Tilman (1980) critiques the Lotka-Volterra equations as "more phenomenological than mechanistic and thus more descriptive than predictive," and replaces competition coefficients with a graphical theory built from zero-net-growth isoclines (ZNGIs), consumption vectors, and resource supply points . Resources are classified pairwise as essential, hemi-essential, or substitutable (complementary, perfectly substitutable, antagonistic, switching), and a single central stability criterion emerges: each species must consume relatively more of the resource that more limits its own growth. The framework unifies competition and predation as consumer-resource interactions.
Tilman's own chemostat tests with Asterionella formosa and Cyclotella meneghiniana competing for phosphate and silicate showed close agreement between predicted and observed dominance/coexistence regions, and the model explained >70% of variance in relative abundance along a Lake Michigan resource gradient . Forty-five years later, a mechanistic consumer-resource model applying Tilman's rules predicted 960 phytoplankton communities with ~83.4% accuracy (vs 53.5% null model), and confirmed the core theoretical prediction that coexistence probability is higher for substitutable (22.7%) than essential (12.1%) resources .
Simulated-context note: values are reported experimental percentages from the 2025 validation study, not simulated data.
Key assumptions are acknowledged by Tilman himself: species interact only through resources (no direct interference), resource supply is equable, and resources are non-interactive . Subsequent work shows these exclusions matter: interference competition can promote coexistence without requiring intraspecific dominance , and mixotrophic intraguild predation enables coexistence under single-resource limitation not captured by pure resource competition . The 2025 study also found Tilman's two-resource rules were met in only 30-60% of empirical pairs, indicating additional ecological factors . The theory is equilibrium-based and ignores nonequilibrium dynamics later explored in Filippov switching models .
A landmark synthesis: rigorous, falsifiable, and validated across 45 years, though its pure resource-competition scope deliberately excludes interference, facilitation, and nonequilibrium dynamics. What would change the assessment: systematic experimental failures of the consumption-limitation stability criterion in systems where resources are correctly classified.
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