Question 3: How do spatial simulation models incorporate and handle real world system uncertainty?
The models are representations of reality, reflecting what we think what are the most influencing and most important reality’s traits and what are their main interactions. Following different philosophical approaches, focused on models’ outcome explicitness, models can be divided into 2 types:
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deterministic
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stochastic.
In deterministic models, e. g. an idea of ‘clockwork universe’ is applied. Thus, the universe is predictable if all its parts and interactions are known and thus predictable (ideas developed after Isaac Newton’s discoveries of Laws of motion explaining behavior of both terrestrial objects and the solar system).
However, the majority of complex systems’ interactions are still not well described neither well understood. And they are not reacting in simple action-reaction law but these reactions can vary over time and space. In addition, there is an existence of emergent system properties, that system is not only the sum of all its particles. Equally, in living systems, the intensity of influencing factors may vary over time (influence of climatic conditions on mosquito population) or should be of different importance (plant growth rate on shiny versus shady conditions).
In this reason, the principle of stochasticity is actually added to models to make them more realistic and thus less predictable.
There is several ways how to include uncertainty and degree of randomness in the model, depending mostly on selected model. In general, the random variable is included.
For agents, their properties (variables) can follow a Gaussian distribution (to represent energy level …, Figure 1) or other types of distribution (Crunchy walk for seed dispersal, correlated random walk to enhance foraging success …). In principle, the entity have not only limited number of possible responses to changing environment (are not “deterministic” = the same expected output for every run) but react less independently on decisions of other agents and stable or changing environment. Equally, the amount of acting agents is included, where every agent follows only simple behavioral rules and the stochasticity is represented by interaction among agents and their environment or among agents themselves.
Figure 1: Entities energy following Gaussian distribution
In models evaluating during the Lab class, the stochasticity is presented in existing path dependence, where the subsequent decisions are influenced by preliminary made decisions and by fact that the agent is almost never able to use holistic approach to take its decision (preferring the highest utility value but from sub-setted amount of patches). The location of sub-setted patches is random, the amount is user defined.
In Fire model, the stochasticity is represented by configuration of the “trees (1 tree = 1 patch)”. In this reason, the threshold density value of 59% leads in ½ cases to reach the opposite site of the world. Below this value (<58%), the fire is not spreading over whole world, beyond the threshold value (>60%), the fire reach the opposite world site in every run.
Fire model reaching the opposite end of world (density threshold value 59%)
Fire model not reaching the opposite end of world (density threshold value 59%)
In segregation model, the stochasticity is handled by the availability of vacant patches in agents’ neighborhood, thus influencing the resulting segregation pattern. As a result, the spatially different pattern is produced every model’s run, however fulfilling the condition of neighbors favorite characteristics.
Different spatial output pattern or Segregation model for similar neighbor preference wanted: 50%)
Uncertainty in the model is also presented by several suns of model, including different outcome of running process. This provide us multiple results, nd thus we can identify with certain probability the final amount of variability in expected results.
Variation of emergent propeties of observed pattern. In Uncertainty region, the reached values of multiple runs are localised
Question 2:
Describe the difference between models of aggregation, mobility, and percolation. Provide an example for each.
Aggregation -
the rules governing cell state changes are expressed solely in terms of the sum of the state values of neighbouring cells.
The governing rules can be different: averaging, averaging with noise, majority rules.. Also, the definituion of neigborhood can be different as in Turing's reaction-diffusion model, explaining the apparence of animals' coat patterns by eliptic neighborhood and zones of inhibition and activation region. All the rules follow the basic principle of geography, thus that the "patches in close proximity are commonly more alike (...) than those which are further appart" (Fisher 1996) creating the patchy landscape pattern. One of the exemple of emerging patchy process from randomly distribuded pixels' states we can observe on Figure 1 by method of simle averaging values in advaning time step. each time step the state of the state is recallalated and replaced by the average number of the state of its neighbours.
Figure 1. Local aggregation (Right to left)
 3.1-local-average view_19.pngLocal averaging |
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Models of aggregation favour the local aggregation of similar things. Models elements change to become more like neighboring elements, but it can be also product of the segregation tendencies (favouring dissimilation of dissimilar entities). A simple process operating locally produces clustered aggregated outcome.
In competing contact process
Long-range-2? OFF – probalilities for death (δ) for 2 population are the same δ1 =δ2
Sustaible survival (undefinite coexistence of two states)
Figure 2. Competing contact process, long-range-2 OFF
If Long-range-2? ON – probalities for death (δ) for 2 population are the same δ1 =δ2. But the long-range prefer the survival of Population 2 (black)
Figure 3. Competing contact process, long-range-2 ON
Important the competition for space: even if the δ are low for both states (slightly different) => we expect the high survival rates , the populations don’t have to survive because of competition for space
Figure4. Competing contact processcompetition for space
Production of patchy landscape by rules of succestion and growth: Simple grass-bush-trees model. Bush leave place to trees (succestion growth), grass leave the place to trees and bushes . Following the plot, the system is sensitive to birth-rate-1 and birth-rate-2 – if it is slightly different (1.8 - 2) the success of grass – high proportion if tree birth-rate-2 is 1.8.
Model produces patchy landscape following the rules: if you are grass, nothing happens, but if you are bush/tree, you set particle into neighboring cells (neighbor4).
Figure 5. Patchy landscape surface created by succession rules (possibility to seed if cell is tree or shrub)
Individual mobile entities = agents movement
In individual mobile entities we observe the movement of agents, not only the changing state of neighboring cells. Individual movement can be defined by several rules influencing their :
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direction (turn angle)
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step lenght (the same/following distribution rules?)
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laziness (have to move or can stay on the same location? )
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dependence of previous step length and direction (correlation?)
Figure 6. Different types of random walk
 4.1-random-walks interface_simple.pngSimple RW, random direction (can come back), same step lenght |  4.1-random-walks interface_normally.pngNormal RW - step lenght is randomly selected from normal distribution, the most of the step lenght is about average value |  4.1-random-walks interface_lattice.pngRW on lattice - lenght step only by integer number |
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 4.1-random-walks interface_expon.pngexponential RW - randomly selected step length following power low distribution |  4.1-random-walks interface_corr.pngCorrelated RW (next step is correlated to previous one - by lenght and direction) -> smooth curve |  4.1-random-walks interface_cauchy.pngRW with step length generated randomly from Cauchy distribution -using Levy flight |
Random walks can have a target (looking for target, foraging (Simon’s model)) – can have the vision and than move directly to the source, influence by the distribution of the sources (Moneky foraging, Seasonal pattern regrowth, Figure 7). They can also change their random walk depending on the flock behavior (Flocking model, with density map) but not correspond to landscape features.
Figure 7. Seasonal foraging walk
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Percolation
is the process on which we can be focused from different perspectives:
1. how is is spreading throught landscape (system), where one of the most important question is how to describe the emergent geometric properties of spanning cluster .
How do the random properties of a medium influence the percolation of a "fluid" throught it, how the system responds to the changing proportion of p (occupied sites?).
at p=pc (critical value where the system behavior changes rapidly), the size-frequency distribution of cluster follows a power-low distribution , meaning that it is scale-invariant, so that clusters of all sizes are typical.
Propagation/spreading of the phenomenon depends on probability values of neighbouring cells, their degree of connection,
Figure 8: Comparison of movement of blind (down) and myopic ant (up). Note different Y scale on plots "Distance displaced"
 5.2-antLabyrinth interface_myopic.pngMyopic ant (select only from neighbors that are occupied) |  5.2-antLabyrinth interface_blind.pngBlind ant (select one of the 4 neighbor, move if it is occupied) |
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2. Dynamics of growth (or aggregation process) is another way how to look at spread. In p.ex. Eden's growth model, the occupied cell occupied its neighbor randomly. It is mostly the dynamics of the frontal points is analysed.
Figure9: Eden's growth process. The timing of growth is exprimed by colors: red (older), bluewish (younger). The frontal growing cells are in red.
The main difference between 3 types of models are:
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aggregation - cell change its own stete depending on states of neighbors
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mobility - the agent moves across world following specific rules
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percolation - tha changement of cell stated depending on site from which it is spreading, reflecting landscape surface properties (ho to the cells with the highest probability)
Question 1:
What potential new forms of knowledge can spatial simulation provide to your discipline, and more importantly, to your specific graduate research topic?
One of the most amazing secrets of Agent-Based and Cellular Automata modelling is the power to let the system interaction works only just defining individual behavioral traits of interacting agents (insects and trees). These behavioral traits are in many cases already defined by classical approaches in field- or lab- approaches. On individual bark beetle level the information about possible dispersal distance, movement range, perceptual range, moving angle etc. are already known. Spruce tree predisposition to be attacked is characterized by its health condition resp. by its primary (tree related volatiles) and secondary attractiveness (tree’s and insect’s attracting and repulsing pheromones).
The complexity science using cellular automaton provides the environment for interactions among many already knows behavioral rules and to understand how the individual traits influence the emerging pattern of the infestation. Bark beetle - spruce interaction has evolved for thousands years and are depending on one another: weakened tree produces terpenes which attract bark beetles, the infestation success of last ones rest on the host resistance and/or on total number of attacking beetles. During endemic phase the both processes are in equilibrium – bark beetle population survives on naturally weakened trees. After severe abiotic factors (windthrows, drought ...) the number of weakened trees incapable to resist the bark beetle attacks is multiplied resulting to explosive insect population growth. In few years the massive beetle population surpasses even vigor tree resistance ending in large-scale tree mortality. However, the self-regulation in bark beetle population falls in lower population density (lower reproduction success caused by male:female ratio to 1:1 not to 1:3 as in endemic phase, diminishing available foraging resources …).
However, these individual tree - bark beetle interactions producing systematic behavior are still poorly understood and moreover difficult to study in classical field and laboratory conditions. The most challenging question is to understand the trade-off between emerging and dispersing population of beetles and a number of beetles needed to successfully colonize a tree (Byers 2004). The framework studying the emerging infestation patterns of infestation in Ips typographus L. – Picea abies ecosystems was proposed by Kautz et al. 2014. The study is focused on one dispersal wave of infestation, a set of bark beetle behavioral rules and on scenarios of stand health conditions. The temporal and spatial patterns still remain unknown, depending on gradation phase, influence of another influencing factors as weather or possible clear-cut management applications.
The aim of the study can be possibly the identification of changing behavior of bark beetles (Ips typographus L.) in interaction with spruce (Picea abies) forest in influence of severe damage. The Kauthz et al. 2014 study is focused in different trees resistance scenarios, my work based on his approach could be focuses in changed Ips behavior in changing environment conditions. If severe windthrow occurs, the chance of successful bark beetle breeding increased. However the condition of the remaining undisturbed forest will not be necessarily changed. Following actual knowledge about bark beetle gradation dynamics, the system behavior will change creating large-scaled spots of infested trees. However on individual beetle level, the one could not be conscious about the actual gradation phase or about the number of active beetles. Accordingly, the individual beetle should to keep its individual traits to look for weakened trees ignorant the number of active beetles or gradation phases. As the we can observe in the nature, it is not true. Consequently, the bark beetle have to adapt is behavior after disturbance.
Consequences
In linear system dynamic, the act of removing all uprooted trees should be sufficient to prevent further bark beetle outbreak. This is surely not true – both windthrows and clear-cuts are creating forest edges, more susceptible to bark beetle outbreak. The founding about the real influence of not intervened uprooted trees should force close-to-nature forest management implementation in logging technologies and could arises new question and answers about the effects of unlogged uprooted trees on further bark beetle outbreak. Or do the logging forest management efforts only shift the bark beetle outbreak to following years?
References
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Byers, J.A., 2004. Chemical ecology of bark beetles in a complex olfactory landscape. In: Lieutier, F., Day, K.R., Battisti, A., Grégoire, J-C., Evans, H.F. (Eds.), Bark and Wood Boring Insects in Living Trees in Europe, a Synthesis. Kluwer Academic Publishers,
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Kautz, M., Schopf, R., & Imron, M. A. (2014). Individual traits as drivers of spatial dispersal and infestation patterns in a host-bark beetle system. Ecological Modelling, 273, 264–276. http://doi.org/10.1016/j.ecolmodel.2013.11.022
