Institut des Sciences de l'Evolution, Centre National de la Recherche Scientifique, UMR 5554, Université Montpellier II, 34095 Montpellier, France

Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

National Centre for Ecological Analysis and Synthesis, 435 State Street, Suite 300, Santa Barbara, CA 93101-3351, USA

Department of Behavioural Ecology, University of Bern, Wohlenstr. 50a, 3032 Hinterkappelen, Switzerland

Abstract

Background

Recent work on the complexity of life highlights the roles played by evolutionary forces at different levels of individuality. One of the central puzzles in explaining transitions in individuality for entities ranging from complex cells, to multicellular organisms and societies, is how different autonomous units relinquish control over their functions to others in the group. In addition to the necessity of reducing conflict over effecting specialized tasks, differentiating groups must control the exploitation of the commons, or else be out-competed by more fit groups.

Results

We propose that two forms of conflict – access to resources within groups and representation in germ line – may be resolved in tandem through individual and group-level selective effects. Specifically, we employ an optimization model to show the conditions under which different within-group social behaviors (cooperators producing a public good or cheaters exploiting the public good) may be selected to disperse, thereby not affecting the commons and functioning as germ line. We find that partial or complete dispersal specialization of cheaters is a general outcome. The propensity for cheaters to disperse is highest with intermediate benefit:cost ratios of cooperative acts and with high relatedness. An examination of a range of real biological systems tends to support our theory, although additional study is required to provide robust tests.

Conclusion

We suggest that trait linkage between dispersal and cheating should be operative regardless of whether groups ever achieve higher levels of individuality, because individual selection will always tend to increase exploitation, and stronger group structure will tend to increase overall cooperation through kin selected benefits. Cheater specialization as dispersers offers simultaneous solutions to the evolution of cooperation in social groups and the origin of specialization of germ and soma in multicellular organisms.

Background

Cooperation is central to transitions in individuality

Previous work highlights group and kin selection

A key type of subunit specialization in multicellular organisms is the separation of germ and soma

A pervasive feature in a diverse array of social systems is that individuals not contributing to the common good either act as dispersers, or are either rewarded for, or coerced into, cooperating. Examples range from bacteria (e.g.

**(Table S1)**. Examples of group formation for which there is some information on dispersal, relatedness and punishment/policing.

Click here for file

These empirical patterns merit explanation, and we take a first step by employing optimization techniques to evaluate the conditions leading to associations between dispersal and social strategy. Sociality in our models takes the form of cooperation in the production of a public good. Previous study of public goods has shown how cheating, if left unchecked, potentially leads to a "tragedy of the commons"

We develop a model based on kin selection that incorporates dispersal specialization, as suggested by the case studies in Table S1 (see Additional file

Methods

We formalize our verbal arguments given above by developing and analyzing a model of coevolution between exploitation of the commons and dispersal. From the outset, we stress that our model is a highly simplified representation of this process, and not aimed to make quantitative predictions for any given system. Rather, our goal is to identify the qualitatively important drivers in the coevolution of individual strategies and the evolution of multicellularity.

In our model the focal units of selection are individuals themselves, rather than the higher-level unit. A transition to multicellularity is favored when the interests of the individual and the higher-level (the group) are aligned

We analyze an optimization model that takes into account the effect of both the phenotype of the focal individual and the average phenotype of the group in which it lives, on the fitness of the focal individual (see Table

Parameters and variables used in this study.

w

Individual fitness

r

Relatedness between any two randomly selected individuals in the group

s

Individual cost to cooperator growth in the group

k

Number of individuals in a group (an inverse measure of kin selection)

c

Individual cost to cooperator dispersal

e

Individual cost to cheater dispersal

Q

Impact of sedentary cheaters on the individual fitness of group members (via consumption of the public good)

P

Impact of sedentary cooperators on the individual fitness of group members (via production of the public good)

n

Relative frequency of cooperators in the group (1-n is the proportion of cheaters)

z

Relative frequency of cheaters dispersing

y

Relative frequency of cooperators dispersing

d

Overall investment in dispersal. d = yn + z(1-n)

Φ

Overall cooperation with respect to the public good. Φ = n*(1-y*)+(1-n*)z*

σ

Association between dispersal and cooperation. σ = y/(y+z)

Our model makes several assumptions. First, we do not explicitly consider dynamics, such as group founding, group numbers, individual emigration and immigration, and competition for limiting resources within or between groups. Rather, we assume negligible variation in inter-group competition. Second, our model does not explicitly incorporate genetic polymorphisms, meaning that the heritable traits are probabilities to adopt alternatives of each strategy (disperse or stay; cooperate or cheat) depending on environmental and/or social conditions

Life cycle and fitness equations

We assume that a group's life-cycle has three sequential stages: colonization, growth, reproduction and survival of individuals within the group; exhaustion of resources; and the dispersal of survivors. Some of the survivors may stay at the same site of the source group, and others disperse as colonists to other sites.

The model tracks the fitness contribution of a mutant individual

The proportion of cooperators in the group is _{i }(for simplicity, hereafter we denote individual _{i }as the investment of a cooperator in dispersal and _{i }as the investment of a given cheater in dispersal. Both of these quantities take on continuous values between zero and one. The mean proportions of dispersing cooperators and cheaters in group _{j}_{j }and _{j}(1-_{j}), respectively and overall investment in dispersal is _{j }= _{j}_{j }+ _{j}(1-_{j}).

The fitness equation takes the form

_{i }= _{i}, _{i}, _{i}) _{i}, _{i}, _{i}) _{i}, _{i}, _{i}),

where the functions

Dispersal is modeled by considering the fitness contributions of both individuals that stay at the site previously occupied by the group and others that disperse

The function,

_{i}, _{i}, _{i}) = [(1 - _{i }(1-_{i}) - _{i }_{i})/(1 - _{j }(1-_{j}) - _{j }_{j }+ (1-_{i }(1-_{i}) + (1-_{i }_{i})/(1 -

The first term in square brackets describes the fitness of a non-disperser (1 - _{i }(1-_{i}) - _{i }_{i}) relative to the average non-disperser (1 - _{j }(1-_{j}) - _{j }_{j}) and immigrants ((1-_{i }(1-_{i}) + (1-_{i }_{i}) given the competition it faces with residents (1 -

All non-dispersing individuals are selected to exploit, but given our assumption that there is a cost of cooperation (

_{i}, _{i}, _{i}) = [(1-_{i}) (1-_{i}) + (1-s) (1-_{i}) _{i}]/[(1-_{j}) (1-_{j}) + (1-s) (1-_{j}) _{j}],

where the subscript

The overall effect of group investment in the public good on individual fitness is described by

_{i}, _{i}, _{i}) = 1 + P (1-_{j}) _{j }- Q (1-_{j}) (1-_{j}),

where it is assumed that non-dispersing cooperators have a positive effect on the public good (scaled by P) as their frequency, _{j}, increases _{j}, increases. Note that in the absence of cooperators, cheats can persist as long as their impact on the commons is sufficiently low (

Relatedness and numerical simulation methods

We analyze the model by employing the Price Equation, which enables us to express possible fitness maxima as a function of constant parameters and variables, and the relatedness,

_{i}/d_{i }= ∂_{i}/∂_{i }+ _{i}/∂_{j}

from which we can find a steady state(s) when d_{i}/d_{i }= 0 to find any or all

In our model,

^{2 }

This recursion tracks the probability that a given focal individual is identical by descent to another randomly picked individual at time

In the recursion above, the term 1/^{2}). This is multiplied by the relatedness from the previous round. Solving this recursion relation yields the equilibrium relatedness, which is

^{2}).

As we assume weak selection, the probability that a given individual disperses depends on the probability that it is a cooperator and disperses, plus the probability that it is a cheater and disperses, so _{i }= _{j }=

Optimal strategies were solved numerically. This consisted of iterating equation (5) with steps of 0.05 or smaller for a total of 100,000 steps, which was sufficient to identify the steady state in all cases. We found that whereas initial levels of evolving variables did not affect the optimal solution when only dispersal frequencies

Results

We consider two scenarios. In the first (Model 1) only dispersal in cooperators (

In addition to optimal levels of dispersal (Model 1), and of cooperation and dispersal (Model 2), we examine the effects of model parameters on dispersal specialization σ =

Model 1

Optimal solutions always yielded partial or complete specialization, with cooperators tending to disperse more than cheaters (i.e., σ > 0.5) for high costs of cooperation (

Globally optimal associations in dispersal and exploitation strategy for Model 1

**Globally optimal associations in dispersal and exploitation strategy for Model 1**. Axes:

Low effective group size (low

Effects of parameters on optimal dispersal levels for Model 1

**Effects of parameters on optimal dispersal levels for Model 1**. Effects of public good production (

Cheater and cooperator dispersal can be understood as follows. When the group is dominated by cheaters (low

Model 2

Permitting social evolution introduces the possibility that the frequency of cooperators or cheaters fixes to zero or one, in which case associations (σ) between dispersal and social strategies are irrelevant. We find that depending on parameter combinations, either only a single global optimum is obtained, or two alternative local optima are possible. In the latter case, which state is obtained depends on initial levels of

The fraction of simulations in Model 2 leading to different local optima

**The fraction of simulations in Model 2 leading to different local optima**. Results based on 100 simulations in which initial levels of

We observed four basic outcomes (Fig.

Locally optimal associations between dispersal and exploitation strategy

**Locally optimal associations between dispersal and exploitation strategy**. The frequency of dispersal in cooperators (

Whereas in Model 1, the relative cost of cooperator (

Relatedness,

**Relatedness, r*, associated with simulations in Figure 4.**

If we define the functional role of a cooperator as contributing to the public good, and that well functioning groups minimize the impact of cheats on the public good, then, trivially, specialization resulting in mobile cooperators and sedentary cheaters corresponds to a non-social, individualistic scenario, and cannot be considered a group related phenomenon. There are however two ways in which the impact of cheaters on the commons can be reduced: either 1-

Overall cooperation, Φ =

**Overall cooperation, Φ = n *(1 - y*)+(1-n*)z*, associated with simulations in Figure 4.**

Discussion

Our results are in broad agreement with the tenets of kin selection theory for explaining dispersal

The examples presented in Table S1 (see Additional file

Transitions in individuality and social complexity are generally thought to require some form of reduction in genetic variance during the reproductive process

Our findings have precedent, both in the study of symbiotic associations, and investigations of cooperation within species. With regard to host-parasite and symbiotic interactions, previous research has considered how parasite virulence (which is analogous to cheaters exploiting cooperative groups) may evolve spatially (e.g.,

In a model investigating cooperation in spatially viscous environments, van Baalen and Rand

Conclusion

Our results suggest that the establishment of trait linkage between dispersal and the propensity of within-group cheating may be a general phenomenon promoting complex social organization and multicellularity. Importantly, we cautiously suggest this should be operative regardless of whether groups ever achieve higher levels of individuality, because selection on individual components will always tend to increase exploitation, and stronger group structure will tend to increase overall cooperation through kin selected benefits

Authors' contributions

MEH conceived the study, developed and analyzed the model and wrote the manuscript. DJR participated in the design of the study, developed the model and participated in writing the manuscript. MT participated in the design of the study, constructed Table S1, and participated in writing the manuscript. All authors read and approved the final manuscript.

Acknowledgements

We thank Daniel Blumstein, Ross Crozier, Steve Frank, Toby Kiers, Barbara Taborsky, Peter Taylor and Don Waller for helpful discussions, and Steve Frank, Andy Gardner, Paul Rainey, Stuart West and two anonymous reviewers for comments on earlier drafts. MEH acknowledges the Santa Fe Institute (2005), the National Center of Ecological Analysis and Research (2006–2007), and the Centre National de la Recherche Scientifique for financial support. MT and DJR acknowledge the Swiss National Science Foundation for support (SNF-grant 3100A0-105626).