Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities

Figure 4

Dynamical stochastic process of multiplication and selection. Continuous limit, one initial ancestor. Two cardinal examples (a) 𝑛=33 and (b) 𝑛=150. Upper left: probability distribution 𝑊^𝑀_𝑛(𝜈) of finding 𝜈 individuals after multiplication phase 𝑀 of generation 𝑛 (3). Lower left: probability distribution 𝑊^𝑆_𝑛(𝑁) of finding 𝑁 individuals after selection phase 𝑆 of generation 𝑛 (4). Average and standard deviation indicated (correct values only by taking the probability of extinction 𝑊(0) into account). Upper right: probability of extinction 𝑊(0) along generation 𝑛. Lower right: number of individuals 𝜈 and 𝑁 with its standard deviation along generation 𝑛 (least square fit, 𝑅=0.0694, see (7) and (8)). Parameters: Maximal total number 𝑁_max=128, multiplication factor 𝜌=2, and copy probability 𝛼=0.1 (only 10% of individuals that are present before multiplication copy once), surviving probability 𝛽=0.9664.