Lecture 2: Individual-based Modelling Part I Steve Railsback Humboldt State University Department of Mathematics & Lang, Railsback & Associates Arcata, California USA www.langrailsback.com 1
Outline 1. What are IBMs? Why use them? 2. Some example IBMs 3. A conceptual framework for IBMs 4. IBMs and field ecology: How to use pattern-oriented modeling to design and learn from an IBM 5. Software for IBMs 6. Conclusions 2 I. What are IBMs? Why use them? The source... 3
What is an IBM? A model of a system (population, community ) in which system dynamics emerge from how individuals interact with each other and their environment Individuals are not always organisms social groups or families superindividuals representing many organisms grid cells, etc. 4 Why are individuals important? (1) They vary: Size Reproductive status Location (food, risks...)... Young-of-year rainbow trout, October 5
Why are individuals important? (2) Adaptive behavior--- individual decisions that depend on individual s state and local environment affect fitness and ultimately the population 6 Why are individuals important? (3) Because they don t vary in key ways Physiology Behavior (fitness) We can build useful, general models of individuals 7
The promise of IBMs: Simple, general models of individuals physiology interaction adaptive behavior in a virtual environment can reproduce many kinds of system complexities 8 What are real IBMs? Individuals are represented explicitly Individuals vary (location, size, sex, energy ) Interactions of individuals with each other and their environment are represented Life cycles are represented fully Individuals have adaptive behavior
Why do we use IBMs? To address problems where individual variability and adaptive behavior are important Prominent examples: Effects of habitat alteration Trophic interactions mediated by behavior Why do we use IBMs? To avoid the complexity-uncertainty trap of system-level models Useful information is more abundant, easier to obtain at the individual level Complex system dynamics can emerge from simple models of individuals
Why do we use IBMs? Conceptual clarity vs What problems limit use of IBMs?
What problems limit use of IBMs? Lack of a conceptual framework and theory ad hoc assumptions Software: cost reliability observability Analysis and Communication Solutions Theory: Models of what individuals do that have been shown to explain system dynamics of interest Standardized concepts for designing, describing models Software tools and techniques
II. Some example IBMs A simple model of a theoretical problem A (relatively) simple management model: Effects of river flow fluctuations on juvenile fish A complex management model: River management effects on trout populations 16 A simple theoretical IBM DeAngelis et al. 1980. Cannibalism and size dispersal in young-of-the-year largemouth bass: experiment and model. Ecological Modelling 8:133-148. How does the final size distribution of a population depend on the initial size distribution, when the individuals eat each other? 17
Example 1: A simple theoretical IBM 3 phases: SD < 5, SD <= 6, SD > 6 18 Example 2: A simple management IBM Effects of river flow fluctuations on juvenile pikeminnow 19
Effects of flow fluctuations on juvenile pikeminnow in backwaters Daily flow cycles affect backwater size, temperature, food availability How do cycles affect pikeminnow growth & survival? In high densities of exotic fish that compete with and eat pikeminnow? Green River, Utah 20 Example: Effects of flow fluctuations on juvenile Colorado pikeminnow in backwaters 21
Example: Effects of flow fluctuations on juvenile Colorado pikeminnow in backwaters Tentative conclusions: Effects were highly dependent on backwater size, shape Flow fluctuations reduced fish growth by reducing food availability Effects were stronger on red shiners, reducing their predation on pikeminnow But overall effects on pikeminnow were usually negative 22 Example 3: instream An IBM for management of trout streams Objective: Predict the effects on trout populations of changes in Flow, temperature, turbidity regimes Channel shape & complexity Biological conditions (e.g., introduced species, hatchery fish) 23
instream: Description Habitat: Habitat cells: several m 2 Depth, velocity = f(flow) Cover for drift feeding Hiding cover Food availability Daily inputs: flow, temperature, turbidity 24 instream: Description Trout: Feeding & growth Growth = f(velocity, temperature, turbidity, fish size, competition from bigger trout) Mortality Terrestrial predators Fish predators Starvation... 25
instream: Description Trout: Feeding, bioenergetics, growth Mortality Behavior == habitat selection Which cell offers the best tradeoff between growth and risk? Fish move each day to the best available cell 26 instream: Demo 27
Example instream application: Effects of channel restoration on juvenile trout survival and growth Does channel restoration benefit survival and growth? How? How much? Why? (very difficult to evaluate via field studies!) Clear Creek Restoration 3406(b)(12), M. Brown & J. De Staso 28 Example application: Effects of channel restoration on fry incubation Scenarios: Growth & survival of 1000 new trout From birth (1 May) to 31 October Reach: 160 m long, ~10-20 m wide 29
Two channel types Unrestored channel: incised, uniform Restored channel: meandering riffle-pool sequence 30 Two channel types Cells shaded by velocity: lighter = faster 31
Example application: Flows (reservoir releases) 32 Results High mortality in high spring flows Less mortality in restored channel 33
Results High mortality in high spring flows Less mortality in restored channel Higher growth in restored channel rapid growth when populations are low High fall flows are OK 34 What if we also added lots of cover? Clear Creek Restoration 3406(b)(12), M. Brown & J. De Staso 35
What if we also added lots of cover? Survival is much higher (less effect of high spring flow) No effect on growth 36 Conclusions from example IBMs IBMs are useful for hypothetical questions that require consideration of individuals IBMs are especially suited for real ecological management questions because they can address: Effects of environment Interactions among individuals But---these IBMs must include: A virtual environment Physiology Behavior 37
III. A Conceptual Framework for IBMs How do we live without differential equations? Leibnitz 38 Conceptual Framework Useful terms and ideas for describing and designing IBMs: Emergence Adaption Fitness Prediction Interaction Sensing Stochasticity Collectives Scheduling Observation
Concept Origins (1) Emergence Which model outcomes emerge from the adaptive behavior of individuals? (vs. being imposed by model rules?)
Emergence example: Upstream migration by adult salmon
Emergence Model: Turn randomly at each junction If you sense water from your natal stream, swim upstream Else swim downstream Emergence IBMs with few or no emergent outcomes tend to be uninteresting and less useful You don t get out more than you put in More emergence = more complexity of the model of the modeling process
Emergence: Key Issues Which model outcomes need to emerge from individual traits? How do you design adaptive traits of individuals so that useful, realistic system behavior emerges? (2) Adaptive Traits and Behavior What decisions do model individuals make? In response to what internal and environmental conditions? How are these decisions modeled?
Ways of Modeling Adaptive Behavior Rule-based and stochastic methods that reproduce observed behaviors IF age = 3 and sex = male then p (mating) = 0.85 Fitness-seeking methods: Choose the behavior that maximizes some measure of fitness Survival Growth Reproductive output Adaptive Traits and Behavior: Key Research Issues What population phenomena emerge from what individual behaviors? What are useful fitness measures: estimates of future fitness that individuals use to make decisions What predictive abilities do individuals have, and how should we model them?
(3) Interaction A key characteristic of IBMs: interactions are local, not global How do we model how individuals interact with each other? Direct Interaction Explicit predation events (fish cannibalism example) Dominance contests
Mediated Interaction Interaction is indirect and mediated by a resource that individuals produce or consume Competition for food, habitat Interaction Fields Individuals are affected by the combined effect of several neighbors SORTIE; Deutschman et al.
(4) Sensing What information are model individuals assumed to know? How do we model how individuals obtain information? Sensing: Key Questions What kind of information is it important and realistic to assume model individuals to know? about themselves about their environment Is it important to model the sensing process? For each variable that individuals know about their environment: Over what distance? With what accuracy?
(5) Collectives Many IBMs represent aggregations of individuals that: strongly affect behavior and fate of individuals have their own behaviors Examples: Social and family groups (packs of wolves ) Flocks, schools, herds Key Questions for Collectives Are collectives important? Do individuals form groups that: have their own behaviors, and affect the fitness of individuals? How to model collectives? As characteristics of the individuals As explicit entities with their own behaviors, intermediate between individual and population
(6) Observation How we observe a system affects what we believe about it IBMs produce many kinds of results We must determine what we need to observe and how To analyze and understand results To provide testability and believability Observation: What Can We Learn from This:
vs. This: (7) Scheduling What actions are in a model? In what order are the actions executed?
What is an Action? A list of model entities (objects) One or more methods (behaviors, subroutines) the entities execute The order in which the entities are processed All trees execute growth in random order All animals execute habitat selection in order of decreasing size An IBM s Schedule is a Hierarchy of Actions (and an outline of the whole model) Habitat patches: Calculate food production Update mortality risks Animals: Select habitat, in size order Feed and grow, in size order Experience mortality: predation starvation extreme weather Observer: File output Graphical output
Scheduling Issues How to represent time: Discrete time steps (how big?) Continuous time with discrete events In what order are actions executed? Do individuals act in random order or in a specific sequence (hierarchy)? IBM Design Concepts: Summary These concepts are a way to: Think about Describe Design Standardize models such as IBMs that are not well described by standard mathematics Emergence Adaptation Fitness Prediction Interaction Sensing Stochasticity Collectives Scheduling Observation