Navigating simplicity and complexity of social-ecological systems through a dialog between dynamical systems and agent-based models

TL;DR

An iterative procedure for combining DSM and ABM to leverage their strengths and gain insights that surpass insights obtained by each approach separately is developed.

Abstract

Social-ecological systems research aims to understand the nature of social-ecological phenomena, to find ways to foster or manage conditions under which desired phenomena occur or to reduce the negative consequences of undesirable phenomena. Such challenges are often addressed using dynamical systems models (DSM) or agent-based models (ABM). Here we develop an iterative procedure for combining DSM and ABM to leverage their strengths and gain insights that surpass insights obtained by each approach separately. The procedure uses results of an ABM as inputs for a DSM development. In the following steps, results of the DSM analyses guide future analysis of the ABM and vice versa. This dialogue, more than having a tight connection between the models, enables pushing the research frontier, expanding the set of research questions and insights. We illustrate our method with the example of poverty traps and innovation in agricultural systems, but our conclusions are general and can be applied to other DSM-ABM combinations.

Figures (8)

• Figure 1: Illustration of the procedure for combining ABM and DSM. Yellow arrows represent parts of the modeling process that decrease complexity and heterogeneity of the studied system. Green arrows represent modeling processes that bring additional complexity and heterogeneity. Blue arrows stand for mathematical and analytical methods within DSM and ABM. Gray boxes contain explanations obtained from the models.
• Figure 2: Causal loop diagram based on structure of Ag-Innovation ABM. Arrows in blue represent variables operating at meso-level while arrows in green represent variables operating at micro-level.
• Figure 3: Causal loop diagram of the DSM based on assumptions \ref{['A1']}--\ref{['A8']} and Figure \ref{['Figure2']}. State variables are given in blue boxes and parameters are in circles ($a_1$- innovation efficiency, $c_1$- innovation desire, $\delta_i$ - depreciation rate of innovation resources, $r_s$ - soil fertility recovery rate, $s_0$ - savings rate, and $\delta_a$ - assets’ depreciation rate). Yellow circles indicate DSM parameters coming from the ABM, while green circles indicate DSM parameters supported by ecological and economic literature. Full definition of parameters can be found in Table 1 in Appendix B. Blue arrows represent cross-level interactions. Green arrows represent individual-level interactions.
• Figure 4: Stability analysis for innovation with low environmental damage shows a bistable system. $E_p$ denotes the poor attractor, characterized by low assets and innovation levels and high soil fertility. Blue volume is the corresponding basin of attraction. $E_w$ and yellow volume represent the well-being attractor and its basin of attraction.
• Figure 5: Bifurcation analysis with environmental damage ($d_1$) as the bifurcation parameter shows bistability (light red area) for low values of parameter $d_1$ and monostability for high values of parameter $d_1$. In the area of bistability, well-being and poverty attractors coexist and escape from poverty is possible. A sudden jump (regime shift) occurs when parameter $d_1$ increases beyond its threshold value. After regime shift, the system is in the poverty trap regime and escaping from poverty is not possible.