Linköping University | Department of Physics, Chemistry and Biology Bachelor’s thesis, 16 hp | Educational Program: Physics, Chemistry and Biology Spring term 2021 | LITH-IFM-G-EX—21/3996—SE
The effect of imperfect resource
conversion and recurring
perturbations on byproduct
cross-feeding chains in digital
communities
Filippa Frejborg
Examiner, Per Milberg Supervisor, György Barabás
Contents
Abstract ... 1
1 Introduction ... 1
1.1 Cross-feeding interactions ... 1
1.2 Digital evolution ... 2
1.3 The Avida software ... 3
1.4 Perturbation ... 3
2 Materials and Methods ... 4
2.1 Software... 4
2.2 Experimental setup ... 4
2.2.1 Setup of the environment ... 4
2.2.2 Perturbation events ... 5
2.2.3 Conversion rates ... 5
3 Results ... 6
3.1 Communities subjected to 0.5 conversion rate ... 6
3.2 Communities subjected to 0.9 conversion rate ... 6
4 Discussion ... 9
5 Societal and Ethical Considerations ... 12
6 Acknowledgements ... 13
Abstract
The gut microbiome plays a vital role in human health. Disturbances of this microbial system is associated with diseases such as obesity and inflammatory bowel disease. In populations of microbial species, many organisms partake in byproduct cross-feeding interactions, where byproducts from one organism are consumed by other microbes. Using the digital evolution software Avida, I studied the effect of recurring perturbations and imperfect resource conversion on the evolution of byproduct cross-feeding chains in digital communities. To investigate the effect of perturbation and conversion rate on digital organisms, I evolved digital communities for 200,000 updates in an unperturbed environment that could hold 50 different resource types, each produced as a byproduct of consuming another resource. At 200,000 updates, 50 or 60 % of all organisms were removed at various intervals during periods of different lengths, with a conversion rate less than 100 % between resources in the byproduct chain. I found that 0.9 conversion rate caused communities to evolve longer cross-feeding chains. A conversion rate of 0.5 resulted in communities with much shorter chains, more similar in length to byproduct chains in the human gut. Perturbation events seem to affect chain length only under certain conditions when energy is lost between resources, for example when 60 % of all organisms were removed every 50th update on average. It appears that conversion loss
makes digital communities more robust against the effects of perturbations, and that it might protect these communities from going extinct.
Keywords: byproduct cross-feeding, cross-feeding interactions, digital evolution, digital
organisms, gut microbiome, recurring perturbations, resource conversion.
1 Introduction
1.1 Cross-feeding interactions
The human microbiome is a plethora of remarkable diversity that plays a major role in human health (Ley et al., 2006; Blaut, 2011). Disruption of the gut microbiota composition, caused by diet change (Henson & Phalak, 2017) or antibiotics (Dethlefsen & Relman, 2011) for example, is associated with diseases such as obesity (Ley et al., 2005), inflammatory bowel disease (Ley et al., 2006) and type 2 diabetes (Larsen et al., 2010). In the human gut, bacterial and archaeal
partaking in cross-feeding interactions will thus be dependent on other organisms for energy (Lindeman, 1942; Pfeiffer & Bonhoeffer, 2004).
Figure 1. Illustration of a byproduct cross-feeding chain with three organisms and four resources. Resource 1 is consumed by organism A. Organism A produces byproduct 2 as a metabolite which in turn is consumed by organism B. Byproduct 3 is a metabolite produced by organism B and will be consumed by organism C. When organism C consumes byproduct 3, a fourth byproduct is produced.
Between resources in the byproduct chain, energy may be lost if the conversion rate is less than 100 % between them. Conversion rate is defined as “the rate of conversion to the byproduct resource” (Ofria & Wilke, 2004). An imperfect resource conversion refers to a conversion rate that allows energy to be lost between resource and byproduct resource. The exchange of metabolites between microbial species helps explain the diversity within microbial systems (Pacheco et al., 2019). These interactions, although widely studied, are remarkably complex.
In the human gut, Wang and colleagues (2019) discovered roughly four microbial trophic levels at which point the cross-feeding chain could not get any longer. Yet, chains 15 steps in length are possible, however rarely found in natural systems (Sung et al., 2017). It is unknown why most byproduct cross-feeding chains remain short. The belief that recurring perturbations may limit the length of byproduct chains in microbial communities is what inspired the current project.
1.2 Digital evolution
Digital evolution is used to study the evolution of digital organisms. Because digital organisms compare to bacteria (Wilke & Adami, 2002), the ambition of the current project is to apply the results to the gut microbiome. Using digital evolution systems, the biological evolution of organisms can be visualized in a matter of hours or days using computer models (Ofria & Wilke, 2004). These systems are used to test general hypotheses on networks of living organisms (Lenski et al., 1999). Digital organisms are defined as computer programs that self-replicate, mutate, and compete for central processing unit (CPU) cycles. They arise from one ancestor that replicates, mutates and evolves, similar to natural organisms (Lenski et al., 1999; Wilke et
Organism A
al., 2002). In contrast to living organisms, digital organisms evolve to solve computational problems by carrying out instructions encoded in their genomes (Misevic et al., 2006). Digital organisms use specific resources by performing associated computations without error (Cooper & Ofria, 2002). By performing computations, organisms obtain computational power to evolve and reproduce in the environment (Wilke & Adami, 2002).
1.3 The Avida software
The digital evolution software Avida is used to conduct and analyze experiments with digital organisms (Lenski et al., 1999). The three elements of Darwinian evolution – selection, variation and inheritance – are present in the system (Adami, 2006). An ancestral organism seeds the population, and its daughter organisms fill up the Avida world. Organisms in Avida self-replicate and offspring are placed in the population (Ofria & Wilke, 2004). In an experimental environment, Avida makes it possible to control and manipulate variables such as mutation rate to study questions of interest. In the present project, the virtual environment was set up in such a manner that byproducts were generated whenever a resource was consumed by a digital organism. This allowed for cross-feeding interactions, structured by trophic levels, where metabolites were transferred between digital organisms (Yedid et al., 2012). With the help of Avida, many advances have been made in research on evolutionary questions (see for example Lenski et al., 1999; Wilke et al., 2001).
1.4 Perturbation
In this project, perturbation refers to the removal of individuals from the Avida system. If a community of digital organisms cannot accommodate the stresses of perturbation, it may go extinct. Some disturbances are important for species diversity (Solé et al., 2002), and for interactions between organisms (Yodzis, 1988). However, high levels of disruption reduce species diversity due to higher extinction rates among species (Wootton, 1998).
Trying to provide clues as to why most metabolic byproduct chains in the human gut remain short, I use digital organisms to analyze the effect of imperfect resource conversion and recurring perturbations on byproduct cross-feeding chain length.
2 Materials and Methods
I examined the effect of recurring perturbations and imperfect resource conversion on metabolic byproduct chain lengths in populations of digital organisms.
2.1 Software
I performed experiments using the Avida software, version 2.14 (https://avida.devosoft.org/). All experiments were executed on the Tetralith computing cluster of the National Supercomputer Centre (NSC) at Linköping University. I used default settings unless stated otherwise.
2.2 Experimental setup
The organisms used here had a constrained genome length of 100 instructions. On average, every 400th copied programming instruction mutated. I used populations of 100×100 organisms
in a clique topology where all positions in the population were connected. During the first 200,000 updates (a unit used by Avida to measure the passage of time), the organisms evolved unperturbed. Offspring occupied empty cells or replaced random organisms if all cells were populated.
All experiments were started with 20 replicate populations. The replicates within the same experimental setup were started with different random number seeds, and thus differ only in the value of the seed. Random number seeds make it possible to recreate experiments. Given that the 20 replicate populations were set up in identical environments, any observed irregularity across replicates is due to different random number seeds. The difference in number seed cause the replicates to differ in occurrence of random point mutations and where the offspring are placed in the population.
2.2.1 Setup of the environment
The environment was set up with one initial consumable resource. This resource had an initial quantity of 1000 units, inflow rate of 100, and outflow rate of 10 %. When this resource was consumed, a byproduct was generated which itself served as a resource for other organisms in the community. The environments had the capacity to hold 50 different resource types. Forty-nine resource types arose as byproducts of a previous resource when the corresponding computation was executed by an organism. The 49 byproduct types had an outflow rate of 10
%, initial and inflow rate set to zero. All resources were available to all digital organisms. When a resource was consumed its availability decreased in the environment.
In the current project, as in the world of microbial ecology (opposed to community ecology), an organism that consumed the initial resource (e.g., resource 1 in Figure 1) in the byproduct chain was on the highest trophic level, with subsequent byproducts (e.g., resources 2, 3 and 4 in Figure 1) being a trophic level down from the previous resource in the chain. A consumed resource on the lowest trophic level defined where a cross-feeding chain started. An organism using the third and fifth resource (in other words performing the tasks associated with producing byproducts three and five) would have a chain of length five steps.
2.2.2 Perturbation events
At 200,000 updates, I subjected the populations to perturbations on average every 30th, 40th,
50th and 60th update (here called the average waiting time) for a given number of events. The
number of events was altered to 100, 1000 and 2000. During the recurring perturbations, a randomized portion of the population was removed. I used removal rates of 50 and 60 % for the experiments (50 or 60 % of all organisms were removed every perturbation event). Populations evolved for a subsequent 10,000 updates after the last perturbation event.
2.2.3 Conversion rates
The conversion rate was altered from the default 1.0 to 0.5 and 0.9. A conversion rate of 1.0 indicates that there is no loss of energy between trophic levels, in this case between resource and byproduct resource. A 0.9 conversion rate indicates that one unit of the consumed resource is transformed into 0.9 units of the byproduct resource, in other words that 10 % energy is lost between two subsequent levels.
3 Results
3.1 Communities subjected to 0.5 conversion rate
Communities that were subject to a 0.5 conversion rate did not display any consistent reduction in chain length with 50 updates in average waiting time and 50 % removal rate at 100 (Figure 2A), 1000 (Figure 2B) and 2000 (Figure 2C) perturbation events. All communities subjected to 0.5 conversion rate survived the perturbations. Most communities displayed short cross-feeding chains, around 15 levels, during the course of the experiment.
Figure 2. Visualization of chain length in 60 communities with 0.5 conversion rate and an average of 50 updates between perturbations. Perturbation period between black lines. A 20 communities subject to 100 perturbation events during 5000 updates. B 20 communities exposed to 1000 perturbation events during 50,000 updates. C 20 communities subject to 2000 perturbations during 100,000 updates.
3.2 Communities subjected to 0.9 conversion rate
At conversion rate 0.9, an average waiting time of 50 updates and 50 % removal rate, some replicates (especially replicate 5-7 in Figure 3B) showed small decreases in chain length. However, in most replicates nothing indicated a reduced chain length during the perturbation period (see Figure 3A and 3B). Ninety percent of communities survived 1000 perturbations and 80 % survived 2000 events. For both 1000 and 2000 perturbation events, many community chain lengths remained constant during and after the perturbation period, often in lengths above 25 trophic levels.
An average waiting time of 30 and 40 updates was set on some communities exposed to 1000 perturbation events and 50 % removal rate. These communities did show small reductions in some replicates at 0.9 conversion rate. The communities subject to average waiting time 30
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 195000 200000 205000 210000 215000 Update R e p lic a te 10 15 20 25 30 Community chain length A 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 200000 220000 240000 260000 Update R e p lic a te 10 15 20 25 30 Community chain length B 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 200000 225000 250000 275000 300000 Update R e p lic a te 10 15 20 25 30 Community chain length C
updates (45 % community survival) showed somewhat similar chain lengths as the populations exposed to average waiting time 40 (60 % community survival) and 50 updates.
Figure 3. Visualization of digital communities subjected to perturbations events every 50th update on average, a removal rate of 50 % and 0.9 conversion rate. Perturbation events take place between the black lines. A Communities that survived 1000 perturbations during 50,000 updates. B Communities that survived 2000 perturbations during 100,000 updates.
Figure 4 presents 40 communities, subjected to a 0.9 conversion rate, that lived in environments with an average 50 updates between perturbations. Figure 4A depicts communities that were exposed to 100 perturbations and a removal rate of 50 %. Most of these replicates showed no indication of reduced chain length as a result of perturbations. The chain length remained around 30 steps for many of the replicates during the course of the experiment.
Communities presented in Figure 4B were subjected to 100 perturbation events and a removal rate of 60 %. Half the replicates that survived the perturbation events showed a reduction in chain length during or following the perturbation period. Most replicates that showed a decrease in chain length went from 30 trophic levels to under 20 levels.
20 19 18 17 16 15 14 13 12 11 10 9 8 6 5 4 2 1 200000 220000 240000 260000 Update R e p lic a te 10 20 30 Community chain length A 20 19 18 16 15 14 12 11 9 7 6 5 4 3 2 1 200000 225000 250000 275000 300000 Update R e p lic a te 5 10 15 20 25 30 Community chain length B
Figure 4. Visualization of 40 digital communities that survived 100 perturbations with an average 50 updates between perturbations and 0.9 conversion rate. Perturbation period between the black lines. A Communities subjected to a removal rate of 50 %. B Communities subjected to a removal rate of 60 %.
Two sets of communities were subject to an average waiting time of 60 and 40 updates respectively. The communities with 60 updates between perturbations had a 60 % removal rate, and the other communities had a removal rate of 50 %. Both groups were exposed to 100 perturbations. All communities showed chains around length 30, similar to the communities in Figure 3, and most replicates showed no reduction following perturbations. Both groups were subjected to a 0.9 conversion rate and all replicates survived the perturbation events.
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 195000 200000 205000 210000 215000 Update R e p lic a te 25 30 35 40 45 50 Community chain length A 20 19 17 16 15 14 13 11 10 9 8 7 6 5 4 3 2 1 195000 200000 205000 210000 215000 Update R e p lic a te 10 20 30 Community chain length B
4 Discussion
Studying the effect of recurring perturbations, as well as imperfect resource conversion, on the evolution of byproduct cross-feeding chains is of importance due to microbial disturbances playing a role in many diseases. Studies on digital organisms have the advantage of in many cases being exceedingly faster and more efficient than studying evolution of real organisms in real-time. In addition, the study of digital communities eliminates the risks and ethical constrains that naturally follow studies on living organisms.
In the current study, digital communities exposed to 0.5 conversion rate evolved chains that were no longer than 15-20 steps and did not display any length reduction by reason of perturbation. Communities subjected to 0.9 conversion rate evolved cross-feeding chains of at least length 25 steps. Most communities subject to 0.9 conversion rate did not show any reduction in chain length as a result of the disturbance events. Most replicates under any given regime survived the perturbations. These results demonstrated that energy loss between resource and byproduct resource appeared to protect digital communities from cross-feeding chain length reduction due to recurring disturbance events. Furthermore, the results suggested that imperfect resource conversion made digital communities somewhat more robust against the effect of perturbations and protected them from community extinction.
Communities exposed to 0.5 conversion rate evolved only short cross-feeding chains (Figure 2). These results indicated that a 50 % energy loss was too harsh for populations to evolve longer chains, perhaps because too much energy was lost for organisms on the higher levels of the byproduct chain to evolve. However, all replicates survived so they may be better protected against community extinction. These chains were similar in length to the metabolic cross-feeding chains found in the human gut by Wang and colleagues (2019).
Long chains evolved in all communities subject to 10 % energy loss. Two 0.9 conversion rate experiments (Figure 3) suggested that the disturbance events were harsh enough to kill 80-90 % of the replicates, but not harsh enough to cause the chains to reduce in length. Most chains maintained their length (around 25-30 steps) when the perturbations started at 200,000 updates.
suggested that a higher energy loss, compared to a moderate energy loss, better protected against community extinction.
A 0.9 conversion rate in addition to 100 perturbation events and average waiting time 50 updates gave chains of at least 30 steps in length in both perturbed and unperturbed state (Figure 4A). The experiments presented in Figure 4A and Figure 2A differed only in conversion rate, 0.9 and 0.5 respectively. Comparing them, one might conclude that a moderate energy loss gave rise to longer chains, as well as less fluctuating chain lengths, than a larger energy loss. Some replicates subjected to a 0.9 conversion rate in addition to 60 % removal rate showed reduced chain lengths (Figure 4B). This suggested that higher removal rates may not protect all communities from decreasing in chain length. It appeared that a higher removal rate (e.g., 60 %) in addition to a relatively short average waiting time (e.g., 50 updates) reduced the unperturbed chain length (approximately 25 steps) and caused community chain lengths to decrease during the perturbation period (Figure 4B).
In contrast to the digital communities that were subjected to only one kind of disturbance – the recurring removal of organisms – the human microbiome is subject to many perturbations such as antibiotics (Dethlefsen & Relman, 2011) and dietary changes (Henson & Phalak, 2017). The findings of the current project suggested that most digital organisms maintained the function of byproduct cross-feeding in the face of perturbation possibly because they were robust against the effects of perturbations. The robustness of a community allows a system to maintain specific systemic functions in the face of perturbations (Kitano, 2004). Communities that are robust to one type of disturbance are often very fragile to other disturbances (Carlson & Doyle, 2002; Kitano, 2004). If the digital communities had been subjected to more than one kind of disturbance during the perturbation period, another result may have come from this study.
In previous studies on the evolution of cross-feeding chains, it has been proposed that the length of the gut, as well as its restricted movement, play a role in determining the length of byproduct chains (Wang et al., 2019). Furthermore, it has been suggested that the number of trophic levels in ecological communities may be decided by population dynamics (Pimm & Lawton, 1977). The findings of the current project may hint that a high conversion rate plays a role in keeping byproduct chains short in perturbed and unperturbed environments.
Seeing that many diseases (for example obesity and type 2 diabetes) are associated with the gut microbiome being disrupted, it is of significance to recognize the effect of recurring perturbation on digital communities similar in structure to the gut microbiome. Analyzing how metabolic byproduct chains behave in unperturbed and perturbed environments is important in understanding mechanisms of disease. However, it is important not to forgo the fact that digital systems do not completely compare to any real biological system. The current study looked at a simplification of the complex interactions taking place in the human gut between species of microbes.
To conclude, the results from the current project suggested that moderate energy loss between resource and byproduct resource created communities that evolved longer byproduct cross-feeding chains than did a larger energy loss. Furthermore, it appeared that energy loss protected against community extinction. Using a larger conversion rate, more communities seemed to survive harsher perturbations. Regarding the effect of perturbations on chain length, it seemed that perturbations caused a steady reduction in chain length only under certain conditions (e.g., when the removal rate was high combined with a relatively short average waiting time) when energy loss was introduced between resources in the byproduct chain. These results, however far from any real community of organisms, may provide an idea of why metabolic byproduct chains remain short in the human gut.
Moving forward, it is of interest to look into why digital communities seem to be more robust during perturbation events when they are subjected to energy loss between resource and byproduct resource. This can be done by looking into the structure of the communities in their unperturbed state, just before they are exposed to any disturbances, and compare it to the perturbed state, to see what might cause the possible robustness.
5 Societal and Ethical Considerations
In itself, digital evolution is a valuable tool in understanding evolutionary processes and in discovering mechanisms underlying evolutionary patterns. However, there are restrictions with using digital organisms in theoretical projects and applying results to real-life organisms, as the two are not indistinguishable. Of course, real-life microbes partaking in cross-feeding interactions in the gut are influenced by other factors (e.g., the host and viruses) not taken into account in these digital communities. Still, the results from the current project may be used in understanding the dynamics of real-life communities of species. These findings may contribute with general ideas of what influences and properties of the gut microbiome affect the length of the metabolic byproduct chains in cross-feeding interactions.
In trying to understand what properties of communities constrain byproduct cross-feeding chains, using digital organisms do not cause afflictions nor generate any risks, but rather provide the opportunity to examine populations of organisms much faster than biologically possible.
6 Acknowledgements
I thank my supervisor György Barabás for valuable discussions, advice and for making this project happen. I am grateful to Johanna Orsholm for inspiring new ideas and assisting with knowledge on Avida. I would also like to thank Johanna Schwarz for support and helpful discussions, and my reviewers Joakim Mathiasson and Hugo Delin for feedback on my first drafts.
7 References
Adami, C. (2006). Digital genetics: unravelling the genetic basis of evolution. Nat. Rev. Genet., 7, 109–118. https://doi.org/10.1038/nrg1771
Blaut, M. (2011). Ecology and physiology of the intestinal tract. In Dobrindt, U., Hacker, J., Svanborg, C. (Eds.), Between Pathogenicity and Commensalism. Current Topics in
Microbiology and Immunology, 358, 247–272. Springer, Berlin, Heidelberg.
https://doi.org/10.1007/82_2011_192
Carlson, J. M., & Doyle, J. (2002). Complexity and robustness. Proc. Natl. Acad. Sci. USA, 99(Suppl 1), 2538–2545. https://doi.org/10.1073/pnas.012582499
Cooper, T., & Ofria, C. (2002). Evolution of stable ecosystems in populations of digital organisms. In Abbass, Bedau, Standish (Eds.), Proc. Artificial Life VIII, 227–232. MIT press. Dethlefsen, L., & Relman, D. A. (2011). Incomplete recovery and individualized responses of the human distal gut microbiota to repeated antibiotic perturbation. Proc. Natl. Acad. Sci. USA, 108, 4554–4561. https://doi.org/10.1073/pnas.1000087107
Harcombe, W. (2019). Novel cooperation experimentally evolved between species. Evolution, 64, 2166–2172. https://doi.org/10.1111/j.1558-5646.2010.00959.x
Henson, M. A., & Phalak, P. (2017). Byproduct cross feeding and community stability in an in silico biofilm model of the gut microbiome. Processes, 5(1), 13.
https://doi.org/10.3390/pr5010013
Kitano, H. (2004) Biological robustness. Nature Reviews Genetics, 5, 826–837.
https://doi.org/10.1038/nrg1471
Larsen, N., Vogensen, F. K., van den Berg, F. W., Nielsen, D. S., Andreasen, A. S., Pedersen, B. K., Al-Soud, W. A., Sørensen, S. J., Hansen, L. H., & Jakobsen, M. (2010). Gut microbiota in human adults with type 2 diabetes differs from non-diabetic adults. PLOS ONE, 5(2), e9085.
https://doi.org/10.1371/journal.pone.0009085
Lenski, R., Ofria, C., Collier, T., & Adami, C. (1999). Genome complexity, robustness and genetic interactions in digital organisms. Nature, 400, 661–664. https://doi.org/10.1038/23245 Ley, R. E., Bäckhed, F., Turnbaugh, P., Lozupone, C. A., Knight, R. D., & Gordon, J. I. (2005). Obesity alters gut microbial ecology. Proc. Natl. Acad. Sci. USA, 102, 11070–11075.
https://doi.org/10.1073/pnas.0504978102
Ley, R. E., Peterson, D. A., & Gordon, J. I. (2006). Ecological and evolutionary forces shaping microbial diversity in the human intestine. Cell, 124, 837–848.
https://doi.org/10.1016/j.cell.2006.02.017
Lindeman, R. L. (1942). The trophic-dynamic aspect of ecology. Ecology, 23, 399–417.
Misevic, D., Ofria, C., & Lenski, R. E. (2006). Sexual reproduction reshapes the genetic architecture of digital organisms. Proc. R. Soc. B., 273, 457–464.
https://doi.org/10.1098/rspb.2005.3338
Ofria, C., & Wilke, C. O. (2004). Avida: A software platform for research in computational evolutionary biology. Artif. Life, 10, 191–229. https://doi.org/10.1162/106454604773563612 Pacheco, A. R., Moel, M., & Segrè, D. (2019). Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems. Nat. Commun., 10, 103.
https://doi.org/10.1038/s41467-018-07946-9
Pfeiffer, T., & Bonhoeffer, S. (2004). Evolution of cross-feeding in microbial populations. The
American Naturalist, 163, E126–135. https://doi.org/10.1086/383593
Pimm, S. L, & Lawton, J. H. (1977). Number of trophic levels in ecological communities.
Nature, 268, 329–331. https://doi.org/10.1038/268329a0
Solé, R. V., Montoya, J. M., & Erwin, D. H. (2002). Recovery after mass extinction: evolutionary assembly in large-scale biosphere dynamics. Phil. Trans. R. Soc. B, 357, 697–707.
https://doi.org/10.1098/rstb.2001.0987
Sung, J., Kim, S., Cabatbat, J., Jang, S., Jin, Y.-S., Jung, G. Y., Chia, N., & Kim, P.-J. (2017). Global metabolic interaction network of the human gut microbiota for context-specific community-scale analysis. Nat. Commun., 8, 15393. https://doi.org/10.1038/ncomms15393 Wang, T., Goyal, A., Dubinkina, V., & Maslov, S. (2019). Evidence for a multi-level trophic organization of the human gut microbiome. PLOS Comput. Biol., 15(12), e1007524. https://doi.org/10.1371/journal.pcbi.1007524
Wilke, C. O., & Adami, C. (2002). The biology of digital organisms. Trends Ecol. Evol., 17, 528–532. https://doi.org/10.1016/S0169-5347(02)02612-5
Wilke, C., Wang, J., Ofria, C., Lenski, R. E., & Adami, C. (2001). Evolution of digital organisms at high mutation rates leads to survival of the flattest. Nature, 412, 331–333.
https://doi.org/10.1038/35085569
Wootton, J. T. (1998). Effects of disturbance on species diversity: a multitrophic perspective.
Am. Nat., 152, 803–825. https://doi.org/10.1086/286210
Yedid, G., Stredwich, J., Ofria, C. A., & Agapow, P.-M. (2012). A comparison of the effects of random and selective mass extinctions on erosion of evolutionary history in communities of digital organisms. PLOS ONE, 7, e37233. https://doi.org/10.1371/journal.pone.0037233 Yodzis, P. (1988). The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology, 69, 508–515. https://doi.org/10.2307/1940449
