Wild yeast (mostly Saccharomyces and Kazachstania species) and lactic-acid bacteria (Lactobacillus) both grow logistically, dN/dt = r·N·(1 − N/K), competing for the same finite sugar pool released by starch-degrading enzymes in the flour. Yeast respire/ferment sugar into CO₂ and ethanol; bacteria ferment sugar into lactic and acetic acid, dropping pH from a neutral ~6.5 toward ~3.5–4.
Growth rate follows a Q10 temperature coefficient: metabolic rate roughly doubles for every 10 °C rise (rate(T) = rate(24°C) · Q10^((T−24)/10), Q10 ≈ 2), which is why cold retard (4 °C) nearly stalls fermentation while a warm 35–40 °C kitchen accelerates it — until heat starts denaturing enzymes and yeast viability drops past ~45 °C. Dough volume rises as CO₂ produced by yeast respiration gets trapped in the gluten network as gas bubbles, then plateaus once available sugar is exhausted (logistic ceiling) or the population's own acid and alcohol byproducts inhibit further growth.