Behavioural Strategies in Cyclic Models: The Effects of Directional Movement Tactics

Behavioural Strategies in Cyclic Models: The Effects of Directional Movement Tactics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Behavioural Strategies in Cyclic Models: The Effects of Directional Movement Tactics Beatriz Moura, Josinaldo Menezes da Silva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-119510/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Mar, 2021 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract We investigate behavioural strategies in stochastic simulations of systems with cyclic nonhierarchical dominance, as a generalisation of the rock-paper-scissors game. We introduce directional movement tactics to one out of the species, whose individuals move according to an innate or a conditioned response to a stimulus; individuals of the other species move randomly. The directional movement tactics allow the individuals to conquer or maintain territory, either attacking or anticipating or Safeguarding themselves. We study the effects of the behavioural strategies for individuals with different levels of perception of the neighbourhood. Besides, we investigate the case where not all individuals are conditioned to perform the behavioural strategy or where individuals that do not use the tactic for every move. We found that self-preservation behaviour is more profitable in terms of population growth, where the best result is achieved for individuals with large perception radius that always move according to the movement tactic. Our findings show that the attack tactics is more gainful for short perception radius and if the individuals alternate the tactic with random movement. For anticipation, the best result is achieved for individuals with long-range perception using the tactics rarely. Finally, we calculated the coexistence probability and found that, in addition to providing a greater spatial density for the species, the Safeguarding tactic is the least jeopardising to biodiversity. Our results may be useful for experimental and theoretical biologists to understand systems of species whose individuals behave strategically, and how coexistence is maintained in an uneven scenario. Biotechnology and Bioengineering investigate behavioural strategies stochastic simulations behavioural strategies least jeopardising to biodiversity Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Full Text Cite Share Download PDF Status: Published Journal Publication published 19 Mar, 2021 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Major revision 24 Dec, 2020 Reviews received at journal 10 Dec, 2020 Reviewers agreed at journal 07 Dec, 2020 Reviews received at journal 07 Dec, 2020 Reviewers agreed at journal 07 Dec, 2020 Reviewers invited by journal 07 Dec, 2020 Editor assigned by journal 07 Dec, 2020 Editor invited by journal 07 Dec, 2020 Submission checks completed at journal 07 Dec, 2020 First submitted to journal 01 Dec, 2020 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-119510","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":5961512,"identity":"a16aaa00-0520-4008-99bb-2d497e272f15","order_by":0,"name":"Beatriz Moura","email":"","orcid":"","institution":"Federal University of Rio Grande do Norte","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Beatriz","middleName":"","lastName":"Moura","suffix":""},{"id":5961514,"identity":"237671a0-5212-4330-82f1-77e1b32670ca","order_by":1,"name":"Josinaldo Menezes da Silva","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACxgYogx9CyQExD5FaJBvAbGPCWuDA4ACxWpinHT724MMfG3vj483PHzC2GeSbM/Ae+4DXYbPT0g1n8KQlbjtzzLABqMVyZwNf8gz8WnLMpHkkDieY3chhBGr5Y2BwgMcYr8MYZ+d/k/5j8N/eeP4bkBYDYrTksEkzJBxg3CDBQ7SWNDPJngPJiTPOpBnOSDgH1HKYLxmvFsPZyc8kfvyxs+dvP/zgw4cyoJbjvYfxa2lA5iWACGa8GhgY5AnIj4JRMApGwShgYAAA4rxFPFdJ+foAAAAASUVORK5CYII=","orcid":"","institution":"Federal University of Rio Grande do Norte","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Josinaldo","middleName":"Menezes da","lastName":"Silva","suffix":""}],"badges":[],"createdAt":"2020-12-01 12:29:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-119510/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-119510/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-021-85590-y","type":"published","date":"2021-03-19T19:10:57+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":4130078,"identity":"83bda134-d23d-4386-b3ea-9f058c482f7a","added_by":"auto","created_at":"2020-12-09 16:44:27","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":29202,"visible":true,"origin":"","legend":"Selection rules and movement tactics for the case N = 5. (a) Illustration of the selection rules among the species, which represents a generalisation of the rock-paper-scissors game. (b) Illustration of the directional movement tactics for individuals of species 1. The solid green line represents the Attack tactic, where individuals move towards the direction with more individuals of species 2. The dashed green line shows the Anticipation tactic, that is a movement towards the path with more individuals of species 3. The dashed-dotted green line illustrates how individuals move when they perform the Safeguard tactic, going towards the direction with more individuals of species 4. The concentric circumference arcs in the right panel illustrate that individuals of species 2, 3, 4, and 5 always move randomly.","description":"","filename":"Fig1.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/fb9ef68addb4806aaa16d901.JPG"},{"id":4130079,"identity":"87625665-e3b0-4686-8507-2b20a9612bfb","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":91250,"visible":true,"origin":"","legend":"Snapshots of 5002 simulations of the generalisation of the rock-paper-scissors game illustrated in Fig. 1. Each dot shows either an individual (according to the colour scheme in Fig. 1) or an empty site (white dot). All simulations started from the same random initial conditions, and we captured the snapshots after 5000 generations. The snapshots show the spatial patterns for the standard model (a), Attack (b), Anticipation (c), and Safeguard (d) tactics, respectively. See also the videos for the whole simulation for the Standard case (https://youtu.be/Hd1XSpbB3Ac), Attack (https://youtu.be/5MTclpRL638), Anticipation (https://youtu.be/mSJFpQpYvqU), and Safeguard (https://youtu.be/PWLr9v3I5bA). The results were obtained for the same perception radius, R = 3.","description":"","filename":"Fig2.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/8532e702d802a92871dfe31c.JPG"},{"id":4130080,"identity":"ebb97fbe-3348-450a-9dc1-a5a9defc1cac","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84970,"visible":true,"origin":"","legend":"Temporal changes of the species densities ri during the simulations presented in Fig. 2. The colours indicate the species following the scheme in Fig. 1, while the grey line shows the density of empty spaces. (a) Standard case, https://youtu.be/Hd1XSpbB3Ac. (b) Attack tactic, https://youtu.be/5MTclpRL638. (c) Anticipation tactic, https://youtu.be/mSJFpQpYvqU. (d) Safeguard tactic, https://youtu.be/PWLr9v3I5bA.","description":"","filename":"Fig3.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/4e8b404988c75cac7bd548d8.JPG"},{"id":4130081,"identity":"60278411-b111-4ac2-b9ff-75a038bc9889","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":75430,"visible":true,"origin":"","legend":"Dynamics of the selection risks of the species densities zi for the simulations presented in Fig. 2. The colours indicate the species following the scheme in Fig. 1. (a) Standard case, https://youtu.be/Hd1XSpbB3Ac. (b) Attack tactic, https://youtu.be/5MTclpRL638. (c) Anticipation tactic, https://youtu.be/mSJFpQpYvqU. (d) Safeguard tactic, https://youtu.be/PWLr9v3I5bA.","description":"","filename":"Fig4.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/c6349209b8489f687d70b836.JPG"},{"id":4130082,"identity":"ac289235-7453-4061-a263-885288c6e07f","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":36769,"visible":true,"origin":"","legend":"Autocorrelation functions Ci for each movement tactic. The colours follow the scheme in Fig. 1. (a), (b) , and (c) depict the cases where individuals of species 1 use Attack, Anticipation, and Safeguard tactics, respectively. The results were obtained using R = 3. The dashed black line represents the autocorrelation function for the standard case (std), that is the same for all species. The horizontal purple dashed line indicates the threshold assumed to calculate the characteristic length.","description":"","filename":"Fig5.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/e55d795d75e1322d0990dacc.JPG"},{"id":4130083,"identity":"a0399d13-8195-40c3-a8d2-c4485afd0619","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":65059,"visible":true,"origin":"","legend":"Mean species densities hrii and mean selection risks hzii for a range of perception radius R. The results were averaged from a set of 5002 simulations with 100 different random initial conditions. R = 0 represents the standard case. (a), (b), and (c) show hrii for Attack, Anticipation, and Safeguard tactics, respectively. (a), (b), and (c) show hrii for Attack, Anticipation, and Safeguard tactics, respectively. (d), (e), and (f) depict hzii for Attack, Anticipation, and Safeguard tactics, respectively. (a), (b), and (c) show hrii for Attack, Anticipation, and Safeguard tactics, respectively.","description":"","filename":"Fig6.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/0fe172650cdb10e65d0dc54d.JPG"},{"id":4130084,"identity":"d8b178e5-911c-4ab5-a859-2595891afa71","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":27962,"visible":true,"origin":"","legend":"Average density of species 1, hr1i, in terms of the conditioning factor a. The green, pink, and yellow lines show the results for the case of individuals of species 1 moving according to Attack, Anticipation, and Safeguard directional tactics, respectively. a = 0 represents the standard case. The results were obtained using R = 3.","description":"","filename":"Fig7.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/468f0af393a33324971a6419.JPG"},{"id":4130085,"identity":"67e51f6d-c2d1-4c3a-80a5-b088cff20894","added_by":"auto","created_at":"2020-12-09 16:44:28","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":34808,"visible":true,"origin":"","legend":"Coexistence probability as a function of the mobility probability m. The solid grey line shows the coexistence probability for the standard model. The green, pink, and yellow lines show the results for the case of individuals of species 1 moving according to Attack, Anticipation, and Safeguard directional tactics, respectively. Solid lines and dashed lines show the results for R = 2 and R = 4, respectively.","description":"","filename":"Fig8.JPG","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1/afc85d6e75c045058ad8d841.JPG"},{"id":13563686,"identity":"b243158c-9a0e-4ec1-871e-2adbaa1dd42d","added_by":"auto","created_at":"2021-09-17 03:17:40","extension":"pdf","order_by":8,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1746940,"visible":true,"origin":"","legend":"","description":"","filename":"BehaviouralStrategiesinRPS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1_covered.pdf"},{"id":4130086,"identity":"bf5af3cf-4c5d-4cd4-bf26-a5965b4832c0","added_by":"auto","created_at":"2020-12-09 16:44:39","extension":"pdf","order_by":8,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1638019,"visible":true,"origin":"","legend":"","description":"","filename":"BehaviouralStrategiesinRPS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-119510/v1_stamped.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eBehavioural Strategies in Cyclic Models: The Effects of Directional Movement Tactics\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-119510/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"investigate behavioural strategies, stochastic simulations, behavioural strategies, least jeopardising to biodiversity","lastPublishedDoi":"10.21203/rs.3.rs-119510/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-119510/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate behavioural strategies in stochastic simulations of systems with cyclic nonhierarchical dominance, as a\u003c/p\u003e\u003cp\u003egeneralisation of the rock-paper-scissors game. We introduce directional movement tactics to one out of the species, whose individuals move according to an innate or a conditioned response to a stimulus; individuals of the other species move randomly. The directional movement tactics allow the individuals to conquer or maintain territory, either attacking or anticipating or Safeguarding themselves. We study the effects of the behavioural strategies for individuals with different levels of perception of the neighbourhood. Besides, we investigate the case where not all individuals are conditioned to perform the behavioural strategy or where individuals that do not use the tactic for every move. We found that self-preservation behaviour is more profitable in terms of population growth, where the best result is achieved for individuals with large perception radius that always move according to the movement tactic. Our findings show that the attack tactics is more gainful for short perception radius and if the individuals alternate the tactic with random movement. For anticipation, the best result is achieved for individuals with long-range perception using the tactics rarely. Finally, we calculated the coexistence probability and found that, in addition to providing a greater spatial density for the species, the Safeguarding tactic is the least jeopardising to biodiversity. Our results may be useful for experimental and theoretical biologists to understand systems of species whose individuals behave strategically, and how coexistence is maintained in an uneven scenario.\u003c/p\u003e","manuscriptTitle":"Behavioural Strategies in Cyclic Models: The Effects of Directional Movement Tactics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-12-09 16:44:26","doi":"10.21203/rs.3.rs-119510/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2020-12-24T09:42:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2020-12-10T17:04:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"5b02ef6e-7f7d-4d1c-80df-266716329b96","date":"2020-12-08T04:38:01+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2020-12-07T16:22:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48b7bd26-b611-49bf-86bc-107a7ba1b466","date":"2020-12-07T15:25:40+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2020-12-07T15:20:16+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2020-12-07T15:07:50+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2020-12-07T09:17:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2020-12-07T08:31:36+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2020-12-01T12:23:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3ce6302a-ecb2-487b-8c17-c97e75122498","owner":[],"postedDate":"December 9th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":1401041,"name":"Biotechnology and Bioengineering"}],"tags":[],"updatedAt":"2021-08-18T19:31:36+00:00","versionOfRecord":{"articleIdentity":"rs-119510","link":"https://doi.org/10.1038/s41598-021-85590-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2021-03-19 19:10:57","publishedOnDateReadable":"March 19th, 2021"},"versionCreatedAt":"2020-12-09 16:44:26","video":"","vorDoi":"10.1038/s41598-021-85590-y","vorDoiUrl":"https://doi.org/10.1038/s41598-021-85590-y","workflowStages":[]},"version":"v1","identity":"rs-119510","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-119510","identity":"rs-119510","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}