Define the edge before drawing it
A graph G = (V, E) contains a set of vertices and a set of edges. For a colony model, a vertex might represent an animal, a chamber, or a host sponge. An edge might represent physical access, observed contact, or a hypothesised information pathway. These choices describe different systems and must not be merged casually.
AESRD proposes to make the construction of the graph a central scientific question, rather than a preparatory step that disappears once the figure is attractive.
Structure is not mechanism
Network measures can describe connectivity, bottlenecks, or clustering, but they do not by themselves explain why interactions occur. The Watts–Strogatz model is an important reference for studying how topology can affect dynamics. It supplies a comparison model, not a default description of a shrimp colony.
A high-degree individual could be socially influential, centrally positioned, more visible to an observer, or all three. Choosing among those accounts requires additional evidence.
A programme of transparent comparisons
Initial work would compare synthetic spatial graphs with graphs formed under alternative contact rules. Analyses would report the observation window, edge threshold, directionality, and treatment of missing observations. Time-aggregated networks would be compared with event sequences where possible.
Null models would preserve features relevant to the question. A comparison that removes the physical constraints under study may exaggerate the apparent importance of a biological mechanism.
Mathematics with an audit trail
Proposed outputs include derivations, accessible diagrams, and worked examples that can be independently checked. The programme would publish the reason for selecting a measure and how the interpretation changes under plausible alternatives.
The desired result is a disciplined conversation between mathematical structure and biological measurement. An equation would be a precise statement of assumptions, not an ornament suggesting that uncertainty has been eliminated.