sign in sign up
<<
Home , Percolation, Systems biology

The tradeoff between division of labor and in complex, adaptive is shaped by environmental stability

Authors: Cole Mathis1, Yu Liu2, José Aguilar-Rodríguez3,4, Stojan Davidovic5, Rohan Mehta6, Emília Garcia-Casademont7, Zhi Qiao 8, Ali Kharrazi9, Renske Vroomans10, Sean M. Gibbons11,12,*

Author Affiliations:

1 Department, Arizona State University, U.S.A. 2 Department, Uppsala University, Sweden 3 University of Zurich, Institute of Evolutionary and Environmental Studies, Zurich, Switzerland 4 Swiss Institute of , Lausanne, Switzerland 5 Center for Adaptive Behavior and Cognition, Max Plank Institute, Germany 6 Biology Department, Stanford University, U.S.A. 7 Institute of , CSIC-UPF, Barcelona, Spain 8 NUS Graduate School for Integrative Sciences and , National University of Singapore, Singapore 9 Graduate School of Public Policy, University of Tokyo, Japan 10 Theoretical Biology Group, Utrecht University, Holland 11 Graduate Program in Biophysical Sciences, University of Chicago, U.S.A. 12 Institute for and Systems Biology, Argonne National Laboratory, U.S.A. *Corresponding author: [email protected]

Abstract

We propose the existence of a fundamental tradeoff between division of labor (i.e. cooperation, lack of redundancy, or interconnectedness) and robustness in complex, adaptive systems. It is unlikely that a universal optimum for this tradeoff exists, and we suggest that context-dependent optima are likely tuned by the stability of the environment in which a evolves. Here, we describe the mechanistic basis for this tradeoff in both natural and social systems, and show how these systems should self-organize under differing levels of environmental noise. We use agent-based modeling to explore the way simple, generalized systems optimize along this tradeoff curve under different perturbation regimes. We then investigate real-world data sets from qualitatively different environments, with differing levels of stability. We also look at more quantitative relationships between environmental disturbances and structure, using microbial mesocosms under controlled laboratory conditions. Finally, we compare structural properties of natural systems to our model outputs. Overall, we find that complex networks maintain a high degree of connectivity under a large range of environmental variability, but the prevalence of high-degree nodes (agents/ with large numbers of connections) drops to zero above a noise threshold.

I. Introduction

Division of labor is a common emergent property in complex systems, and is inversely proportional to the self-sufficiency of the actors. This phenomenon is driven by individual and systems-level cost reduction, leading to improved efficiency; for example, partitioning tasks minimizes the costs associated with task switching (1) and loss of individual traits reduces the cost of maintaining expensive genetic or metabolic infrastructure (2). However, the more entities rely upon their surroundings, the more vulnerable they are to fluctuations in the environment. On one end of the tradeoff spectrum, a system is minimally redundant and maximally efficient, but very sensitive to perturbations. On the other end, a system is highly redundant/inefficient, but robust to disturbances. Thus, when controlling for the size of a network (number of nodes), two parameters govern the placement of a system in this space: 1) the magnitude of efficiency gain achieved by labor division, and 2) the rate at which perturbations disrupt the system and overwhelm the deterministic progression towards higher efficiency. In this report, we explore this cost curve in different types of environments, ranging from stable to noisy

(Fig. 1).

We hypothesize that natural systems will evolve to maximize their efficiency up to a fragility threshold, and that this threshold will be determined by the level of background noise in the environment. In this paper we elaborate on the of this fundamental tradeoff in a few distinct types of complex systems, then we describe a generalized model for this tradeoff and compare the results of experiments with data collected from naturally occurring microbial communities and microbial mesocosms in controlled laboratory studies.

Division of Division Laborof

Environmental Noise

Figure 1. Putative relationship between division of labor and environmental noise, based on the proposed tradeoff.

Biological Systems

Metabolic Networks

Free-living organisms are sustained by metabolic networks: complex chemical reaction networks that contain hundreds to thousands of reactions catalyzed by

(3). These networks convert nutrients into biomass or and produce chemicals that play a role in different biological processes: energy storage, defense, communication, etc.

(4). At present, in modern , there is an “efficient division of metabolic labor between enzymes” (5). Enzymes tend to be highly specialized in catalyzing a given reaction. However, it is very likely that the ancestral was different. In 1976,

Jensen proposed that primitive enzymes had much broader specificities and were not specialized to one substrate or reaction (6). Therefore, a relatively few generalist enzymes of low efficiency, acting on several different substrates, were enough to confer a wide range of metabolic capabilities. If we measure the efficiency of a metabolism in terms of the flux of matter trough a or in terms of the growth that it can sustain (7), the primordial metabolism envisioned by Jensen was not very efficient.

However, we can hypothesize that the ancient metabolism was robust to genetic perturbations. In a metabolism where enzymes tend to be multifunctional, the chance that an could compensate for the activity of another knocked-out enzyme is higher than in a metabolism where all enzymes are highly specific. It is known that in

Escherichia coli, the overexpression of promiscuous enzymes can compensate for the loss of otherwise essential enzymes (8). If it were not for gene duplication, primordial enzymes would have been trapped in a situation in which mutational improvements in the specificity (and efficiency) of a reaction would diminish the specificity of the other promiscuous activities catalyzed by the same enzyme (6, 9). However, gene duplication, followed by the sub-functionalization of the two copies of the enzyme (10), allowed the selective divergence of generalist enzymes into the current specialist enzymes and increased metabolic efficiency.

Therefore, a tradeoff between division of metabolic labor and robustness could have shaped the of metabolism. The predictions of this hypothesis remain to be tested empirically. For example, given that even in modern metabolism we find specialist and generalists enzymes (11, 12), the fraction of promiscuous or generalist enzymes should be higher in less efficient but more robust metabolic networks. A theoretical study has shown how metabolic networks that evolve in fluctuating environments acquire greater robustness to single-gene deletions than networks evolved in stable environments

(12). Networks computationally evolved in changing environments become more robust partially through the acquisition of multifunctional enzymes. This metabolic study seems to support our thesis that the tradeoff between division of labor and robustness in complex networks is controlled by environmental pressure.

Ecology and Evolution

In evolutionary biology, the rise of cooperation has been a controversial topic due to the implication of group-level selection (13, 14). Equivocal evidence has been found for strong group selection in biological systems (15, 16). In order to circumvent group selection, kin selection (cooperation between related entities) has often been invoked as a selfish for altruistic behavior between similar 'types' (17). However, cooperation often occurs between unrelated organisms in real-world (e.g. flowering plants and their pollinators, Egyptian plovers and crocodiles, mycorrhizal fungi and land-plants). A recent theory in called the Black Queen Hypothesis (BQH) proposed a novel ecological mechanism for how interdependencies may evolve between unrelated entities due to adaptive trait loss in the presence of 'leaky' ecological functions

(2, 18, 19). The BQH (18) describes the evolution of functional dependencies in microbial ecosystems through adaptive gene loss. The BQH relies on two basic assumptions: 1) organisms unavoidably produce public goods (e.g. the excretion of metabolic by-products); and 2) organisms that make use of these public goods will delete their own costly metabolic infrastructure needed for producing them (19). This results in a subset of organisms getting stuck with providing necessary services for the rest of the . Organisms that can outsource essential functions escape the cost of performing these activities and expand the number of resources available for their growth and . Although this process of adaptive gene loss starts out as selfish, and may appear unstable, it has been shown to lead to long-term ecotype co-existence (20).

However, this process should make the more delicate, as the destruction of key species will eliminate their crucial service(s) and potentially lead to system collapse

(19).

A. B.

Figure 2. Panel A: the largest connected component (bold red edges) grows as the number of randomly placed edges is increased in a graph with 150 nodes (p = percentage of all possible non-redundant connections between nodes). Panel B shows a critical transition in the size of the largest component when p = 0.009.

Apart from the mechanism by which division of labor evolves, the degree to which division of labor is possible in the face of environmental variability is still an open question. There is work in many fields showing that the connectivity of a network is inversely proportional to network resilience, and that different network architectures are optimal for maintaining maximal connectivity and resilience in an unpredictable world

(21). Ecological networks have been shown to be ‘robust, yet fragile’, meaning that they are resistant to random shocks, but vulnerable to targeted attacks on key species (22, 23).

This suggests that the evolved network structure can support a rather large number of connections before there is a significant reduction in robustness. This type of effect is reminiscent of (24), and the growth of giant components in random graphs (Fig. 2). In fact, most ecological networks are highly connected (25) and have likely evolved to be adjacent to such a tradeoff threshold (26), allowing them to achieve high levels of efficiency without incurring a large cost to their robustness.

Social Systems

Economics

Issues of competition and cooperation have been particularly important in economics.

Similar to the role of selfish gene in biological evolution, the founder of modern economics, Adam Smith (1776), identified self-interest as the key generator of a functioning . From that point on economics has become, primarily, a study of competition among selfish individuals. However, Smith recognized the importance of division of labor and its benefits for the economy. He observed that division of labor leads to qualitative increases in productivity, which naturally emerge from economic interactions. Smith marked avoidance of task switching costs and development of expertise as main reasons for improvement in labor productivity. Smith’s arguments have at least two direct parallels in biology. First, recent evidence supports the minimization of task switching costs in the evolution of division of labor in natural systems (1). Another analog to biology, which sparked significant attention in economics, is Smith’s observation that the power of division of labor is limited by the size of the market (27-29). In biological systems, it has been shown that division of labor emerges only when group (colony) size exceeds a certain point (30). This mirrors established work in and recent ecological theory, which shows selective (deterministic) forces (i.e. propensity of a system to evolve towards higher efficiency) are overwhelmed by stochastic effects below a certain threshold in the system’s size (31, 32). This scaling idea also relates to the economic literature, which has considered division of labor as the main force behind economies of scale (33, 34).

More recently economists have devoted considerable thought to questioning whether or not the integration of international markets leads to more specialization (35).

Even though division of labor has been recognized as a factor in market structuring and increasing interconnectedness, there was little evidence about its impact on stability of the markets. The financial crisis of 2007-2009 is an extreme example for how specialization is a very important factor in the organization of global economy. This crisis has revealed how entire economies depend on particular functions provided by a few specialized financial institutions (36). The failure of a specialized, but essential, in a financial system - like interbank markets - can lead to the collapse of the global economy (37).

II. Results and Discussion

Model and Results

We define a kinetic agent-based model to explore the effects of environmental noise and perturbations on network division of labor and robustness. We assume an initially well-mixed population of interacting agents. Each agent has three vector properties: � is the production capability of an agent, � represents the consumption needs of the agent (both normalized to unity), and �, which represents the resources currently in the agent’s possession. There is a fixed rate of raw material influx, which is uniformly distributed amongst the agents. Agents produce resources from this raw material based on their production capabilities at a rate �!. Agents have a consumption rate, �!, which defines the minimum amount of resources they require to sustain function and increase fitness. When an agent has more resources than its consumption needs (�! > �!�! for all i), it consumes its resources first to maintain itself, and then to increase its fitness (f). After agents maximize their own fitness, (i.e. �! < �!�! for any i), they have a certain probability of donating any excess resources they have to other agents who need that resource. This donation is biased by the history of the agent, where they are more likely to donate to agents that have received resources from them in the past, and less likely to give it to any other agent. Thus, as the system evolves, it transitions from ‘well-mixed’ to ‘spatially-distributed,’ or from homogenous to heterogeneous.

When agents are unable to meet their consumption needs, they may be removed from the system. The probability of being removed from the system is proportional to time since the agent has met its consumption needs. New agents are added to the model as mutated copies of the fittest individuals. The propensity of an agent being added to the system is inversely proportional the death rate, thus the total number of agents in the system is free to vary and typically fluctuates. Agents that are more specialized in their production (i.e., produce one resource more than others) have a lower consumption rate than other agents, which reflects the fact that they have a lower ‘genetic overhead’ to maintain. When an exchange occurs, there is a certain probability that it will be lost from the system, and we refer to this probability as environmental noise, which is simply due to small-scale stochastic fluctuations. There can also be externally applied perturbations in which a fraction of the population is removed from the system. These shocks can be random, harming all agents indiscriminately, or targeted harming only those agents whose are specialized in production of a specific resource.

It is important to note that this is an open system with a constant flux of energy coming in (energy used to manufacture resources), so that mean fitness is always increasing within the system. However, energy flux is fixed in this model, meaning that if more agents are added, then every agent produces fewer resources in a fixed time interval. We investigated the case where all agents produced resources from the environment at a uniform rate, �! = 1, for all agents. However �! was a linearly decreasing function in the agent’s specialization, so more specialized agents require fewer resources to sustain themselves.

Our model results indicate that the degree of random environmental noise has little impact on the network structure of the community (i.e., the proportion of generalists vs. specialists), up to a critical threshold (Fig. 3). Beyond this threshold, the system loses its highest-degree nodes (i.e., ‘hub’ species, with large numbers of connections; Fig 3E).

Even at the highest noise level tested, the largest connected sub-graph spans almost the entire network. Thus, we find that in our model system, rather than a in the size of the (e.g. Fig. 2), we see a switch in the presence or absence of highly connected hub-species at high levels of environmental noise. These results, however, are rather tenuous, as they are based on a small number of simulations. We will reinforce these results by running replicate simulations, with a denser sampling of parameter space.

A. C. count

B. D. count

degree degree E. 40

30

20

10

HighestDegree Node 30 40 50 60 70 80 Environmental Variability

Figure 3. Agent-based model results. Panels A-D show the network structures for model simulations under varying levels of noise (noise defined as probability that a resource is lost during an exchange between actors: A = 30%, B = 40%, C = 60%, and D = 80%). Colors denote the three different resource types included in the model. Bar graphs show degree distribution for each network. Panel E shows the magnitude of the highest degree node as environmental noise increases. The dashed line is not a fit, but a qualitative estimate of the relationship between highest degree and environmental noise. This qualitative relationship is very preliminary, and will require many replicate simulations with a denser sampling of parameter space.

Microbial Time Series Analysis

We investigated the relationship between ambient environmental noise levels and the network structure of microbial interactions by analyzing time series data from four qualitatively different natural environments: human skin, human feces, freshwater lake, and the English Channel. Direct or indirect species-species interactions were estimated by calculating significant pairwise correlations between Operational Taxonomic Units

(OTUs, i.e., ‘species’; see Methods). Networks were then built with OTUs as nodes and correlations as edges (Fig. 3A-D; inset plots). We hypothesized that human skin would be the most variable environment due to the behavior of the host (i.e., showering, application of lotion, sweating, exposure to sunlight, etc.) and the ocean would be the most stable. Further, we suspected that the fecal and lake data sets would be intermediate to these two extremes. Analysis of the correlation structure of these environments showed that the ocean environment had the largest proportion of high-degree nodes (OTUs with many connections), while the skin environment had a degree distribution weighted toward lower-degree nodes (Fig. 3).

Overall, our correlation matrices show a high degree of connectivity across all environments, but edges are more evenly distributed across nodes in noisier environments

(Fig. 3). This result mirrors prior work in ecology, showing that ecological networks are highly connected (25, 38). However, our results indicate that individual organisms with large numbers of connections are less favored in noisy environments. The loss of these species could have a disproportionately negative effect on the food web (22, 23, 25, 39).

Reliance of the ecological network on these hub species might be too costly in a highly variable environment, with greater risks of stochastic extinctions in noisy systems. On the other hand, these highly connected organisms likely increase the efficiency, productivity, and functionality of stable ecosystems, which is why they should arise under permissive conditions (39-41). Individual connections with a hub species may be subject to different tradeoff optima, where higher gains in efficiency may tolerate stronger fluctuations than minor gains. Further, the proportion of obligate vs. facultative interrelationships between taxa would also determine a network’s ability to restructure itself as noise levels change.

A. B. count

C. D. count

degree degree

Figure 3. Histograms showing degree distributions for correlation networks from four different environmental time series: human skin (A); human feces (B); freshwater lake (C); and the English Channel (D). Network structures derived from the environmental correlation matrices are shown in each panel.

Microbial Mesocosm Experiment

We ran a series of experiments on replicate microbial mesocosms in order to explicitly test how perturbations influence microbial correlation network structure. Replicate communities, inoculated from the same source enrichment, were grown up in 96 well plates. The control communities receive no applied disturbance for 40 days, while disturbance replicates were subjected to different regimes of periodic disturbance

(ranging in magnitude: low, medium, and high; and in type: biomass removal and ultraviolet radiation). At the end of the experiment, the control replicates were subjected to a single point disturbance (heat shock at 50° C for 2 hrs). Independent of whether the disturbance was applied periodically over the growth period or as a single high-intensity disturbance at the end of the experiment, and independent of the type or magnitude of disturbance, the effect was the same (Fig. 4). In the control community, the highest degree node had 19 connections, and the average ‘disturbed’ community’s highest degree node had only 8.2 connections (± 1.3, SE). Thus, our experimental results mirror our environmental data, showing that high levels of environmental noise reduce the number of high-degree nodes in an ecological interaction network. Interestingly, the largest connected component in all of these treatments spanned almost the entire network, showing again that these ecological networks are highly connected, and that the degree distribution is the primary network measure constrained by environmental noise.

Figure 4. Bar plot showing the highest degree node from OTU correlation networks derived from mesocosm treatment replicate treatments. For the control treatments, ‘before’ and ‘after’ refer to before and after the application of a single point disturbance (heat shock at 50° C for 2 hrs). For the remaining biomass removal (BR) and ultraviolet (UV) treatments, ‘low’, ‘medium’, and ‘high’ refer to the magnitudes of periodically applied disturbance treatments. Dotted line shows average value over all disturbance replicates (excluding the ‘before’ control).

III. Conclusion

Our original hypotheses were that a fundamental tradeoff between division of labor and system robustness exists, and that this tradeoff is tuned to the amount of environmental variability that a system experiences during its development. It is clear from the literature that such a tradeoff exists across a number of systems (e.g. social, biological, physical), and our model simulations and empirical results verify that this tradeoff is tuned to the level of environmental variance that a system is exposed to. Specifically, we show the occurrence of high-degree nodes (i.e., hubs) in a network has a non-linear dependence upon the level of environmental noise. Contrary to our original hypothesis, biological networks - and the networks produced by our model - are able to maintain high overall connectivity under a large range of environmental conditions. Thus, the size of the giant component (largest connected sub-graph, normalized to the number of nodes in the system) does not change. However, beyond an upper environmental noise threshold, the frequency of high degree nodes quickly drops to zero. Therefore, we find that natural systems are able to maintain a large amount of low-degree of connectivity independent of environmental fluctuations, but highly specialized entities with many connections will not persist in noisy environments. Future work will focus on in-depth characterization of the seemingly non-linear transition in the degree distribution as a function environmental noise. Our results can be applied broadly to many different fields involving complex, adaptive systems: e.g., environmental conservation (i.e. conservation of keystone species in the face of climate change), evolutionary theory (i.e. efficiency, robustness, and evolvability in noisy environments), metabolic engineering (i.e. generalist vs. specialist enzymes in different environmental regimes), or policy making (i.e. division of labor and robustness in the economies of stable vs. war-torn countries). We hope our work will help spark new avenues of research focused on identifying general laws that shape complex, adaptive systems.

IV. Methods

Models

Model code is available upon request from [email protected] and supplemental model code is available upon request from [email protected].

Microbial data analysis

Microbial time series data were obtained from the Earth Project (EMP) data portal: www.microbio.me/emp. For each data set, we ran closed reference OTU picking

(≥ 97% sequence identity) against the Greengenes (May, 2013 release) to build the phylotype-abundance matrix, with default setting in the Quantitative Insights into

Microbial Ecology (QIIME) analysis package (42-44). Taxonomic identities were determined using the RDP classifier (45). Only abundant taxa were retained for each analysis (at least 0.1% relative abundance across a data set). OTU matrices containing abundant taxa were normalized to an even sequence depth across samples. The resulting matrices were then processed using SparCC, to calculate all pairwise linear correlations between OTUs across the time series (46). Correlation matrices were filtered to only include significant correlations (p < 0.05) with rho-values ≥ 0.3. This filtered correlation matrix was then used to construct a network, where each OTU represents a node and each correlation an edge. Network statistics were then calculated using the NetworkX package in python, and plotting was done using Matplotlib (47, 48).

Mesocosm Experiments Microbial communities were enriched from the surface water of Lake Ontario, and grown on BG11 medium (49) for several months. Initially, cyclohexamide was added to the medium (0.5 µg mL-1) to prevent the growth of eukaryotes. Mesocosm experiments were inoculated into 96-well plates from this enrichment culture (1:1 culture to fresh medium), and grown over the course of a month with varying regimes of disturbance. Biomass removal disturbances were applied by removing a percentage of the culture from a well

(5%, 10%, or 15%) and replacing it with an equivalent volume of fresh medium. UV disturbances were applied by allowing wells to sit uncovered beneath a UV sterilization lamp for varying lengths of time (5, 10, or 15 minutes; G15T8 bulb; emission peak at 254 nm, 5 W). Samples were harvested by spinning down cells for 15 minutes at 5,000 RCUs.

DNA extractions and PCR amplification of the V4 region of the 16S gene were carried out using EMP standard protocols (http://www.earthmicrobiome.org/emp-standard- protocols/). Samples were sequenced at the Argonne National Laboratory Illumina sequencing facility. Data was processed using QIIME and SparCC, as described in the previous section.

V. Acknowledgements

This study was made possible by the 2014 Complex Systems Summer School (CSSS) at the , NM, USA. Thanks to the Santa Fe Institute faculty and staff for helpful advice and discussion. Special thanks to the CSSS 2014 summer school organizers and to our fellow attendees for an inspirational month of interdisciplinary science.

VI. References

1. Goldsby HJ, Dornhaus A, Kerr B, & Ofria C (2012) Task-switching costs promote the evolution of division of labor and shifts in individuality. Proceedings of the National Academy of Sciences 109(34):13686-13691. 2. Ellers J, Toby Kiers E, Currie CR, McDonald BR, & Visser B (2012) Ecological interactions drive evolutionary loss of traits. Ecology letters 15(10):1071-1082. 3. Berg JMTJLSL (2012) (W.H. Freeman, Basingstoke). 4. Wagner A (2011) The origins of evolutionary innovations: a theory of transformative change in living systems (Oxford University Press). 5. Szathmary E & Maynard Smith J (2004) The major transitions in evolution (Oxford University Press). 6. Jensen RA (1976) Enzyme recruitment in evolution of new function. Annual Reviews in 30(1):409-425. 7. Wagner A (2013) Robustness and evolvability in living systems (Princeton University Press). 8. Patrick WM, Quandt EM, Swartzlander DB, & Matsumura I (2007) Multicopy suppression underpins metabolic evolvability. and evolution 24(12):2716-2722. 9. Kacser H & Beeby R (1984) Evolution of catalytic . Journal of molecular evolution 20(1):38-51. 10. Force A, et al. (1999) Preservation of duplicate genes by complementary, degenerative . Genetics 151(4):1531-1545. 11. Tawfik OK & S D (2010) Enzyme promiscuity: a mechanistic and evolutionary perspective. Annual review of biochemistry 79:471-505. 12. Nam H, et al. (2012) Network context and selection in the evolution to enzyme specificity. Science 337(6098):1101-1104. 13. Wilson DS (1975) A theory of group selection. Proceedings of the National Academy of Sciences 72(1):143-146. 14. Traulsen A & Nowak MA (2006) Evolution of cooperation by multilevel selection. Proceedings of the National Academy of Sciences 103(29):10952- 10955. 15. Wade MJ (1978) A critical review of the models of group selection. Quarterly Review of Biology:101-114. 16. LEIGH J (2010) The group selection controversy. Journal of Evolutionary Biology 23(1):6-19. 17. Riolo RL, Cohen MD, & Axelrod R (2001) Evolution of cooperation without reciprocity. Nature 414(6862):441-443. 18. Morris JJ, Lenski RE, & Zinser ER (2012) The Black Queen Hypothesis: Evolution of Dependencies through Adaptive Gene Loss. mBio 3(2). 19. Sachs J & Hollowell A (2012) The origins of cooperative bacterial communities. mBio 3(3):e00099-00012. 20. Morris JJ, Papoulis SE, & Lenski RE (2014) Coexistence of evolving bacteria stabilized by a shared black queen function. Evolution. 21. Shargel B, Sayama H, Epstein IR, & Bar-Yam Y (2003) Optimization of robustness and connectivity in complex networks. Physical Review Letters 90(6):068701. 22. Dunne JA & Williams RJ (2009) Cascading extinctions and community collapse in model food webs. Philosophical Transactions of the Royal Society B: Biological Sciences 364(1524):1711-1723. 23. Montoya JM, Pimm SL, & Solé RV (2006) Ecological networks and their fragility. Nature 442(7100):259-264. 24. Shante VK & Kirkpatrick S (1971) An introduction to percolation theory. Advances in Physics 20(85):325-357. 25. Dunne JA, Williams RJ, & Martinez ND (2002) Network structure and loss in food webs: robustness increases with connectance. Ecology Letters 5(4):558-567. 26. Solé RV, Manrubia SC, Luque B, Delgado J, & Bascompte J (1996) Phase transitions and complex systems. Complexity 1(4):13-26. 27. Chaney T & Ossa R (2013) Market size, division of labor, and firm productivity. Journal of International Economics 90(1):177-180. 28. Adam S (1776) An Inquiry into the Nature and Causes of the Wealth of Nations. Edwin Cannan's Annotated Edition. 29. Stigler GJ (1951) The division of labor is limited by the extent of the market. The Journal of Political Economy:185-193. 30. Jeanson R, Fewell JH, Gorelick R, & Bertram SM (2007) of increased division of labor as a function of group size. Behavioral Ecology and 62(2):289-298. 31. Gillespie JH (2001) Is the population size of a species relevant to its evolution? Evolution 55(11):2161-2169. 32. Fisher CK & Mehta P (2014) The transition between the niche and neutral regimes in ecology. Proceedings of the National Academy of Sciences 111(36):13111-13116. 33. Bell FW & Murphy NB (1968) Economies of scale and division of labor in commercial banking. Southern Economic Journal:131-139. 34. Edwards BK & Starr RM (1987) A note on indivisibilities, specialization, and economies of scale. The American Economic Review:192-194. 35. Krugman P & Venables AJ (1996) Integration, specialization, and adjustment. European Economic Review 40(3):959-967. 36. Gai P & Kapadia S (2010) Contagion in financial networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science:rspa20090410. 37. Arinaminpathy N, Kapadia S, & May RM (2012) Size and complexity in model financial systems. Proceedings of the National Academy of Sciences 109(45):18338-18343. 38. Dunne JA, Williams RJ, & Martinez ND (2002) Food-web structure and : the role of connectance and size. Proceedings of the National Academy of Sciences 99(20):12917-12922. 39. Albert R, Jeong H, & Barabási A-L (2000) Error and attack tolerance of complex networks. Nature 406(6794):378-382. 40. Stueffer J, De Kroon H, & During H (1996) Exploitation of environmental hetergeneity by spatial division of labor in a clonal plant. Functional Ecology:328-334. 41. Wilson EO (1980) Caste and division of labor in leaf-cutter ants (Hymenoptera: Formicidae: Atta). Behavioral Ecology and Sociobiology 7(2):157-165. 42. Caporaso JG, et al. (2010) QIIME allows analysis of high-throughput community sequencing data. Nature Methods 7(5):335-336. 43. McDonald D, et al. (2012) An improved Greengenes with explicit ranks for ecological and evolutionary analyses of bacteria and archaea. ISME Journal 6(3):610-618. 44. Rideout JR, et al. (2014) Subsampled open-reference clustering creates consistent, comprehensive OTU definitions and scales to billions of sequences. PeerJ 2:e545. 45. Wang Q, Garrity GM, Tiedje JM, & Cole JR (2007) Naïve Bayesian Classifier for Rapid Assignment of rRNA Sequences into the New Bacterial Taxonomy. Applied and Environmental Microbiology 73(16):5261-5267. 46. Friedman J & Alm EJ (2012) Inferring correlation networks from genomic survey data. PLoS 8(9):e1002687. 47. Hunter JD (2007) Matplotlib: A 2D graphics environment. Computing in Science & Engineering:90-95. 48. Hagberg A, Swart P, & S Chult D (2008) Exploring network structure, dynamics, and function using NetworkX. (Los Alamos National Laboratory (LANL)). 49. Stanier R, Kunisawa R, Mandel M, & Cohen-Bazire G (1971) Purification and properties of unicellular blue-green algae (order Chroococcales). Bacteriological Reviews 35(2):171.

VII. Supplemental Materials

An Alternative Model

Introduction

Specialization and division of labor are everywhere in nature. As described above, division of labor can arise when species lose their ability to perform a particular function and must rely on their environment to supplement this deficit (BQH).

In this model, we assume that all the individuals have the same needs to survive

(e.g. 1 A + 1 B + 1 C) and these needs never change. However, the ability to gather a given resource (A, B, or C) can mutate.

General Description of the Model

This model is agent-based, and does not take spatial effects into account. Every individual has a '' which can be inherited and mutated. The genome records an agent’s ability to gather resources, and its consumption rate for each resource. Each agent is able to store a certain number of unused resources, which can be exchanged between individuals. At every time step, individuals have the opportunity to trade their inventory with other agents. The rule for trading is that both individuals attempt to maximize their lifespans by asking for resources that they need to increase their fitness, but neither party can lose out in the trade (neither agent comes away from the trade with lower fitness). In addition, every time step, individuals have a set of probabilities for gathering resources, reproducing (with every reproduction event there is a probability of mutating the resource production rates of the offspring) or dying. If an individual runs out of a limiting resource then it dies.

Definitions

We define the stability of the system as the magnitude of its response to an external perturbation. For the same perturbation, a larger response denotes lower stability.

Specifically, we consider the change in population size as the response variable. There are two kinds of perturbation we will investigate: 1) perturbation of resource inputs, and

2) perturbation of species abundances (i.e., mortality rate). Interestingly, these perturbation types could have different effects. We consider two systems: one uniquely composed of self-sufficient generalists, called system X, another uniquely composed of interdependent specialists, called system Y.

Resource input perturbations

In both systems X and Y, if we decrease resource A input by 10%, the size of the entire population will drop by 10%, rendering 10% of resources B and C unusable, as each agent needs an equal amount of each resource. The effect of this disturbance is the same whether or not the system is comprised of generalist or specialists.

Species perturbation

In system X, if we remove 10% of the individuals, the size of the whole population decreases by 10%. However, in system Y, if we remove 10% (with respect to the whole population) of only specialists that gather resource A (i.e. a ‘targeted attack’), other specialists who gather B and C will also decrease in abundance by 10%, as they require

A, which can only be obtained through trading with the A-gathering specialists. Thus, the overall population size of system Y will decline by 30%. Therefore, the specialist- community is more fragile than the generalist-community when faced with targeted attacks (targeted attacks are not possible in a generalist system, where all agents are identical).

Results and Discussion

Perfect specialization will evolve if 1) specialists are more efficient at gathering their resource than a generalist, and 2) the whole system has a carrying capacity, which means it cannot support infinite number of individuals (carrying capacity depends on resource inputs, physical dimension, etc.). Thus, specialization will reduce the maintenance cost of individuals, and increase the overall carrying capacity of the system. However, this process may be disrupted by perturbations. 120 1000

100 800

80 600

60 400 Total Population 40 200 Average Exchange Amount 20 0 0 100 200 300 400 0 100 200 300 400

1

2500 0.8 2000 0.6 1500 0.4 1000

500 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 20 40 60 80 0 100 200 300 400 Time Step Time Step

Figure S1. Shows the progression of our model system toward perfect specialization over time.

Figure S2 shows how more specialized systems are more sensitive to disturbances. If we remove a certain number of individuals (denoted as m) from a non- specialized system, this perturbation will not propagate any further throughout the system, because the agents are self-sufficient and do not depend on one other. However, if we kill m individuals in a perfectly specialized system (like in Fig. S2 at T = 250), it is likely that more individuals would die afterwards since they are dependent on trading with each other (however, if an equal number of each specialist type is removed, then the perturbation will not propagate). To illustrate this point, we can see that in Figure S2, at T = 250, when we remove ~20 randomly chosen specialists, the total population size drops by ~60 individuals (3-fold amplification of the original disturbance).

1200

1000 100 800

600

50 400 Total Population 200 Average Exchange Amount 0 0 0 100 200 300 400 500 0 100 200 300 400 500

1 4000

0.8 3000 0.6 2000 0.4

1000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 50 100 150 0 100 200 300 400 500 Time Step Time Step

Figure S2. Following shocks, specialization continues to increase, and rarely decreases. Red vertical lines represent random species removal events.

We hypothesized that our model system would eventually stabilize at a certain degree of specialization, which would depend on the noisiness of the environment. The larger the number of perturbations, the lower the steady-state specialization level.

However, our simulations show that specialization almost always increases, and will continue to increase until perfect specialization is attained. Large disturbances can crash the system, or slow/pause the development of specialists, but as long as the system is not destroyed it continues to advance towards perfect specialization (see Figure S3-S6). In summary, our model system always moves towards perfect specialization, but perturbations will temporarily disrupt this process. The more specialized the system is when perturbations occur, the longer the system needs to recover, but perturbations almost never force specialization go backwards.

120 800

100 600 80

60 400

40 Total Population 200 20 Average Exchange Amount 0 0 0 100 200 300 400 500 0 100 200 300 400 500

1 3000

2500 0.8

2000 0.6 1500 0.4 1000 0.2 500 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 20 40 60 80 100 0 100 200 300 400 500 Time Step Time Step

Figure S3. The system is collapsed by a large perturbation at T = 320.

120 1200 100 1000 80 800

60 600

40 400 Total Population

20 200 Average Exchange Amount 0 0 0 100 200 300 400 500 0 100 200 300 400 500

1 4000

0.8 3000 0.6 2000 0.4

1000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 50 100 150 0 100 200 300 400 500 Time Step Time Step

Figure S4. The population size drops following a perturbation at T=300. 120 800 100

80 600

60 400 40 Total Population 200 20 Average Exchange Amount 0 0 0 100 200 300 400 500 0 100 200 300 400 500

1

3000 0.8

0.6 2000 0.4 1000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 20 40 60 80 0 100 200 300 400 500 Time Step Time Step

Figure S5. High-frequency perturbations do not prevent the attainment of perfect specialization, although they do slow the process down.

1200

1000 100 800

600

50 400 Total Population 200 Average Exchange Amount 0 0 0 100 200 300 400 500 0 100 200 300 400 500

1 4000

0.8 3000 0.6 2000 0.4

1000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 50 100 150 0 100 200 300 400 500 Time Step Time Step

Figure S6. Low-frequency perturbations do not slow the attainment of perfect specialization as much as high-frequency perturbations do.

In the prior simulations, we only discussed systems where individuals can efficiently exchange with each other. The exchange efficiency is determined by the parameters ‘Trialpercent’ and ‘IntelligenceDegree’. If we set the two parameters to be low, then there is a higher chance that an attempted exchange is aborted. This reduced efficiency could be considered as another kind of perturbation (i.e. an exchange perturbation). This exchange perturbation would be a major cost to specialization, and we hypothesized that perfect specialization would be impossible in the presence of this perturbation. However, simulation results seem to invalidate our initial hypothesis. The higher the exchange perturbation, the more time is needed to reach perfect specialization, but if the system evolves for infinite time then perfect specialization will always be reached. Thus, in this model, we find that perfect specialization is the only global equilibrium, although there may be several sub-equilibria.

Figures S1-S6 above have the parameters ‘Trialpercent = 1’ and

‘IntelligenceDegree = 60’, in most cases, perfect specialization can be reached before T =

500. However, if we set these parameters lower (see Figure S7), more time is required to reach perfect specialization. 120 80

100 60 80

60 40

40 Total Population 20 20 Average Exchange Amount 0 0 0 500 1000 1500 2000 0 500 1000 1500 2000

4 x 10 1 15000 2 1 0.8 0 0 500 10000 0.6

0.4 5000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 10 20 30 0 500 1000 1500 2000 Time Step Time Step

Figure S7. Trialpercent = 0.1 and IntelligenceDegree = 30. 1500 time steps are needed to reach perfect specialization.

When keep Trialpercent as 0.1, and set IntelligenceDegree lower, e.g. 20 as shown in Figure S8-S10, we can see that the degree of specialization is still low at T =

2000. However, given enough time, we predict that specialists will eventually displace generalists. 60 100 50 80 40 60 30 40 20 Total Population 20 10 Average Exchange Amount 0 0 0 500 1000 1500 2000 0 500 1000 1500 2000

4 x 10 1 15000 2 1 0.8 0 0 500 10000 0.6

0.4 5000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 10 20 30 0 500 1000 1500 2000 Time Step Time Step

Figure S8. Trialpercent = 0.1 and IntelligenceDegree = 20. Perfect specialization is not yet achieved by 2000th time step.

100 25

80 20

60 15

40 10 Total Population 20 5 Average Exchange Amount 0 0 0 500 1000 1500 2000 0 500 1000 1500 2000

4 x 10 1 15000 2 1 0.8 0 0 200 400 10000 0.6

0.4 5000 0.2 Natural Lifetime Distribution 0 Average Specialization Degree 0 0 10 20 30 0 500 1000 1500 2000 Time Step Time Step

Figure S9. Trialpercent = 0.1 and IntelligenceDegree = 10. Perfect specialization is not yet achieved by the 2000th time step.

There are many reasons why real-world systems do not exhibit perfect specializations. First, the time that the system has had to evolve may not be long enough for it to have reached equilibrium. Second, highly specialized systems are very fragile, and it is possible that they are destroyed regularly by stochastic perturbations and are thus forced to restart the specialization process over and over again (i.e., an evolutionary successional process). Third, heterogeneity in the consumptive needs and production capabilities of evolving entities could give rise to partial specialization, as niche space expands and the number of ways to make a living continuously grows. Finally, environmental heterogeneity likely plays a more nuanced role in specialization, preventing trading partners from interacting and imposing an adaptive cost on specialization, but this simplified model is somehow not capturing this process.

Thus, in this model, perfect specialization will always happen if specialization is adaptive. Specifically, selection pressure will be applied if the following conditions are satisfied: specialization has higher efficiency, exchanges are possible, and resources are limited. Different levels of environmental noise only affect the time needed to reach perfect specialization.