Download Examples of Allometry Metabolic Rate

Distributions, physiological ecology,
and allometry
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Individual species distributions
Ecological implications of body size
Body size patterns
Allometry and allometric patterns
Allometry of metabolic rate
Metabolic Rate
O2
Examples of Allometry
• Physiological
metabolic rate
brain size
heartbeat
Ecological
mammal litter size
lifespan
bird clutch mass
Populations
density
-0.30
0.25
0.75
-0.98
Metabolic rate – comparisons across animals of
different body sizes
log O2
mass
b
0.75
0.73
-0.25
log mass
• Metabolic rate ! a*(mass)0.75
Note: both axes
are on log scale
Mass specific metabolic rate
Mass specific metabolic rate – comparisons
across animals of different body sizes
• To get mass specific metabolic rate (e.g. how
much it costs to run each gram of tissue), divide
by mass:
Met rate/mass ! a*(mass)0.75/mass ! (mass)-0.25
log O2
/mass
log O2
log mass
log mass
Note: y-axis is not log-transformed, so relationship is not linear in this graph
Mass specific metabolic rate
Implications of b = 0.75 for whole organism
and b = -0.25 for mass specific MR:
1. Diet: tiny organisms need energy rich
fuel!
Mass specific metabolic rate
Implications of b = 0.75 for whole organism and
b = -0.25 for mass specific MR:
2. Bigger things can last longer! fat stored ! mass1
Endurance time ! mass/metabolic rate
! mass1/mass0.75 = m0.25
log mass
/log O2
log mass
Behavioral and Evolutionary
Ecology
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What is behavioral/evolutionary ecology?
Optimality models
Example with clutch size in birds
Optimal foraging
Do animals gamble?
Behavioral and Evolutionary
Ecology
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1. Variation in a trait
2. Heritability of trait
3. Fitness consequences
" The resulting genotypic and phenotypic
changes
Behavioral and Evolutionary
Ecology
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Focus is on adaptations
Ideally we would like to study the entire
process of natural selection
1. Variation in a trait
2. Heritability of trait
3. Fitness consequences
" The resulting genotypic and phenotypic
changes
Focus is on adaptations
Ideally we would like to study the entire
process of natural selection
Behavioral and Evolutionary
Ecology
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Often this is not possible to study the
entire process of natural selection
because:
1.
2.
3.
Behavioral and Evolutionary
Ecology
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An alternative is to focus on phenotypic
selection (i.e. the fitness consequences
of variation in a trait)
Behavioral and Evolutionary
Ecology
These questions have at least two answers
or two levels of analysis:
• Example: Why do birds sing in spring?
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1. Functional / Ultimate level:
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2. Proximate level (e.g. how):
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This is the Optimality Approach
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Optimality Approach: Example with
clutch size in birds
Optimality Approach: Example with
clutch size in birds
• Model (theoretical) approach
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– Models are “cartoons” of the world
– Try to simplify thing by looking at a few key
factors (parameters)
– Graphs, math, paragraph of ideas
– Allows us to seek generalities
– Must clarify assumptions!
Clutch size optimality model (Lack – 1950’s)
Pattern: robins lay 4 eggs per nest
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Why 4? Why not more or less?
Prediction: 4 is maximum number of chicks that parents
can adequately feed
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Kids = fitness
Limit to how much food parents can provide
Want lots of kids, but want quality kids too
Optimality Approach: Example with
clutch size in birds
Optimality Approach: Example with
clutch size in birds
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• Clutch size optimality model
Clutch size optimality model
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Currency = kids that survive to next year
Constraint = rate at which parents can feed
Decision variable = how many eggs to lay
Want to optimize # eggs given food availability
" Parents want to optimize # eggs given food
availability
The theoretical model
# Chicks
surviving
to next
year
2
Optimality Approach: Example with
clutch size in birds
• Clutch size optimality model
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Next step: test the model – How?
Go to nests and add or subtract eggs, measure how
many chicks survive
# Chicks
surviving
to next
year
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4
# Eggs laid
4
# Eggs laid
5
6
Optimal foraging
• Foraging can be crucial to an organism’s fitness
• Organisms must make critical decisions while
foraging
• Example: central place forager such as a mother
bird feeding her chicks
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Possible results
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3
5
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Food patch
Nest
Food patch
Optimal foraging
• Example: mother bird feeding her chicks
– Currency: max rate of food return to nest
– Decision: How long to stay in a patch
– Constraints: Rate of forage in a patch diminishes with
time
In Travel
Optimal foraging
• Predictions of Optimal Foraging Model:
– Comparing near vs. far patches
– Assuming that each patch has same amount of food
Patch A: Near
Patch B: Far
# Worms
In Travel
In Patch
Time Spent
Test of the optimal foraging model
• Prediction: For a given quality of patch, birds
should
• Study done on European starlings (Kacelnick)
In Patch
Time Spent
Test of the optimal foraging model
• Prediction: For a given patch, birds should
• Experimental Design of study on starlings:
– Treehole nesters (can use bird boxes)
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Distance A
Nest
Distance C
Distance B
Do animals gamble?
Test of the optimal foraging model
• Results:
• Risk sensitive foraging: when a foraging animal
is sensitive to the variability in the food reward,
not just the average of the reward
• The “risk” here refers to the chance of the animal
receiving a low foraging payoff (not risk of being
preyed upon)
Do animals gamble?
Do animals gamble?
• Experiment to test whether or not animals have
risk-sensitive foraging:
– Currency = consistency of food intake
– Treatments: hold mean intake rate the same, but vary
constancy
Constant
average
=
Risky
average
=
Constant Tray
CAGE
Risky Tray
• Results:
“Risk-prone”
“Risk-adverse”
% Time
visiting
risky tray
High
Low
Food intake rate prior to
experiment