Bacteria Competition: Growth, Diffusion and the Fight for Nutrients

Logistic growth on a finite dish

A single bacterial population on a dish with finite food doesn't grow forever - division slows as nutrients are used up and waste accumulates, following the logistic equation dN/dt = rN(1 - N/K), where r is the intrinsic growth rate and K, the carrying capacity, is set by how much nutrient the dish can supply. Two competing species turn this into a coupled system.

dN1/dt = r1·N1·(1 - (N1 + a12·N2) / K1)      Lotka-Volterra
dN2/dt = r2·N2·(1 - (N2 + a21·N1) / K2)      competition equations

a12, a21 = competition coefficients (how much one species'
           growth is suppressed per individual of the other)

Whether the two populations settle into stable coexistence, one competitively excludes the other, or the outcome depends on starting proportions is determined entirely by how the four parameters r1, r2, a12, a21 compare to each other.

It's not just growth rate: resource competition theory

A more mechanistic view asks what nutrient concentration each species needs just to break even - its R*. In a well-mixed system with a single limiting resource, the competitive exclusion principle predicts that whichever species can survive on the lowest R* will eventually drive the other to extinction, regardless of which one grows faster when nutrients are abundant. A species that divides quickly but needs a lot of food to sustain itself can still lose to a slower, more frugal competitor once the easy nutrients run out.

Diffusion turns competition into geometry

A shaken flask is well-mixed; a petri dish is not. Nutrient diffuses inward from the surrounding agar while the growing colony consumes it at the edge, so each colony carves out a local depletion zone rather than competing against a single shared pool. The shape that results depends on how starved the colony's growing edge is: rich, well-diffused media give smooth compact discs (growth limited by division machinery, not food supply), while nutrient-poor or high-viscosity media starve the crowded interior far more than the exposed tips, producing jagged, fractal, diffusion-limited-aggregation-style branching patterns.

Coexistence tricks

Real bacterial competition rarely plays out as cleanly as the well-mixed R* theory predicts, because spatial structure, waste products that shift local pH, and chemical warfare via bacteriocins (antimicrobial proteins targeted at close relatives) all give slower or weaker competitors ways to persist. Colonies that would lose in a shaken flask can carve out a stable local niche on a plate simply because diffusion never lets the "winning" colony reach every corner of the dish before resources locally run low.

Frequently asked questions

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