Qualitative Reasoning about Population and Community Ecology

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Qualitative Reasoning about Population and
Community Ecology

• Evgeniya Khusnitdinova

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• The presentation is based on an article by
• Paulo Salles and Bert Bredeweg, published in
• AI Magazine, Winter 2003.

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Why use qualitative representation for ecology?

• Ecological modeling mathematical model building
• Math models require numeric data of good quality
• But ecological data are often difficult to obtain
  (long term observation, experimentation with real
  systems)

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Why use qualitative representation for ecology?

• So ecological knowledge includes both
  quantitative and qualitative aspects
• Its imprecise, incomplete, qualitative and fuzzy
• So qualitative modeling is used to represent
  these knowledges

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Why use qualitative representation for ecology?

• Qualitative representation
• Captures commonsense knowledge about ecological
  systems and uses it to derive conclusions without
  any numeric data
• Enables reusability by constructung libraries of
  partial-behavior descriptions
• Qualitative models provide causal explanations of
  system behavior

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A Qualitative Approach to Population Dynamics

• GARP (General Architecture for Reasoning about
  Physics)
• A reasoning engine
• Compositional modelling approach
• Three main constructs
• - Scenarios
• - Model Fragments
• - Transition Rules

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Basic Architecture of the Qualitative Reasoning
Engine
Scenarios
Qualitative Reasoning Engine

• Initial Values

Behavior Graph
Assumptions
Transition Rules
Library of Model Fragments
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Basic Processes

• Compositional modeling gt constructing model
  fragments that represent elementary behavioral
  units
• General Growth Equation
• Nof(t1)Nof(t) (B Im) - (D E)
• Nof number of individuals
• B birth rate
• D death rate
• Im immigration rate
• E emigration rate

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Causal Dependencies

• Positive and Negative direct influences
• (I, I-)
• Indirect influences (proportionality)
• (P, P-)

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Causal Dependencies Capturing Natality as a Basic
Process

Upper Limit?
Upper Limit?
I
Born
Number_of (or size)
Intermediate Landmark(s)?
P
0
0
Q-space
Q-space
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Four Basic Processes

• Natality
• I(Nof, B) P(B, Nof)
• Mortality
• I-(Nof, D) P(D, Nof)
• Immigration
• I(Nof, Im)
• Emigration
• I-(Nof, E) P(E, Nof)

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Quantity Spaces

• Q-spaces in GARP consist of an ordered set of
  alternating points and intervals
• Quantity values are represented as
  magnitude-derivative pairs ltmag, dergt
• Usually Nof QS zero, normal, maximum
• For B, D, Im, E QS zero, plus
• For derivatives QS -, 0,

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Landmarks

• Difficult to determine meaningful q-values for
  the magnitudes of quantities in qualitative
  models about population
• Unlike in physics, in ecological systems there
  are not many obvious landmarks that characterize
  qualitative distinct behavior
• Idea of minimum required variation
• max for a limit to the population growth
• zero for extinct or not existing population
• normal for the size between extreme points

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Capturing Additional Knowledge

• Distinction between situations in which
  population exists (Nof gt zero) and doesnt exist
  (Nof zero) gt
• Processes Natality, Mortality, Emigration are
  active, when the model fragment existing
  population is active and do not become active
  if the fragment nonexisting population is
  active.

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Capturing Additional Knowledge

• Immigration
• existing population gt immigration process
• nonexisting population gt colonization
  process

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Growth Process

• Inflow B Im
• Outflow D E
• Growth Inflow Outflow
• Model fragment population growth
• I(Nof, Growth) P(Growth, Nof)
• QS minus, zero, plus

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Migratory Movements

• closed population (ImEzero, dImdE0)
• gt model fragment assume closed-population
• Otherwise open population

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Simulation Single-Population Behavior

• Initial scenario
• - objects biological entity and population
• - quantities Nof, B, D, Im, E, Inflow, Outflow
  and Growth with no values assigned to them
• - B D
• Simulator produces eight initial states
• ltzero,0gt ltzero,gt ltnormal,-gt ltnormal,0gt
  ltnormal,gt ltmax,-gt ltmax,0gt ltmax,gt
• Further, it generates all possible transitions
  between states

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Simulation of a Populations Behavior, with
Undefined Initial Values
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Qualitative Models of Interactions between Two
Populations

• Effect of interaction -, 0,
• The change of the population is designed ()
  when it changes in opposite (same) direction
  compared to changes in the other population
• Population is designed 0 if it is not influenced
• Example (A, B) is classified as (,-)

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Base Model for Interacting Populations

• Neutralism (0, 0) no interaction, cross-product
  of all possible behaviors of each population
• Comensalism (0, )
• Predation (, -)
• Symbiosis (, )
• Competition (-, -)

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Base Model for Interactions between Two
Populations
(We assume that both populations are
closed-populations)
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Defining Interaction Types

• Define the Effect quantities that represent the
  interaction (ex., predation, effect of the
  predator on the prey is consumption and of the
  prey on the predator is supply)
• Establish causal links between Nof, Effect, B and
  D for both population
• Define other assumptions between Nof, Effect, B
  and D
• Represent condition for nonexisting populations
  (ex., predator population cannot survive when the
  prey population goes extinct)

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Example Simulation Predation

• Predation model (, -)
• Im E
• Supply influences both Natality and Mortality
• Consumption influences only Mortality of the prey
• Predator population cannot become bigger than the
  prey population

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Causal Model for Predation
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Simulation with the Predation Model
(Starting from Nof ltnormal, ?gt for both
populations)

• Balanced coexistence 2
• Population to a maximum 1-(11)-10
• Population to extinction 4-(5)-6
• Predator to extinction 3-(9/7)-8

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Application Brazilian Cerrado Vegetation

• This vegetation consists of many different
  physiognomies, from open grassland to rather
  closed forests
• Composition determined by fire, soil fertility
  and water availability
• Ex., fire frequency increases gt woody components
  decrease gt vegetation becomes less dense
• Cerrado succession hypotheses (CSH)

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Cerrado Community Types

• Cerrado communities consist of three
  populations tree (T), shrub (S), grass (G)
• Different proportions of them characterize
  different types of cerrado communities
• For Nof QS zero, low, medium, high, max
• Campo Limpo no trees, no shrubs, only grass
• Cerradao dense forest, no grass, only tree and
  shrub populations

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Causal Model of the Cerrado Succession Hypotheses
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Simulation the Cerrado Succession Hypothesis
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The End