Scaling and Animal Abundance

1
Scaling and Animal Abundance

• Isnt ecology the study of the factors that
  affect the abundance of animals?

2
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.

3
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

4
My image sucks!
5
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

6
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.

7
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

8
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)

9
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?

10
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

11
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)

12
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

13
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.

14
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? --gt
15
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.

16
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.

17
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 (BiF)/?(BiF) ?Ii Where F is arbitrary
  constant
• So the amount of total food a population demands
  is taken from everybody elses death. The more
  of you there are, the more die.
• Total ingestion therefore Total mortality
• So all organisms eat the same foodso 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.

18
What does the model say?

• Firstly, lets look back at the equation Mi
  (BiF)/?(BiF) ?Ii
• Remember F? Well when F1, mortality loss is
  directly proportional to abundance. But since
  small things are more sex-hungry, 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 gt 1, all of the size classes persist.
  Larger values of F leads to larger representation
  by big animals. But small sizes always dominate.

19
F!

• A, B, C are F 1, 2, and 3

20
What the F more can it do?

• As F goes up
• 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

21
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

22
Copes Law

• Larger soecies tend to appear later in a groups
  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 dont control body
  temp),larger offspring, increased capacity to
  learn, and more specialization

23
Explanations of Copes 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 lets just say being small is just as good as
  being big.
• Stanley (1973) rephrased Copes 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 isnt 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 arent many big things to
  begin with.

24
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

25
How useful are these relationships?

• Wellhow 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).

26
So like normal

• Size and abundance relationships could be
  interesting
• Too bad we dont have great data
• Too bad we dont have a reliable mechanism
• Too bad there are conflicting views and numbers