Tragedy of the commons in the chemostat

Abstract

We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. Whereas the tragedy is commonly set in a game theoretical context, and attributed to an underlying Prisoner’s Dilemma, we take an alternative approach based on basic mechanistic principles of species growth that does not rely on the specification of payoffs which may be difficult to determine in practice. We establish the tragedy in the context of a general chemostat model with two species, the cooperator and the cheater. Both species have the same growth rate function and yield constant, but the cooperator allocates a portion of the nutrient uptake towards the production of a public good -the “Commons” in the Tragedy- which is needed to digest the externally supplied nutrient. The cheater on the other hand does not produce this enzyme, and allocates all nutrient uptake towards its own growth. We prove that when the cheater is present initially, both the cooperator and the cheater will eventually go extinct, hereby confirming the occurrence of the tragedy. We also show that without the cheater, the cooperator can survive indefinitely, provided that at least a low level of public good or processed nutrient is available initially. Our results provide a predictive framework for the analysis of cooperator-cheater dynamics in a powerful model system of experimental evolution.

Ecology drives the evolution of diverse siderophore-production strategies in the opportunistic human pathogenPseudomonas aeruginosa

“…the fixation of cheaters and the concomitant collapse of populations. Such a scenario has been proposed for several microbial social traits (Rankin et al 2007; Kümmerli et al 2015; Schuster et al 2017). One possible explanation for its absence is that most cheater clones still produced some pyoverdine, allowing them to grow even in the absence of regular pyoverdine producers (Fig.…”

“…It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for this this version posted January 27, 2021. ; https://doi.org/10.1101/2021.01.27.427959 doi: bioRxiv preprint collapse of populations. Such a scenario has been proposed for several microbial social traits (Rankin et al 2007;Kümmerli et al 2015;Schuster et al 2017). One possible explanation for its absence is that most cheater clones still produced some pyoverdine, allowing them to grow even in the absence of regular pyoverdine producers (Fig.…”

Competition for nutritional resources masks the true frequency of bacterial mutants

“…Cheaters are better able to exploit the cooperators in dense populations and when the cheaters themselves are less frequent than the cooperators [ 68 ]. However, if the magnitude of cheating increases such that the number of cheaters far exceeds the number of cooperators, the whole community collapses resulting in a situation known as the tragedy of the commons [ 21 , 69 , 70 ]. The unfair competition between cheaters and cooperators is aggravated by the fact that the cooperators, carrying the burden of producing the public goods (AP in our case), display a lower relative fitness compared to the cheaters [ 71 ].…”

“…The glycerol produced by the PCMs leaches out and is sequestered by the overwhelming presence of surrounding wild-type cells. Since the concentration of glycerol is not sufficient to support the growth of both PCM and wild-type cells, the population collapses, as in a “tragedy of the commons-like” case [ 21 – 23 ]. Only a tiny fraction of the PCMs eventually manage to grow and form colonies.…”

Fluctuating Environment Can Negate Cheater Success Due to Speed-Agility Trade-Off

“…When unchecked, cheaters in a community can proliferate and disrupt the system's stability, leading to collapse (Fiegna & Velicer, 2003;Kümmerli et al, 2015;Rainey & Rainey, 2003;Rankin et al, 2007;Ross-Gillespie et al, 2007;Schuster et al, 2017). This extreme outcome would not only require cheater emergence (constrained mostly by stochastic mechanisms), but also cheater proliferation (constrained mostly by non-random, selective mechanisms) (Fiegna & Velicer, 2003).…”