Bayesian Networks for Causal Analysis in Socioecological Systems

TL;DR

This work advances causal analysis in socioecological systems by applying structural causal models (SCMs) to observational data and leveraging EMCC to bound counterfactual queries. It extends Bayesian networks with post-intervention and twin (counterfactual) models to quantify necessity and sufficiency relations among socioecological variables, demonstrated on a southern Spain case study of land-use and population dynamics. Key findings show immigration as a strong, often necessary and sufficient driver of population growth, and geography and density as critical factors shaping land-use outcomes, illustrating the added value of counterfactual reasoning over conventional BN analyses. The methodology enables policy-relevant insights where interventional data are unavailable, with broader applicability to ecosystem services, risk assessment, and adaptive management in environmental science.

Abstract

Causal and counterfactual reasoning are emerging directions in data science that allow us to reason about hypothetical scenarios. This is particularly useful in fields like environmental and ecological sciences, where interventional data are usually not available. Structural causal models are probabilistic models for causal analysis that simplify this kind of reasoning due to their graphical representation. They can be regarded as extensions of the so-called Bayesian networks, a well known modeling tool commonly used in environmental and ecological problems. The main contribution of this paper is to analyze the relations of necessity and sufficiency between the variables of a socioecological system using counterfactual reasoning with Bayesian networks. In particular, we consider a case study involving socioeconomic factors and land-uses in southern Spain. In addition, this paper aims to be a coherent overview of the fundamental concepts for applying counterfactual reasoning, so that environmental researchers with a background in Bayesian networks can easily take advantage of the structural causal model formalism.

Figures (16)

• Figure 1: BN obtained from the observational data in Table \ref{['tab:intro_data']}.
• Figure 2: Study area (Andalusia, Spain) (a) and municipalities within the study area, color-coded based on their primary geomorphological unit (b), their main land-use (c), and their population growth rate (d). For (b) and (c), in cases where a municipality encompasses more than one geomorphological unit or land-use, the color represents the larger or dominant one within that municipality.
• Figure 3: BN obtained from the model in a previous study maldonado2018 by restricting it to our variables of interest and by limiting the number of parents to 3.
• Figure 4: Markovian SCM used for intended counterfactual analysis. All the SEs are asumed to be canonical. Each endogenous variable has only one exogenous cause, and each exogenous variable is cause of only one endogenous one.
• Figure 5: Intervals for the queries with EGR as effect variable. The x-axis represents each cause variable, according to the graph in Figure \ref{['fig:exp_bn']}, while the y-axis shows the query metric. Panels (a) to (f) depict different types of analysis: (a) conventional BN analysis, (b) causal analysis, and (c-f) counterfactual analysis. The metrics illustrated are (a) the difference in conditional probability, $P(y|x)-P(y|x')$; (b), the average causal effect, ACE; (c) the probability of necessity, PN; (d) the probability of necessity with reverse cause, PNrc; (e) the probability of sufficiency, PS; and (f) the probability of necessity and sufficiency, PNS. Note that metrics in panels (a) and (b) can take negative values, as they are defined as differences of probabilities.

Theorems & Definitions (1)

• Definition 1: Structural causal model (SCM)