{"paper_id":"026b6eb5-7495-4817-a570-e5b49520d783","body_text":"Host Age Structure Defines Interactions with Pathogens: Grandparent Effect under Collaboration and Virulent Mutualism under Competition | 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 Host Age Structure Defines Interactions with Pathogens: Grandparent Effect under Collaboration and Virulent Mutualism under Competition Carsten O.S. Portner, Edward G. Rong, Jared A. Ramirez, Yuri I. Wolf, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1972333/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Background: Symbiotic relationships are ubiquitous in the biosphere. Inter-species symbiosis is impacted by intra-specific distinctions, in particular, those defined by the age structure of a population. Older individuals compete with younger individuals for resources despite being less likely to reproduce, diminishing the fitness of the population. Conversely, however, older individuals can support the reproduction of younger individuals, increasing the population fitness. Parasitic relationships are commonly age structured, typically, more adversely affecting older hosts. Results: We employ mathematical modeling to explore the differential effects of collaborative or competitive host age structures on host-parasite relationships. A classical epidemiological compartment model is constructed with three disease states: susceptible, infected, and recovered. Each of these three states is partitioned into two compartments representing young, potentially reproductive, and old, post-reproductive, hosts, yielding 6 compartments in total. In order to describe competition and collaboration between old and young compartments, we model the reproductive success to depend on the fraction of young individuals in the population. Collaborative populations with relatively greater numbers of post-reproductive hosts enjoy greater reproductive success whereas in purely competitive populations, increase of the post-reproductive subpopulation reduces reproductive success. However, in competitive populations, virulent pathogens preferentially targeting old individuals can increase the population fitness. Conclusions: We demonstrate that, in collaborative host populations, pathogens strictly impacting older, post-reproductive individuals can reduce population fitness even more than pathogens that directly impact younger, potentially reproductive individuals. In purely competitive populations, the reverse is observed, and we demonstrate that endemic, virulent pathogens can oxymoronically form a mutualistic relationship with the host, increasing the fitness of the host population. Applications to endangered species conservation and invasive species containment are discussed. Virulence Mutualism Age Structure Epidemic Compartment Model Host-Pathogen Interactions Figures Figure 1 Figure 2 Figure 3 Background Despite having acquired a positive connotation when used informally, the term “symbiosis” may refer to any sustained inter- (but not intra-) species relationship(1). This relationship can be mutualistic (beneficial for all species involved), commensal (beneficial or neutral for all species), or parasitic (beneficial for some and deleterious for others) as well as obligate or facultative (beneficial but not required for survival). The diversity of inter-species symbioses is broadened still by intra-species diversity such that the nature of the symbiosis varies among individuals within each species. Pathogenic (that is, involved in strongly asymmetric, parasitic relationships(2)) human viruses provide well-characterized examples. For almost all pathogenic viruses, a period of host immunity follows infection, compartmentalizing the population into two groups, only one of which would engage in symbiosis with the virus(3). For common viruses that confer lifelong immunity following initial infection (or vaccination), these two groups can be often well approximated by age whereby young individuals who have never been exposed are susceptible to infection and older individuals, who were most likely exposed when they were themselves younger, are immune. Indeed, the age structure of human populations plays an important role in forecasting the impact of novel pathogens because, even among apparently susceptible hosts, increased age may be a predictor of increased(4, 5) or decreased(5, 6) morbidity and mortality. Although post-reproductive lifespans appear to be rare in nature, even among mammals(7), senescence has been observed in all major branches of the tree of life, from animals(8, 9) and plants(10) to yeast(11) and bacteria(12). Senescent members are inherently costly to the population as they consume shared resources but reproduce with reduced (down to zero) efficiency. However, senescent individuals also can increase the overall growth rate of populations if they increase the efficiency with which other members reproduce. Such collaborative populations foster selection for post-reproductive lifespans, commonly referred to as “the grandmother hypothesis,” best demonstrated among humans(13–15) and orca whales(16). In this work, we sought to explore the impact of host age-structure dynamics on the introduction of a pathogen with age-dependent virulence. We consider two diverse host populations: a competitive population modelled after rotifers(17, 18) (as well as an additional case modeled after solitary bees(19, 20) with qualitatively similar behavior addressed in the supplement) and a collaborative population modelled after humans. We demonstrate that, in competitive populations, a virulent pathogen can paradoxically increase the population growth rate. Conversely, in collaborative populations, the loss of a single post-reproductive member due to infection can result in a growth rate drop that exceeds that resulting from the loss of a single reproductive member. Results Model Construction A classical epidemiological compartment model (Fig. 1 A) was constructed with three disease states: susceptible, infected, and recovered. Each of these three states is partitioned into two compartments representing young, potentially reproductive, and old, post-reproductive, hosts, yielding 6 compartments in total. All hosts are born susceptible (at rate k B ) to infection; age into the post-reproductive compartment (at rate k A ); and die from causes unrelated to infection (at rate k D ). Susceptible hosts may become infected (proportional to rate k I ) and recover or die due to infection (at rate k R or the age-specific rates k DYI or k DOI respectively). Recovered hosts can lose immunity and return to a susceptible compartment (at rate k L ). For each population, the birth rate, death rate, and rate of aging from young to old compartments were fixed across all simulations (for a complete list of all parameters, see Table 1 ). In order to model competition and collaboration between old and young compartments, we sought to make the reproductive success (which may represent the fraction of young hosts which are fertile or the probability that a birth will result in viable offspring) dependent on the proportion of the young individuals in the population, \\(\\frac{Y}{Y+O}\\) , where \\(Y\\) and \\(O\\) are the cumulative sizes of all young and old compartments, respectively. First let us consider a collaborative population. In the limiting case where all but a single host (or mating pair) is post-reproductive, and aiding in the reproduction of that single host, we assume 100% reproductive success. The more collaborative the population, or conversely the greater the degree to which young hosts depend on post-reproductive hosts, the more steeply the reproductive success declines with relatively fewer post-reproductive hosts. Under conditions without any post-reproductive hosts, we assume the limiting case where the reproductive success is zero. We further assume this behavior saturates with respect to either limit. The converse argument applies to competitive populations: reproductive success is inversely proportional to the relative number of post-reproductive hosts. Although cooperation and competition are not necessarily strictly symmetrical, for formal convenience, we considered the family of functions: $$f\\left(\\frac{Y}{Y+O}\\right)={cos}^{10a}\\left(\\frac{\\pi }{2}\\frac{Y}{Y+O}\\right){sin}^{10b}\\left(\\frac{\\pi }{2}\\frac{Y}{Y+O}\\right)$$ where \\(a=0, 0<b\\le \\frac{1}{2}\\) and \\(b=0 , 0<a\\le \\frac{1}{2}\\) represent competitive and collaborative populations, respectively (Fig. 1 B), which possess the properties described above. We also emphasize that competition between parameter regimes is not assessed in this work. Only the relative fitness of disease free and endemic equilibria are considered. Each simulation was conducted as follows. Parameters \\(a\\) and \\(b\\) were selected and the equilibrium age distribution, \\(\\frac{Y}{Y+O}\\) , as well as the exponential growth rate, \\(\\frac{dN/dt}{N}\\) where \\(N\\) is the cumulative size of all compartments, were computed (for details, see Extended Data A). Compartments are initialized to respect the equilibrium age distribution, with infected compartments initialized to be 0.1% of the total population. The solution is then propagated using Python scipy method solve_ivp until a state of endemic equilibrium is reached where the measured rate of change of compartment proportions is negligible. The new growth rate at endemic equilibrium is then computed. For details, see Extended Data B. Loss of post-reproductive hosts is costly for collaborative populations A human population was modelled consistent with an average reproductive life span of 25 years; post-reproductive life span of 45 years; a birth rate of 0.14 births/year; and reproductive success determined by \\(a=\\left\\{\\text{0.1,0.2,0.3,0.4,0.5}\\right\\}\\) . The pathogen was modelled with an infectivity (the product of the rate of host contact and the probability of infection given contact) of 2/week, mean duration of infection 2 weeks, and mean duration of immunity 1 year for all hosts, but a probability of death roughly 1% for old hosts and zero for young hosts. These parameters well represent a range of human respiratory viruses(21) but we note this model does not account for the complex behavior associated with time varying contact rates(22, 23). The epidemic trajectory for \\(a=0.2\\) is shown in Fig. 2 A. Due to the loss of old hosts as a result of infection, the young fraction of the population increases throughout the epidemic phase and into endemicity (Fig. 2 B). In every case, the growth rate substantially declines (and can become negative) during the epidemic phase before gradually increasing (subject to oscillations) to a value reduced relative to the pre-epidemic level (Fig. 2 C). The cost to the population (decreased growth rate) as a result of endemic infection is greater for more collaborative populations (larger \\(a\\) , Fig. 2 D). Death rate due to infection was then varied, ranging from 0.25/year to 0.45/year among old hosts, remaining at zero for young hosts. For each final growth rate, the equivalent death rate due to infection under conditions where only young hosts die as a result of infection was computed such that the final growth rate attained was the same for both models. Under sufficiently collaborative conditions, \\(a\\ge 0.2\\) , the equivalent death rate among young hosts resulting in the same growth rate reduction was greater than that among old hosts (Fig. 2 E). In other words, in a highly collaborative population, the cost of the loss of a post-reproductive member due to infection is greater than the cost of the loss of a young, potentially reproductive member. The relative cost of losing young vs. post-reproductive hosts depends on the reproductive success function, \\(f\\left(\\frac{Y}{Y+O}\\right)\\) . When reproductive success remains near one until \\(\\frac{Y}{Y+O}\\) approaches one and then sharply declines, representing the case where the population is insensitive to the abundance of post-reproductive hosts, the loss of a young host always has a greater impact than the loss of a post-reproductive host (see Supplemental Fig. 1). Virulent mutualism in competitive populations A competitive population was modelled using the data available for rotifer populations, with an average reproductive life span of 8 days; post-reproductive life span of 9 days; a birth rate of 1.3/day(17); and reproductive success determined by \\(b=\\left\\{\\text{0.1,0.2,0.3,0.4,0.5}\\right\\}\\) . The pathogen was modelled with an infectivity of 4/day, mean duration of infection 3 days, and mean duration of immunity 17 days for all hosts, but a probability of death near 100% for old hosts and zero for young hosts. These parameters, apart from age dependence, are modelled after a fungal pathogen of the genus Rotiferophthora (18). The epidemic trajectory for \\(b=0.2\\) is shown in Fig. 3 A. Note that the timescale of the epidemic is much shorter than that in the model of a collaborative population due to the major difference in member lifespans, and oscillations are not observed in these trajectories. Due to the loss of old hosts as a result of infection, the young fraction of the population increases logistically over the epidemic phase and into endemicity (Fig. 3 B). While the exponential growth rate ( \\(\\frac{dN/dt}{N}\\) , which is not the birth rate) still declines during the epidemic phase due to the loss of post-reproductive members, it remains positive and the endemic growth rate is elevated relative to the disease-free state (Fig. 3 C). The benefit to the population (increased growth rate) as a result of endemic infection is greater for more competitive populations (larger \\(b\\) , Fig. 2 D). As for the collaborative case, the death rate due to infection was then varied, ranging from 0.33/day to 0.52/day among old hosts, remaining at zero for young hosts. For each final growth rate, the equivalent birth rate for a disease-free state was computed such that the final growth rate attained was the same for both models. Note that even a 1% change in the exponential growth rate under these conditions results in a 50% larger population within the time span of 3 generations. The introduction of a virulent pathogen significantly increased the population growth rate, in some cases equivalent to increasing the birth rate by more than 2% (Fig. 3 E). An additional competitive population was loosely modelled after sweat bees(19) introduced to a pathogen resembling acute bee paralysis virus(20), resulting in qualitatively similar behavior (see Supplemental Fig. 2). Discussion Parasites, by definition, decrease host fitness and the introduction of a parasite into one or more competing host species can substantially alter the ecological landscape resulting in or preventing the extinction of one competitor(24, 25). Symbionts that are parasitic in the absence of inter-species host competition but which increase the competitiveness of infected hosts (for example, through allelopathy(26)) establish a seemingly surprising, mutualistic relationship. Similarly, host competition can admit the persistence of a parasite under conditions where persistence within a single host population is not supported(25). Furthermore, even within a single host species, symbionts that are parasitic in one environment can provide a fitness advantage due to specialized adaptations in another environment, for example, promoting resistance to drought(27). Parasitic interactions can also substantially alter intra-species competition due to variability in tolerance or transmissibility influenced by genomic or nongenomic factors including host density(28) and age. In previous human epidemics, advanced age has been commonly associated with increased(4, 5) or occasionally decreased(5, 6) morbidity and mortality. More generally, species lifespans are likely influenced by pathogen interactions. Populations of species with short lifespans are able to clear pathogens faster, and being short-lived decreases the probability of crossing the species barrier, which typically requires major adaptations to emerge within the first infected novel host to mediate efficient transmission(29). Age structure substantially alters transmission dynamics, and can reduce the likelihood of an epidemic while increasing the magnitude in the event of an outbreak(30). The presence of immune post-reproductive hosts decreases the density of susceptible hosts and reduces the rate of infection; however, susceptible, and senescent, post-reproductive hosts can increase the cumulative number of mortalities. The disparity in predicted outcomes between homogenous (which may already lead to diverse results(31, 32)) and age-structured populations is exacerbated in the event of vaccination(33). Here we demonstrate that host age structure, associated with differential susceptibility to a parasite, can determine whether a virulent pathogen, as defined by its relationship with individual hosts, is a parasite or a mutualist with respect to the population as a whole. In competitive populations where older, post-reproductive hosts share resources with younger, potentially reproductive hosts, virulent pathogens that disproportionately affect non-reproductive hosts increase the population growth rate. Conversely, in collaborative populations where older, post-reproductive hosts aid in the reproduction of younger hosts, the cost of the loss of a non-reproductive host can be even greater than that of a young host. Although post-reproductive lifespans appear to be rare, even among mammals(7), most if not all cellular life forms exhibit some form of senescence(8–12). Therefore, although advanced social roles for post-reproductive members have not yet been identified outside of mammals, costs and potentially benefits associated with the presence of senescent hosts are likely widespread even for unicellular life. Among prokaryotes, horizontal gene transfer from dead, maximally senescent, cells can prevent irreversible genomic deterioration, Muller’s rachet(34). In addition to chronological age, altering the stationary cell cycle phase distribution(35, 36) can modify the fitness landscape by altering phase-dependent gene expression(37) potentially delegating different functions to individuals in different phases. Thus, collaborative populations might be far more common across the diversity of life than is immediately obvious. These, often complex, impacts of age structure have to be taken into account prior to formulating a strategy for intervention against a pathogen, mitigation of invasive species, or preservation of an endangered population(38). For example, food provisioning both increases resource availability and host aggregation, potentially amplifying pathogen invasion(39). Thus, in the context of competition, which may itself be magnified as a result of host aggregation, the effect of a pathogen likely enhances conservation efforts, whereas in the case of collaboration, this straightforward intervention could lead to population decline. Declarations Authors’ information COSP, EGR, and JAR are students in the Montgomery Blair High School Magnet Program supervised by APB. YIW, EVK, and NDR hold intramural positions at the NIH. Authors’ Contributions YIW, APB, EVK, and NDR designed the study; COSP, EGR, and JAR programed the model; COSP, EGR, JAR, YIW, and NDR conducted the analysis; COSP, EVK, and NDR wrote the manuscript that was edited and approved by all authors. Acknowledgements The authors thank Koonin group members for helpful discussions. Funding YIW, NDR, and EVK are supported by the Intramural Research Program of the National Institutes of Health. Availability of supporting data Supplementary figures and extended data are available for download as a single pdf. Competing Interests The authors have no competing interests to declare. Consent for publication All authors have provided consent for publication. Human Ethics Not applicable. Ethical Approval and Consent to participate Not applicable. References Paracer S & Ahmadjian V (2000) Symbiosis: an introduction to biological associations (Oxford University Press). Casadevall A & Pirofski L-a (1999) Host-pathogen interactions: redefining the basic concepts of virulence and pathogenicity. Infection and immunity 67(8):3703-3713. Amanna IJ, Carlson NE, & Slifka MK (2007) Duration of humoral immunity to common viral and vaccine antigens. New England Journal of Medicine 357(19):1903-1915. 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Table Table 1 Human Rotifer Sweat Bee Rate of Infection 2 week -1 4 days -1 1.9 weeks -1 Rate of Recovery 0.5 week -1 0.059 days -1 0.06 weeks -1 Rate of Loss of Immunity 1 years -1 0.059 days -1 0.06 weeks -1 Birth Rate 0.14 years -1 1.3 days -1 1.5 weeks -1 Aging Rate 0.04 years -1 0.125 days -1 0.14 weeks -1 Post-Reproductive Death Rate 0.022 years -1 0.11 days -1 0.14 weeks -1 Post-Reproductive Infection Death Rate 0.25 years -1 0.33 days -1 1.4 weeks -1 Additional Declarations No competing interests reported. Supplementary Files virulentMutalistSupplement.pdf SupplementalFigurelegends.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 21 Sep, 2022 Reviews received at journal 23 Aug, 2022 Reviewers agreed at journal 23 Aug, 2022 Reviewers invited by journal 23 Aug, 2022 Editor assigned by journal 23 Aug, 2022 Submission checks completed at journal 22 Aug, 2022 First submitted to journal 17 Aug, 2022 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-1972333\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":130722487,\"identity\":\"28e43dc7-d9e3-46bb-ae8d-23ebb9fe2968\",\"order_by\":0,\"name\":\"Carsten O.S. Portner\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Montgomery Blair High School\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Carsten\",\"middleName\":\"O.S.\",\"lastName\":\"Portner\",\"suffix\":\"\"},{\"id\":130722488,\"identity\":\"09b545ab-56c5-4dea-ba91-6fccadaa3d36\",\"order_by\":1,\"name\":\"Edward G. Rong\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Montgomery Blair High School\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Edward\",\"middleName\":\"G.\",\"lastName\":\"Rong\",\"suffix\":\"\"},{\"id\":130722491,\"identity\":\"34de1dbe-2269-498d-932d-236416e60b1a\",\"order_by\":2,\"name\":\"Jared A. Ramirez\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Montgomery Blair High School\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jared\",\"middleName\":\"A.\",\"lastName\":\"Ramirez\",\"suffix\":\"\"},{\"id\":130722492,\"identity\":\"8b8c40f5-9573-4d56-8935-d908da28c225\",\"order_by\":3,\"name\":\"Yuri I. Wolf\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"National Institutes of Health\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Yuri\",\"middleName\":\"I.\",\"lastName\":\"Wolf\",\"suffix\":\"\"},{\"id\":130722493,\"identity\":\"1c0f8b1d-3f7e-4b0f-a9c0-57606d26ee48\",\"order_by\":4,\"name\":\"Angelique P. Bosse\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Montgomery Blair High School\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Angelique\",\"middleName\":\"P.\",\"lastName\":\"Bosse\",\"suffix\":\"\"},{\"id\":130722494,\"identity\":\"92c38145-83f4-4e60-829f-63ed75a64a50\",\"order_by\":5,\"name\":\"Eugene V. Koonin\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"National Institutes of Health\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Eugene\",\"middleName\":\"V.\",\"lastName\":\"Koonin\",\"suffix\":\"\"},{\"id\":130722495,\"identity\":\"9d156268-3d0e-424f-bd65-69c292e1906f\",\"order_by\":6,\"name\":\"Nash D. Rochman\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYHACNjBpACI+MEgkkKaFcQbJWph5GBgIazFnP/7sAeMeG3lzscPPHtvusMhj4F98TAKfFsueHHMDhmdphjtnp5kb556RKGaQeJaGV4vBgRw2CYYDhxMMbieYSee2SSQ2SJwxNsCr5fzzZ1At6d+kLYnSciPBDKolx0yaEaSFv8fwAX4tb8wkEg6kGW64nVMm2QvU0ibBlohfy/n0ZxIfDtjIAx22TeJnW11iP//hAwfwaQGDBGQOG3GxiQL4CdsxCkbBKBgFIwsAACKbSJgCtyguAAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"National Institutes of Health\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Nash\",\"middleName\":\"D.\",\"lastName\":\"Rochman\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2022-08-17 20:29:14\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-1972333/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-1972333/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":25621803,\"identity\":\"c2e3e685-2404-443c-a307-a745547960c1\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:08:26\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":370996,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e See image above for figure legend.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/00f13177648801488e50a9b3.png\"},{\"id\":25621498,\"identity\":\"34ba2181-18ba-4d01-9779-b6b7b725ec37\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:03:26\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":647832,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e See image above for figure legend.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/1c5ab0b4122c538f80e98584.png\"},{\"id\":25621501,\"identity\":\"44668e30-1de1-41b2-808d-94492fca15fd\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:03:26\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":634676,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e See image above for figure legend.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/e122bac6fa78f2ed4ada66d2.png\"},{\"id\":25622160,\"identity\":\"b8669586-fe2e-400a-a16e-5d85758cad85\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:13:29\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":287761,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/9d734e05-0ab1-4039-aefe-0275e819ac3e.pdf\"},{\"id\":25622132,\"identity\":\"d8d95840-77a2-4127-95bc-7b5e3728437e\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:13:26\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":1607316,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"virulentMutalistSupplement.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/229a64e000209ea206195de6.pdf\"},{\"id\":25621500,\"identity\":\"1c442ebd-1865-427c-a990-ae718ac4c1f4\",\"added_by\":\"auto\",\"created_at\":\"2022-08-24 17:03:26\",\"extension\":\"docx\",\"order_by\":2,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":12804,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"SupplementalFigurelegends.docx\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-1972333/v1/02281ed532665202eb9d6639.docx\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Host Age Structure Defines Interactions with Pathogens: Grandparent Effect under Collaboration and Virulent Mutualism under Competition\",\"fulltext\":[{\"header\":\"Background\",\"content\":\"\\u003cp\\u003eDespite having acquired a positive connotation when used informally, the term \\u0026ldquo;symbiosis\\u0026rdquo; may refer to any sustained inter- (but not intra-) species relationship(1). This relationship can be mutualistic (beneficial for all species involved), commensal (beneficial or neutral for all species), or parasitic (beneficial for some and deleterious for others) as well as obligate or facultative (beneficial but not required for survival). The diversity of inter-species symbioses is broadened still by intra-species diversity such that the nature of the symbiosis varies among individuals within each species. Pathogenic (that is, involved in strongly asymmetric, parasitic relationships(2)) human viruses provide well-characterized examples. For almost all pathogenic viruses, a period of host immunity follows infection, compartmentalizing the population into two groups, only one of which would engage in symbiosis with the virus(3). For common viruses that confer lifelong immunity following initial infection (or vaccination), these two groups can be often well approximated by age whereby young individuals who have never been exposed are susceptible to infection and older individuals, who were most likely exposed when they were themselves younger, are immune.\\u003c/p\\u003e \\u003cp\\u003eIndeed, the age structure of human populations plays an important role in forecasting the impact of novel pathogens because, even among apparently susceptible hosts, increased age may be a predictor of increased(4, 5) or decreased(5, 6) morbidity and mortality. Although post-reproductive lifespans appear to be rare in nature, even among mammals(7), senescence has been observed in all major branches of the tree of life, from animals(8, 9) and plants(10) to yeast(11) and bacteria(12). Senescent members are inherently costly to the population as they consume shared resources but reproduce with reduced (down to zero) efficiency. However, senescent individuals also can increase the overall growth rate of populations if they increase the efficiency with which other members reproduce. Such collaborative populations foster selection for post-reproductive lifespans, commonly referred to as \\u0026ldquo;the grandmother hypothesis,\\u0026rdquo; best demonstrated among humans(13\\u0026ndash;15) and orca whales(16).\\u003c/p\\u003e \\u003cp\\u003eIn this work, we sought to explore the impact of host age-structure dynamics on the introduction of a pathogen with age-dependent virulence. We consider two diverse host populations: a competitive population modelled after rotifers(17, 18) (as well as an additional case modeled after solitary bees(19, 20) with qualitatively similar behavior addressed in the supplement) and a collaborative population modelled after humans. We demonstrate that, in competitive populations, a virulent pathogen can paradoxically increase the population growth rate. Conversely, in collaborative populations, the loss of a single post-reproductive member due to infection can result in a growth rate drop that exceeds that resulting from the loss of a single reproductive member.\\u003c/p\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cdiv class=\\\"Section2\\\" id=\\\"Sec3\\\"\\u003e\\n \\u003ch2\\u003eModel Construction\\u003c/h2\\u003e\\n \\u003cp\\u003eA classical epidemiological compartment model (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003eA) was constructed with three disease states: susceptible, infected, and recovered. Each of these three states is partitioned into two compartments representing young, potentially reproductive, and old, post-reproductive, hosts, yielding 6 compartments in total. All hosts are born susceptible (at rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eB\\u003c/em\\u003e\\u003c/sub\\u003e) to infection; age into the post-reproductive compartment (at rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eA\\u003c/em\\u003e\\u003c/sub\\u003e); and die from causes unrelated to infection (at rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eD\\u003c/em\\u003e\\u003c/sub\\u003e). Susceptible hosts may become infected (proportional to rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eI\\u003c/em\\u003e\\u003c/sub\\u003e) and recover or die due to infection (at rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eR\\u003c/em\\u003e\\u003c/sub\\u003e or the age-specific rates \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eDYI\\u003c/em\\u003e\\u003c/sub\\u003e or \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eDOI\\u003c/em\\u003e\\u003c/sub\\u003e respectively). Recovered hosts can lose immunity and return to a susceptible compartment (at rate \\u003cem\\u003ek\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eL\\u003c/em\\u003e\\u003c/sub\\u003e). For each population, the birth rate, death rate, and rate of aging from young to old compartments were fixed across all simulations (for a complete list of all parameters, see Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e).\\u003c/p\\u003e\\n \\u003cp\\u003eIn order to model competition and collaboration between old and young compartments, we sought to make the reproductive success (which may represent the fraction of young hosts which are fertile or the probability that a birth will result in viable offspring) dependent on the proportion of the young individuals in the population, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{Y}{Y+O}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, where \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(Y\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(O\\\\)\\u003c/span\\u003e\\u003c/span\\u003e are the cumulative sizes of all young and old compartments, respectively. First let us consider a collaborative population. In the limiting case where all but a single host (or mating pair) is post-reproductive, and aiding in the reproduction of that single host, we assume 100% reproductive success. The more collaborative the population, or conversely the greater the degree to which young hosts depend on post-reproductive hosts, the more steeply the reproductive success declines with relatively fewer post-reproductive hosts. Under conditions without any post-reproductive hosts, we assume the limiting case where the reproductive success is zero. We further assume this behavior saturates with respect to either limit.\\u003c/p\\u003e\\n \\u003cp\\u003eThe converse argument applies to competitive populations: reproductive success is inversely proportional to the relative number of post-reproductive hosts. Although cooperation and competition are not necessarily strictly symmetrical, for formal convenience, we considered the family of functions:\\u003c/p\\u003e\\n \\u003cdiv class=\\\"Equation\\\" id=\\\"Equa\\\"\\u003e\\n \\u003cdiv class=\\\"mathdisplay\\\" id=\\\"FileID_Equa\\\" name=\\\"EquationSource\\\"\\u003e$$f\\\\left(\\\\frac{Y}{Y+O}\\\\right)={cos}^{10a}\\\\left(\\\\frac{\\\\pi }{2}\\\\frac{Y}{Y+O}\\\\right){sin}^{10b}\\\\left(\\\\frac{\\\\pi }{2}\\\\frac{Y}{Y+O}\\\\right)$$\\u003c/div\\u003e\\n \\u003c/div\\u003e\\n \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a=0, 0\\u0026lt;b\\\\le \\\\frac{1}{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(b=0 , 0\\u0026lt;a\\\\le \\\\frac{1}{2}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e represent competitive and collaborative populations, respectively (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003eB), which possess the properties described above. We also emphasize that competition between parameter regimes is not assessed in this work. Only the relative fitness of disease free and endemic equilibria are considered.\\u003c/p\\u003e\\n \\u003cp\\u003eEach simulation was conducted as follows. Parameters \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(b\\\\)\\u003c/span\\u003e\\u003c/span\\u003e were selected and the equilibrium age distribution, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{Y}{Y+O}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, as well as the exponential growth rate, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{dN/dt}{N}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e where \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(N\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the cumulative size of all compartments, were computed (for details, see Extended Data A). Compartments are initialized to respect the equilibrium age distribution, with infected compartments initialized to be 0.1% of the total population. The solution is then propagated using Python scipy method solve_ivp until a state of endemic equilibrium is reached where the measured rate of change of compartment proportions is negligible. The new growth rate at endemic equilibrium is then computed. For details, see Extended Data B.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"Section2\\\" id=\\\"Sec4\\\"\\u003e\\n \\u003ch2\\u003eLoss of post-reproductive hosts is costly for collaborative populations\\u003c/h2\\u003e\\n \\u003cp\\u003eA human population was modelled consistent with an average reproductive life span of 25 years; post-reproductive life span of 45 years; a birth rate of 0.14 births/year; and reproductive success determined by \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a=\\\\left\\\\{\\\\text{0.1,0.2,0.3,0.4,0.5}\\\\right\\\\}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. The pathogen was modelled with an infectivity (the product of the rate of host contact and the probability of infection given contact) of 2/week, mean duration of infection 2 weeks, and mean duration of immunity 1 year for all hosts, but a probability of death roughly 1% for old hosts and zero for young hosts. These parameters well represent a range of human respiratory viruses(21) but we note this model does not account for the complex behavior associated with time varying contact rates(22, 23). The epidemic trajectory for \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a=0.2\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is shown in Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eA.\\u003c/p\\u003e\\n \\u003cp\\u003eDue to the loss of old hosts as a result of infection, the young fraction of the population increases throughout the epidemic phase and into endemicity (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eB). In every case, the growth rate substantially declines (and can become negative) during the epidemic phase before gradually increasing (subject to oscillations) to a value reduced relative to the pre-epidemic level (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eC). The cost to the population (decreased growth rate) as a result of endemic infection is greater for more collaborative populations (larger \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eD).\\u003c/p\\u003e\\n \\u003cp\\u003eDeath rate due to infection was then varied, ranging from 0.25/year to 0.45/year among old hosts, remaining at zero for young hosts. For each final growth rate, the equivalent death rate due to infection under conditions where only young hosts die as a result of infection was computed such that the final growth rate attained was the same for both models. Under sufficiently collaborative conditions, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(a\\\\ge 0.2\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, the equivalent death rate among young hosts resulting in the same growth rate reduction was greater than that among old hosts (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eE). In other words, in a highly collaborative population, the cost of the loss of a post-reproductive member due to infection is greater than the cost of the loss of a young, potentially reproductive member.\\u003c/p\\u003e\\n \\u003cp\\u003eThe relative cost of losing young vs. post-reproductive hosts depends on the reproductive success function, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(f\\\\left(\\\\frac{Y}{Y+O}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. When reproductive success remains near one until \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{Y}{Y+O}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e approaches one and then sharply declines, representing the case where the population is insensitive to the abundance of post-reproductive hosts, the loss of a young host always has a greater impact than the loss of a post-reproductive host (see Supplemental Fig.\\u0026nbsp;1).\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"Section2\\\" id=\\\"Sec5\\\"\\u003e\\n \\u003ch2\\u003eVirulent mutualism in competitive populations\\u003c/h2\\u003e\\n \\u003cp\\u003eA competitive population was modelled using the data available for rotifer populations, with an average reproductive life span of 8 days; post-reproductive life span of 9 days; a birth rate of 1.3/day(17); and reproductive success determined by \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(b=\\\\left\\\\{\\\\text{0.1,0.2,0.3,0.4,0.5}\\\\right\\\\}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. The pathogen was modelled with an infectivity of 4/day, mean duration of infection 3 days, and mean duration of immunity 17 days for all hosts, but a probability of death near 100% for old hosts and zero for young hosts. These parameters, apart from age dependence, are modelled after a fungal pathogen of the genus \\u003cem\\u003eRotiferophthora\\u003c/em\\u003e(18). The epidemic trajectory for \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(b=0.2\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is shown in Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003eA. Note that the timescale of the epidemic is much shorter than that in the model of a collaborative population due to the major difference in member lifespans, and oscillations are not observed in these trajectories.\\u003c/p\\u003e\\n \\u003cp\\u003eDue to the loss of old hosts as a result of infection, the young fraction of the population increases logistically over the epidemic phase and into endemicity (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003eB). While the exponential growth rate (\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{dN/dt}{N}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, which is not the birth rate) still declines during the epidemic phase due to the loss of post-reproductive members, it remains positive and the endemic growth rate is elevated relative to the disease-free state (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003eC). The benefit to the population (increased growth rate) as a result of endemic infection is greater for more competitive populations (larger \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(b\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eD).\\u003c/p\\u003e\\n \\u003cp\\u003eAs for the collaborative case, the death rate due to infection was then varied, ranging from 0.33/day to 0.52/day among old hosts, remaining at zero for young hosts. For each final growth rate, the equivalent birth rate for a disease-free state was computed such that the final growth rate attained was the same for both models. Note that even a 1% change in the exponential growth rate under these conditions results in a 50% larger population within the time span of 3 generations. The introduction of a virulent pathogen significantly increased the population growth rate, in some cases equivalent to increasing the birth rate by more than 2% (Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003eE). An additional competitive population was loosely modelled after sweat bees(19) introduced to a pathogen resembling acute bee paralysis virus(20), resulting in qualitatively similar behavior (see Supplemental Fig.\\u0026nbsp;2).\\u003c/p\\u003e\\n\\u003c/div\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cp\\u003eParasites, by definition, decrease host fitness and the introduction of a parasite into one or more competing host species can substantially alter the ecological landscape resulting in or preventing the extinction of one competitor(24, 25). Symbionts that are parasitic in the absence of inter-species host competition but which increase the competitiveness of infected hosts (for example, through allelopathy(26)) establish a seemingly surprising, mutualistic relationship. Similarly, host competition can admit the persistence of a parasite under conditions where persistence within a single host population is not supported(25). Furthermore, even within a single host species, symbionts that are parasitic in one environment can provide a fitness advantage due to specialized adaptations in another environment, for example, promoting resistance to drought(27).\\u003c/p\\u003e \\u003cp\\u003eParasitic interactions can also substantially alter intra-species competition due to variability in tolerance or transmissibility influenced by genomic or nongenomic factors including host density(28) and age. In previous human epidemics, advanced age has been commonly associated with increased(4, 5) or occasionally decreased(5, 6) morbidity and mortality. More generally, species lifespans are likely influenced by pathogen interactions. Populations of species with short lifespans are able to clear pathogens faster, and being short-lived decreases the probability of crossing the species barrier, which typically requires major adaptations to emerge within the first infected novel host to mediate efficient transmission(29).\\u003c/p\\u003e \\u003cp\\u003eAge structure substantially alters transmission dynamics, and can reduce the likelihood of an epidemic while increasing the magnitude in the event of an outbreak(30). The presence of immune post-reproductive hosts decreases the density of susceptible hosts and reduces the rate of infection; however, susceptible, and senescent, post-reproductive hosts can increase the cumulative number of mortalities. The disparity in predicted outcomes between homogenous (which may already lead to diverse results(31, 32)) and age-structured populations is exacerbated in the event of vaccination(33).\\u003c/p\\u003e \\u003cp\\u003eHere we demonstrate that host age structure, associated with differential susceptibility to a parasite, can determine whether a virulent pathogen, as defined by its relationship with individual hosts, is a parasite or a mutualist with respect to the population as a whole. In competitive populations where older, post-reproductive hosts share resources with younger, potentially reproductive hosts, virulent pathogens that disproportionately affect non-reproductive hosts increase the population growth rate. Conversely, in collaborative populations where older, post-reproductive hosts aid in the reproduction of younger hosts, the cost of the loss of a non-reproductive host can be even greater than that of a young host.\\u003c/p\\u003e \\u003cp\\u003eAlthough post-reproductive lifespans appear to be rare, even among mammals(7), most if not all cellular life forms exhibit some form of senescence(8\\u0026ndash;12). Therefore, although advanced social roles for post-reproductive members have not yet been identified outside of mammals, costs and potentially benefits associated with the presence of senescent hosts are likely widespread even for unicellular life. Among prokaryotes, horizontal gene transfer from dead, maximally senescent, cells can prevent irreversible genomic deterioration, Muller\\u0026rsquo;s rachet(34). In addition to chronological age, altering the stationary cell cycle phase distribution(35, 36) can modify the fitness landscape by altering phase-dependent gene expression(37) potentially delegating different functions to individuals in different phases. Thus, collaborative populations might be far more common across the diversity of life than is immediately obvious.\\u003c/p\\u003e \\u003cp\\u003eThese, often complex, impacts of age structure have to be taken into account prior to formulating a strategy for intervention against a pathogen, mitigation of invasive species, or preservation of an endangered population(38). For example, food provisioning both increases resource availability and host aggregation, potentially amplifying pathogen invasion(39). Thus, in the context of competition, which may itself be magnified as a result of host aggregation, the effect of a pathogen likely enhances conservation efforts, whereas in the case of collaboration, this straightforward intervention could lead to population decline.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eAuthors\\u0026rsquo; information\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eCOSP, EGR, and JAR are students in the Montgomery Blair High School Magnet Program supervised by APB. YIW, EVK, and NDR hold intramural positions at the NIH.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAuthors\\u0026rsquo; Contributions\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eYIW, APB, EVK, and NDR designed the study; COSP, EGR, and JAR programed the model; COSP, EGR, JAR, YIW, and NDR conducted the analysis; COSP, EVK, and NDR wrote the manuscript that was edited and approved by all authors.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAcknowledgements\\u0026nbsp;\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors thank Koonin group members for helpful discussions.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eFunding\\u0026nbsp;\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eYIW, NDR, and EVK are supported by the Intramural Research Program of the National Institutes of Health.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAvailability of supporting data\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eSupplementary figures and extended data are available for download as a single pdf.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCompeting Interests\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors have no competing interests to declare.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eConsent for publication\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eAll authors have provided consent for publication.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eHuman Ethics\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eNot applicable.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eEthical Approval and Consent to participate\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eNot applicable.\\u003cbr\\u003e\\u0026nbsp;\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n \\u003cli\\u003eParacer S \\u0026amp; 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Pugliese A (2009) Epidemics in two competing species. \\u003cem\\u003eNonlinear Analysis: Real World Applications\\u003c/em\\u003e 10(2):723-744.\\u003c/li\\u003e\\n \\u003cli\\u003eMATTNER SW (2006) The impact of pathogens on plant interference and allelopathy. \\u003cem\\u003eAllelochemicals: Biological control of plant pathogens and diseases\\u003c/em\\u003e:79-101.\\u003c/li\\u003e\\n \\u003cli\\u003eGonz\\u0026aacute;lez R\\u003cem\\u003e, et al.\\u003c/em\\u003e (2021) Plant virus evolution under strong drought conditions results in a transition from parasitism to mutualism. \\u003cem\\u003eProceedings of the National Academy of Sciences\\u003c/em\\u003e 118(6):e2020990118.\\u003c/li\\u003e\\n \\u003cli\\u003eAlexander HM \\u0026amp; Holt RD (1998) The interaction between plant competition and disease. \\u003cem\\u003ePerspectives in Plant Ecology, Evolution and Systematics\\u003c/em\\u003e 1(2):206-220.\\u003c/li\\u003e\\n \\u003cli\\u003eLidsky PV \\u0026amp; Andino R (2020) Epidemics as an adaptive driving force determining lifespan setpoints. \\u003cem\\u003eProceedings of the National Academy of Sciences\\u003c/em\\u003e 117(30):17937-17948.\\u003c/li\\u003e\\n \\u003cli\\u003eClark J, McNally L, \\u0026amp; Little TJ (2021) Pathogen dynamics across the diversity of aging. \\u003cem\\u003eThe American Naturalist\\u003c/em\\u003e 197(2):203-215.\\u003c/li\\u003e\\n \\u003cli\\u003eCastro M, Ares S, Cuesta JA, \\u0026amp; Manrubia S (2020) The turning point and end of an expanding epidemic cannot be precisely forecast. \\u003cem\\u003eProceedings of the National Academy of Sciences\\u003c/em\\u003e 117(42):26190-26196.\\u003c/li\\u003e\\n \\u003cli\\u003eWilke CO \\u0026amp; Bergstrom CT (2020) Predicting an epidemic trajectory is difficult. \\u003cem\\u003eProceedings of the National Academy of Sciences\\u003c/em\\u003e 117(46):28549-28551.\\u003c/li\\u003e\\n \\u003cli\\u003eMagpantay F, King A, \\u0026amp; Rohani P (2019) Age-structure and transient dynamics in epidemiological systems. \\u003cem\\u003eJournal of the Royal Society Interface\\u003c/em\\u003e 16(156):20190151.\\u003c/li\\u003e\\n \\u003cli\\u003eTakeuchi N, Kaneko K, \\u0026amp; Koonin EV (2014) Horizontal gene transfer can rescue prokaryotes from Muller\\u0026rsquo;s ratchet: benefit of DNA from dead cells and population subdivision. \\u003cem\\u003eG3: Genes, Genomes, Genetics\\u003c/em\\u003e 4(2):325-339.\\u003c/li\\u003e\\n \\u003cli\\u003eRochman ND, Popescu DM, \\u0026amp; Sun SX (2018) Ergodicity, hidden bias and the growth rate gain. \\u003cem\\u003ePhysical biology\\u003c/em\\u003e 15(3):036006.\\u003c/li\\u003e\\n \\u003cli\\u003eBarnum KJ \\u0026amp; O\\u0026rsquo;Connell MJ (2014) Cell cycle regulation by checkpoints. \\u003cem\\u003eCell cycle control\\u003c/em\\u003e, (Springer), pp 29-40.\\u003c/li\\u003e\\n \\u003cli\\u003eFischer M, Schade AE, Branigan TB, M\\u0026uuml;ller GA, \\u0026amp; DeCaprio JA (2022) Coordinating gene expression during the cell cycle. \\u003cem\\u003eTrends in Biochemical Sciences\\u003c/em\\u003e.\\u003c/li\\u003e\\n \\u003cli\\u003eHudson PJ\\u003cem\\u003e, et al.\\u003c/em\\u003e (2002) Trophic interactions and population growth rates: describing patterns and identifying mechanisms. \\u003cem\\u003ePhilosophical Transactions of the Royal Society of London. Series B: Biological Sciences\\u003c/em\\u003e 357(1425):1259-1271.\\u003c/li\\u003e\\n \\u003cli\\u003eBecker DJ, Streicker DG, \\u0026amp; Altizer S (2015) Linking anthropogenic resources to wildlife\\u0026ndash;pathogen dynamics: a review and meta‐analysis. \\u003cem\\u003eEcology letters\\u003c/em\\u003e 18(5):483-495.\\u003cstrong\\u003e\\u003c/strong\\u003e\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"},{\"header\":\"Table\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eTable 1\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellpadding=\\\"0\\\" cellspacing=\\\"0\\\" width=\\\"0\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e\\u0026nbsp;\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003eHuman\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003eRotifer\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eSweat Bee\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eRate of Infection\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e2 week\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e4 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e1.9 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eRate of Recovery\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e0.5 week\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e0.059 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e0.06 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eRate of Loss of Immunity\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e1 years\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e0.059 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e0.06 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eBirth Rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e0.14 years\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e1.3 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e1.5 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003eAging Rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e0.04 years\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e0.125 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e0.14 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003ePost-Reproductive Death Rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e0.022 years\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e0.11 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e0.14 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003ePost-Reproductive Infection Death Rate\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25.16025641025641%\\\"\\u003e\\n \\u003cp\\u003e0.25 years\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"24.83974358974359%\\\"\\u003e\\n \\u003cp\\u003e0.33 days\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd valign=\\\"top\\\" width=\\\"25%\\\"\\u003e\\n \\u003cp\\u003e1.4 weeks\\u003csup\\u003e-1\\u003c/sup\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"biology-direct\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"bdir\",\"sideBox\":\"Learn more about [Biology Direct](http://biologydirect.biomedcentral.com)\",\"snPcode\":\"13062\",\"submissionUrl\":\"https://submission.nature.com/new-submission/13062/3\",\"title\":\"Biology Direct\",\"twitterHandle\":\"@Biology_Direct\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"BMC/SO AJ\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Virulence, Mutualism, Age Structure, Epidemic Compartment Model, Host-Pathogen Interactions\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-1972333/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-1972333/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003e\\u003cstrong\\u003eBackground:\\u003c/strong\\u003e Symbiotic relationships are ubiquitous in the biosphere. Inter-species symbiosis is impacted by intra-specific distinctions, in particular, those defined by the age structure of a population. Older individuals compete with younger individuals for resources despite being less likely to reproduce, diminishing the fitness of the population. Conversely, however, older individuals can support the reproduction of younger individuals, increasing the population fitness. Parasitic relationships are commonly age structured, typically, more adversely affecting older hosts.\\u003c/p\\u003e\\u003cp\\u003e\\u003cstrong\\u003eResults:\\u003c/strong\\u003e We employ mathematical modeling to explore the differential effects of collaborative or competitive host age structures on host-parasite relationships. A classical epidemiological compartment model is constructed with three disease states: susceptible, infected, and recovered. Each of these three states is partitioned into two compartments representing young, potentially reproductive, and old, post-reproductive, hosts, yielding 6 compartments in total. In order to describe competition and collaboration between old and young compartments, we model the reproductive success to depend on the fraction of young individuals in the population. Collaborative populations with relatively greater numbers of post-reproductive hosts enjoy greater reproductive success whereas in purely competitive populations, increase of the post-reproductive subpopulation reduces reproductive success. However, in competitive populations, virulent pathogens preferentially targeting old individuals can increase the population fitness.\\u003c/p\\u003e\\u003cp\\u003e\\u003cstrong\\u003eConclusions:\\u003c/strong\\u003e We demonstrate that, in collaborative host populations, pathogens strictly impacting older, post-reproductive individuals can reduce population fitness even more than pathogens that directly impact younger, potentially reproductive individuals. In purely competitive populations, the reverse is observed, and we demonstrate that endemic, virulent pathogens can oxymoronically form a mutualistic relationship with the host, increasing the fitness of the host population. Applications to endangered species conservation and invasive species containment are discussed.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Host Age Structure Defines Interactions with Pathogens: Grandparent Effect under Collaboration and Virulent Mutualism under Competition\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2022-08-24 17:03:24\",\"doi\":\"10.21203/rs.3.rs-1972333/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Major revision\",\"date\":\"2022-09-21T11:51:15+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2022-08-24T03:48:56+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"02d18dd5-60b4-4a03-9136-1c98b650e9d0\",\"date\":\"2022-08-23T15:06:42+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2022-08-23T06:46:43+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2022-08-23T06:39:30+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2022-08-22T12:28:39+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Biology Direct\",\"date\":\"2022-08-17T20:23:49+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"biology-direct\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"bdir\",\"sideBox\":\"Learn more about [Biology Direct](http://biologydirect.biomedcentral.com)\",\"snPcode\":\"13062\",\"submissionUrl\":\"https://submission.nature.com/new-submission/13062/3\",\"title\":\"Biology Direct\",\"twitterHandle\":\"@Biology_Direct\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"BMC/SO AJ\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"768df0fe-64ab-4fe5-ae7c-a9d34fae7cfc\",\"owner\":[],\"postedDate\":\"August 24th, 2022\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"under-review\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2022-10-14T09:14:18+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2022-08-24 17:03:24\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-1972333\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-1972333\",\"identity\":\"rs-1972333\",\"version\":[\"v1\"]},\"buildId\":\"_2-kVJe1T_tPrBINL-cwx\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}