Grognard Frédéric, Masci Pierre, Benoît Eric, Bernard Olivier
INRIA Sophia-Antipolis-Team BIOCORE, 2004 route des lucioles, BP 93, 06902 , Sophia Antipolis, France,
J Math Biol. 2015 Apr;70(5):959-1006. doi: 10.1007/s00285-014-0783-x. Epub 2014 Apr 20.
Resource-based competition between microorganisms species in continuous culture has been studied extensively both experimentally and theoretically, mostly for bacteria through Monod and Contois "constant yield" models, or for phytoplankton through the Droop "variable yield" models. For homogeneous populations of N bacterial species (Monod) or N phytoplanktonic species (Droop), with one limiting substrate and under constant controls, the theoretical studies indicated that competitive exclusion occurs: only one species wins the competition and displaces all the others (Armstrong and McGehee in Am Nat 115:151, 1980; Hsu and Hsu in SIAM J Appl Math 68:1600-1617, 2008). The winning species expected from theory is the one with the lowest "substrate subsistence concentration" s([star]), such that its corresponding equilibrium growth rate is equal to the dilution rate D. This theoretical result was validated experimentally with phytoplankton (Tilman and Sterner in Oecologia 61(2):197-200, 1984) and bacteria (Hansen and Hubell in Science 207(4438):1491-1493, 1980), and observed in a lake with microalgae (Tilman in Ecology 58(22):338-348, 1977). On the contrary for aggregating bacterial species described by a Contois model, theory predicts coexistence between several species (Grognard et al. in Discrete Contin Dyn Syst Ser B 8(1):73-93, 2007). In this paper we present a generalization of these results by studying a competition between three different types of microorganisms: planktonic (or free) bacteria (represented by a generalized Monod model), aggregating bacteria (represented by a Contois model) and free phytoplankton (represented by a Droop model). We prove that the outcome of the competition is a coexistence between several aggregating bacterial species with a free species of bacteria or phytoplankton, all the other free species being washed out. This demonstration is based mainly on the study of the substrate concentration's evolution caused by competition; it converges towards the lowest subsistence concentration s([star]), leading to three different types of competition outcomes: (1) the best free bacteria or phytoplankton competitor excludes all other species; (2) only some aggregating bacterial species coexist in the chemostat; (3) A coexistence between the single best free species, with one or several aggregating species.
在连续培养中，微生物物种之间基于资源的竞争已在实验和理论上得到广泛研究，主要是针对细菌通过莫诺德（Monod）和康托伊斯（Contois）的“恒定产量”模型，或者针对浮游植物通过德鲁普（Droop）的“可变产量”模型。对于由N种细菌（莫诺德模型）或N种浮游植物（德鲁普模型）组成的同质种群，在一种限制性底物和恒定控制条件下，理论研究表明会发生竞争排斥：只有一个物种赢得竞争并取代所有其他物种（阿姆斯特朗和麦吉hee，《美国博物学家》，115:151，1980；许和许，《工业与应用数学学会应用数学杂志》，68:1600 - 1617，2008）。理论上预期的获胜物种是具有最低“底物维持浓度”s([星号])的物种，使得其相应的平衡生长速率等于稀释率D。这一理论结果已通过浮游植物实验（蒂尔曼和斯特纳，《生态学》，61(2):197 - 200，1984）和细菌实验（汉森和哈贝尔，《科学》，207(4438):1491 - 1493，1980）得到验证，并在一个有微藻的湖泊中观察到（蒂尔曼，《生态学》，58(22):338 - 348，1977）。相反，对于由康托伊斯模型描述的聚集性细菌物种，理论预测几种物种会共存（格罗尼亚德等人，《离散与连续动力系统系列B》，8(1):73 - 93，2007）。在本文中，我们通过研究三种不同类型微生物之间的竞争对这些结果进行了推广：浮游（或自由）细菌（由广义莫诺德模型表示）、聚集性细菌（由康托伊斯模型表示）和自由浮游植物（由德鲁普模型表示）。我们证明竞争的结果是几种聚集性细菌物种与一种自由细菌或浮游植物物种共存，所有其他自由物种被冲走。这一证明主要基于对竞争引起的底物浓度演变的研究；它趋向于最低维持浓度s([星号])，导致三种不同类型的竞争结果：（1）最佳的自由细菌或浮游植物竞争者排除所有其他物种；（2）只有一些聚集性细菌物种在恒化器中共存；（3）单一最佳自由物种与一种或几种聚集性物种共存。
