Natural regulation of population size in large mammals by means of two new delayed density-dependent fertility mechanisms

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We have used information on physiological reproductive mechanisms in humans in a stochastic computer simulation study to explore how known density-dependent fertility mechanisms in humans could regulate population size in a hypothetical large mammal species, assuming no deliberate interference with sexual or reproductive processes. Two physiological reproductive mechanisms in women are dependent on nutrition in utero or early life: age at menarche and post-partum amenorrhea during lactation and were included in the model. If large female mammals in general have physiological reproductive mechanisms similar to human females, strong density-dependence mechanisms will be the result, but with a substantial delay, 20 to 50 years. The model results are discussed in relation to what is known about populations of the Eastern North Pacific gray whales ( Eschrichtius robustus ), Antarctic minke whales ( Balaenoptera bonaerensis ) and elephants ( Loxodonta africana ) in Amboseli National Park, Kenya. Biological sciences/Computational biology and bioinformatics Biological sciences/Ecology Biological sciences/Physiology Biological sciences/Zoology delayed density-dependence fertility mechanisms elephants large whales stochastic simulation model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Many populations of wild animals show fluctuations, sometimes large, in population size, and these fluctuations are often correlated with stochastic changes in the environment. The biological mechanisms that are sometimes able to keep population size approximately constant and at other times cause fluctuations correlated with changes in environment are likely to be density-dependent (Nicholson 1933 ). Sinclair (Sinclair 1989 ) summarized the theoretical basis for population regulation and reviewed the empirical evidence for density dependence in a number of populations. For large mammals, species with long life spans, low reproductive rates and high parental investment in offspring, there seems to be agreement in the literature that density-dependent mechanisms are strongest for high population levels, near the carrying capacity for the habitat (Fowler 1981 , 1987 ; Sinclair 1989 ). There is only a limited number of potential density-dependent mechanisms in large mammal populations. What about the possibility of density-dependent changes in fertility in large mammals (Laws et al. 1975 , Ohsumi 1986 , Williams et al. 2013 )? The type of model for density-dependent population regulation that many have explored is to assume that poor nutrition one or two years reduces the fertility of the adult females or increases the mortality of the young animals one or two years later (Wang et al 2013 ; Witting 2003 ; Punt and Wade 2010 ). Other authors have not found evidence of such density-dependent regulation in elephants (Gough and Kerley 2006 ). Modern humans are the only large terrestrial species for which substantial amounts of information are available on fertility. The main difficulty in using information on fertility from human populations is the influence of cultural variables, especially how fecundity early in life is influenced by traditions and rules for adolescent sexual activity, and also later in life how pregnancies can be prevented by conscious decisions. As a way of avoiding these difficulties, we here discuss the available human information in relation to a hypothetical human species, which has physiological reproductive mechanisms similar to those of modern humans, but no conscious interference with sexual or reproductive processes. Two physiological reproductive mechanisms that in women are dependent on nutrition in utero or early life were included in the model: age at menarche and post-partum amenorrhea during lactation. This hypothetical human-like species could perhaps be thought of as a very early Homo species, although we do not argue that such a species has ever existed. Our main objective in this article is to explore how effectively these density-dependent physiological fertility mechanisms could regulate populations of large mammals like whales and elephants if they operated alone, and how delayed the population response would be after a step change in available resources. We have assumed constant age-dependent mortality and the existence of reproductive mechanisms observed in modern Western human populations from the 19th century and in hunting and gathering people in South Africa (Howell 1979 ), South America (Early and Peters 1990 ; Loponte and Mazza 2021 ) and New Guinea (Wood et al. 1985a , b ; Tracer 1996 ) in the 1950s and 60s. The investigation was carried out by computer simulation of relevant hypothetical populations. Methods The hypothetical humanlike population was studied by stochastic simulation of the total reproductive life history of a large number of women, using a continuous time model. Each important event in the life histories of the women was recorded and could be subject to statistical analysis. Simulations were run using the CLASS SIMULATION in the computer language SIMULA (Birtwistle et al. 1973 ). Simulated population Each simulation run starts at time zero, when a number of women are created with properties drawn from the relevant distributions relating to their reproductive life history (these are discussed below). These women are treated individually, and each of them is given a personal number. In the starting phase, 20 women are created each year until the population reaches 500 women. This takes 25 years. The probability that the child is a girl and is assigned a personal number is 0.5. Each simulation run lasts for 2000 years. The first 300–400 years must be regarded as the ‘running in’ period needed for the female population to achieve an approximately constant age distribution. The simulation results for the first 400 years of each run are therefore not plotted in the figures. During the rest of the 2000-year period, the availability of natural resources (≈ food) is changed three times, after 500 years, 1000 years and 1500 years. In most simulation runs, these changes are abrupt, to better show the effect of the assumed regulatory mechanisms, but we have also explored gradual changes in resources. The important reproductive events throughout each woman’s life are simulated, with all timings determined at birth. The waiting times to the events are drawn from the relevant probability distributions (see below). Males are also simulated and are assigned birth dates and death dates drawn from the same distributions as the females. Since no density-dependent mechanisms operate on the male segment of the population, they only appear in the results in plots of intervals between births and distributions of number of children. Fertility mechanisms in human females dependent on nutrition early in life Two physiological reproductive mechanisms in females have been shown to be dependent on nutrition in utero or early in life: age at menarche (= first menstruation, the first ovulation follows somewhat later, see below) (Liestøl 1982 ) and post-partum amenorrhea (= period without menstruation (ovulation) following childbirth) during lactation (Liestøl et al. 1988 ). The first ovulation occurs some months after the first menstruation, see later for details. The age at menarche is approximately normally distributed both in Dobe ¡Kung (Howell 1979 ) and in modern female (Brundtland and Walløe 1973 ) populations. In the simulations, we assumed that the mean of the distributions could vary between 10 and 21 years with a coefficient of variation of 0.1. These distributions approximate to what has been observed in hunting and gathering peoples and in modern populations under varying nutritional levels. For post-partum amenorrhea, we used observations from our own investigations (Liestøl et al. 1988 ). A logistic relationship between post-partum amenorrhea and age at menarche, based on observations in working class women in Christiania (Oslo) in 1840–1900 (Liestøl et al. 1988 ), was used in the model (Liestøl et al. 1988 ). The resources in the environment were modelled as a term n between 0 and 10, 10 representing the most abundant resources and 0 the most limited resources. The mean age at menarche µ is a linear function of two terms, n and p, where p is the size of the female population. µ = 148.9*n + p -1979 The slope 148.9 and the constant 1979 have been chosen to fit the observations by Liestøl et al ( 1988 ). The mean age at menarche has a lower limit of 10 years and an upper limit of 21 years, corresponding to what has been observed in modern human populations under extreme living conditions. It was assumed that menstruation never resumes during the first two months after birth. The additional duration of post-partum amenorrhea during lactation was modelled as an Erlang distribution of order 3 with coefficient of variation of 0.75 (Liestøl et al. 1988 ). The mean duration of postpartum amenorrhea was modelled as a cumulative logistic distribution with mean 19 months for age at menarche of 16 years and slope 3.25 months/year in the middle section. Asymptotes at 9 and 29 months. In most simulation runs, both these density-dependent mechanisms were active. However, we also included simulation runs where one of these two variables was kept at its mean value (either mean age at menarche = 17 years or postpartum amenorrhea = 19 months) to explore the effect of each mechanism alone. Adolescent sexual activity In the simulation model, we assumed that adolescent girls start sexual activity as soon as they are sexually mature. Physiologically, there is a varying delay between the first menstruation and the first ovulation (Wood et al. 1985a ). This is modelled as a constant equal to 2.5 years, plus a varying waiting time until conception similar to the waiting time after post-partum amenorrhea (see below). Mortality In the model, we assumed constant age-dependent mortality. This was divided into two phases, infant mortality of about 40%, similar to what has been found in many aboriginal human populations and mortality for older children and adults. Infant mortality, which occurs during the breastfeeding period, was modelled as a negative exponential distribution with half time 15 months. For children who survived until weaned, the duration of additional life was drawn from a uniform distribution between 0 and 80 (Hassan 1981 ). Other distributions were also tested, but without any marked changes in the results. Breastfeeding The duration of breastfeeding was modelled as a normal distribution with mean 3 years and standard deviation 1 year, which is similar to what has been observed in Dobe ¡Kung(Howell 1979 ) and many other human populations (Dupras et al. 2001 ; Bourbou et al. 2013 ; Stantis et al. 2020 ) and in the gorilla (Stewart 1988 ). When breastfeeding is terminated, either because the infant dies or because it is weaned, menstruation resumes after two months. Interval between births The interval between succeeding births is the sum of three terms: duration of post-partum amenorrhea, waiting time until conception and 9 months pregnancy. This interval was about 4 years in Dobe ¡Kung and similar in many other aboriginal populations. Again, a third order Erlang distribution with mean 16 months for the waiting time until conception gives the right distribution of intervals between births. Duration of a woman’s fertile period We modelled the end of a woman’s fertile period in two different ways. The simplest was to use the observed age at last birth in Dobe ¡Kung, which is approximately a normal distribution with mean 35 years and SD = 3 years (Howell 1979 ). The alternative was to use normally distributed age at menopause with mean 47 years and standard deviation 1 year, and a 10% probability of permanent sterility after each birth. The two models gave similar results for population development. In the results we present here, the simplest method was used. Results The results for total female population size during a simulation run of 2000 years are shown in figure 1(a). The ‘environment resources’ term starts at 1 (very limited resources available), changes abruptly to 8 at 500 years (abundant resources available), changes back to more limited resources at 1000 years (resource level 3) and finally back to 6 at 1500 years (Fig 1 d). The time development of mean age at menarche and mean duration of post-partum amenorrhea are shown in figures 1 (b) and (c). The development of the female population size during the years 500 to 1000 is shown at higher time resolution in figure 2(a). Much of the first 500 years should be regarded as a running-in period for the simulation model, and the results for this period should therefore be ignored. The figures clearly show a transitional period of approximately 200 years after each abrupt change in living conditions. After the transitional periods, the female population size shows only small fluctuations. Both age at menarche and duration of post-partum amenorrhea are approximately constant and the same in all three periods (figures 1(b) and (c)). Figure 2(a) clearly shows that the female population increases more than twentyfold during the first 200 years after an abrupt change in living conditions (≈available food), but also that the increase is slow to appear. It takes more than 50 years for the population to double. The effects of the two fertility mechanisms were studied separately by keeping either the mean age at menarche or the mean duration of post-partum amenorrhea constant at the long-term values shown in figures 1 (b) and (c). The corresponding changes in female population size following two abrupt changes in natural resources are shown in figures 2 (a) and (b). The effect of changing the resources term gradually instead of abruptly is shown in figure 2(c). The figure shows the age at menarche when the availability of resources term is allowed to decrease linearly over a period of 100 years. The changes in age at menarche are roughly delayed one hundred years but are largely the same as following a step decrease. Figures 1 and 2 show the mean values of the relevant variables. The figures show an overshoot in the population response after year 500 resulting in a damped oscillation. Since the simulation is stochastic, each variable has a distribution. Figures 3 (a), (b) and (c) show three typical distributions. Figure 4 (a) shows the distribution of time intervals between births for women born in a stable period. Figure 4 (b) shows the mean number of children plotted for the year of birth of the women. Figure 5 shows two distributions of the number of children, one from a stable period, and one from a period with a growing population. Discussion The population effects of two density-dependent physiological fertility mechanisms were explored by stochastic simulation. One of the mechanisms assumes that age at sexual maturity is dependent on nutrition early in life. We have evidence for this mechanism both from the investigations by McCance and Widdowson ( 1974 ) and by Liestøl ( 1982 ). In addition, other biological and medical conditions in humans have been shown to be dependent on conditions in utero or in early life (fetal programming, physiological imprinting, the Baker hypothesis) (Baker and Osmond 1986 ; Baker 1995 ). The mean duration of post-partum amenorrhea has been shown to be dependent on age at menarche but has not been shown to be directly related to living conditions near the time of a woman’s birth. We have assumed that this linear relationship can also be extended back through the age at menarche to the period near a woman’s birth. Using only two density-dependent fertility mechanisms known from observations on human females result in strong regulation of population size in our simulated populations. Either of the two mechanisms could regulate the population on its own, without the help of the other (Fig. 2 ). All the situations displayed in Fig. 2 show a much-delayed response. It is not until 50 years after the running-in period that a small response can be seen, and only after nearly one hundred years that the population increase reaches its maximal rate. The rate of increase in the female component of the population between years 600 and 700 is then 6.0 women/year for the model where age at menarche was kept constant, 9.6 women/year for the model where the mean duration of post-partum amenorrhea was kept constant, and 17.5 women/year where both were allowed to vary. The population response was found to be much faster when the environment was abruptly changed to harsher in the year 1000, but the response was still considerably delayed. As regards the growth of real Homo populations, it is possible that an increase in fertility has been important during periods of expansion into new and possibly richer habitats in human prehistory. One likely example is the rapid population growth indicated by archaeological evidence following the first arrival of a maximum of a few hundred Homo sapiens (including about 70 women) in New Zealand around 1280 AD (Holdaway and Jacomb 2000 ; Wilmshurst et al. 2008 ). To our knowledge, there is no aboriginal human population today in which the two main assumptions of our model are approximately fulfilled. In all known populations, there are cultural restrictions on early sexual activity. The situation in populations of non-human large mammals is different. There is some, but only weak, evidence of density-dependent fertility regulation of populations of whales (Gambell 1973 ; Laws 1977 ; Kato 1986 , 1987 ; Ohsumi 1986 ) and elephants (Laws et al. 1975 ; Moss 1988 ; Lee et al. 2016 ). Witting discussed the population dynamics of eastern Pacific gray whales over the last 150 years (Witting 2003 ) and found, like others before him (Lankester and Beddington 1986 ), that a “hypothesis of density-regulated growth does not reconcile the known historical catches with the recent trajectory in abundance estimates”. This is different for population growth models with delayed density regulation. Witting explored population growth in ‘inertial age-structured models’ and obtained a reasonable fit to observations of abundance and catches during the last 150 years. However, he did not have any reasonable biological explanation for his assumptions of a delayed response in the fertility rate or of a delayed age at sexual maturity in female gray whales. We believe that the delayed fertility mechanisms known from human females, which we have explored in this paper, may be the biological mechanisms Witting would have needed in his model. However, including these mechanisms in his model would probably result in different predictions from those made by Witting from his original mathematical model. Many different biological mechanisms could in theory be responsible for delayed density regulation in whales, but the two mechanisms explored in the present paper are obvious candidates. The most likely candidate is age at sexual maturity. For gray whales, age at sexual maturity has been determined to be between 6 and 12 years, and females give birth every one to three years. Neither of the two variables has been related to stock size during the last 50 years, mainly because of a lack of relevant observations. However, relevant observations have been obtained for other whale species, especially the Antarctic minke whale (Kato 1987 ). Individual minke whales are a little smaller than gray whales, but the life history variables are similar. For Antarctic minke whales, age at sexual maturity decreased from 13 to 7 years during the period 1920 to 1960 when the large baleen whales (blue whales, humpback whales and later fin whales) were hunted down to very low population levels in the Southern Ocean. All these whale species competed with minke whales for krill. As numbers of the other whale species were reduced, more krill became available for the minke whales – “The krill surplus hypothesis” (Laws 1977 ). The other fertility mechanism explored for humans, the duration of post-partum amenorrhea, is perhaps not so likely to be important in animals with estrus restricted to specific times of year. However, even in gray whales the time between births vary between one and three years and possibly even longer. The model’s assumption of constant age-dependent mortality is not realistic in real-world situations when available natural resources decrease rapidly (e.g. in model year 1000). In such situations, mortality is likely to increase. The simulation results show that even without an increase in mortality, the fertility mechanisms investigated would result in a rapid reduction in population size, but only starting after a delay of about 20 years. It is not easy to investigate whether the assumptions of our model simulations based on observations from human populations are fulfilled for populations of other large mammal species. Based on our limited knowledge, only two populations have been studied over a sufficiently long period and in enough detail to be potentially interesting: the eastern North Pacific stock of gray whales (Witting 2003 ; Punt and Wade 2010 ) and the elephant population in Amboseli National park, Kenya (Moss 1988 ; Lee et al. 2016 ). For both populations, the critical factor is the level of detail in the available information about age at sexual maturity. Some of the published observations on the elephants indicate that our model could be relevant: “Early reproducers(< 12.5 years) had higher age-specific fertility rates than did females who commenced reproduction late (15 + years) with no difference in survival between these groups.” (Lee et al. 2016 ). Age at sexual maturity is not known to be a function of living conditions or nutrition near the time of birth either in elephants or in gray whales. However, for both species a large range of values has been published for age at sexual maturity for different areas and/or time periods. Observation from minke whales indicate a functional relationship similar to that we have found for humans. Assuming that this relationship also applies to elephants and gray whales, the results shown in our graphs should be approximately valid for these two species as well and should be able to explain delayed density-dependent fertility mechanisms in these species. The most surprising result is perhaps how large the delay may be. In this case, it was more than 50 years before an effect could be seen on the population size after an abrupt improvement in living conditions. For elephants, the delay would be expected to be of this order of magnitude, for gray whales perhaps somewhat smaller, since they reach sexual maturity at a somewhat younger age than humans do. The population response is faster when the environment changes from abundant to more harsh conditions, but even then, more than 20 years before a significant fall in population size can be seen (Fig. 2 (b)). Under such circumstances, our model assumption about constant mortality is in addition unrealistic, and we would expect an immediate density-dependent increase in mortality. This can explain Fowler and Sinclair’s observation (Fowler 1981 ; Sinclair 1989 ) that density-dependent mechanisms in large mammals operate near the carrying capacity of the environment. The delayed density-dependent fertility mechanisms we are proposing for large mammals could also be relevant to the current discussion and the model investigations related to the regrowth of baleen whale populations (blue, fin and humpback whales) in the Antarctic Ocean after commercial whaling was stopped, and their competition with minke whales, seals and penguins for the krill resources (Laws 1977 ; Cunen et al. 2021 ). "The simulation program is written in the old SIMULA language. Interested readers may contact the corresponding author: [email protected] " Declarations Author Contribution Author contributionsS-M B wrote the SIMULA program and ran the simulations as part of her master thesis in informatics, instructed about the biological model and supervised by L W, who also wrote the manuscript. Acknowledgement AcknowledgementsThe mechanisms presented in this article were discussed with CW Fowler who gave positive feedback comments in 2001 at a meeting of the Scientific Committee of the International Whaling Commission in London. Additional comments and suggestions were provided by Nils Christian Stenseth, both when he was external examiner for S-M H B’s master thesis, and more recently. Data Availability The simulation program is written in the old SIMULA language. Interested readers may contact the corresponding author: [email protected] References Baker DJP (1995) The fetal origins of adult disease. Proc R Soc Lond B 262:37–43 Baker DJP, Osmond C (1986) Infant mortality, childhood nutrition, and ischaemic heart disease in England and Wales. Lancet 1077–1081 Birtwistle GM, Dahl O-J, Myhrhaug B, Nygaard K (1973) SIMULA begin. Auerbach Publishers, Philadelphia Bourbou C, Fuller BT, Garvie-Lok SJ, Richards MP (2013) Nursing mothers and feeding bottles: reconstructing breastfeeding and weaning patterns in Greek Byzantine populations (6th-15th centuries AD) using carbon and nitrogen stable isotopratios. J Archaeol Sci 40:3903–3913. https://doi.org/10.1016/j.jas.2013.04.020 Brundtland GH, Walløe L (1973) Menacheal age in Norway. Nature 241:478–479 Cunen C, Walløe L, Konishi K, Hjort NL (2021) Decline in enegry storage in the Antarctic minke whale (Balaenoptera bonaerensis) in the Southern Ocean during the 1990s. Polar Biol 44:259–273 Dupras TL, Schwarcz HP, Fairgrieve SI (2001) Infant feeding and weaning practices in Roman Egypt. Am J Phys Anthr 115:204–212 Early JD, Peters JF (1990) The population dynamicsof the Mucajai Yanomama. Academic Press Fowler CW (1987) A review of density dependence in populations of large mammals. In: H H Genoways (ed): Current mammology. Plenum press, New York, pp 401–441 Fowler CW (1981) Density dependence as related to life history strategy. Ecology 62:602–610 Gambell R (1973) Some effects of exploitation on reproduction in whales. J Reprod Fert Suppl 19:533–553 Gough KF, Kerley GIH (2006) Demography and population dynamics in the elephants Loxodonta africana of Addo Elephant National Park, South Africa: Is there evidence of density dependent regulation. Oryx 40:434–441 Hassan FA (1981) Demographic archaeology. Academic Press Holdaway R, Jacomb C (2000) Rapid extinction of the moas (Aves:Dinornithiformes): Model, test and implications. Science 287:2250–2254 Howell N (1979) Demography of The Dobe !Kung. Academic Press Kato H (1986) Changes in biological parameters of balaenopterid whales in the Antarctic, with special reference to southern minke whale. Mem Natl Inst Polar Res 40:330–344 Kato H (1987) Density dependent changes in growth parameters of the southernminke whale. Sci Rep Whales Res Inst 47–73 Lankester K, Beddington JR (1986) An age structured population model applied to the gray whale (Eschrichtius robustus). Rep int whal commn 36:353-358 Laws RM (1977) Seals and whales in the Southern Ocean. Phil Trans R Soc Lond B 279:81–96 Laws RM, Parker ISC, Johnstone ICB (1975) Elephants and their habitats: the ecology of elephants in North Bunyoro, Uganda. Oxford University Press Lee PC, Fishlock V, Webber CE, Moss CJ (2016) The reproductive advantage of a long life: longevity and senescence in wild female African elephants. Behav Ecol Sociobiol 70:337–345 Lett PF, Mohn RK, Gray DF (1981) Density-dependent processes and management strategy for the Northwest Atlantic harp seal population. In: C W Fowler & T D Smith: Dynamics of large mammal populations. John Wiley, New York, pp 135–157 Liestøl K (1982) Social conditions and menarcheal age: the importance of early years of life. Ann Hum Biol 9:521–537. https://doi.org/10.1080/03014468200006051 Liestøl K, Rosenberg M, Walløe L (1988) Lactation and post-partum amenorrhoea: a study based on data from three Norwegian cities 1860-1964. J Biosoc Sci 20:423–434 Loponte D, Mazza B (2021) Breastfeeding and weaning in Late Holocene hunter-gatherers of lower Parana wetland, South America. Am J Phys Anthr 176:504–520. https://doi.org/10.1002/ajpa.24381 McCance RA, Widdowson EM (1974) The determinants of growth and form. Proc R Soc Lond B 185:1–17 Moss CJ (2001) The demography of an African elephant (Loxodonta africana) population in Amboseli, Kenya. J Zool Lond 255:145–156 Moss CJ (1988) Elephant Memories - Thirteen years in the life of an elephant family. In: Chapter 9 - Population dynamics. pp 239–268 Nicholson AJ (1933) The balance of animal populations. J Anim Ecol 2:131–178 Ohsumi S (1986) Yearly change in age and body length at sexual maturity of a fin whale stock in the eastern North pacific. Sci Rep Whales Res Inst 1–16 Punt AE, Wade PR (2010) Population status of the eastern North Pacific stock of gray whales in 2009. Sinclair ARE (1989) Population regulation in animals. In: J M Cherrett: Ecological Concepts. Blackwell, Oxford Stantis C, Schutkowski H, Softysiak A (2020) Reconstructing breastfeeding and weaning practices in the bronze age Near East using stable nitrogen isotopes. Am J Phys Anthr 172: Stewart K (1988) Suckling and lactational anoestrus in wild gorillas (Gorilla gorilla). J Reprod Fert 83:627–634 Tracer DP (1996) Lactation, nutrition and postpartum amenorrhea in lowlans Papua New Guinea. Hum Biol 68:277–292 Wang GM et al (2013) Comparative population dynamics of large and small mammals in the Northern Hemisphere: deterministic and stochastic forces. Ecography 36;439-446, doi:10.1111j.1600-0587.2011.07156.x Williams R, Vikingsson GA, Gislason A (2013) Evidence for density-dependent changes in body condition and pregnancy rate of North Atlantic fin whales over four decades of varying environmental conditions. ICES J Mar Sci 70:1273–1280 Wilmshurst JM, Anderson AJ, Higham TF, Worthy TH (2008) Dating the late prehistoric dispersal of Polynesians to New Zealand using the commersal Pacific rat. Proc Natl Acad Sci USA 105:7676–7680 Witting L (2003) Reconstructing the population dynamics of eastern Pacific gray whales over ther past 150 to 400 years. J Cetacean Res Manage 5:45–54 Wood JW, Johnson PL, Caåmpbell KL (1985a) Demographic and endocrinological aspects of low natural fertility in highland New Guinea. J Biosoc Sci 17:57–79 Wood JW, Lai D, Johnson PL, et al (1985b) Lactation and birth spacing in highland New Guinea. J Biosoc Sci Suppl 9:159–173 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 12 May, 2025 Reviews received at journal 05 May, 2025 Reviewers agreed at journal 25 Apr, 2025 Reviews received at journal 15 Apr, 2025 Reviewers agreed at journal 07 Apr, 2025 Reviewers invited by journal 26 Mar, 2025 Editor assigned by journal 26 Mar, 2025 Editor invited by journal 03 Mar, 2025 Submission checks completed at journal 28 Feb, 2025 First submitted to journal 20 Feb, 2025 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. 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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-6072541","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":422239278,"identity":"e823088d-574c-4d3b-a9d3-ca9f743f1456","order_by":0,"name":"Lars Walløe","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYBACPigtA2QwPmBgYOZhYAbxDXBrYYPSPEAGswHJWtgkGCDq8QM29rOPPzC22fGwsTcfq7pRYS0j3857gJmnwIbBnL0BuxaedDMJxrZkHjaeY2m3c86k8xgc5ktg5jFIY7DsOYDDYWlsDIzbmHnYJHLMbue2HeYxYAajwwwGNxKwa+F/xvyBcVs9UEv+t+Lcf4d55JsJaZFIY5Bg3HYYZAsbc27DYR6GwwS1PGOTSPx3HOQXY+mcYyC/8BgcnGOQxmNwBrtf+PnTmD98OFMtx8/e/PBzTo21vXz/GcMHb/7YyBkcxx5iYIDhAJDxPLjVj4JRMApGwSggBACkCUkTKnIaKQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Oslo","correspondingAuthor":true,"prefix":"","firstName":"Lars","middleName":"","lastName":"Walløe","suffix":""},{"id":422239280,"identity":"8e0568a2-91ca-4cdf-bcc2-e7f5fe67bcd1","order_by":1,"name":"Signe-Marie Bjerke","email":"","orcid":"","institution":"Teambyggerne, 1350 Lommedalen","correspondingAuthor":false,"prefix":"","firstName":"Signe-Marie","middleName":"","lastName":"Bjerke","suffix":""}],"badges":[],"createdAt":"2025-02-20 13:53:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6072541/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6072541/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-22992-2","type":"published","date":"2025-11-11T15:57:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":77625196,"identity":"451e485a-3966-4550-9f1b-1601ca1c3dba","added_by":"auto","created_at":"2025-03-03 16:29:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":53354,"visible":true,"origin":"","legend":"\u003cp\u003eThe total female population size as a function of time over a 2000-year period (a). Mean age at menarche (b) and mean duration of post-partum amenorrhea (c) over this period. In (b) and (c), the mean values are plotted for the year of birth of the women. Figure (d) shows an index of the environment resources. The first 300-400 years should be regarded as a running-in period, and the simulation results are not plotted. The environment resources term in the model changes abruptly from 1 to 8 at 500 years, from 8 to 3 at 1000 years, and from 3 to 6 at 1500 years.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/430d209edca1e64e3a6fb39f.png"},{"id":77625197,"identity":"7d4dd6d9-aacf-4158-8cb6-64b889f8246c","added_by":"auto","created_at":"2025-03-03 16:29:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":47775,"visible":true,"origin":"","legend":"\u003cp\u003eFemale population size from year 500 to year 1000 (a) and from year 1000 to year 1500 (b), in a model where density-dependent mechanisms operate only on the duration of post-partum amenorrhea, while age at menarche is kept constant at 17 years (broken line), in a model where density-dependent mechanisms operate only on the age at menarche, while the mean age of post-partum amenorrhea is kept constant at 19 months (dotted line), and in a model in which both mechanisms are operating (unbroken line). (c) Time development of the mean age at menarche in a model where the environment resources term increases abruptly from 1 to 8 at 500 years (broken line), or linearly from 1 to 8 from year 500 to year 600 (unbroken line).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/899d48ea19d0c00992a36b14.png"},{"id":77626682,"identity":"30e4a15c-a9ff-42c2-b875-3fc9f1ce0c86","added_by":"auto","created_at":"2025-03-03 16:45:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36079,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of distribution of age at menarche ((a) and (b)), and distribution of duration of post-partum amenorrhea (c). (a) During a stable period, years 1300-1400, mean age 17.0 years, N = 1129, (b) during linear increase of the environment resources term, year 600-700, mean age 12.0 years, N = 410, and (c) during a stable period, years 1300-1400, mean duration 19.1 months, N = 3770.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/ed7eea8b31f7c6b6001e4ded.png"},{"id":77625203,"identity":"31800d28-2ae4-46da-b4f5-581d36018c71","added_by":"auto","created_at":"2025-03-03 16:29:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":30011,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of time distances between births for women born in a stable period, years 1300-1400, mean distance 3.5 years, N = 2880 (a), and mean number of children (girls and boys) in the population plotted for the year of birth of the women (b). All women: unbroken line, women who have survived the menopause: broken line.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/56e687e974ddb6e4de36cdcd.png"},{"id":77625624,"identity":"f8ee98c2-5169-400b-acf3-a755fe8ec247","added_by":"auto","created_at":"2025-03-03 16:37:22","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":19901,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of number of children in a stable period (year 1300-1400) for women surviving menopause, mean size 4.6 children/woman, N = 662, (a), and for women born in the period 500 to 550, and surviving menopause, mean size = 8.0 children/woman, N = 118 (b).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/0218da03423047432d315ef8.png"},{"id":96104978,"identity":"cfc93aed-a63d-49ed-98e8-708d77ec0bb1","added_by":"auto","created_at":"2025-11-17 16:05:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":598401,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6072541/v1/9c4d7813-e32c-4904-8471-3feaf374edc5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Natural regulation of population size in large mammals by means of two new delayed density-dependent fertility mechanisms","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMany populations of wild animals show fluctuations, sometimes large, in population size, and these fluctuations are often correlated with stochastic changes in the environment. The biological mechanisms that are sometimes able to keep population size approximately constant and at other times cause fluctuations correlated with changes in environment are likely to be density-dependent (Nicholson \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1933\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSinclair (Sinclair \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1989\u003c/span\u003e) summarized the theoretical basis for population regulation and reviewed the empirical evidence for density dependence in a number of populations. For large mammals, species with long life spans, low reproductive rates and high parental investment in offspring, there seems to be agreement in the literature that density-dependent mechanisms are strongest for high population levels, near the carrying capacity for the habitat (Fowler \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1981\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Sinclair \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). There is only a limited number of potential density-dependent mechanisms in large mammal populations.\u003c/p\u003e \u003cp\u003eWhat about the possibility of density-dependent changes in fertility in large mammals (Laws et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1975\u003c/span\u003e, Ohsumi \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1986\u003c/span\u003e, Williams et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2013\u003c/span\u003e)? The type of model for density-dependent population regulation that many have explored is to assume that poor nutrition one or two years reduces the fertility of the adult females or increases the mortality of the young animals one or two years later (Wang et al \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Witting \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Punt and Wade \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Other authors have not found evidence of such density-dependent regulation in elephants (Gough and Kerley \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eModern humans are the only large terrestrial species for which substantial amounts of information are available on fertility. The main difficulty in using information on fertility from human populations is the influence of cultural variables, especially how fecundity early in life is influenced by traditions and rules for adolescent sexual activity, and also later in life how pregnancies can be prevented by conscious decisions. As a way of avoiding these difficulties, we here discuss the available human information in relation to a hypothetical human species, which has physiological reproductive mechanisms similar to those of modern humans, but no conscious interference with sexual or reproductive processes. Two physiological reproductive mechanisms that in women are dependent on nutrition in utero or early life were included in the model: age at menarche and post-partum amenorrhea during lactation. This hypothetical human-like species could perhaps be thought of as a very early \u003cem\u003eHomo\u003c/em\u003e species, although we do not argue that such a species has ever existed.\u003c/p\u003e \u003cp\u003eOur main objective in this article is to explore how effectively these density-dependent physiological fertility mechanisms could regulate populations of large mammals like whales and elephants if they operated alone, and how delayed the population response would be after a step change in available resources. We have assumed constant age-dependent mortality and the existence of reproductive mechanisms observed in modern Western human populations from the 19th century and in hunting and gathering people in South Africa (Howell \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1979\u003c/span\u003e), South America (Early and Peters \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Loponte and Mazza \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and New Guinea (Wood et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1985a\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003eb\u003c/span\u003e; Tracer \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1996\u003c/span\u003e) in the 1950s and 60s. The investigation was carried out by computer simulation of relevant hypothetical populations.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe hypothetical humanlike population was studied by stochastic simulation of the total reproductive life history of a large number of women, using a continuous time model. Each important event in the life histories of the women was recorded and could be subject to statistical analysis. Simulations were run using the CLASS SIMULATION in the computer language SIMULA (Birtwistle et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1973\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSimulated population\u003c/h2\u003e \u003cp\u003eEach simulation run starts at time zero, when a number of women are created with properties drawn from the relevant distributions relating to their reproductive life history (these are discussed below). These women are treated individually, and each of them is given a personal number. In the starting phase, 20 women are created each year until the population reaches 500 women. This takes 25 years. The probability that the child is a girl and is assigned a personal number is 0.5. Each simulation run lasts for 2000 years. The first 300\u0026ndash;400 years must be regarded as the \u0026lsquo;running in\u0026rsquo; period needed for the female population to achieve an approximately constant age distribution. The simulation results for the first 400 years of each run are therefore not plotted in the figures. During the rest of the 2000-year period, the availability of natural resources (\u0026asymp;\u0026thinsp;food) is changed three times, after 500 years, 1000 years and 1500 years. In most simulation runs, these changes are abrupt, to better show the effect of the assumed regulatory mechanisms, but we have also explored gradual changes in resources.\u003c/p\u003e \u003cp\u003eThe important reproductive events throughout each woman\u0026rsquo;s life are simulated, with all timings determined at birth. The waiting times to the events are drawn from the relevant probability distributions (see below).\u003c/p\u003e \u003cp\u003eMales are also simulated and are assigned birth dates and death dates drawn from the same distributions as the females. Since no density-dependent mechanisms operate on the male segment of the population, they only appear in the results in plots of intervals between births and distributions of number of children.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eFertility mechanisms in human females dependent on nutrition early in life\u003c/h3\u003e\n\u003cp\u003eTwo physiological reproductive mechanisms in females have been shown to be dependent on nutrition in utero or early in life: age at menarche (=\u0026thinsp;first menstruation, the first ovulation follows somewhat later, see below) (Liest\u0026oslash;l \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1982\u003c/span\u003e) and post-partum amenorrhea (=\u0026thinsp;period without menstruation (ovulation) following childbirth) during lactation (Liest\u0026oslash;l et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). The first ovulation occurs some months after the first menstruation, see later for details. The age at menarche is approximately normally distributed both in Dobe \u0026iexcl;Kung (Howell \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1979\u003c/span\u003e) and in modern female (Brundtland and Wall\u0026oslash;e \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1973\u003c/span\u003e) populations. In the simulations, we assumed that the mean of the distributions could vary between 10 and 21 years with a coefficient of variation of 0.1. These distributions approximate to what has been observed in hunting and gathering peoples and in modern populations under varying nutritional levels. For post-partum amenorrhea, we used observations from our own investigations (Liest\u0026oslash;l et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). A logistic relationship between post-partum amenorrhea and age at menarche, based on observations in working class women in Christiania (Oslo) in 1840\u0026ndash;1900 (Liest\u0026oslash;l et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e), was used in the model (Liest\u0026oslash;l et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe resources in the environment were modelled as a term n between 0 and 10, 10 representing the most abundant resources and 0 the most limited resources.\u003c/p\u003e \u003cp\u003eThe mean age at menarche \u0026micro; is a linear function of two terms, n and p, where p is the size of the female population.\u003c/p\u003e \u003cp\u003e\u0026micro;\u0026thinsp;=\u0026thinsp;148.9*n\u0026thinsp;+\u0026thinsp;p -1979\u003c/p\u003e \u003cp\u003eThe slope 148.9 and the constant 1979 have been chosen to fit the observations by Liest\u0026oslash;l et al (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). The mean age at menarche has a lower limit of 10 years and an upper limit of 21 years, corresponding to what has been observed in modern human populations under extreme living conditions.\u003c/p\u003e \u003cp\u003eIt was assumed that menstruation never resumes during the first two months after birth. The additional duration of post-partum amenorrhea during lactation was modelled as an Erlang distribution of order 3 with coefficient of variation of 0.75 (Liest\u0026oslash;l et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1988\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe mean duration of postpartum amenorrhea was modelled as a cumulative logistic distribution with mean 19 months for age at menarche of 16 years and slope 3.25 months/year in the middle section. Asymptotes at 9 and 29 months.\u003c/p\u003e \u003cp\u003eIn most simulation runs, both these density-dependent mechanisms were active. However, we also included simulation runs where one of these two variables was kept at its mean value (either mean age at menarche\u0026thinsp;=\u0026thinsp;17 years or postpartum amenorrhea\u0026thinsp;=\u0026thinsp;19 months) to explore the effect of each mechanism alone.\u003c/p\u003e\n\u003ch3\u003eAdolescent sexual activity\u003c/h3\u003e\n\u003cp\u003eIn the simulation model, we assumed that adolescent girls start sexual activity as soon as they are sexually mature. Physiologically, there is a varying delay between the first menstruation and the first ovulation (Wood et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1985a\u003c/span\u003e). This is modelled as a constant equal to 2.5 years, plus a varying waiting time until conception similar to the waiting time after post-partum amenorrhea (see below).\u003c/p\u003e\n\u003ch3\u003eMortality\u003c/h3\u003e\n\u003cp\u003eIn the model, we assumed constant age-dependent mortality. This was divided into two phases, infant mortality of about 40%, similar to what has been found in many aboriginal human populations and mortality for older children and adults. Infant mortality, which occurs during the breastfeeding period, was modelled as a negative exponential distribution with half time 15 months.\u003c/p\u003e \u003cp\u003eFor children who survived until weaned, the duration of additional life was drawn from a uniform distribution between 0 and 80 (Hassan \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1981\u003c/span\u003e). Other distributions were also tested, but without any marked changes in the results.\u003c/p\u003e\n\u003ch3\u003eBreastfeeding\u003c/h3\u003e\n\u003cp\u003eThe duration of breastfeeding was modelled as a normal distribution with mean 3 years and standard deviation 1 year, which is similar to what has been observed in Dobe \u0026iexcl;Kung(Howell \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1979\u003c/span\u003e) and many other human populations (Dupras et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Bourbou et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Stantis et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and in the gorilla (Stewart \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). When breastfeeding is terminated, either because the infant dies or because it is weaned, menstruation resumes after two months.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eInterval between births\u003c/h2\u003e \u003cp\u003eThe interval between succeeding births is the sum of three terms: duration of post-partum amenorrhea, waiting time until conception and 9 months pregnancy. This interval was about 4 years in Dobe \u0026iexcl;Kung and similar in many other aboriginal populations. Again, a third order Erlang distribution with mean 16 months for the waiting time until conception gives the right distribution of intervals between births.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eDuration of a woman’s fertile period\u003c/h3\u003e\n\u003cp\u003eWe modelled the end of a woman\u0026rsquo;s fertile period in two different ways. The simplest was to use the observed age at last birth in Dobe \u0026iexcl;Kung, which is approximately a normal distribution with mean 35 years and SD\u0026thinsp;=\u0026thinsp;3 years (Howell \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1979\u003c/span\u003e). The alternative was to use normally distributed age at menopause with mean 47 years and standard deviation 1 year, and a 10% probability of permanent sterility after each birth. The two models gave similar results for population development. In the results we present here, the simplest method was used.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe results for total female population size during a simulation run of 2000 years are shown in figure 1(a). The \u0026lsquo;environment resources\u0026rsquo; term starts at 1 (very limited resources available), changes abruptly to 8 at 500 years (abundant resources available), changes back to more limited resources at 1000 years (resource level 3) and finally back to 6 at 1500 years (Fig 1 d).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe time development of mean age at menarche and mean duration of post-partum amenorrhea are shown in figures 1 (b) and (c). The development of the female population size during the years 500 to 1000 is shown at higher time resolution in figure 2(a).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMuch of the first 500 years should be regarded as a running-in period for the simulation model, and the results for this period should therefore be ignored. The figures clearly show a transitional period of approximately 200 years after each abrupt change in living conditions. After the transitional periods, the female population size shows only small fluctuations. Both age at menarche and duration of post-partum amenorrhea are approximately constant and the same in all three periods (figures 1(b) and (c)). Figure 2(a) clearly shows that the female population increases more than twentyfold during the first 200 years after an abrupt change in living conditions (\u0026asymp;available food), but also that the increase is slow to appear. It takes more than 50 years for the population to double.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe effects of the two fertility mechanisms were studied separately by keeping either the mean age at menarche or the mean duration of post-partum amenorrhea constant at the long-term values shown in figures 1 (b) and (c). The corresponding changes in female population size following two abrupt changes in natural resources are shown in figures 2 (a) and (b).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe effect of changing the resources term gradually instead of abruptly is shown in figure 2(c). The figure shows the age at menarche when the availability of resources term is allowed to decrease linearly over a period of 100 years. The changes in age at menarche are roughly delayed one hundred years but are largely the same as following a step decrease.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigures 1 and 2 show the mean values of the relevant variables. The figures show an overshoot in the population response after year 500 resulting in a damped oscillation. Since the simulation is stochastic, each variable has a distribution. Figures 3 (a), (b) and (c) show three typical distributions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 4 (a) shows the distribution of time intervals between births for women born in a stable period. Figure 4 (b) shows the mean number of children plotted for the year of birth of the women.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 5 shows two distributions of the number of children, one from a stable period, and one from a period with a growing population.\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe population effects of two density-dependent physiological fertility mechanisms were explored by stochastic simulation. One of the mechanisms assumes that age at sexual maturity is dependent on nutrition early in life. We have evidence for this mechanism both from the investigations by McCance and Widdowson (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1974\u003c/span\u003e) and by Liest\u0026oslash;l (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1982\u003c/span\u003e). In addition, other biological and medical conditions in humans have been shown to be dependent on conditions in utero or in early life (fetal programming, physiological imprinting, the Baker hypothesis) (Baker and Osmond \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1986\u003c/span\u003e; Baker \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1995\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe mean duration of post-partum amenorrhea has been shown to be dependent on age at menarche but has not been shown to be directly related to living conditions near the time of a woman\u0026rsquo;s birth. We have assumed that this linear relationship can also be extended back through the age at menarche to the period near a woman\u0026rsquo;s birth. Using only two density-dependent fertility mechanisms known from observations on human females result in strong regulation of population size in our simulated populations. Either of the two mechanisms could regulate the population on its own, without the help of the other (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAll the situations displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e show a much-delayed response. It is not until 50 years after the running-in period that a small response can be seen, and only after nearly one hundred years that the population increase reaches its maximal rate. The rate of increase in the female component of the population between years 600 and 700 is then 6.0 women/year for the model where age at menarche was kept constant, 9.6 women/year for the model where the mean duration of post-partum amenorrhea was kept constant, and 17.5 women/year where both were allowed to vary. The population response was found to be much faster when the environment was abruptly changed to harsher in the year 1000, but the response was still considerably delayed.\u003c/p\u003e \u003cp\u003eAs regards the growth of real \u003cem\u003eHomo\u003c/em\u003e populations, it is possible that an increase in fertility has been important during periods of expansion into new and possibly richer habitats in human prehistory. One likely example is the rapid population growth indicated by archaeological evidence following the first arrival of a maximum of a few hundred \u003cem\u003eHomo sapiens\u003c/em\u003e (including about 70 women) in New Zealand around 1280 AD (Holdaway and Jacomb \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Wilmshurst et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo our knowledge, there is no aboriginal human population today in which the two main assumptions of our model are approximately fulfilled. In all known populations, there are cultural restrictions on early sexual activity. The situation in populations of non-human large mammals is different. There is some, but only weak, evidence of density-dependent fertility regulation of populations of whales (Gambell \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1973\u003c/span\u003e; Laws \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e; Kato \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1986\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Ohsumi \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1986\u003c/span\u003e) and elephants (Laws et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1975\u003c/span\u003e; Moss \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Lee et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Witting discussed the population dynamics of eastern Pacific gray whales over the last 150 years (Witting \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) and found, like others before him (Lankester and Beddington \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1986\u003c/span\u003e), that a \u0026ldquo;hypothesis of density-regulated growth does not reconcile the known historical catches with the recent trajectory in abundance estimates\u0026rdquo;. This is different for population growth models with delayed density regulation. Witting explored population growth in \u0026lsquo;inertial age-structured models\u0026rsquo; and obtained a reasonable fit to observations of abundance and catches during the last 150 years. However, he did not have any reasonable biological explanation for his assumptions of a delayed response in the fertility rate or of a delayed age at sexual maturity in female gray whales. We believe that the delayed fertility mechanisms known from human females, which we have explored in this paper, may be the biological mechanisms Witting would have needed in his model. However, including these mechanisms in his model would probably result in different predictions from those made by Witting from his original mathematical model.\u003c/p\u003e \u003cp\u003eMany different biological mechanisms could in theory be responsible for delayed density regulation in whales, but the two mechanisms explored in the present paper are obvious candidates. The most likely candidate is age at sexual maturity. For gray whales, age at sexual maturity has been determined to be between 6 and 12 years, and females give birth every one to three years. Neither of the two variables has been related to stock size during the last 50 years, mainly because of a lack of relevant observations. However, relevant observations have been obtained for other whale species, especially the Antarctic minke whale (Kato \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Individual minke whales are a little smaller than gray whales, but the life history variables are similar. For Antarctic minke whales, age at sexual maturity decreased from 13 to 7 years during the period 1920 to 1960 when the large baleen whales (blue whales, humpback whales and later fin whales) were hunted down to very low population levels in the Southern Ocean. All these whale species competed with minke whales for krill. As numbers of the other whale species were reduced, more krill became available for the minke whales \u0026ndash; \u0026ldquo;The krill surplus hypothesis\u0026rdquo; (Laws \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e). The other fertility mechanism explored for humans, the duration of post-partum amenorrhea, is perhaps not so likely to be important in animals with estrus restricted to specific times of year. However, even in gray whales the time between births vary between one and three years and possibly even longer.\u003c/p\u003e \u003cp\u003eThe model\u0026rsquo;s assumption of constant age-dependent mortality is not realistic in real-world situations when available natural resources decrease rapidly (e.g. in model year 1000). In such situations, mortality is likely to increase. The simulation results show that even without an increase in mortality, the fertility mechanisms investigated would result in a rapid reduction in population size, but only starting after a delay of about 20 years.\u003c/p\u003e \u003cp\u003eIt is not easy to investigate whether the assumptions of our model simulations based on observations from human populations are fulfilled for populations of other large mammal species. Based on our limited knowledge, only two populations have been studied over a sufficiently long period and in enough detail to be potentially interesting: the eastern North Pacific stock of gray whales (Witting \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Punt and Wade \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and the elephant population in Amboseli National park, Kenya (Moss \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Lee et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). For both populations, the critical factor is the level of detail in the available information about age at sexual maturity. Some of the published observations on the elephants indicate that our model could be relevant: \u0026ldquo;Early reproducers(\u0026lt;\u0026thinsp;12.5 years) had higher age-specific fertility rates than did females who commenced reproduction late (15\u0026thinsp;+\u0026thinsp;years) with no difference in survival between these groups.\u0026rdquo; (Lee et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAge at sexual maturity is not known to be a function of living conditions or nutrition near the time of birth either in elephants or in gray whales. However, for both species a large range of values has been published for age at sexual maturity for different areas and/or time periods. Observation from minke whales indicate a functional relationship similar to that we have found for humans. Assuming that this relationship also applies to elephants and gray whales, the results shown in our graphs should be approximately valid for these two species as well and should be able to explain delayed density-dependent fertility mechanisms in these species. The most surprising result is perhaps how large the delay may be. In this case, it was more than 50 years before an effect could be seen on the population size after an abrupt improvement in living conditions. For elephants, the delay would be expected to be of this order of magnitude, for gray whales perhaps somewhat smaller, since they reach sexual maturity at a somewhat younger age than humans do.\u003c/p\u003e \u003cp\u003eThe population response is faster when the environment changes from abundant to more harsh conditions, but even then, more than 20 years before a significant fall in population size can be seen (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b)). Under such circumstances, our model assumption about constant mortality is in addition unrealistic, and we would expect an immediate density-dependent increase in mortality. This can explain Fowler and Sinclair\u0026rsquo;s observation (Fowler \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1981\u003c/span\u003e; Sinclair \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1989\u003c/span\u003e) that density-dependent mechanisms in large mammals operate near the carrying capacity of the environment.\u003c/p\u003e \u003cp\u003eThe delayed density-dependent fertility mechanisms we are proposing for large mammals could also be relevant to the current discussion and the model investigations related to the regrowth of baleen whale populations (blue, fin and humpback whales) in the Antarctic Ocean after commercial whaling was stopped, and their competition with minke whales, seals and penguins for the krill resources (Laws \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e; Cunen et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e\"The simulation program is written in the old SIMULA language. Interested readers may contact the corresponding author: [email protected]\"\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor contributionsS-M B wrote the SIMULA program and ran the simulations as part of her master thesis in informatics, instructed about the biological model and supervised by L W, who also wrote the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eAcknowledgementsThe mechanisms presented in this article were discussed with CW Fowler who gave positive feedback comments in 2001 at a meeting of the Scientific Committee of the International Whaling Commission in London. Additional comments and suggestions were provided by Nils Christian Stenseth, both when he was external examiner for S-M H B\u0026rsquo;s master thesis, and more recently.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe simulation program is written in the old SIMULA language. Interested readers may contact the corresponding author: [email protected]\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBaker DJP (1995) The fetal origins of adult disease. Proc R Soc Lond B 262:37\u0026ndash;43\u003c/li\u003e\n\u003cli\u003eBaker DJP, Osmond C (1986) Infant mortality, childhood nutrition, and ischaemic heart disease in England and Wales. Lancet 1077\u0026ndash;1081\u003c/li\u003e\n\u003cli\u003eBirtwistle GM, Dahl O-J, Myhrhaug B, Nygaard K (1973) SIMULA begin. Auerbach Publishers, Philadelphia\u003c/li\u003e\n\u003cli\u003eBourbou C, Fuller BT, Garvie-Lok SJ, Richards MP (2013) Nursing mothers and feeding bottles: reconstructing breastfeeding and weaning patterns in Greek Byzantine populations (6th-15th centuries AD) using carbon and nitrogen stable isotopratios. J Archaeol Sci 40:3903\u0026ndash;3913. https://doi.org/10.1016/j.jas.2013.04.020\u003c/li\u003e\n\u003cli\u003eBrundtland GH, Wall\u0026oslash;e L (1973) Menacheal age in Norway. Nature 241:478\u0026ndash;479\u003c/li\u003e\n\u003cli\u003eCunen C, Wall\u0026oslash;e L, Konishi K, Hjort NL (2021) Decline in enegry storage in the Antarctic minke whale (Balaenoptera bonaerensis) in the Southern Ocean during the 1990s. Polar Biol 44:259\u0026ndash;273\u003c/li\u003e\n\u003cli\u003eDupras TL, Schwarcz HP, Fairgrieve SI (2001) Infant feeding and weaning practices in Roman Egypt. Am J Phys Anthr 115:204\u0026ndash;212\u003c/li\u003e\n\u003cli\u003eEarly JD, Peters JF (1990) The population dynamicsof the Mucajai Yanomama. Academic Press\u003c/li\u003e\n\u003cli\u003eFowler CW (1987) A review of density dependence in populations of large mammals. In: H H Genoways (ed): Current mammology. Plenum press, New York, pp 401\u0026ndash;441\u003c/li\u003e\n\u003cli\u003eFowler CW (1981) Density dependence as related to life history strategy. Ecology 62:602\u0026ndash;610\u003c/li\u003e\n\u003cli\u003eGambell R (1973) Some effects of exploitation on reproduction in whales. J Reprod Fert Suppl 19:533\u0026ndash;553\u003c/li\u003e\n\u003cli\u003eGough KF, Kerley GIH (2006) Demography and population dynamics in the elephants Loxodonta africana of Addo Elephant National Park, South Africa: Is there evidence of density dependent regulation. Oryx 40:434\u0026ndash;441\u003c/li\u003e\n\u003cli\u003eHassan FA (1981) Demographic archaeology. Academic Press\u003c/li\u003e\n\u003cli\u003eHoldaway R, Jacomb C (2000) Rapid extinction of the moas (Aves:Dinornithiformes): Model, test and implications. Science 287:2250\u0026ndash;2254\u003c/li\u003e\n\u003cli\u003eHowell N (1979) Demography of The Dobe !Kung. Academic Press\u003c/li\u003e\n\u003cli\u003eKato H (1986) Changes in biological parameters of balaenopterid whales in the Antarctic, with special reference to southern minke whale. Mem Natl Inst Polar Res 40:330\u0026ndash;344\u003c/li\u003e\n\u003cli\u003eKato H (1987) Density dependent changes in growth parameters of the southernminke whale. Sci Rep Whales Res Inst 47\u0026ndash;73\u003c/li\u003e\n\u003cli\u003eLankester K, Beddington JR (1986) An age structured population model applied to the gray whale (Eschrichtius robustus). Rep int whal commn 36:353-358 \u003c/li\u003e\n\u003cli\u003eLaws RM (1977) Seals and whales in the Southern Ocean. Phil Trans R Soc Lond B 279:81\u0026ndash;96\u003c/li\u003e\n\u003cli\u003eLaws RM, Parker ISC, Johnstone ICB (1975) Elephants and their habitats: the ecology of elephants in North Bunyoro, Uganda. Oxford University Press\u003c/li\u003e\n\u003cli\u003eLee PC, Fishlock V, Webber CE, Moss CJ (2016) The reproductive advantage of a long life: longevity and senescence in wild female African elephants. Behav Ecol Sociobiol 70:337\u0026ndash;345\u003c/li\u003e\n\u003cli\u003eLett PF, Mohn RK, Gray DF (1981) Density-dependent processes and management strategy for the Northwest Atlantic harp seal population. In: C W Fowler \u0026amp; T D Smith: Dynamics of large mammal populations. John Wiley, New York, pp 135\u0026ndash;157\u003c/li\u003e\n\u003cli\u003eLiest\u0026oslash;l K (1982) Social conditions and menarcheal age: the importance of early years of life. Ann Hum Biol 9:521\u0026ndash;537. https://doi.org/10.1080/03014468200006051\u003c/li\u003e\n\u003cli\u003eLiest\u0026oslash;l K, Rosenberg M, Wall\u0026oslash;e L (1988) Lactation and post-partum amenorrhoea: a study based on data from three Norwegian cities 1860-1964. J Biosoc Sci 20:423\u0026ndash;434\u003c/li\u003e\n\u003cli\u003eLoponte D, Mazza B (2021) Breastfeeding and weaning in Late Holocene hunter-gatherers of lower Parana wetland, South America. Am J Phys Anthr 176:504\u0026ndash;520. https://doi.org/10.1002/ajpa.24381\u003c/li\u003e\n\u003cli\u003eMcCance RA, Widdowson EM (1974) The determinants of growth and form. Proc R Soc Lond B 185:1\u0026ndash;17\u003c/li\u003e\n\u003cli\u003eMoss CJ (2001) The demography of an African elephant (Loxodonta africana) population in Amboseli, Kenya. J Zool Lond 255:145\u0026ndash;156\u003c/li\u003e\n\u003cli\u003eMoss CJ (1988) Elephant Memories - Thirteen years in the life of an elephant family. In: Chapter 9 - Population dynamics. pp 239\u0026ndash;268\u003c/li\u003e\n\u003cli\u003eNicholson AJ (1933) The balance of animal populations. J Anim Ecol 2:131\u0026ndash;178\u003c/li\u003e\n\u003cli\u003eOhsumi S (1986) Yearly change in age and body length at sexual maturity of a fin whale stock in the eastern North pacific. Sci Rep Whales Res Inst 1\u0026ndash;16\u003c/li\u003e\n\u003cli\u003ePunt AE, Wade PR (2010) Population status of the eastern North Pacific stock of gray whales in 2009.\u003c/li\u003e\n\u003cli\u003eSinclair ARE (1989) Population regulation in animals. In: J M Cherrett: Ecological Concepts. Blackwell, Oxford\u003c/li\u003e\n\u003cli\u003eStantis C, Schutkowski H, Softysiak A (2020) Reconstructing breastfeeding and weaning practices in the bronze age Near East using stable nitrogen isotopes. Am J Phys Anthr 172:\u003c/li\u003e\n\u003cli\u003eStewart K (1988) Suckling and lactational anoestrus in wild gorillas (Gorilla gorilla). J Reprod Fert 83:627\u0026ndash;634\u003c/li\u003e\n\u003cli\u003eTracer DP (1996) Lactation, nutrition and postpartum amenorrhea in lowlans Papua New Guinea. Hum Biol 68:277\u0026ndash;292\u003c/li\u003e\n\u003cli\u003eWang GM et al (2013) Comparative population dynamics of large and small mammals in the Northern Hemisphere: deterministic and stochastic forces. Ecography 36;439-446, doi:10.1111j.1600-0587.2011.07156.x\u003c/li\u003e\n\u003cli\u003eWilliams R, Vikingsson GA, Gislason A (2013) Evidence for density-dependent changes in body condition and pregnancy rate of North Atlantic fin whales over four decades of varying environmental conditions. ICES J Mar Sci 70:1273\u0026ndash;1280\u003c/li\u003e\n\u003cli\u003eWilmshurst JM, Anderson AJ, Higham TF, Worthy TH (2008) Dating the late prehistoric dispersal of Polynesians to New Zealand using the commersal Pacific rat. Proc Natl Acad Sci USA 105:7676\u0026ndash;7680\u003c/li\u003e\n\u003cli\u003eWitting L (2003) Reconstructing the population dynamics of eastern Pacific gray whales over ther past 150 to 400 years. J Cetacean Res Manage 5:45\u0026ndash;54\u003c/li\u003e\n\u003cli\u003eWood JW, Johnson PL, Ca\u0026aring;mpbell KL (1985a) Demographic and endocrinological aspects of low natural fertility in highland New Guinea. J Biosoc Sci 17:57\u0026ndash;79\u003c/li\u003e\n\u003cli\u003eWood JW, Lai D, Johnson PL, et al (1985b) Lactation and birth spacing in highland New Guinea. J Biosoc Sci Suppl 9:159\u0026ndash;173\u003c/li\u003e\n\u003c/ol\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":"[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":"delayed density-dependence, fertility mechanisms, elephants, large whales, stochastic simulation model ","lastPublishedDoi":"10.21203/rs.3.rs-6072541/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6072541/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIt is generally assumed that population size of all wild animal species is regulated through density-dependent mechanisms, but the mechanisms responsible have been difficult to identify for elephants and large whales. We have used information on physiological reproductive mechanisms in humans in a stochastic computer simulation study to explore how known density-dependent fertility mechanisms in humans could regulate population size in a hypothetical large mammal species, assuming no deliberate interference with sexual or reproductive processes. Two physiological reproductive mechanisms in women are dependent on nutrition in utero or early life: age at menarche and post-partum amenorrhea during lactation and were included in the model. If large female mammals in general have physiological reproductive mechanisms similar to human females, strong density-dependence mechanisms will be the result, but with a substantial delay, 20 to 50 years. The model results are discussed in relation to what is known about populations of the Eastern North Pacific gray whales (\u003cem\u003eEschrichtius robustus\u003c/em\u003e), Antarctic minke whales (\u003cem\u003eBalaenoptera bonaerensis\u003c/em\u003e) and elephants (\u003cem\u003eLoxodonta africana\u003c/em\u003e) in Amboseli National Park, Kenya.\u003c/p\u003e","manuscriptTitle":"Natural regulation of population size in large mammals by means of two new delayed density-dependent fertility mechanisms","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-03 16:29:17","doi":"10.21203/rs.3.rs-6072541/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-05-12T07:13:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-05T21:01:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315814146621666937997389470365919225466","date":"2025-04-25T16:14:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-15T16:06:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105092723829784999334339206344137579516","date":"2025-04-07T05:16:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-26T20:29:01+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-26T20:28:03+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-03-03T14:27:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-02-28T10:25:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-02-20T13:46:36+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":"f68e3042-d69c-4031-95af-a7785f8e7cc1","owner":[],"postedDate":"March 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":45008462,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":45008463,"name":"Biological sciences/Ecology"},{"id":45008464,"name":"Biological sciences/Physiology"},{"id":45008465,"name":"Biological sciences/Zoology"}],"tags":[],"updatedAt":"2025-11-17T16:00:06+00:00","versionOfRecord":{"articleIdentity":"rs-6072541","link":"https://doi.org/10.1038/s41598-025-22992-2","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-11-11 15:57:16","publishedOnDateReadable":"November 11th, 2025"},"versionCreatedAt":"2025-03-03 16:29:17","video":"","vorDoi":"10.1038/s41598-025-22992-2","vorDoiUrl":"https://doi.org/10.1038/s41598-025-22992-2","workflowStages":[]},"version":"v1","identity":"rs-6072541","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6072541","identity":"rs-6072541","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}