Why mussels stick together: spatial self-organization affects the evolution of cooperation
Cooperation with neighbours may be crucial for the persistence of populations in stressful environments. Yet, cooperation is often not evolutionarily stable, since non-cooperative individuals can reap the benefits of cooperation without having to pay the costs associated with cooperation. Here we show that active aggregation leading to self-organized spatial pattern formation can promote the evolution of cooperativeness. To this end, we study the effect of movement strategies on the evolution of cooperation in mussel beds. Mussels cooperate by attaching themselves to neighbours via byssal threads, thereby providing mutual protection. Using an individual-based model for mussel bed formation, we first demonstrate that the spatial pattern and the corresponding number of neighbours strongly depends on the movement strategies of the mussels. With an evolutionary model, we then show that this has important implications for the evolution of cooperation, since the evolved level of cooperativeness (the number of byssus threads produced) strongly depends on the number of neighbours and on the harshness and variability of the environment. Our results suggest that spatial aggregation, abundantly found in self-organized ecosystems, may promote the evolution of cooperation.
KeywordsCooperation Spatial structure Eco-evolutionary dynamics Mytilus edulis Mussels
Cooperation between neighbouring individuals is often essential for survival in stressful environments (Bertness and Callaway 1994; Callaway and Walker 1997; Holmgren et al. 1997; Stachowicz 2001). Organisms ameliorate their environment locally, for instance by providing shade or by drawing moisture and nutrients towards themselves and close neighbours (Schlesinger et al. 1996; Aguiar and Sala 1999), which allows others to survive in an otherwise hostile world. To what extent cooperation evolves in a population depends on the nature and intensity of interactions between individuals (Hamilton 1963; Axelrod and Hamilton 1981; Nowak and May 1992; Rainey and Rainey 2003; Doebeli and Hauert 2005; Santos and Pacheco 2005; Ohtsuki et al. 2006; Santos et al. 2006; West et al. 2007; Masuda 2007; Van Dyken and Wade 2012). The number of cooperating individuals an organism interacts with likely determines the effectiveness of its cooperation strategy and may affect the degree of cooperativeness that evolves within a population (Vainstein and Arenzon 2001; Zhang et al. 2005; Ohtsuki et al. 2006; Hui and McGeoch 2007).
Even if cooperation is profitable for all interacting individuals, it is intrinsically unstable when recipients can reap the benefits of cooperation without helping others in return. Such a social dilemma can be solved to a certain extent by spatial population structure (Axelrod and Hamilton 1981; Nowak and May 1992; West et al. 2002). Especially in highly viscous populations, where cooperative traits are transferred locally, the effects of network structure and neighborhood size have been studied extensively (Pfeiffer and Bonhoeffer 2003; Rainey and Rainey 2003; Santos and Pacheco 2005; Ohtsuki et al. 2006; Santos et al. 2006; Masuda 2007). Yet, little is known about the evolution of local cooperation in species that disperse their offspring over a wide range, but interact locally. This is, in particular, the case for widely dispersing organisms that upon settlement, move into a self-organized spatial structure.
Systems as diverse as mussel beds, coral reefs, marsh tussocks, tidal wetlands, peat lands, arid ecosystems, and ribbon forests are highly structured in space due to the interplay of local facilitation and long-range inhibition (Klausmeier 1999; Mistr and Bercovici 2003; Rietkerk et al. 2004a, b; van de Koppel et al. 2005, 2008; van de Koppel and Crain 2006; Rietkerk and Van de Koppel 2008; Eppinga et al. 2009). In these systems, the number of potentially cooperating neighbours depends on the spatial scale and distribution pattern of the population. In many systems, the spatial pattern results from the active movement of organisms (Theraulaz et al. 2003; Jeanson et al. 2005; van de Koppel et al. 2008; de Jager et al. 2011; Hemelrijk and Hildenbrandt 2012). Accordingly, the movement strategies of these organisms can indirectly affect the number of neighbours an individual will encounter. In situations where costs and benefits of facilitation depend on the availability and density of local neighbours, the movement strategy therefore affects the evolution of facilitation.
An example of active pattern formation can be found in intertidal mussel beds. Mussels self-organize into large-scale labyrinth-like patterns (van de Koppel et al. 2005, 2008). They use their foot to aggregate into a group of conspecifics after wide dispersion by the currents during the larval stage (Geesteranus 1942). Because mussels are well-mixed during their larval stage, relatedness between neighbouring individuals is, on average, equal to the relatedness between distant individuals within the same mussel bed (Ferguson et al. 2013). When aggregated, mussels facilitate each other by attaching byssus threads (a glue-like substance made of protein strands, which are costly to produce; Eckroat and Steele 1993) to the shells of conspecifics that are within reach. These attachments decrease the risks of dislodgement and predation for both the attaching mussel and the one receiving the byssus thread (Hunt and Scheibling 2001, 2002). Mussels that are sufficiently affixed by neighbours do not need to create attachments themselves and can therefore avoid the costs of producing byssus threads. Through active aggregation into mussel clumps with various densities, mussels can modify the number of neighbours within their attachment range. By self-organizing into the labyrinth-like patterns that are characteristic for intertidal mussel beds, mussels attain an intermediate number of neighbours, which lies between the few neighbours that are within attachment distance in scattered distributions and many neighbours in dense mussel clumps.
In this paper, we investigate how spatial patterns affect the evolution of cooperativeness in self-organized mussel beds. For this purpose, three questions regarding cooperation in mussel beds will be addressed. First, we investigate how the aggregation strategy of mussels affects the spatial pattern and, in particular, the number of neighbours available for cooperation. Aggregation in mussels typically leads to the formation of a spatial pattern consisting of regularly spaced strings and clumps (van de Koppel et al. 2005, 2008). With an individual-based model (IBM), we investigate how the number of neighbours a mussel experiences is related to this self-organized pattern. Second, we examine, by means of an adaptive dynamics approach, how the number of neighbours affects the tendency to attach costly byssus threads to neighbours, which we interpret as the cooperativeness of an individual. Building on the fundamental assumption that the spatial pattern relates to the average number of neighbours that a mussel can attach its byssus threads to, investigating how the number of neighbours affects the evolution of the attachment tendency of mussels gives us insight into whether and how aggregation strategies promote or hamper cooperation. Third, we study the effect of harshness of the environment. It is likely that this affects the evolution of cooperation, since for mussels, survival under stressful conditions depends on how well they are attached to their neighbours. Furthermore, we take into account that environmental stress likely differs substantially between generations, which may further affect the evolution of cooperativeness.
An individual-based model of self-organized patterning
We modelled the effect of individual aggregation strategies on the formation of mussel beds with an IBM. As the self-organized pattern in mussel beds is a compromise between reducing wave stress and predation risk (requiring dense aggregations) on the one hand and minimizing food competition (requiring low densities on a larger spatial scale) on the other (van de Koppel et al. 2005, 2008), mussels move around until they find a location where local mussel densities are sufficiently high and densities at a larger scale are low enough to permanently establish in the mussel bed. We developed an IBM that describes pattern formation in mussels by relating the chance of movement to the density of the mussels at two spatial scales, i.e. within a short-distance of 2 cm and a long distance of 7.5 cm, following de Jager et al. (2011). We consider 1600 circular individuals with a diameter of 1 cm that are initially spread homogeneously on a 30 × 30 cm surface. In each of the 500 time steps within a simulation, all individuals get a chance to move in random order. Whether a mussel moves or not depends on the density of mussels within the local attachment range of 1.1 cm ø (i.e. the ‘local density’) and the density of mussels within the larger, 3.3 cm ø competition range (i.e. the ‘long-range density’); a mussel moves when the local density is lower than a certain settlement threshold (which we will vary below) and/or when the long-range density is higher than 0.7 individuals/cm2. These parameter values were estimated using a regression analysis of experimental data (van de Koppel et al. 2008; de Jager et al. 2011). We modelled the movement of individuals in correspondance to natural mussel movements, using a heavy-tailed step length distribution (a Lévy walk with μ = 2; de Jager et al. 2011), where steps are made in random directions and their lengths are drawn from a power law distribution. A mussel ends its step prematurely when it encounters a conspecific (de Jager et al. 2014). In our model, mussels cooperate after (and not during) pattern formation; therefore the attachment of byssus threads does not impair mussel movement. To examine the relation between the number of neighbours within the facilitation range and the spatial structure that emerges in the self-organized mussel bed, we simulated mussel bed formation for a range of settlement thresholds, e.g. the minimum mussel density required for local aggregation. We plotted the emergent spatial patterns and calculated the average number of neighbours ±SE within attachment range for each simulation.
A model for the evolution of between-mussel cooperation
The parameter E in Eq. 3 represents environmental conditions, such as wave stress and predation risk. In harsh environments, E will take on a larger value than in benign environments. We will examine the evolution of attachment for a range of environmental conditions. Furthermore, environmental conditions are likely to vary between generations. Hence, we will also investigate the effect of alternating environments on the evolution of cooperation.
Spatial patterning relates to number of neighbours
Evolution of the attachment tendency A
Changing environmental stress levels
Because mussels disperse over a wide range as larvae before settling on a mussel bed, environmental conditions are most likely different between generations. Adaptation of between-mussel cooperation to a particular stress level is therefore difficult and evolution of cooperation becomes more challenging than described above. We investigate the robustness of our results above to variability in the environmental conditions that are encountered during the adaptation process. In Fig. 4b, we considered the three situations where the environmental stress level a generation encounters is variable; drawn from a random distribution (μ = 6) with low (σ = 1), intermediate (σ = 3), and high (σ = 5) variation in stress. When variation in E is high, the evolutionarily stable attachment tendency is very low for all n. With a mean stress level μ = 6, only at low variation in environmental stress do we find a hump-shaped relation between the number of neighbours and the average number of attachments a mussel produces. This confirms the results we obtained in the absence of environmental variation between generations (Fig. 4a).
Cooperation is often a necessity for survival in harsh environments and is therefore found in many species. Organisms utilize a multitude of supporting traits and behaviours, such as local dispersal, reciprocity, and punishment, to maintain high levels of cooperation (West et al. 2007). Our theoretical analysis reveals that in intertidal mussels, movement into spatial aggregations stimulates the evolution of cooperation. Because mussels benefit from any attachment of byssus threads with neighbouring individuals, some degree of between-mussel cooperation evolves in any type of mussel bed, irrespective of the number of neighbours. However, our analysis shows that the number of neighbours that maximizes investment in cooperation depends on environmental conditions and overall mussel density. In low stress environments with little inter-generational variation in stress, aggregating in scattered distributions maximizes investment in cooperation. In contrast, investment in cooperation is maximized when mussels aggregate in dense clumps in high stress environments with considerable variation in stress between generations. Yet, aggregating in labyrinth-like patterns, which mussels do in natural mussel beds, only maximizes investment in byssal attachments in a small range of environments with intermediate stress levels and corresponding inter-generational variation in stress. Based on our results and those of others (Ohtsuki et al. 2006; Santos et al. 2006; Masuda 2007), we can conclude that forming spatial aggregations can substantially influence the degree of cooperativeness that evolves in a population.
For simplicity, we did not take the correlation between environmental stress and food availability into account. In most intertidal ecosystems, an extensive range of environmental conditions can be encountered at any time, from very benign habitats that also provide little food, to very hash conditions where food is often abundant. Mussel offspring is likely to reach all of these habitats, as is wittnessed by the high availability of mussel spat on artificial settlement structures. This implies that the offspring of any mussels can spread itself over different habitats where a more harsh environment implies a better food supply. Further research may show whether the inclusion of this relationship between environmental stress and food availability will give different results. It is likely that the levels of cooperation that are found in real-world mussels reflects an adaptation to the habitat where they can generate the highest number of offspring, taking into account the availability of the habitat in the overall area.
We furthermore adopted a number of simplifying assumptions that do not precisely reflect the conditions that mussels, or any real-world organism, would encounter. In mussels, reproductive output per unit of biomass increases with age, as growth takes an ever smaller part of energy. Under most circumstances, our simplification of semelparity has little consequences, yet it might become important in temporally variable environments. We assumed a fixed self-organizing behavior within each and throughout generations; in each simulation of our IBM, all individuals used the same set of rules, including the settlement threshold, to move into a spatial pattern. This is an unrealistic assumption for several reasons. For example, generations are likely to differ in initial overall density; a scattered population in a dense mussel bed will result in a higher number of neighbours within attachment distance than in less dense but patterned beds. In this case, mussels in our model will never stop moving and hence never attach to any neighbours, because the long-range mussel density remains too high. Furthermore, individuals might differ in their self-organizing strategy; though some are aggregating in dense clumps, others may be strategically moving away from dense mussel clusters. A further simplification is that we only examined one aspect of spatial patterning on mussel survival: the effect of the number of direct neighbours. Irrespective of the overall mussel density, the number of neighbours is lowest for a scattered distribution, intermediate for a labyrinth-like pattern, and highest in dense clumps. Still, depending on the overall mussel density, an equal number of neighbours, and hence a similar degree of cooperation, can be achieved in all three patterns. It is conceivable that not only the number of neighbours, but also the spatial patterning of the neighbourhood is of importance for the evolution of cooperation. Spatial population structure plays an important role in mussel beds, as it defines not only the number of primary connections, but also secondary and tertiary connections between mussels, which bond many mussels into a single clump. Production of clumps generates an additional selection pressure, as larger clumps are less likely to become dislodged by wave stress. Though we do not consider the effect of spatial patterning on group size and higher-order selection processes in the current paper, we do analyse these effects in a separate study (de Jager 2015).
Our study demonstrates that active self-organization can have substantial consequences for the degree of cooperation between neighbours that evolves in a population. Inversely, self-organized spatial patterns have been described in a wide range of ecosystems, and many of these studies highlight the importance of cooperative interactions for the formation of these spatial patterns. In patterned arid bushlands, for instance, plants promote the infitration of water into the soil, facilitating other plants (Klausmeier 1999). This highlights the potential importance of feedback interaction between pattern formation processes on the one hand, and cooperation on the other. Whereas studies on the evolution of multicellularity have shown that feedback between pattern formation and evolution of cooperation/division of labour can drive evolution of unicellular to multicellular organisms (Pfeiffer and Bonhoeffer 2003; Rainey and Rainey 2003; Ratcliff et al. 2012), our study system may provide a suitable template to investigate such feedback in populations of non-related individuals. So far, the evolution of cooperative interactions other than aggregation and the pattern forming characteristics of organisms, such as their aggregative behavior, have been studied in isolation. Although our conclusions—that evolution of cooperation depends on spatial aggregation within the population—can be drawn without the explicit inclusion of joint evolution, the joint evolution of pattern forming and cooperative traits is a promising subject for further investigation.
M.J. was supported by a Grant from the Netherlands Organisation for Scientific Research—Earth and Life Sciences (NWO-ALW), and Project Group Movement Ecology by the KNAW Strategic Fund.
- de Jager M (2015) Eco-evolutionary feedbacks in self-organized ecosystems. Dissertation, University of GroningenGoogle Scholar
- Dercole F, Rinaldi S (2008) Analysis of evolutionary processes: the adaptive dynamics approach and its applications. Princeton University Press, PrincetonGoogle Scholar
- Eckroat L, Steele L (1993) Comparative morphology of the byssi of Dreissena-polymorpha and Mytilus edulis. Am Malacol Bull 10:103–108Google Scholar
- Hunt HL, Scheibling RE (2002) Movement and wave dislodgment of mussels on a wave-exposed rocky shore. Veliger 45:273–277Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.