[Population Modeling] Paragraph for paper

Fri Apr 22 12:40:33 PDT 2016

Hello to everyone,

Here is my contribution to the joint paper.

EcoSim, a platform to investigate theoretical ecological and evolutionary questions

We designed, EcoSim [1, 2], a simulation platform for theoretical ecological modeling. EcoSim is an individual-based model including three trophic levels (primary producers, prey and predators individuals) in a large (1000x1000 cells) toroidal discrete world. Each individual possesses its proper behavioral model implemented by a Fuzzy Cognitive Map [3] composed of perception, internal and action concepts linked by excitatory and inhibitory edges allowing for positive and negative feedback loops to appear. The behavioral model and the physical characteristics (such as size, speed and vision range) of each individual are coded in its genome allowing for the evolution of new behaviors and physical characteristics. Species are also represented as populations of individuals with high genomic similarities. Species can emerge or disappear at any time step due to the evolution, birth and death of their individuals [4]. Each individual is also associated with a reserve of energy that can be refilled through food consumption and a metabolism function determining its energy usage based on its physical characteristics, the complexity of its behavioral model and the type of action performed, sexual reproduction being a particularly costly one. An important property of our model is that it does not rely on any pre-defined fitness function [5]. Instead fitness emerges from the multiple interactions between the individuals and their changing environment.
With hundreds of thousands of unique individuals simultaneously living in a large and dynamic environment and being subject to evolution for thousands of generations, many biological and ecological theories can be investigate through EcoSim. EcoSim has been validated through several studies showing clear coherence of the features generated by the simulation with empirical data such as species abundance pattern [6], chaotic [7] and multifractal [8] patterns and species-area relationship [9]. EcoSim has also been use in many different studies such as the effect of movement restriction on speciation [10], the prediction of species extinction [11], the effect of predation on prey evolution [12] and the impact of PCB exposure on prey population. We are currently working on several new subjects including the search for an explanation to the prevalence of sexual reproduction over asexual reproduction, the evolutionary responses of female mating preference to predation risk, the emergence of basic communication abilities, the understanding of the environmental and behavioral conditions favoring species invasion and the emergence of altruistic behaviors.

[1] Gras R., Devaurs D., Wozniak A., Aspinall A., An individual-based evolving predator-prey ecosystem simulation using a Fuzzy Cognitive Map model of behavior, Artificial Life, 15(4), 423-463, 2009.

[2] Gras R., Golestani A., Hosseini M., Khater M., Majdabadi Farahani Y., Mashayekhi M., Sina M., Sajadi A., Salehi E. and Scott R., EcoSim: an individual-based platform for studying evolution, European Conference on Artificial Life 2011, Advances In Artificial Life, ECAL 2011, 284-285

[3] Kosko, B. (1986). Fuzzy cognitive maps. Int. J. Man-Machine Studies, 24: 65 – 75.

[4] Aspinal A., Gras R., K-Means Clustering as a Speciation Method within an Individual-Based Evolving Predator-Prey Ecosystem Simulation, Lecture Notes in Computer Science, 6335, 318-329, 2010, Toronto,August, IEEE International Conferences on Active Media Technology.

[5] Gras R., Golestani A, Hendry A., Cristescu M., Speciation without pre-defined fitness functions, PLOS ONE, DOI: 10.1371/journal.pone.0137838, 2015

[6] Devaurs D., Gras R., Species abundance patterns in an ecosystem simulation studied through Fisher's log series, Simulation Modelling Practice and Theory, 18, 100-123, 2010.

[7] Golestani A., Gras R., Regularity Analysis of an individual-based Ecosystem Simulation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 20 (043120) 2010.

[8] Golestani A., Gras R., Identifying Origin of Self-Similarity in EcoSim, an Individual-Based Ecosystem Simulation, Using Wavelet-based Multifractal Analysis,  Proceedings of the World Congress on Engineering and Computer Science 2012 (WCECS 2012), San Francisco, 1275-1282.

[9] Mashayekhi M., MacPherson B., Gras R., Species-area relationship and a tentative interpretation of the function coefficients in an ecosystem simulation, Ecological Complexity, 19, 84-95, 2014.

[10] Golestani A., Gras R., Cristescu M., Speciation with gene flow in a heterogeneous virtual world: can physical obstacles accelerate speciation?, Proceedings of the Royal Society B: Biological Sciences, 279(1740), doi: 10.1098/rspb.2012.0466, 3055-3064, 2012.

[11] Mashayekhi M., MacPherson B., Gras R., A machine learning approach to investigate the reasons behind species extinction, Ecological Informatics, 20, 58-66, March 2014.

[13] Khater M., Murariu D., Gras R., Contemporary Evolution and Genetic Change of Prey as a Response to Predator Removal, Ecological Informatics, 22, 13-22, July 2014.

[14] Karim Pour M., Bhattacharjee S., Gras R., Drouillard K., The integration of an individual-based model into toxicokinetics to enhance ecological realism in evaluating population-level impacts of exposure to PCB, 3rd World conference on Complex Systems, November, 2015, In Press.

Dr. Robin GRAS
Associate Professor, Canada Research Chair
School of Computer Science
Cross-appointed by the Biology Department
Cross-appointed by the Great Lakes Institute for Environmental Research
8111 LAM, University of Windsor
401 Sunset Avenue, Windsor, ON  N9B 3P4
Phone:  519.253.3000 ext. 2994
Fax: 519 973 7093, Email:rgras at uwindsor.ca
Web Page: http://sites.google.com/site/ecosimgroup/home

________________________________________
From: popmodwkgrpimag-news-bounces at simtk.org <popmodwkgrpimag-news-bounces at simtk.org> on behalf of Matthias Chung <mcchung at vt.edu>
Sent: April 22, 2016 9:09 AM
To: IMAG (popmodwkgrpimag-news at simtk.org)
Subject: [Population Modeling] Paragraph for paper

Hi everyone,

Here is my paragraph.

Best,

Tia

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Title of paragraph: Parameter estimation for population dynamical models.

Author: Matthias Chung, Department of Mathematics, Computational Modeling & Data Analytics, Virginia Tech

Inferring information from observed population dynamics onto population interactions is inherently difficult. We consider parameter estimation methods to overcome such obstacles.

Lets assume the dynamics of interacting species can mathematically be modelled by a generalized Lotka-Volterra system y' = diag(y)(r + A y).
Here the vector function y describes the time dependent dynamic, r captures the intrinsic growth, and A describes the interaction between species y. Notice that in higher dimensions (more than two species) dynamics of y are highly sensitive to small changes in the interaction A. Hence inferring A from longitudinal observations d is notably difficult.

Single and multiple shooting methods are standard methods for point estimation of ordinary differential equation. However, these methods are known fail for highly sensitive equations such as population dynamical systems. To overcome this issue the underlying parameter estimation problem is reformulated as

min || m(s) - d || + a || s' - diag(s)(r + A s) ||,

where s is an adequate parameterized function approximation of y and m is a projection of that function onto the observation space. Further, || . || is the Euclidian norm and a is an appropriate regularization parameter, while we optimize over A and s. These continuous shooting methods have been shown to generate robust estimates for the inferred parameters A, [1,2].

References:

[1] J. Ramsay, Principal differential analysis: data reduction by differential operators, J R Stat Soc Series B Methodol, 58 (1996), pp. 495-508.

[2] M. Chung, J. Krueger, M. Pop, Robust Parameter Estimation for Biological Systems: A Study on the Dynamics of Microbial Communities.  ArXiv http://arxiv.org/abs/1509.06926, (2015), pp. 1-33.
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