Cooperation and Hamilton's rule in a simple synthetic microbial system

Abstract

A fundamental problem in biology is understanding the evolutionary emergence and maintenance of altruistic behaviors. A well-recognized conceptual insight is provided by a general mathematical relation, Hamilton's rule. This rule can in principle be invoked to explain natural examples of cooperation, but measuring the variables that it involves is a particularly challenging problem and controlling these variables experimentally an even more daunting task. Here, we overcome these difficulties by using a simple synthetic microbial system of producers and nonproducers of an extracellular growth-enhancing molecule, which acts as a 'common good.' For this system, we are able to manipulate the intrinsic growth difference between producers and nonproducers, as well as the impact of the common good on the growth rate of its recipients. Our synthetic system is thus uniquely suited for studying the relation between the parameters entering Hamilton's rule and the quantities governing the systems' behavior. The experimental results highlight a crucial effect of nonlinearities in the response to the common good, which in general tend to limit the predictive value of Hamilton's rule.

Figure 1

Decreasing the relative growth of producers versus nonproducers reverses the direction of selection. (A) Schematic of a modified producer–nonproducer system composed of Arg⁻ (arginine auxotroph) producers and Arg⁺ nonproducers (see text and Materials and methods for details). (B) Growth curves of Arg⁻ versus Arg⁺ producers grown in minimal media lacking antibiotic at 30°C with varying arginine concentrations (different colors; 1 × = 520 μM arginine). (C) The overall proportion of producers, Δp̄, decreases under selective conditions (in antibiotic; producer–nonproducer mixtures with p_g distributed uniformly) when the arginine concentration is decreased. (Insets) Growth curves of producer–nonproducer mixtures (differing in p_g) corresponding to two conditions of low (0.05 × ) and intermediate (0.3 × ) arginine concentrations. Note: With argHΔ, limiting arginine does not have large effects on growth rates, but rather overall growth levels—this does not affect our conclusions as what matters here is only how much growth occurred during the selection phase in antibiotic.

Figure 2

Increasing the antibiotic resistance response to autoinducer reverses the direction of selection. (A) Schematic of a modified producer–nonproducer system in which all autoinducer recipients have increased dosage (‘extra rhlR') of the autoinducer-responsive transcription factor gene, rhlR (see text and Materials and methods for details). (B) Growth curves of extra rhlR nonproducers versus control nonproducers in antibiotic in the presence of varying amounts of exogenously added autoinducer. (C) The overall proportion of producers, Δp̄, decreases under selective conditions (in antibiotic; producer–nonproducer mixtures with p_g distributed uniformly) when autoinducer recipient cells were made more responsive to autoinducer by increased rhlR dosage (‘extra rhlR'). (Insets) Growth curves of producer–nonproducer mixtures (differing in p_g) from the extra rhlR system (left) versus the control system (right).

Figure 3

Interpretation of the ‘benefit' parameter b in the presence of nonlinearities. (A) Two different systems (blue and red) have different nonlinear relations between the initial proportion of cooperators, p_g, in a mixed group, g, and the factor by which such a population is multiplied, w_g. When different groups of equal size are formed, here two groups with proportion of producers p₁ and p₂, the value of b entering Hamilton's rule, Equation (1) of Box 1, is given by the regression coefficient b defined in Equation (3) of Box 1. This regression coefficient corresponds here to the slope of the line joining the two points associated with p₁ and p₂ on the curve (in the presence of more than two groups, b would correspond to the slope of the best linear interpolation between the different points). In this example b_blue>b_red in spite of the fact that the red system systematically outgrows the blue system with any given fraction of cooperators, i.e., w_blue(p_g)<w_red(p_g) for all p_g. (B) Growth rates of extra rhlR (circles) and control (squares) nonproducers in the presence of varying amounts of Rhl autoinducer and antibiotic (Cm). Growth rates were determined by fitting growth curves to a logistic equation. The approximate range of autoinducer concentrations experienced by cells during an experiment of Figure 2C is outlined in the dashed magenta box.