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Individual-based Model (IBMs) in Ecology

• Occasionally used since 1960s
• Established and widely used since ca. 1990
• I like IBMs - no I like the idea of IBMs
• Have been made possible by increase in computer
  power
• Are also in other disciplines (agent-based),
  e.g. economy, sociology, engineering, ...
  (complex adaptive systems)

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Exponential increase of number of papers using
IBMs (see grimm99.pdf on Q\tmp\IBM\volker)
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Types of Models
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• Limitations of top-down models (TM)
• Ecological systems ARE complex, because they
  consist of many different components. TMs ignore
  this complexity, based on the argument models
  have to be simple to gain understanding.
• TMs transfer the idea of theory from physics to
  ecology. But classical physics doesnt deal with
  complex (adaptive) systems.

• TMs ignore that individuals
• are different
• usually interact locally (in particular sessiles)
• have a life cycle
• change themselves and their environment
• exist only for a short time
• release more (potential) offspring than necessary
  to replace themselves (natural selection)
• follow a program fittness-seeking
• show adaptive behavior, i.e. behavior which
  apapts to the current environmental conditions.
• By themselves use models to decide what to do

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Individual-based Models

• Describe individuals as discrete units, which are
  characterized by a set of variables (e.g., age,
  weight, energy reserves, social rank, sex,
  location, identity)
• Take into account the life cycle of individuals
  (growth, development)
• Take into account resources and their dynamics
• Are most often spatially explicit (most often
  grid-based)
• Have to be implemented as computer programs
• Are most often stochastic, i.e. include random
  processes and probabilities
• Often include probabilistic if-then rules

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• Disadvantages of IBMs
• Many parameters, many individuals, heterogeneous
  environment IBMs are complex
• Complex models are harder to develop, understand,
  test and communicate
• Are most often tailored to specific species and
  therefore much less general than minimal models
• Are not acknowledged by the theory establishment
  (math for president!)

All these problems are real and severe - they
have been underestimated by the pioneers of the
IBM approach But there is a (relatively) new
scientific discipline (complex adaptive
systems) with the credo it must be possible to
develop a general theory of complex systems
(stock markets, ant societies, neocortex, social
groups, ecological systems, immun system...) In
all these systems there are emergent
properties, which do not exist at the level of
the parts (the agents) of the system. More
about this in Ze Book (Grimm and Railsback 2005)
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August 2002 there was a IBM course in Denmark.
The powerpoint presentation and course material
is available at
http//www.zi.ku.dk/ibpm-net/norfa/ http//www.zi.
ku.dk/ibpm-net/norfa/S-Drive/Teachersppt/
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Example The Alpine Marmot (PVA)

• Social behaviour
• Overwintering in groups
• alpha-couple
• Metapopulation
• of territories
• of clusters of territories
• Model
• individual-based
• spatially explicit

Dorndorf 1999 Grimm et al. 2003 www.oesa.ufz.de/vo
lker
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Problem How does viability depend on
environmental variation (winter length),
population size and social behavior? Related
species solitary species live in lowlands,
group-living in the mountains Model
individual Juvenil/Yearling/Subordinate/Territori
al, Alpha, Floater, Age, Sex, Territory Yearly
time steps, 100 years or more, spatial scale
several km
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Spatial distribution of territories
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/ Reproduction With probability fecund a
female produces 1-6 babies. The number of babies
is normally distributed.
/ TerritoriumReproduction() int
reproduced 0 / Check, if there was a
change in the male alpha position / if
((m_AlphaMale m_OldAlpha) (m_AlphaMale gt 0)
(m_AlphaFemale gt 0)(ran1(ZufallInit) lt
gl_fecund)) / clutch size from normal
distribution / int litter
round(normal(gl_litter_mean, gl_litter_std)) i
f (litter lt 1) litter 1 if
(litter gt 6) litter 6
reproduced 1 / Determine mean
weaning weight / int gewicht
gl_weaning_mean - 35.238litter int
gewicht_std gl_weaning_std int sex 0
for (int i 0 i lt litter i) //
Determine sex // if (ran1(ZufallInit) lt
gl_sex_ratio) sex MALE else sex
FEMALE Ind00 Newborn(sex, 0, m_ID, 0,
m_AlphaFemale, m_AlphaMale) int temp
round(normal(gewicht, gewicht_std))
Newborn.Set_Weaning(temp) if
(Newborn.Get_Sex()1) Set_Male(Newborn) else
Set_Female(Newborn) //
Newborn.PrintOut()
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Results Validation
Group-size distribution
Time series
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Mean time to extinction vs. Number of territories
Result resemble theoretical curves for the case
of very weak environmental noise, but
environmental variations (winter length) are in
fact very strong. Why dont we see an effect of
environmental variation?
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Idea social living helps marmot to buffer the
harshness and the variability of the winter
(which allows them to liver higher in the
mountains than solitary species) How does social
behavior affect model individuals? For
territorials, winter mortality - interpreted as
the probability of dying in a certain winter -
is (1) P ter 1 exp(6.82 - 0.286 A - 0.028
WS 0.395 SUBY)-1 where A is the age, WS
winter strength, and SUBY the number of
subdominants (including yearlings) present in a
group. Eqn. (1) states that the winter mortality
of dominants increases with the severity of
overwintering conditions and with age, but
decreases with the number of subdominants and
yearlings. Now, let us manipulate this positive
effect of the subdominants in a group (there is
a similar effect for juveniles)
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Social behaviour buffers environmental noise
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Summary Marmots

• Social behavior buffers effect of environmental
  variation and is therefore decisive for viability
  of the population.
• To simple (minimal) models (for example
  age-dependent mortalities) would not capture this
  effect!
• To simple models can be dangerous for PVA because
  they might suggest that enlarging the habitat
  would not pay, although in reality this might be
  the case.

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Summary IBMs

• Have the potential, to advance both basic and
  applied ecology.
• Problems with complexity exist, but it is
  possible to cope with them
• Research program formulate (alternative) simple
  models about the traits of adaptive behavior and
  test in IBMs of these models are capable of
  reproducing system-level patterns of the real
  system (pattern-oriented modeling).