Source-linked AI summary
Sensitivity Analysis of Decision Rules in an Agent-Based Agro-Ecological Model
Benjamin Pianet, Baptiste Lesquoy, Paul Saves, Benoit Gaudou, Jean Villerd, Nicolas Verstaevel, Olivier Therond
TL;DR
Classical global sensitivity analysis assumes independent inputs over a fixed Cartesian product, while agro-ecological decisions can activate parameters conditionally. The paper encodes MAELIA’s crop-management choices as a hierarchical design space and analyzes them with random-forest-supervised HSIC-ANOVA; the results identify fertilisation doses as the leading family across three outputs, with the next-ranked family differing by output.
Problem
Classical GSA assumes independent inputs over a fixed Cartesian product, an assumption violated by branched decision spaces with conditionally active parameters.
Source: §1 · p. 2Method
The paper encodes MAELIA’s crop-management itinerary as a hierarchical design space and applies random-forest-supervised HSIC-ANOVA to rank effects and interactions.
Source: §4 · p. 8, §6 · p. 15Results
Fertilisation doses lead across nitrogen leaching, soil organic-carbon variation, and yield; the next-ranked family is timing, sowing and harvest calendar, and itinerary structure, respectively.
Source: §6 · p. 16Takeaways & Limitations
Within the analyzed structured space, first-order effects carry most dependence, while the observed interactions remain secondary.
Source: §6 · p. 16A head-to-head comparison with classical variance-based GSA is not well posed because branched spaces violate its independent-input, fixed-Cartesian-product assumption.
Source: §6 · p. 16
Abstract
from arXiv · showhide
Agent-based models are well-suited for modelling agro-ecological systems for decision-making, yet turning their simulations into actionable insight requires identifying which decisions actually drive the behaviours. In such a context, sensitivity analysis stumbles upon a structural feature of many complex systems: the parameters are not a flat vector but a decision tree in which many parameters appear only when a higher-level choice activates them. Classical global sensitivity analysis presupposes independent inputs over a fixed Cartesian product and is ill-posed on such a branched space and biased by construction. We instead treat the structure of the decisions as a first-class modelling object. Using advanced surrogate modelling techniques, we encode the crop-management itinerary of the high-resolution agro-ecological modelling platform MAELIA as a hierarchical design space featuring both categorical and numerical variables. We propose a novel dedicated method to analyse this kind of hierarchical space, a random-forest-supervised HSIC-ANOVA, which ranks main effects and interactions natively on the tree while placing rarely and always active decisions on an equal footing. We show how, when applied to simulation outputs such as nitrogen leaching, soil organic carbon variation, and yield predictions, it can deliver an interpretable, decision-oriented reading.
1 Introduction
MAELIA’s coupled processes and outputs make it difficult to attribute outcomes to individual inputs, and its crop-management parameters form a conditional decision tree rather than a flat vector. The paper encodes that hierarchy and proposes a structure-aware sensitivity-analysis pipeline for a complex agro-ecological simulator.
1 Introduction
- MAELIA couples agricultural activity, hydrology, and water-resource governance daily across spatial scales, producing many indicators whose outcomes emerge from interacting components.These coupled processes make attribution to an isolated input difficult.Source: §1 · pp. 1–2
- Hierarchical inputs violate classical GSA’s independent-input assumption; flattening them creates invalid combinations and imputed values can mask upstream decisions.Variance-based indices also require many model evaluations, which can be prohibitive for time-consuming ABMs.Source: §1 · p. 2
- The study addresses the open challenge of applying sensitivity analysis to a complex agro-ecological simulator with a genuinely hierarchical parameter space.It encodes MAELIA’s crop-management itinerary as 14 potential meta and decreed variables, including operation switches and their dependent counts, depths, doses, and dates.Source: §1 · p. 2
- Random-forest-supervised HSIC-ANOVA ranks influential variables, then decomposes output dependence into main effects and interactions on the hierarchical space.The random forest identifies influential variables; HSIC-ANOVA handles categorical and numerical inputs alike.Source: §1 · pp. 2–3
2 Related Work
Prior sensitivity-analysis work addresses ABM stochasticity and costly simulations, but methods based on independent inputs do not directly fit optional, hierarchical agricultural operations. Related work on hierarchical design spaces and surrogate-assisted exploration informs the paper’s approach.
Sensitivity Analysis of Agent-Based Models
- Variance-based GSA captures main and interaction effects, while ABM applications must address stochasticity, output selection, and replication limits.Prior work reports that variance-based GSA can enhance the analytical and policy relevance of agro-ecological ABMs, but these approaches are inadequate for optional, hierarchical operations.Source: §2 · p. 3
Hierarchical and Mixed-Variable Design Spaces
- Agricultural itineraries combine continuous, integer, and categorical variables, with some variables active only under specific parent decisions.Hierarchical design-space frameworks represent these as meta-variables and conditionally active decreed variables, with graph-structured distances.Source: §2 · p. 3
Surrogate-Assisted, Multi-Stage Exploration
- Surrogate-assisted workflows reduce the cost of ABM sensitivity analysis, and a prior two-phase workflow screens factors before training a surrogate for indices and explanations.This paper adapts that approach by representing the agricultural parameter space as a genuinely hierarchical directed acyclic graph.Source: §2 · p. 3
3 The MAELIA platform
MAELIA links farmer decisions with crop, soil, and water processes across daily simulations. This study directly specifies crop-management itineraries, then structures their operation choices and parameters as a constrained hierarchy for analysis.
3.1 Main Features and Capabilities
- MAELIA simulates daily interactions among crop growth, soil water, carbon and nitrogen cycles, water resources, and farmer activities across fields and territories.Its modular platform supports configurations tailored to different territories and research questions.Source: §3.1 · pp. 3–4
3.2 MAELIA architecture
- Farmer agents’ technical operations respond to crop, soil, weather, and workforce conditions, while operations in turn alter the soil state that informs later decisions.The study examines nitrogen leaching, soil organic-carbon variation, and yield; these outputs are defined by the model’s drainage, soil-carbon balance, and crop-stress mechanisms.Source: §3.2 · pp. 4–5
3.3 Model Parameters
- Date-dose input specifies itineraries directly, and its replay of a rule-generated itinerary yields identical outputs and intermediary variables.The design space covers 14 potential variables: tillage and fertilisation counts activate dependent operation parameters, while date constraints enforce agronomic order. It excludes several operation types and requires restrictions to keep itineraries agronomically admissible.Source: §3.3 · pp. 6–7
4 Sensitivity Analysis over a Hierarchical Space
The pipeline analyzes MAELIA crop-management decisions on their hierarchical design-space graph, combining random-forest supervision with HSIC-ANOVA and an activation-frequency correction. Its stages encode conditional activation, focus the analysis on influential variables, decompose dependence into effects and interactions, and account for decisions that are active only on some itineraries.
4 Sensitivity Analysis over a Hierarchical Space
- Random-forest-supervised HSIC-ANOVA ranks decisions and their combinations directly on the hierarchical space, without imputing inactive variables.The pipeline takes simulated itineraries and their outputs and returns a ranked list of decisions and combinations for each output.Source: §4 · pp. 7–8, Figure 1 · p. 8
4.1 Encoding the Itinerary and its Activation Pattern
- The 14-parameter design graph uses two structural counts to activate nine variables, while sowing date, sowing depth, and harvest date are always active.Inactive variables are represented as absent, and continuous variables are rescaled to a uniform range.Source: §4.1 · pp. 8–9, Figure 2 · p. 9
4.2 Learning What Matters with a Random Forest
- Conditional permutation importance ranks parameters only among itineraries where they are active, while randomized inactive entries prevent the forest from using branch status as a shortcut.Parameters below τ = 0.1% importance are pruned; retained importances set the kernel length scales.Source: §4.2 · pp. 9–10
4.3 Measuring and Decomposing Dependence on the Design Space Graph
- Conditional algebraic distance treats jointly absent operations as identical, absent-versus-active operations as maximally different, and jointly active values by numeric distance.HSIC-ANOVA then decomposes dependence into orthogonal main-effect and interaction shares; pruning makes interactions up to four decisions tractable.Source: §4.3 · pp. 10–11
4.4 Comparing Rare and Common Decisions Fairly
- Activation-frequency correction estimates a decision’s influence among itineraries where it is taken, then renormalizes shares so rarely active choices can be compared with always-active variables.This intrinsic view complements the global ranking.Source: §4.4 · p. 11
4.5 Novelty with Respect to the State of the Art
- The pipeline combines conditional distances for hierarchical spaces with dependence measures and ANOVA decomposition, extending hierarchical-space methods beyond optimization and prediction to global sensitivity analysis.Random-forest pruning keeps interaction analysis tractable, and activation-frequency correction supports a single structure-aware decomposition.Source: §4.5 · pp. 11–12
5 Results
Across the homogenised winter-wheat setup, sensitivity results show mostly additive main effects, with output-specific leading levers and a distinct secondary decision family for each output.
5.1 Experimental Setup
- The 5,000 configurations use hierarchical Latin hypercube sampling, with conditional activation respected and outputs averaged over ten weather years.The setup holds terrain, soil type, geometry, and weather zone constant, and restricts analysis to winter wheat and three aggregated outputs.Source: §5.1 · p. 12
5.2 Per-Output Sensitivity
- Most retained HSIC-ANOVA terms are main effects; the strongest interactions couple fertilisation count with applied doses.The analysis ranks terms by their share of global input-output dependence across the three outputs.Source: Figure 3 · p. 13, §5.2 · p. 13
- For nitrogen leaching, the leading shares are second dose 12.1%, fertilisation count 9.4%, second date 9.2%, first dose 8.6%, and third dose 6.9%.The authors relate this profile to synchronisation between nitrogen supply and crop uptake.Source: §5.2 · p. 13
- For soil organic-carbon variation, harvest date leads at 25.8%, ahead of the second dose 12.8%, first dose 11.2%, fertilisation count 10.2%, and preparation count 8.5%.It has the most visible higher-order interactions, including three third-order terms above the threshold, each described as small.Source: §5.2 · pp. 13–14
- For yield, the second, first, and third doses contribute 20.6%, 19.0%, and 8.7%, while fertilisation count contributes 17.6%; its strongest interaction is count with first dose at 7.7%.Yield has the strongest interaction structure among the three outputs, including a third-order count-and-dose interaction at 4.7%.Source: §5.2 · p. 14
- For yield, global dose shares rank second 20.6%, first 19.0%, third 8.7%, while intrinsic shares reverse the order to third 28.0%, second 16.1%, first 6.6%.The intrinsic reading measures a decision's influence among itineraries where it is active; the global reading weights influence across all itineraries.Source: §5.2 · p. 14, Table 2 · p. 14
5.3 Aggregation by Decision Family
- The analysis groups parameters into four decision families and divides interaction contributions equally among constituent parameters before aggregation.Working depths of tillage and sowing are omitted because their dependence is negligible for all three outputs.Source: §5.3 · pp. 14–15
- Fertilisation doses lead all three decision-family profiles, while the next-largest family differs: timing for leaching, crop calendar for carbon, and management structure for yield.Doses and timing account for 46.9% and 23.7% of leaching dependence; doses, crop calendar, and structure account for 37.3%, 32.2%, and 25.5% for carbon; doses and structure account for 66.0% and 27.8% for yield.Source: §5.3 · p. 15
6 Conclusion and Perspectives
The paper encodes MAELIA’s crop-management itinerary as a hierarchical design space and applies random-forest-supervised HSIC-ANOVA to analyze decisions within that structure. Across three outputs, fertilisation doses lead, while the next influential family differs by output.
6 Conclusion and Perspectives
- The crop-management itinerary is encoded as a hierarchical design space, with random-forest-supervised HSIC-ANOVA defined to analyze decisions within it.The itinerary uses date-dose formalism and meta and decreed variables.Source: §6 · p. 15
- Fertilisation doses lead across nitrogen leaching, soil organic-carbon variation, and yield, while the next influential family differs by output.Number of fertilisations is top-ranked throughout; first-order effects carry most dependence, and interactions, mostly with doses, remain secondary. Figure 4 reports no sufficient retained sowing-and-harvest-calendar term for yield.Source: Figure 4 · p. 15, §6 · p. 16
- A head-to-head comparison with classical variance-based GSA is not well-posed because its independent-input, fixed-product assumptions conflict with the branched design space.Flattening the space would require arbitrary values for inactive variables, distorting variance decomposition and masking upstream decisions.Source: §6 · p. 16
- Robustness tests could reintroduce pedo-climatic variation and additional crops, while applying the pipeline to other GAMA-based models could probe generality.These are proposed directions for future work.Source: §6 · p. 16
- The structured space could also support Bayesian optimization, and an interactive interface enables real-time exploration with partial-dependence plots and individual conditional-expectation curves.The interface uses the smt-explainability library.Source: §6 · p. 16