Project paper

Individual-based ecosystem evolution simulation Chenzhe Qian1 and Dr. Christian Jacob1,2 ? . 1 2 Dept. of Computer Sci...

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Individual-based ecosystem evolution simulation Chenzhe Qian1 and Dr. Christian Jacob1,2 ? . 1

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Dept. of Computer Science, Faculty of Science, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4 [email protected], [email protected] Dept. of Biochemistry & Molecular Biology, Faculty of Science, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4 [email protected]

Abstract. In this paper, I will present an agent-based model to measure the changes within populations, within an environment, and across populations and environment responding to the changes of ecosystem factors. Agents will survive, compete and mate in a simulated environment. Environment will also respond changes of agents. In general, the goal of the simulation is to answer the agents with specific genome with eight genes that best fit the specific simulated environment.In specific, the simulation focuses on the energy usage of agents respecting to the environment where they are sitting. It aims to explore the best combination(s) of energy usage for agents, in other words, fitness, under a particular environment. The genome will be analyzed and output as well as the rate and degree of changes within a population and within an environment.

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Introduction

Ecological modeling is the crossroad between theoretical ecology, mathematics and computer science.[1]. Ecosystem models aim to characterize the major dynamics of ecosystems, for a better understanding of such systems, and to allow predictions of their behavior.[2]. Ecosystem models simplify the natural ecosystems, and this simplification allows for the development of computer-aided ecosystem simulations that are tractable [3]. Using the model developed in this project, we will be able to measure how intensive the environment and internal population changes will affect the ecosystem.[4]. Agents may compete and mate with each other, and may survive or die from environment pressure. More precisely, agents will evolve to have longer lifespan, higher temperature tolerance, and higher efficiency to utilize energy to perform behaviors (respiration, growth and mating) in order to survive from the environment and pass the genetic materials down to the next generation. Respectively, energy usage will contain three parts, one for metabolism, one for growth and one for breeding. The problem remains for agents is that how much energy should be used for three different behaviors to make them being best ?

Dr. Larry R Liton, Afshin Esmaeili

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Chenzhe Qian and Dr. Christian Jacob.

fitted to the environment which is equivalent to ask where the fitness function is. The user will be able to modify either the environmental variables or population variables. During the simulation, the program will show how the population reacts to environment changes and how the environment reacts to population(s) changes. The program will be able to analyze the rate and intensity of changes that population(s) and environment made in the evolutionary process and answer the question about where the fitness function is.

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Method

The project implements an ecological modeling by using the individual-based model. The environment has two components, temperature and food, that are linked by two types of functions, linear equation and Michaelis Menten equation. The agents have the genomes which contain genes valued from 0.0 to 1.0. These genes can apply the genetic algorithm (single crossover and single mutation) and pass them down to filial generation. According to their genomes, all agents will perform three behaviors in order to survive, compete and mating. Energy is the bridge that links the genomes and behaviors, which can be considered as the translation of a genotype into a phenotype. The energy is consisted of three sub-energy pools, each of which is related to a specific behavior. The particular behavior can be applied only if the energy stored in the corresponding energy pool is sufficient to do so. The energy cannot be withdrawn from other energy pools, which forms a trade-off of energy utility. As a consequence, the square sum of last three genes is restricted to at most 1.

Fig. 1. Illustration of Energy Usage

As there are only three ways to consume energy, we can consider this into 3D coordinates, with each axis valued from 0 to 1 so that the functional space is a one eighth sphere. The unknown fitness function will intersect the functional space, be tangent to the functional space or locate outside the functional space.

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Agents with larger size can obtain a greater amount of food; however, as a cost, they will pay more energy on respiration. This is another trade-off and can be considered as intra-competition. Agents under the same simulated environment can be paired tested as there are two major types of agents genomes, Control and Off-Control. Control means the square sum of three energy usage genes is restricted to 1. This restriction implies that all agents will fully use energy without any waste. Also, there is no GA rules can be applied to Control agents. Off-Control means the square sum of three energy usage genes is restricted to at most 1, which implies agents will have chance to generate waste instead of fully energy utility. Therefore, Off-Control agents will have a lot more genetic freedom and they can apply GA rules. As time being, the number of agents related to the food-reproduction capability of simulated environment displays a constant pattern. The evolutionary mechanism over the time selects the suitable agents and kills the ones that cannot survive.

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Project Details Setting of Environment

The temperature increases from top to bottom linearly The functions of food reproduce rate depend on the temperature are the followings: T ypeI(Linear) : y = k ∗ x + m, wherekandmarevariables T ypeII(M ichaelisM enten) : V =

Vmax ∗ T , whereV maxandKmarevariables Km + T

Fig. 2. demonstration of Michaelis Menten Curve

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Setting of Agents

Genome has eight genes: Sex: either male or female Temperature tolerance: higher tolerance, larger range of living area Growth energy threshold: minimum amount of energy to perform growth Breeding energy threshold: minimum amount of energy to perform breeding Metabolism energy proportion: the proportion of energy used for respiration Growth energy proportion: the proportion of energy used for growth Breeding energy proportion: the proportion of energy used for breeding Agents either starve to die or reach maximum lifespan to die. 3.3

Agents Reproducing Rules

The rules are based on natural rules and artificially created. Only female will choose the mating partner and male displays. The number of offspring produced per time is dependent on the energy that stored in parents breeding energy pool. Each offspring is independent via genetic algorithm. 3.4

Interactions

The size determine the amount of food a agent can obtain per time f ood = size ∗ f ood − eaten − size − ratio The size also affect the metabolism rate of a agent 3

matabolism − rate(R) = size 4 The metabolism rates of agents depend on the temperatures of their own unique location that we apply Q10 function here 10

Q10 = (

3.5

R2 T2 −T1 ) R1

Output Graphic Results

As each agent has eight genes, seven of them will apply GA rules except sex gene, and each gene valued from 0.0 to 1.0, it is not possible to distinct by colors also it is not easy to understand by reading pure numbers. Thus, the graphic visualized approaches need to be applied. Fig. 3 outputs the ArrayPlot of genomes in each agent. Each column represents a specific gene and each row represents a agent at a particular time point. Fig. 4 outputs the 3DListPlot of the energy usage genes (metabolism propportion, growth propportion and breeding propportion). Each point represents a combination of these three genes of a agent.

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Fig. 3. First column represents lifespan, second column represents temperature tolerance, third column represents growth threshold, forth column represents breeding threshold, fifth column represents metabolism proportion, sixth column represents growth proportion, seventh column represents breeding proportion. The color indicates the value of gene, white is 0.0 and black is 1.0

Fig. 4. The X axis represents metabolism proportion, the Y axis represents growth proportion, the Z axis represents breeding proportion

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Results

As there are more than ten variables users can play with, it is not possible to generate all results of all permutations of variables. We are only interested in some particular cases. 4.1

standard test

Fig. 5. Standard Test Condition

Fig. 6. standard test, at time tick 1, population 914

As the Fig.6 and Fig. 7 shown, the agents with random genomes converged to higher lifespan and higher temperature tolerance as expected. Furthermore,

Individual-based ecosystem evolution simulation

Fig. 7. standard test, at time tick 20000, population 20670

Fig. 8. standard test, population plot

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most agents preferred to use most energy for respiration, least energy for growth and media energy for mating. Also, there were some agents used least energy for respiration, media for growth and most for mating. The 3D plot in Fig.5 showed the fitness function of agents under the standard test condition. 4.2

standard test with Control

Switch the ”control” on, and keep other variables same

Fig. 9. standard test with Control, at time tick 1, population 912

Fig. 10. standard test with Control, at time tick 20000, population 21758

As the Fig.10 shown, the agents survived had similar genomes compared to standard test without control. Hence, the fitness function of this test was close

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to the previous test. However, as the 3D plot in Fig. 10 shown, the agents had less diversity than those without control. 4.3

test2

Only change is to assign food-eaten-size-ratio = 1, and keep other variables same to standard test

Fig. 11. test 2, at time tick 20000, population 13980

As the Fig. 11 shown, all agents would like to use energy for growth in order to be able to get food more efficiently. Compared with standard test, agents with less food-eaten-size-ratio sacrifice mating energy to had sufficient energy for growth. 4.4

test3

Change Vmax to 1 and mm-intersection to 15. Keep other variables same to standard test Fig.12 indicated that the agents kept small size and consumed energy only for respiration and mating equivalently. The population size was dramatically less than standard test as well, which Fig. 13 showed about 20 times less. 4.5

genetic algoritm test

This test only change max-lifespan to 100 and change mut-strength from 0.0 to 1.0 at different time. In addition, it keeps other variables same to standard test as well. Agents without applying any GA rules (in Control) could survive and live happily. Agents with applying only crossover also could also survive but less comfortable. Agents with applying both crossover and mutation lived much worse and/or eventually went to extinction as the mutation strength increased.

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Fig. 12. test 3, at time tick 20000, population 668

Fig. 13. test 3, population plot

Fig. 14. on Control, population plot

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Fig. 15. without Control, mut-strength 0.0 population plot

Fig. 16. without Control, mut-strength 0.1, population plot

Fig. 17. without Control, mut-strength 0.3, population plot

Fig. 18. without Control, mut-strength 0.5, population plot

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Fig. 19. without Control, mut-strength 0.7, population plot

Fig. 20. without Control, mut-strength 1.0, population plot

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Discussion

For the standard test, the results generated from the simulation figured out where the fitness function was. In an environment with large temperature range, the agents were able to have multiply choices to spend energy for different purposes so that they could survive. For the standard test with control, the agents started from more restricted genomes so ended in fewer choices to spend energy than that without control. As Control, agents were not allowed to apply any GA rules; hence the results could be used to verify the validity of GAs. Moreover, this test clearly illustrates the difference between GAs and non-GAs. For the test 2, since the food-eaten-size-ratio was ten times less than the standard test, the agents were inefficient to incept food. In order to have more food and enhance the survivability, the agents were willing to spend more energy on growth. As a consequence, they would have enough amount of energy to perform other behaviors. However, the key issues to be successful in the environment are to keep alive and produce offspring. Thus, agents would still spend quite lot energy on either metabolism or breeding. For the test 3, as the food reproduce rate and food producible area was also much smaller than standard test, the agents were under a tough environment. Only fewer agents with right fitted genomes could survive. All agents kept in small size and used almost all energy for respiration and mating in order to be successful in the environment.

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For genetic algorithm test, each agent has up to 100 time tick lifespan, thus the age pressure become key issue. Agents like this will respond more sensitive to the changes of genome. As seen, the higher mutation strength, the higher failure probability of the entire population. In the simulation, the higher mutation strength led to higher mutation failure due to the restriction. More importantly, the higher mutation ratio would occur the higher chance that jumping over the best fit point to other less fit point. Biologically, this can be considered as a genetic performance failure. Furthermore, the higher mutation ratio caused quicker extinction.

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Conculsion

In conculsion, the simulation generally follows the biological principles. It can simulate the responses of changes from agents to environment, from agents to agents and from environment to agents. The program will generate a genome map, a fitness function and a population plot of a species under a particular simulated environment. The output data is visualized and easy to understand. The simulation is not only functional to give an answer after a constant time tick, but also able to generate results at any time point and is functional to respond to changes of the variables in running time. As the simulation can generally answer the question about where the fitness function of a particular environment is, it can be used to predict the properties of a species at a simulated similar environment. Furthermore, it can help environment designers to verify the validity and compute the fitness of the designed environment. However, the simulation still contains a few artificial rules and some magic numbers so that the simulation is only generally scientifically valid not specifically and precisely correct. Furture development of the simulation will focus on enhancing the intracompetition of agents, building more complex (realistic) biological genetic rules via GAs. Further direction will be to specify either a species simulation or an environment simulation

References 1. Gras, R., Golestani, A.: Regularity analysis of an individual-based ecosystem simulation. Chaos 20(043120) (2010) 13 2. Wolfe, J.R., Zweiga, R.D., Engstroma, D.G.: A computer simulation model of the solar-algae pond ecosystemstarl. Ecological Modelling 34 (1986) 1–59 3. Gras, R., Devaurs, D., Wozniak, A., Aspinall, A.: An individual-based evolving predator-prey ecosystem simulation using a fuzzy cognitive map as the behavior model. Artificial Life 15 (2009) 423–463 4. Lin, W., Lin, Y., Li, L.: Computer simulation of the pattern formation of a spatial ecosystem. Natural Computation, 2009. ICNC ’09. Fifth International Conference on (2009) 464–467