Elsevier

Journal of Theoretical Biology

Volume 299, 21 April 2012, Pages 31-41
Journal of Theoretical Biology

Understanding microbial cooperation

https://doi.org/10.1016/j.jtbi.2011.03.008Get rights and content

Abstract

The field of microbial cooperation has grown enormously over the last decade, leading to improved experimental techniques and a growing awareness of collective behavior in microbes. Unfortunately, many of our theoretical tools and concepts for understanding cooperation fail to take into account the peculiarities of the microbial world, namely strong selection strengths, unique population structure, and non-linear dynamics. Worse yet, common verbal arguments are often far removed from the math involved, leading to confusion and mistakes. Here, we review the general mathematical forms of Price's equation, Hamilton's rule, and multilevel selection as they are applied to microbes and provide some intuition on these otherwise abstract formulas. However, these sometimes overly general equations can lack specificity and predictive power, ultimately forcing us to advocate for more direct modeling techniques.

Introduction

Cooperation presents a fundamental challenge to customary evolutionary thinking. If only the fittest organisms survive, why would an individual ever pay a fitness cost for another organism to benefit? Traditionally, kin selection and group selection have been the most prominent explanations for the maintenance of cooperation in nature. Kin selection refers to cooperative behaviors being favored when they are preferentially directed towards relatives (Hamilton, 1964). In turn, group selection, also known as multilevel selection, suggests that altruistic traits can be favored because of their beneficial effect on a group, despite the individual cost of such behaviors (Wilson, 1975).

While the connection between kin and multilevel selection was initially unclear, recent theoretical work has elucidated many of the similarities and differences between the two concepts (Nowak, 2006b, Page and Nowak, 2002, Fletcher and Zwick, 2006, Wenseleers et al., 2009). In particular, the underlying theme behind all mechanisms for the evolution of altruism is the assortment of similar individuals (Fletcher and Doebeli, 2009). When similar individuals are assorted, cooperators are more likely than average to interact with other cooperators and non-cooperating defectors are, in turn, more likely to interact with defectors. This assortment is ascribed to relatedness in kin selection and between-group variance in multilevel selection models. Both methods are equivalent when applied correctly and under certain assumptions. Unfortunately, when these assumptions do not hold, both methods resort to abstract generalities, making application difficult and prone to error.

Microbes present a unique opportunity for scientists interested in the evolution of cooperation because of their well-characterized and simple genetics, fast generation times, and easily manipulated and measured interactions. While these advantages are often well appreciated, other differences between organisms of the microscopic and macroscopic world are sometimes forgotten when transferring ideas and methods from the study of animals to that of microbes. Important differences include strong selection strengths, fast evolution times, high levels of diversity, and non-linear dynamics, all of which invalidate many less general techniques derived using specific assumptions, a fact too often ignored or simply unknown by non-theorists.

In this review, we examine the standard techniques used to understand cooperation, as they are applied to microbes. This allows us to make several simplifications, particularly in genetics, but it also means that we will not cover any technique inappropriate to microbes. With that said, many of our points are pertinent to any scientist in the field of cooperation or microbial biology, but some may only be valid when considering microbial cooperation.

Section snippets

Four basic classes of cooperation

To begin, let us define cooperation as any act that increases the fitness of others. Now, if we have two strains of a microbe, one an obligate cooperator and the other a defector that never cooperates, there are still four fundamentally different classes of interactions that fit within this definition of cooperation. For example, imagine mixing the two strains at different relative fractions in a test tube, either: one strain performs better than the other at every frequency, or one strain

Price's equation

The Price equation provides a general and exact mathematical description of evolution, with applications in kin and multilevel selection models (Price, 1970, Page and Nowak, 2002). First assume each individual, i, has a genotype, Gi, that can be quantitatively described. For example, Gi is often arbitrarily set to 1 if the (haploid) individual has the cooperative gene and 0 if it does not, a convention we will repeat in this paper. Now, if we want to know how the genotype frequency changes in

Hamilton's rule

In 1964, Hamilton stated his famous rule: a cooperative act will be favored by natural selection if the cost, c, of performing the cooperative act is less than the benefit, b, given to the other individual times the relatedness, r, between the two individuals, or equivalently ifrbc>0.

While pleasingly simple, the assumptions that went into deriving this rule almost never hold even in simple models, much less microbial systems (Cavalli-Sforza and Feldman, 1978, Karlin and Matessi, 1983, Nowak et

Weak selection

Before moving on to alternative methods of conceptualizing and analyzing cooperation, let us discuss why the simple form of Hamilton's rule – without any regressions – is usually inappropriate for the study of microbes. Hamilton thought of evolution as a very slow and gradual process where each mutant varied only slightly from the wild type and this can be seen in many of the assumptions used in deriving the simple form of Hamilton's rule, namely the assumption of weak selection (Hamilton, 1964

Multilevel selection

Multilevel selection, also known as group selection, has gone through its ups and downs, from once being completely discredited to now being acknowledged as an important organizing principle that can aid in the evolution of cooperation (Traulsen and Nowak, 2006, Nowak, 2006b). Multilevel selection occurs whenever selection acts on multiple levels, such as when individuals are partitioned into groups and the groups themselves compete – either directly or indirectly – in addition to the

Common misconceptions

Perhaps the biggest misconception in the study of the evolution of cooperation is that there is something special, or even magical, about kin selection that allows it to explain phenomena that other theories cannot. Inclusive fitness, the basis of kin selection, is the effect of an individual's action on everyone's fitness weighted by the relatedness between the individuals; this is simply an alternative accounting scheme and, therefore, cannot produce novel predictions outside of the scope of

Discussion

For researchers studying microbial interactions, the most important steps towards understanding the system are experimental measurements and modeling (Brännström and Dieckmann, 2005, MacLean and Gudelj, 2006, Xavier and Foster, 2007). Without even a rough model of the interaction, no predictions or explanations of phenomena can be made. Unfortunately, the simplicity of Hamilton's rule often discourages researchers from doing any modeling beyond the simple idea that cooperators pay a fixed cost,

Acknowledgements

We would like to thank j. smith, M. van Veelen, E. Yurtsev, S. Serene, A. Velenich, K. Korolev, and the rest of the laboratory for stimulating discussions and constructive criticisms. We are also thankful to the two anonymous reviewers for their useful comments. The laboratory acknowledges financial support through an NIH K99 Pathways to Independence Award.

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