perform the name matching while creating the GH length categories. However, one complicating factor with these data is that wrAdd() expects a string in species (and, thus, thesaurus=) rather than a numeric like specCode. Thus, specCode is converted to a character below before using wrAdd().
BGHRfish <- BGHRfish |>
mutate(specCode=as.character(specCode),
Wr=wrAdd(weight~length+specCode,thesaurus=thes))
peek(BGHRfish,n=10)
#> UID fishID specCode length weight count Wr
#> 1 1 1 116 100 NA 1 NA
#> 30 2 7 118 317 390 1 85.72306
#> 59 4 9 122 151 90 1 126.69368
#> 89 6 NA 122 180 NA 2 NA
#> 118 10 2 116 356 520 1 75.92125
#> 148 12 3 122 152 80 1 110.17845
#> 177 15 4 118 311 370 1 86.57589
#> 207 19 4 118 304 350 1 88.23133
#> 236 20 NA 118 80 NA 1 NA
#> 266 20 21 122 171 120 1 111.83201“Bad” Names, Groups, and Multiple Equations
The use of wrAdd() can become complicated for data.frames with species names other than what WSlit expects, with species for which standard weight equations exist for sub-groups, especially if more than one sub-group is in the data, and for species with multiple standard weight equations. The hypothetical data set PSDWRtest distributed with FSA can be used to illustrate how to handle these “issues”.
peek(PSDWRtest,n=20)
#> species location len wt sex
#> 1 Bluegill Sunfish Bass Lake 107 25.8 <NA>
#> 53 Bluegill Sunfish Bass Lake 116 34.8 <NA>
#> 107 Bluegill Sunfish Bass Lake 191 138.3 <NA>
#> 160 Brook Trout Trout Lake 291 NA <NA>
#> 214 Brown Trout Trout Lake 151 45.4 <NA>
#> 267 Brown Trout Trout Lake 190 86.3 <NA>
#> 321 Brown Trout Brushy Creek 318 198.4 M
#> 374 Brown Trout Brushy Creek 446 533.4 F
#> 428 Largemouth Bass Bass Lake 199 70.1 <NA>
#> 481 Largemouth Bass Bass Lake 306 311.9 <NA>
#> 535 Lean Lake Trout Trout Lake 529 1480.0 F
#> 588 Lean Lake Trout Trout Lake 809 5448.1 F
#> 642 Muskellunge Long Lake 1097 11376.4 U
#> 695 Walleye Bass Lake 72 3.5 <NA>
#> 749 Walleye Bass Lake 307 273.6 M
#> 802 Walleye Bass Lake 345 429.8 F
#> 856 Yellow Perch Bass Lake 165 59.4 F
#> 909 Yellow Perch Bass Lake 150 40.2 F
#> 963 Yellow Perch Bass Lake 241 187.9 F
#> 1016 Yellow Perch Bass Lake 322 520.0 FwrAdd() will produce some informative error messages, but it is best that you have a full understanding of the issues that may arise with your data by carefully examining your data and understanding the standard weight (and Gabelhouse length categories) for the species in your data. The “issues” that need to be addressed with the PSDWRtest data are as follows:
- “Bluegill Sunfish” was used rather than “Bluegill”.
- “Lean Lake Trout” was used rather than “Lake Trout”.
- Brook Trout sampled from a lotic (“Trout Lake”) system, for which there are standard weight equations for sub-groups.
- Brown Trout sampled from a lotic (“Trout Lake”) and lentic (“Brush Creek”) system, for which there are standard weight equations for sub-groups.
- Muskellunge for which sex is known for some and not for others, and there is a desire to use the sex-specific standard weight equation when sex is known (and use the overall equation when it is not).
- Walleye of sizes for which separate standard weight equations may be used.
- Ruffe for which the reference quantile of the standard weight equation must be specified.
The easiest way to deal with most of these “issues” is to create a new “species” variable (i.e., species2 below) that appends the specific groups in parentheses to the species name. There are a variety of ways to do this and which way (is best or works) may depend on the specifics of the situation. Here, we primarily use case_when() from dplyr with a series of statements that begin with a “condition” to the left of the ~ and new species “name” for that condition to the right of the ~. The .default=species at the end puts the name from species into species2 for all situations where none of the conditions above it are met (e.g., if species is “Yellow Perch” then species2 will be “Yellow Perch”).
PSDWRtest <- PSDWRtest |>
mutate(species2=case_when(
species=="Bluegill Sunfish" ~ "Bluegill",
species=="Lean Lake Trout" ~ "Lake Trout",
species=="Brown Trout" & location=="Trout Lake" ~ "Brown Trout (lotic)",
species=="Brown Trout" & location=="Brushy Creek" ~ "Brown Trout (lentic)",
species=="Brook Trout" & location=="Trout Lake" ~ "Brook Trout (lotic)",
species=="Muskellunge" & sex=="M" ~ "Muskellunge (male)",
species=="Muskellunge" & sex=="F" ~ "Muskellunge (female)",
species=="Muskellunge" & sex=="U" ~ "Muskellunge (overall)",
species=="Muskellunge" & is.na(sex) ~ "Muskellunge (overall)",
species=="Walleye" & len>=150 ~ "Walleye (overall)",
species=="Walleye" & len<150 ~ "Walleye (30-149 mm)",
.default=species
))
peek(PSDWRtest,n=20)
#> species location len wt sex species2
#> 1 Bluegill Sunfish Bass Lake 107 25.8 <NA> Bluegill
#> 53 Bluegill Sunfish Bass Lake 116 34.8 <NA> Bluegill
#> 107 Bluegill Sunfish Bass Lake 191 138.3 <NA> Bluegill
#> 160 Brook Trout Trout Lake 291 NA <NA> Brook Trout (lotic)
#> 214 Brown Trout Trout Lake 151 45.4 <NA> Brown Trout (lotic)
#> 267 Brown Trout Trout Lake 190 86.3 <NA> Brown Trout (lotic)
#> 321 Brown Trout Brushy Creek 318 198.4 M Brown Trout (lentic)
#> 374 Brown Trout Brushy Creek 446 533.4 F Brown Trout (lentic)
#> 428 Largemouth Bass Bass Lake 199 70.1 <NA> Largemouth Bass
#> 481 Largemouth Bass Bass Lake 306 311.9 <NA> Largemouth Bass
#> 535 Lean Lake Trout Trout Lake 529 1480.0 F Lake Trout
#> 588 Lean Lake Trout Trout Lake 809 5448.1 F Lake Trout
#> 642 Muskellunge Long Lake 1097 11376.4 U Muskellunge (overall)
#> 695 Walleye Bass Lake 72 3.5 <NA> Walleye (30-149 mm)
#> 749 Walleye Bass Lake 307 273.6 M Walleye (overall)
#> 802 Walleye Bass Lake 345 429.8 F Walleye (overall)
#> 856 Yellow Perch Bass Lake 165 59.4 F Yellow Perch
#> 909 Yellow Perch Bass Lake 150 40.2 F Yellow Perch
#> 963 Yellow Perch Bass Lake 241 187.9 F Yellow Perch
#> 1016 Yellow Perch Bass Lake 322 520.0 F Yellow PerchThe relative weights for each fish (for species with standard weight equations) is added to this data.drame with wrAdd() as described above, noting the use of the “new” species variable species2. Further note the use of wsOpts= to define which reference quantile to use for the Ruffe standard weight equation.
PSDWRtest$wr <- wrAdd(wt~len+species2,data=PSDWRtest,
WsOpts=list(Ruffe=list(ref=75)))
peek(PSDWRtest,n=20)
#> species location len wt sex species2
#> 1 Bluegill Sunfish Bass Lake 107 25.8 <NA> Bluegill
#> 53 Bluegill Sunfish Bass Lake 116 34.8 <NA> Bluegill
#> 107 Bluegill Sunfish Bass Lake 191 138.3 <NA> Bluegill
#> 160 Brook Trout Trout Lake 291 NA <NA> Brook Trout (lotic)
#> 214 Brown Trout Trout Lake 151 45.4 <NA> Brown Trout (lotic)
#> 267 Brown Trout Trout Lake 190 86.3 <NA> Brown Trout (lotic)
#> 321 Brown Trout Brushy Creek 318 198.4 M Brown Trout (lentic)
#> 374 Brown Trout Brushy Creek 446 533.4 F Brown Trout (lentic)
#> 428 Largemouth Bass Bass Lake 199 70.1 <NA> Largemouth Bass
#> 481 Largemouth Bass Bass Lake 306 311.9 <NA> Largemouth Bass
#> 535 Lean Lake Trout Trout Lake 529 1480.0 F Lake Trout
#> 588 Lean Lake Trout Trout Lake 809 5448.1 F Lake Trout
#> 642 Muskellunge Long Lake 1097 11376.4 U Muskellunge (overall)
#> 695 Walleye Bass Lake 72 3.5 <NA> Walleye (30-149 mm)
#> 749 Walleye Bass Lake 307 273.6 M Walleye (overall)
#> 802 Walleye Bass Lake 345 429.8 F Walleye (overall)
#> 856 Yellow Perch Bass Lake 165 59.4 F Yellow Perch
#> 909 Yellow Perch Bass Lake 150 40.2 F Yellow Perch
#> 963 Yellow Perch Bass Lake 241 187.9 F Yellow Perch
#> 1016 Yellow Perch Bass Lake 322 520.0 F Yellow Perch
#> wr
#> 1 113.81070
#> 53 117.44555
#> 107 89.31318
#> 160 NA
#> 214 118.65447
#> 267 114.26156
#> 321 53.30764
#> 374 48.64940
#> 428 70.72483
#> 481 76.95718
#> 535 102.54739
#> 588 95.07015
#> 642 103.11404
#> 695 104.56374
#> 749 95.72295
#> 802 103.75325
#> 856 99.38328
#> 909 91.50636
#> 963 92.47232
#> 1016 100.37577Summarizing Relative Weights
Single Species
As an illustration, the mean and standard deviation of relative weights for Cisco (in CiscoTL from above) are computed below (along with validn which is the number of non-NA (i.e., non-missing) relative weights).20 These results suggest that this population of Cisco is substantially “skinnier” (i.e., under-weight) than the standard for the species (because the mean relative weight is substantially less than 100).
Multiple Species
The mean and sd of relative weight for all species in PSDWRtest from above is shown below. It is important to carefully examine these results because a species could have no mean relative weight calculated because there is no standard weight equation for that species (in WSlit) or because the species name is not spelled as expected (in WSlit). The only species below with no mean relative weight (i.e., Iowa Darter) does, indeed, not have a known standard weight equation.
PSDWRtest |>
group_by(species,location) |>
summarize(validn=sum(!is.na(wr)),
mnWr=mean(wr,na.rm=TRUE),
sdWr=sd(wr,na.rm=TRUE)) |>
as.data.frame()
#> `summarise()` has grouped output by 'species'. You can override using the
#> `.groups` argument.
#> species location validn mnWr sdWr
#> 1 Bluegill Sunfish Bass Lake 111 101.77768 9.689499
#> 2 Brook Trout Trout Lake 73 109.45569 1.191287
#> 3 Brown Trout Brushy Creek 91 56.91065 5.724542
#> 4 Brown Trout Trout Lake 72 102.97181 10.372980
#> 5 Iowa Darter Bass Lake 0 NaN NA
#> 6 Largemouth Bass Bass Lake 87 70.00372 6.558304
#> 7 Lean Lake Trout Trout Lake 92 97.51835 9.643417
#> 8 Muskellunge Long Lake 44 110.93352 11.695635
#> 9 Ruffe Round Lake 36 84.17434 7.423376
#> 10 Walleye Bass Lake 154 99.46820 9.000269
#> 11 Yellow Perch Bass Lake 160 102.25132 9.927675