MODEL OF CARRYING CAPACITY SYSTEM DYNAMICS IN NETLOGO AND STELLA

Size: px

Start display at page:

Download "MODEL OF CARRYING CAPACITY SYSTEM DYNAMICS IN NETLOGO AND STELLA"

Dwain Wilkerson
6 years ago
Views:

1 MODEL OF CARRYING CAPACITY SYSTEM DYNAMICS IN NETLOGO AND STELLA Kamila Olševičová, Richard Cimler, Hana Tomášková, Alžběta Danielisová University of Hradec Králové Institute of Archaeology of Academy of Sciences of the Czech Republic Key words: carrying capacity model NetLogo social simulation Stella system dynamics Abstract: We compare implementations of system dynamics of Celtic settlement using two tools NetLogo and Stella. The objective of the model is to catch the relations among the population growth, the production growth and the land use with respect to agricultural strategies. Our main objective is to better understand the Celtic society and economy and its sudden collapse. More broadly we are interested in the applicability of multimethod simulation (agent-based approach enhanced with system dynamics and process modelling) in archaeological research. Introduction Our objective is to explore the complexity of the society in late Iron Age in central Europe where fortified agglomerations the oppida came into picture. They appeared as a part of an economically advanced environment, together with a distinctive intensification of settlement patterns. Archaeological record shows that dynamics of their occupation includes fast growth and then even more rapid decline: the population density peaked within ca. 70 years, and then, within two generations it decreased extensively. Causes for gradual trend of depopulation can be seen in both endogenous and exogenous factors (organizational and political, environmental or ecological). Computational simulation can help us to get insight into the causes of the collapse. Our previous research was focused mainly on the agent-based simulations; see e.g. our 117

2 NetLogo [1] model of population dynamics [2] or model of agricultural strategies [3]. The simulation of synthetic population (size, structure and subsistence needs) was accompanied with the model of agricultural practices with the aim of investigating the sustainability of the long-term means of production and means of subsistence. Up-to-date simulation software such as AnyLogic [4] supports the multi-method simulations combining agent-based approach with system dynamics model and discrete event model. Each of the three methodologies assumes certain level of abstraction and quantification, namely in case of complex models of economies. We built two models of the carrying capacity of the Celtic settlement to learn more about the benefits and limits of system dynamics modelling. The first model was implemented using System Dynamics Modeler in NetLogo, the second was created using Stella software [5]. The models are presented in the rest of the paper. 1. System Dynamics Modelling with NetLogo and Stella With the agent-based approach the behaviour and interactions of individual agents are defined. The system dynamics model catches how populations behave as a whole. Both NetLogo and Stella provide intuitive icon-based graphical interfaces for creating the diagram that defines populations and how they affect each other (Fig. 1, 2). In NetLogo, its System Dynamics Modeler directly generates the appropriate NetLogo code (global variables, procedures and reporters). The diagram is composed of four types of elements: stock accumulates or drains, flow defines and controls stock s input/output, variable is a value (a constant or an equation that depends on other variables), link transmits a number from a variable or a stock into a stock or a flow. Similarly, Stella provides four types elements: stock and flow do not differ from corresponding NetLogo elements, converter manipulates inputs into outputs (holds values for constants, defines external inputs to the model, calculates algebraic relationships, serves as the repository for graphical functions), connector passes information between pairs of elements. 118

The population growth parameters (birth-rates, mortality and migration) are specified by domain experts.

3 FIG. 1: Part of the diagram in NetLogo FIG. 2: Part of the diagram in Stella 2. The carrying capacity models The population of the Celtic settlement increases from 600 up to 2000 inhabitants during 120 years. The population growth parameters (birth-rates, mortality and migration) are specified by domain experts. The total carrying capacity of the settlement depends mainly on the available strong workforce and available arable land. The amount of strong workforce is defined by the number of adult men between 15 and 45 years capable of hard agricultural work. The area of fields differs for intensive and extensive agricultural strategy which operates with fallow. About 70% of the population consumption is covered by cereals; further 20% diet consists of animal proteins (beef, 119

4 pork, lamb and horse meat and milk). The proportions of herds are given: large family of approx. 20 people cared about 2 cows, 2 sheep, 3 pigs and 1 horse. Animals require food from meadows and woodland and provide manure. With manure the crop grows from kg/ha up to kg/ha. The food production is restricted by constraints such as maximum of slaughtered cattle or approx. cereal losses during the winter. Food energy tables are used for mapping amount of wheat and milk on the consumption of each age group from toddlers to elderly. The map of the initial proportion of arable land, woodland and meadows is given as well as rules expressing the spreading of fields and the process of deforestation. The system dynamics models are created as follows. The stock of the human population is modified by birth- and immigrationinflows and death- and emigration- outflows. The stocks of animals population are modified by birth-inflows and slaughteroutflows. The stock of food contains calories from all sources of food. The stock of cereals is decomposed into three sub-stocks of one, two and three years old storages. The oldest storage is consumed with the highest priority while part of the newest crop is used as seed for the next season. The stock of arable land defines the current area of fields and together with the stock of woodland area and the stock of grasslands gives the total land use. 120

(archaeological and environmental records) to dynamic modelling that incorporates feedback mechanisms and nonlinear

5 FIG. 3: Population growth graph in Stella FIG. 4: Interface of NetLogo model Conclusion We intended to demonstrate the ability to move from a static data set (archaeological and environmental records) to dynamic modelling that incorporates feedback mechanisms and nonlinear responses to a wide range of input data. This approach can help to analyse past socio-economic processes, determine possible crisis factors and understand ecological and cultural changes. 121

6 Results obtained with the system dynamics simulation of carrying capacity of late Iron Age oppida show limits of the sustainable economy practiced by a constantly growing population under particular environmental settings. The immediate or gradual impact of the success rate in the food production and its potential influences on the social processes including the oppida abandonment can be also addressed. In NetLogo, the system dynamics can be enriched with the agent-based component (for example of the interface, see fig. 4). The system dynamics model of the settlement population and food production will be extended with the agent-based model of villages in the hinterland. Villages with its individual characteristics will be represented by agents and organized in the network. This is the way how to simulate the suppliercustomer relationships and to experiment with hypotheses about the level of selfsufficiency and the likely share of importing food and exporting craft products. Stella software does not allow us to continue with modelling individuals. The model is limited in several aspects, e.g. the graph cannot contain more than 5 lines (fig. 3). The main advantage of Stella is that it helps us to check the consistency of the model and to ensure the model outputs do not depend on the implementation tool. Acknowledgement: The research described was supported by grant GACR-405/12/0926 Social modeling as a tool for understanding Celtic society and cultural changes at the end of the Iron Age and the project No. CZ.1.07/2.2.00/ Innovation and support of doctoral study program (INDOP), financed from EU and Czech Republic funds. 122

7 References: [1] NetLogo homepage. [online] [2] OLŠEVIČOVÁ, K., CIMLER, R., MACHÁLEK, T. (2012) Agent-based Model of Celtic Population Growth: NetLogo and Python. In: N.T. Nguyen et al. (Eds.) Advanced Methods for Computational Collective Intelligence, Studies in Computational Intelligence 457, Springer-Verlag Berlin Heidelberg 2013, pp [3] MACHÁLEK, T., CIMLER, R., OLŠEVIČOVÁ, K., DANIELISOVÁ, A. (2013) Fuzzy Methods in Land Use Modeling for Archaeology. In: Proc. of 31st International Conference on Mathematical Methods in Economics 2013, Jihlava, part II, pp [4] AnyLogic homepage [online] [5] Stella homepage. [online]

Introduction to System Dynamics

Introduction to System Dynamics Stella Guide Compounding and Draining Processes John Hayward Church Growth Modelling www.churchmodel.org.uk Page 2 System Dynamics System dynamics is a methodology that