Description Usage Arguments Details Value Warning Author(s) References See Also Examples
Calculate the peak value, the timetopeak, the duration and the magnitude of the Specific Dynamic Action (SDA, i.e., Heat Increment of Feeding, postprandial metabolic rate, etc.) from oxygen uptake data recorded with a fed fish for which the standard metabolic rate (SMR) is known. SMR is required to calculate the magnitude of SDA (area bounded by the SDA curve and the SMR). A nonparametric quantile regression is used to fit the SDA curve, a technique that is robust against changes in activity level during digestion.
1 2 3 4 5 6 7 8 9 10 11 12 
X 
A numeric vector or data frame column containing the time relative
to the meal (which it at time zero) for each oxygen uptake measurement.
Measurements obtained before the meal, if present, have negative X values.
See 
Y 
A numeric vector or data frame column containing oxygen uptake measurements. 
my.smr 
The Standard Metabolic Rate (SMR) for the animal. Same units
as 
tau 
A parameter that varies between 0 and 1. As with a quantile, the

lambda 
A penalty parameter used by 
postfeed.acclim 
Duration (in same units as X axis, typically hours)
of a period, right after feeding, which is skipped before fitting the SDA
curve with 
tol 
How close to SMR should the SDA curve return to declare SDA complete. Ideally the curve returns to SMR (tol == 0). In practice, small fluctuations in MO2 around SMR, or experiments that end a bit too early for the fit to return to SMR will result in curve that do not return to SMR and SDA will have no end, no duration, and the magnitude will not be reliable. A solution is to allow for a tolerance about SMR to declare that SDA has ended. A good value is 5% of SMR, expressed as a proportion (0.05). 
tol.type 
If 
MO2.time.unit 
Time unit over which MO2 is expressed, 
X.time.unit 
Time can be in 
The rqss
function of the quantreg
package is used for this
nonparametric quantile regression that results in a curve that tracks the
bottom of the MO2 values on a plot of MO2 x time, keeping a proportion
tau
of values below the line. Thus the same assumption is made than
when estimating SMR: SMR is not taken as the lowest value of MO2 that can be
observed, but as a normal distribution describing the MO2 when an animal is
fasted and quiet, and some values are below the mean of this distribution.
In practice, when measuring SMR, a method that fits several normal
distributions, should reveal SMR, which is the lowest of these
distributions. In practice, it does not work in all cases (See Chabot et al.
2016b) and simply assuming that 20% of the MO2 values are below SMR works
well. This same principle is used to fit a curve tracing SDA. Without
ignoring a few hours at the beginning of SDA, it is difficult to get a fit
that begins close to SMR at time zero. The practical, if not particularly
elegant, solution is to start the fit a few hours hours after the meal and
to force a straight line from SMR at time zero, to the beginning of the SDA
fit at time postfeed.acclim
.
A list with two object:
sda.fit 
A data frame containing the fitted values of SDA every 0.25 hour, which can then be used to plot SDA. The variables of this data frame are:

sda.var 
A list that contains the calculated parameters of SDA:

The parameters tau and lambda are not independent from each other. If changing one, check if the results are acceptable, otherwise adjust the second parameter.
Denis Chabot, Institut MauriceLamontagne, Department of Fisheries and Oceans.
Chabot, Denis, Koenker, Roger and Farrell, Anthony P. (2016a) The measurement of the specific dynamic action in fishes. Journal of Fish Biology 88, 152172.
Chabot, Denis, Steffensen, John F. and Farrell, Anthony P. (2016b) The determination of the standard metabolic rate in fishes. Journal of Fish Biology 88, 81121.
Koenker, Roger (2005) Quantile regression. Cambridge University Press, Cambridge. 366 p.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  # using juvenile cod data included in the package, minimum acceptable r2 is
# 0.96 and SMR is 81.2; see calcSMR for how it was obtained
data("codSDA")
sda.data = subset(codSDA, r2 >= 0.96)
# Logtime_hr is time in hours relative to time of feeding, a required variable.
# MO2cor is in micromoles per min per kg and the "cor" in the name means that
# the MO2 values soon after feeding were corrected for the effect of the feeding procedure
SDA= calcSDA(X=sda.data$Logtime_hr, Y=sda.data$MO2cor, my.smr=81.2,
tau=0.2, lambda=30,
postfeed.acclim=3, tol=0.05, tol.type="proportion",
MO2.time.unit="min", X.time.unit="hour")
names(SDA)
SDA$sda.var

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