### Abstract

We investigate the effects of random motility on the ability of a microbial population to survive in pure culture and to be a good competitor for scarce nutrient in mixed culture in a flow reactor model consisting of a nonlinear parabolic system of partial differential equations. For pure culture (a single population), a sharp condition is derived which distinguishes between the two outcomes: (1) washout of the population from the reactor or (2) persistence of the population and the existence of a unique single-population steady state. Our simulations suggest that this steady state is globally attracting. For the case of two populations competing for scarce nutrient, we obtain sufficient conditions for the uniform persistence of the two populations, for the existence of a `coexistence' steady state, and for the ability of one population to competitively exclude a rival. Extensive simulations are reported which suggest that (1) all solutions approach some steady state solution, (2) all possible outcomes exhibited by the classical competitive Lotka-Volterra ODE model can occur in our model, and (3) the outcome of competition between two bacterial strains can depend rather subtly on their respective random motility coefficients.

Original language | English (US) |
---|---|

Pages (from-to) | 573-596 |

Number of pages | 24 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 59 |

Issue number | 2 |

State | Published - Nov 1998 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*59*(2), 573-596.

**Effects of random motility on microbial growth and competition in a flow reactor.** / Ballyk, Mary; Dung, Le; Jones, Donald; Smith, Hal.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 59, no. 2, pp. 573-596.

}

TY - JOUR

T1 - Effects of random motility on microbial growth and competition in a flow reactor

AU - Ballyk, Mary

AU - Dung, Le

AU - Jones, Donald

AU - Smith, Hal

PY - 1998/11

Y1 - 1998/11

N2 - We investigate the effects of random motility on the ability of a microbial population to survive in pure culture and to be a good competitor for scarce nutrient in mixed culture in a flow reactor model consisting of a nonlinear parabolic system of partial differential equations. For pure culture (a single population), a sharp condition is derived which distinguishes between the two outcomes: (1) washout of the population from the reactor or (2) persistence of the population and the existence of a unique single-population steady state. Our simulations suggest that this steady state is globally attracting. For the case of two populations competing for scarce nutrient, we obtain sufficient conditions for the uniform persistence of the two populations, for the existence of a `coexistence' steady state, and for the ability of one population to competitively exclude a rival. Extensive simulations are reported which suggest that (1) all solutions approach some steady state solution, (2) all possible outcomes exhibited by the classical competitive Lotka-Volterra ODE model can occur in our model, and (3) the outcome of competition between two bacterial strains can depend rather subtly on their respective random motility coefficients.

AB - We investigate the effects of random motility on the ability of a microbial population to survive in pure culture and to be a good competitor for scarce nutrient in mixed culture in a flow reactor model consisting of a nonlinear parabolic system of partial differential equations. For pure culture (a single population), a sharp condition is derived which distinguishes between the two outcomes: (1) washout of the population from the reactor or (2) persistence of the population and the existence of a unique single-population steady state. Our simulations suggest that this steady state is globally attracting. For the case of two populations competing for scarce nutrient, we obtain sufficient conditions for the uniform persistence of the two populations, for the existence of a `coexistence' steady state, and for the ability of one population to competitively exclude a rival. Extensive simulations are reported which suggest that (1) all solutions approach some steady state solution, (2) all possible outcomes exhibited by the classical competitive Lotka-Volterra ODE model can occur in our model, and (3) the outcome of competition between two bacterial strains can depend rather subtly on their respective random motility coefficients.

UR - http://www.scopus.com/inward/record.url?scp=0032201842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032201842&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032201842

VL - 59

SP - 573

EP - 596

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -