Example: Metabolic Rate

1
Start here 18 Jan. 2007
Example Metabolic Rate Amount of (metabolically
active) tissue should dictate the rate at which
an animal produces heat (or consumes
oxygen). Oxygen consumption at rest or during
maximum exertion should be ? M1.00 However,
respiratory exchange surface area should be ?
M0.67 "Houston, we have a problem "
2
Max. O2 consumption is typically10-fold higher
than Resting
log10 scale,Body Mass on X axis
3
What gives? Metabolic rate typically scales with
an exponent less than unity, often 0.7-0.8
(many exceptions). Gas exchange surface area
often scales with an exponent greater than
0.67. But, the slopes do not always
match. Example mammalian maximal oxygen
consumption (measured on motorized treadmill)
scales as M0.872
4
Weibel, E. R., L. D. Bacigalupe, B. Schmitt, and
H. Hoppeler. 2004. Allometric scaling of maximal
metabolic rate in mammals muscle
aerobic capacity as determinant factor.
Respiratory Physiology Neurobiology 140115-132.
5
What gives? Metabolic rate typically scales with
an exponent less than unity, often 0.7-0.8
(many exceptions). Gas exchange surface area
often scales with an exponent greater than
0.67. But, the slopes do not always
match. Example mammalian maximal oxygen
consumption (measured on motorized treadmill)
scales as M0.872 whereas pulmonary diffusing
capacity (measured morphometrically) scales as
M1.084 So, large-bodied species have excess
capacity.
6
Resting and Maximal Metabolic Rates do not always
Scale in Parallel. Example Amphibolurus
(Ctenophorus) nuchalis S.M.R. scales as
M0.830 95 C.I. on slope 0.783 - 0.877 VO2max
scales as M0.948 95 C.I. on slope 0.885 -
1.011
7
Using Allometry as a Tool to Understand
Organismal Design and Adaptation
Deviations from the empirical line of best fit,
for a given kind of animal, may indicate special
adaptations.
Ex. pronghorn have high maximal rate of oxygen
consumption (VO2max)
Ex. humans have large brains
8
Bat
9
Liem et al. 2001, Focus Box 14-2
10
Using Allometry as a Tool to Understand
Organismal Design and Adaptation
These deviations call for explanations at both
proximate and ultimate levels. Ultimate Why did
natural selection, sexual selection or random
genetic drift make them that way? e.g.,
apparently, increasing intelligence was favored
in human ancestors e.g., perhaps pronghorn use
their high aerobic capacity when escaping from
predators
11
Using Allometry as a Tool to Understand
Organismal Design and Adaptation
Proximate How do they do it in terms of
morphology and physiology? e.g., maybe pronghorn
have large lungs, high hemoglobin levels, large
hearts, lots of mitochondria in their muscles ...

12
Metabolic Rate is Often Expressed per unit Mass
of Tissue (e.g., per gram body mass) If
Whole-animal BMR ? M0.75 Then Mass-specific BMR ?
M-0.25
13
Mass-specific metabolic rate scales about as
M-0.25
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
14

M0.75
M-0.25
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
15
Log transformation linearizes the
relationships. This is easier to analyze by
least-squares linear regression. Slope gives the
"allometric scaling exponent."

Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
16
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
17
Statistical Tutorial
18
Correlation (bivariate) - relationship between
two traits or variables Can be positive or
negative Ranges from -1 to 1 Usually assumed to
be linear for purposes of statistical
testing Pearson product-moment correlation assume
s bivariate normality denoted as r or
R Spearman rank correlation is a "nonparametric"
alternative By itself, correlation does not
indicate causation!
19
N 50
R 0.066
2-tailedP 0.649
20
N 50
R 0.293
2-tailedP 0.039
21
N 50
R 0.517
2-tailedP 0.0001
22
N 50
R 0.747
2-tailedP 510-10
23
N 50
R 0.894
2-tailedP 310-18
24
Regression - one type of line of best fit More
formally, "least-squares linear
regression" Distinguishes between "dependent" (Y)
and "independent" (X) variable Typically used
when some degree of causality is
presumed Minimizes sum of the squared vertical
deviations from the line residuals Passes
through point mean X, mean Y Coefficient of
determination (r2 or R2) indicates how much of
the variance in Y is explained by variance in X
25
Assumes no measurement error in the independent
(X) variable If have measurement error in X
variable, then underestimates the slope Not
really appropriate in many biological
studies (including allometry) but used
anyway Reduced Major Axis line is geometric mean
of slope of Y on X plus X on Y can be computed
as least-squares regression slope divided by
r Major Axis line minimizes sum of the
squared perpendicular deviations from the line
26
Least-squares linear regression
N 50
27
Least-squares linear regression
N 50
28
Least-squares linear regression
N 50
29
Least-squares linear regression
N 50
30
Least-squares linear regression
N 50
31
t-test - statistical test based on the t
distribution. Most commonly, a comparison of the
mean (average) value of samples from two
populations Are the means "significantly"
different? Statistically "significant"
traditionally taken as P lt 0.05 1 in 20 chance
of getting a difference that big by chance
alone when you sample randomly from two
populations that actually have the same mean 1
in 20 times you will get a "significant" differe
nce when there really is not one, i.e., commit
a Type I error
32
Lecture 4 Thermoregulation and Resting Metabolism
33
Some Terms from the Student Survey (plus or
minus a few ...) Serves as Partial Review for
Midterm 1 on Tuesday, 30 Jan. 2007 Ecology -
study of relationships between organisms and
their environments, including both biotic (i.e.,
other organisms) and abiotic (i.e., physical
factors) Evolution - change more specifically,
heritable, cross-generational changes in
populations of organisms Physiology - study of
how organisms work
34
Phenotype - physical characteristics of an
organism resulting from gene expression modified
by environmental factors Genotype - genetic
material possessed by an individual organism,
usually in the form of DNA Natural Selection -
correlation between variation in one or more
phenotypic traits and Darwinian fitness (
lifetime reproductive success)
35
Ectotherm - organism that relies on external
sources of heat Endotherm - organism that
produces enough heat by its own metabolic
processes to affect its own body temperature can
increase metabolic rate in response to reduced
ambient temperature Poikilotherm - organism that
experiences variable body temperature, often
closely tracking ambient temperature Homeotherm -
organism that experiences (relatively) constant
body temperature (e.g., 2 C)
36
Fig. 17-9
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
37
Endotherm Tb and Metabolic Rate vs. Ambient
Temperature
NoteTNZ goes from LCT to UCT
Summit metabolism
Thermal conductance
(e.g., evaporative cooling by sweating or panting)
Lower C.T.
Upper C.T.
Fig. 17-21
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
38
Takes little energy. Vasomotor responses -
regulate blood flow between the periphery and
core Insulation adjustments - pilomotor muscles
can raise ("fluff") or lower hairs or feathers
(human "goose bumps" are a vestige of
this) Postural changes - body shape or
orientation affects heat exchange via radiation,
conduction, convection
39
Insulation and Conductance
Fig. 17-25
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
40
Endothermic Homeotherm - most birds and mammals
some insects some large fishes (tuna, sharks)
brooding pythonsa few plants (example later in
this lecture )
41
Ectothermic Poikilotherm - most marine
invertebrates arthropods amphibiansfishes
"reptiles" (not a good name, with respect to
phylogenetic relationships, e.g., birds are
"reptiles" in the old sense of the term)
42
Inertial Homeotherm - relatively constant
Tb because of large body size e.g., some
dinosaurs? Trivial Homeotherm - constant Tb
because of constant environmental
temperature e.g., animals in the deep sea, by
hydrothermal vents, pupfish living in thermal
hot springs Heterotherm - homeotherm whose body
temperature varies somewhat, either over time or
regionally (regional heterothermy)
43
Regional Heterothermy
Fig. 17-24
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
44
Regional Heterothermy
Fig. 17-24
Randall, D., W. Burggren, and K. French. 2002.
Eckert animal physiology mechanisms and
adaptations. 5th ed. W. H. Freeman and Co., New
York.
45
Stopped here 18 Jan. 2007
Many lizards maintain high and stable body
temperatures (35-40 C) when active. Many birds
and mammals, especially small ones, undergo
regulated hypothermia and hypometabolism Daily
torpor in hummingbirds Seasonal hibernation in
small mammals and the Poorwill, discovered by
Dr. Edmund C. Jaeger in 1946 in the Chuckawalla
Mountains Seasonal estivation in response to
heat and/or lack of water, e.g.,
round-tailed ground squirrel in Mojave desert