Transcript Kaz Uyehara.

Scaling and Animal Abundance
Isn’t ecology the study of the
factors that affect the abundance
of animals?
Scaling and ecology vs. scaling
and individuals
 The individual implications of scaling can take on a
different form.
 Excretion, ingestion, growth, and reproduction are
physiological processes that scale to body size.
 When applied to a population of animals they can
become nutrient regeneration, prey mortality, and
production.
Community structure
 Sheldon, Prakash, and Sutcliffe (1972) found that when marine
communities are divided into logarithmic size classes, the
amount of matter in each class is approx. constant. (Remember
that if metabolism and abundance have relationships with (body
size)^(3/4) and (body size)^(-3/4) this is true)
 Bacteria biomass = whale biomass
 Biomass =7,200(individual body mass)^(-1)
 Number individuals = 7,200(individual body mass)^(-2)
 Number of species = 230 (individual body mass)^(-1)
 But all of the numbers kind of sketchy
My image sucks!
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Other studies
 Schwunghamer (1981) tested model to marine benthic
communities. There were 3 biomass peaks, which correspond to
bacteria, meiofauna, and macrofauna.
 This makes sense and is predictable. But there was not constant
biomass across all logarithmicly increasing size classes.
 Schwinghamer suggested that a given environment would favor
some parts of the spectrum, but that there would still be no trend
in overall logarithmic size classes.
 Janzen and Schoener (1968) found nearly constant biomass
across insect communities divided into logarithmic length
classes.
 Side note: may be evidence that connects the size of organisms
to resource availability (limited resources = more small
organisms)
 Overall = sketchy
 Need more research
Mean density
 Not well studied
 Mohr (1947) found that per unit area, the number of animals in a
species (all North American mammal) is inversely proportional to
their body mass. So biomass per unit area is constant
 Damuth (1981) suggests that global herbivore density decreases
as W^(-.75)
 A few other studies show a similar decrease in density with size.
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Differences among organisms
 Temperate mammals maintain higher population
densities than tropical species
 Herbivores have higher density than carnivores
 Non-mammalian species show significantly different
relationships
 But all data could be described by a curve of slope -1,
is this very general relationship better than more
specific ones from smaller data sets?
 Note: People still unsure of what the slope should
be…
Home range
 We can test the population density numbers by
comparing them with data for home ranges.
 If the population densities are good, home range (how
much area an organisms wanders around) should be
close to the inverse of population density.
 Area used by animals ~ area/animals (individual area
used by animal)
 Empirical evidence supports population density
numbers (but not perfect of course)
Energy flux
 (Population density) x (individual energy use) = rate at which
population consumes energy from the environment
 NP = R
 Who claims more of the ecosystem production?
Depends on stability of environment
 In stable ecosystems, Sprules and Munawar (1986) found in
more ‘stable’ ecosystems, smaller organisms consumed more of
the ecosystem energy.
 But in more ‘unstable’ ecosystems larger organisms used more of
the energy.
 Stable = self-sustainable, ocean or large, oligotrophic ( not many
plants = good for animals because decomposition uses oxygen)
 Unstable = shallow lakes/coastal zone, eutrophic (opposite of
oligotrophic), subject to major discharges of
nutrients/contaminents
More studies
 Biddanda et al. (2001) had similar results. In the most stable
aquatic ecosystems, bacteria control 91-98% of energy. In
highly eutrophic water, bacteria respiration only accounts for 9%.
 Li (2002) found that the ratio between population densities of the
smallest phytoplankton and the largest grew with ecosystem
stability. In most stable ecosystem, the exponent B of the power
law ~ -4/3. In unstable, B ~ -1/3.
 Damuth (1993) got results for terrestial animals and found that
closed ecosystems had more negative B values than open
systems (-.88 +/- .31 vs. -.50 +/- .40)
Which means…
 If R is dependent on body mass, ecosystems dominated by
smaller organisms will be more stable
 If energy flux is constant, a lot of small organisms are more
stable than a few big ones
 Example: Better to have your money in many investments than
one
What about plants?
 Plants like trees can be huge because most of their mass (wood)
is not metabolically active. Their leaves/needles take care of the
metabolism.
 If we judge plants by their number of leaves… Whittaker (1975)
found that conifers (needles) dominate boreal forests, rather than
grasses and deciduous trees.
Allometric Simulation Models
 We can use computers to ‘make’ an ecosystem that runs on
allometric models!
 These help us predict qualitative transfers of mass through time
by using a few allometric equations
 Ii = 0.0059Wi^-.25
Gi = 0.0018Wi^-.25
 Ri = 0.0018Wi^-.25 Di = 0.0023Wi^-.25
 Those are ingestion, production, respiration, and defecation
 Note: for poikilotherms
Allometric? -->
A simple model
 There are five different groups of
organisms of mass W (.1, 1, 10, 100,
and 1000 g.)
 Each group starts with some biomass B
 There is this mystical food pool from which all of the organisms
get their energy. This is related to their ingestion, I
 They give back to the mystical pool in relation to the mortality, M
 They maintain their population in relation to their production, G
 All of the energy ‘lost’ in the form of defecation and respiration
goes to a magical pool of detritus, which then gives back to the
food pool such that there is no energy loss in the system.
Things to keep in mind
 The energy flow is whack-tastic
 There are no primary producers
 So the system would just die down because of
respiration and defecation
 To compensate the detritus pool puts back into the
food pool, so it basically represents poop, plants,
and all the animals not shown in the model.
On food
 The trophic relations are interesting
 Ingestion is determined by size and biomass, this
food is drawn from ALL classes through a function
for mortality in relation to the class’ abundance
 Mi = [(Bi^F)/∑(Bi^F)] ∑Ii
Where F is arbitrary constant
 So the amount of total food a population demands is taken from
everybody else’s death. The more of you there are, the more die.
 Total ingestion therefore = Total mortality
 So all organisms eat the same food…so there are no trophic
levels in relation to body size. This model implies that dietary
differences within and between the sizes is not too important
 Other models try to have trophic levels so that larger animals
always eat the next smallest class.
What does the model say?
 Firstly, let’s look back at the equation: Mi = [(Bi^F)/∑(Bi^F)] ∑Ii
 Remember F? Well when F=1, mortality loss is directly
proportional to abundance. But since small things are more sexhungry, they will rapidly dominate the system.
 We need a way to give small populations more protection from
predators and have large populations contribute a lot to the food
pool.
 When F > 1, all of the size classes persist. Larger values of F
leads to larger representation by big animals. But small sizes
always dominate.
F!
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QuickTime™ and a
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A, B, C are F = 1, 2, and 3
What the F more can it do?
 As F goes up:
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Total biomass goes up
Diversity goes up
Average body size goes up
Top line is biomass
Middle line is size diversity
Bottom line is average size
QuickTime™ and a
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So how does the model compare?
 Well it qualitatively agrees with observed trends in succession for
everything that the model can predict (but not necessarily a good
test… this is still unreliable)
 Biomass, individual size, and size class diversity increase over
time
 Bigger organisms are more
resistant to dramatic changes
in the environment
QuickTime™ and a
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Cope’s Law
 Larger soecies tend to appear later in a group’s phylogeny
 That means, large animals usually started out as small animals
 Exceptions are for some birds and amphibians, which are now smaller,
and also really big animals which are now extinct
 Some theorize that this is because large body size is a desirable trait
that is selected over evolutionary time (more control over environmental
effects so less likely to be eaten, dessicated (no water), die from
temperature, and starve)
 Plus big animals are more mobile, better vision, higher fecundity for
poikilotherms (more offspring for animals that don’t control body
temp),larger offspring, increased capacity to learn, and more
specialization
Explanations of Cope’s Law
 But for all of the advantages, many people cite complementary
disadvantages and debate whether larger animals really do have it
better off (more parasites, predators have fewer prey, may not really be
more specialized).
 So let’s just say being small is just as good as being big.
 Stanley (1973) rephrased Cope’s law to ask why many evolutionary lines
started off as small species. He found that over evolutionary time,
maximum size does increase within taxa. But the medium and minimum
sizes are not affected.
 This suggests that being big really isn’t better
 So the real question may be, why did so few species become big
 The easy answer is that most potential ancestors were small. This is
because perhaps being big is a very specialized trait, and they are so
specialized that they are poor potential ancestors and there aren’t many
big things to begin with.
Small Species and Big Species
 Small species are more likely to produce new lines because:
 There are more of them
 They have smaller geographic ranges and less mobility, so it
is easier to be isolated geographically
 Small species produce more offspring, so their will be more
heterogeneity
 They have higher absolute mortality (more selection)
 Large species evolve more slowly because:
 Lower rates of speciation
 High rates of extinction
 Longer generation times, low population numbers,
specialized habitat
 Of course, people disagree! Maybe the evolutionary rates are the
same, but big species have higher extinction rates because of
fewer niches
How useful are these relationships?
 Well…how often do people study two organisms that are in different
logarithmic size groups?
 The relationships break down when comparing things of similar size
(maybe because large size differences dominate over more specific
traits governing abundance)
 There are too many factors! Body size scaling would be sweet.
 A whole paper talked about how our methods for determining population
were poor because of how we determine our census area.
 Read Brown et al. (2004)…next week. Lots of people have problem with
his work and the abundance - body size relationship being legit or try to
show that there is no strong mechanism (energy).
So like normal…
Size and abundance relationships could
be interesting
Too bad we don’t have great data
Too bad we don’t have a reliable
mechanism
Too bad there are conflicting views and
numbers