Whale mass inferred from length

Calculate an estimate of the mass of different species of whale, based on animal length, based on formulae as listed in “Details”.

whaleMassFromLength(L, species = "N. Atl. Right Whale", model = NULL)

Arguments

L: whale length in m.
species: character value specifying the species (see “Details”). If only one value is given, then it will repeated to have the same length as L. Otherwise, its length must match the length of L.
model: either NULL (the default), to choose a model based on the particular species, or a character value specifying the model (see “Details”). If only one value is given, then it will repeated to have the same length as L. Otherwise, its length must match the length of L.

Value

Mass in kg.

Details

The permitted values for model and species are as follows. Note that if model is not provided, then Fortune (2012) is used for "N. Atl. Right Whale", and Lockyer (1976) is used for all other species.

"moore2005" (which only works if species is "N. Atl. Right Whale") yields \(242.988 * exp(0.4 * length)\), which (apart from a unit change on L) is the regression equation shown above Figure 1d in Moore et al. (2005) for right whales. A difficult in the Moore et al. (2005) use of a single nonzero digit in the multiplier on L is illustrated in “Examples”.
"fortune2012" with species="N. Atl. Right Whale" yields the formula \(exp(-10.095 + 2.825*log(100*L))\) for North Atlantic right whales, according to a corrected version of the erroneous formula given in the caption of Figure 4 in Fortune et al (2012). (The error, an exchange of slope and intercept, was confirmed by S. Fortune in an email to D. Kelley dated June 22, 2018.)
"fortune2012" with species="N. Pac. Right Whale" yields the formula \(exp(-12.286 + 3.158*log(100*L))\) for North Pacific right whales, according to a corrected version of the erroneous formula given in the caption of Figure 4 in Fortune et al (2012). (The error, an exchange of slope and intercept, was confirmed by S. Fortune in an email to D. Kelley dated June 22, 2018.)
"lockyer1976" uses formulae from Table 1 of Lockyer (1976). The permitted species and the formulae used are as follows (note that the "Gray Whale" formula is in the table's caption, not in the table itself).
- "Blue Whale": \(2.899 * L^3.25\)
- "Bryde Whale": \(12.965 * L^2.74\)
- "Fin Whale": \(7.996 * L^2.90\)
- "Gray Whale": \(5.4 * L^3.28\)
- "Humpback Whale": \(16.473 * L^2.95\)
- "Minke Whale": \(49.574 * L^2.31\)
- "Pac. Right Whale": \(13.200 * L^3.06\)
- "Sei Whale": \(25.763 * L^2.43\)
- "Sperm Whale": \(6.648 * L^3.18\)

References

Lockyer, C. "Body Weights of Some Species of Large Whales." J. Cons. Int. Explor. Mer. 36, no. 3 (1976): 259-73.
Moore, M.J., A.R. Knowlton, S.D. Kraus, W.A. McLellan, and R.K. Bonde. "Morphometry, Gross Morphology and Available Histopathology in North Atlantic Right Whale (Eubalaena Glacialis) Mortalities (1970 to 2002)." Journal of Cetacean Research and Management 6, no. 3 (2005): 199-214.
Fortune, Sarah M. E., Andrew W. Trites, Wayne L. Perryman, Michael J. Moore, Heather M. Pettis, and Morgan S. Lynn. "Growth and Rapid Early Development of North Atlantic Right Whales (Eubalaena Glacialis)." Journal of Mammalogy 93, no. 5 (2012): 1342-54. doi:10.1644/11-MAMM-A-297.1 .

Author

Dan Kelley

Examples

library(whalestrike)
L <- seq(5, 15, length.out = 100)
kpt <- 1000 # kg per tonne
# Demonstrate (with dashing) the sensitivity involved in the single-digit
# parameter in Moore's formula, and (with colour) the difference to the
# Fortune et al. (2012) formulae.
plot(L, whaleMassFromLength(L, model = "moore2005") / kpt,
    type = "l", lwd = 2,
    xlab = "Right-whale Length [m]", ylab = "Mass [tonne]"
)
lines(L, 242.988 * exp(0.35 * L) / kpt, lty = "dotted", lwd = 2)
lines(L, 242.988 * exp(0.45 * L) / kpt, lty = "dashed", lwd = 2)
lines(L, whaleMassFromLength(L,
    species = "N. Atl. Right Whale",
    model = "fortune2012"
) / kpt, col = 2, lwd = 2)
lines(L, whaleMassFromLength(L,
    species = "N. Pac. Right Whale",
    model = "fortune2012"
) / kpt, col = 3, lwd = 2)
legend("topleft",
    lwd = 2, col = 1:3,
    legend = c("moore2005", "fortune2012 Atlantic", "fortune2012 Pacific")
)


# Emulate Figure 1 of Lockyer (1976), with roughly-chosen plot limits.
L <- seq(0, 18, 0.5)
m <- whaleMassFromLength(L, species = "Pac. Right Whale", model = "lockyer1976") / kpt
plot(L, m,
    col = 1, xlab = "Length [m]", ylab = "Mass [tonne]", type = "l", lwd = 2,
    xaxs = "i", yaxs = "i", xlim = c(3, 30), ylim = c(0, 180)
)
L <- seq(0, 28, 0.5)
m <- whaleMassFromLength(L, species = "Blue Whale", model = "lockyer1976") / kpt
lines(L, m, col = 2, lwd = 2)
L <- seq(0, 24, 0.5)
m <- whaleMassFromLength(L, species = "Fin Whale", model = "lockyer1976") / kpt
lines(L, m, col = 3, lwd = 2)
L <- seq(0, 18, 0.5)
m <- whaleMassFromLength(L, species = "Sei Whale", model = "lockyer1976") / kpt
lines(L, m, col = 1, lty = 2, lwd = 2)
L <- seq(0, 17, 0.5)
m <- whaleMassFromLength(L, species = "Bryde Whale", model = "lockyer1976") / kpt
lines(L, m, col = 2, lty = 2, lwd = 2)
L <- seq(0, 12, 0.5)
m <- whaleMassFromLength(L, species = "Minke Whale", model = "lockyer1976") / kpt
lines(L, m, col = 3, lty = 2, lwd = 2)
L <- seq(0, 17, 0.5)
m <- whaleMassFromLength(L, species = "Humpback Whale", model = "lockyer1976") / kpt
lines(L, m, col = 1, lty = 3, lwd = 2)
L <- seq(0, 18, 0.5)
m <- whaleMassFromLength(L, species = "Sperm Whale", model = "lockyer1976") / kpt
lines(L, m, col = 2, lty = 3, lwd = 2)
L <- seq(0, 15, 0.5)
m <- whaleMassFromLength(L, species = "Gray Whale", model = "lockyer1976") / kpt
lines(L, m, col = 3, lty = 3, lwd = 2)
grid()
legend("topleft",
    col = c(1:3, 1:3, 1:2), lwd = 2, lty = c(rep(1, 3), rep(2, 3), rep(3, 3)),
    legend = c("Right", "Blue", "Fin", "Sei", "Bryde", "Minke", "Humpback", "Sperm", "Gray")
)