Ecology of the collapse of Rapa Nui royalsocietypublishing.org/journal/rspb society M. Lima1,2, E. M. Gayo2,3, C. Latorre1,4,5, C. M. Santoro6, S. A. Estay2,7, N. Cañellas-Boltà8, O. Margalef 9,12, S. Giralt8, A. Sáez10, S. Pla-Rabes11,12 Research and N. Chr. Stenseth13 1 Departamento de Ecología, Pontificia Universidad Católica de Chile, Santiago, Chile Cite this article: Lima M et al. 2020 Ecology 2 Center of Applied Ecology and Sustainability (CAPES), Pontificia Universidad Católica de Chile, Santiago, Chile of the collapse of Rapa Nui society. 3 Center for Climate and Resilience Research (CR2), Santiago, Chile 4 Proc. R. Soc. B 287: 20200662. Centro UC del Desierto de Atacama, Pontificia Universidad Católica de Chile, Santiago, Chile 5 http://dx.doi.org/10.1098/rspb.2020.0662 Institute of Ecology and Biodiversity (IEB), Santiago, Chile 6 Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile 7 Instituto de Ciencias Ambientales y Evolutivas, Universidad Austral de Chile, Valdivia, Chile 8 Institute of Earth Sciences Jaume Almera (ICTJA-CSIC), Lluís Solé Sabarís s/n, E-08028 Barcelona, Spain 9 Consejo Superior de Investigaciones Científicas, Global Ecology Unit CREAF-CSIC-UAB, 08193 Cerdanyola del Received: 24 March 2020 Vallès, Catalonia, Spain 10 Accepted: 29 May 2020 Department of Earth and Ocean Dynamics, Universitat de Barcelona, Marti i Franques s/n, E-08028 Barcelona, Spain 11 BABVE, Universitat Autònoma de Barcelona (UAB), Cerdanyola del Vallès 08193, Spain 12 Center for Ecological Research and Forestry Application (CREAF), E-08193 Cerdanyola del Vallès, Catalonia, Spain 13 Subject Category: Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, Ecology PO Box 1066, Blindern, 0316 Oslo, Norway ML, 0000-0002-3700-2945; SP-R, 0000-0003-3532-9466 Subject Areas: ecology, environmental science Collapses of food producer societies are recurrent events in prehistory and have triggered a growing concern for identifying the underlying causes of convergences/divergences across cultures around the world. One of the Keywords: most studied and used as a paradigmatic case is the population collapse collapse, climate change, Rapa Nui, of the Rapa Nui society. Here, we test different hypotheses about it by devel- overpopulation, population theory oping explicit population dynamic models that integrate feedbacks between climatic, demographic and ecological factors that underpinned the socio- cultural trajectory of these people. We evaluate our model outputs against a reconstruction of past population size based on archaeological radiocarbon Author for correspondence: dates from the island. The resulting estimated demographic declines of the M. Lima Rapa Nui people are linked to the long-term effects of climate change on e-mail: mlima@bio.puc.cl the island’s carrying capacity and, in turn, on the ‘per-capita food supply’. 1. Introduction Prehistoric producer societies provide unique socio-ecological laboratories for understanding the relationship between human population, food production and climate variability, with profound implications for current sustainability problems [1]. Recently, a number of studies covering the Holocene period have used the summed probability densities (SPDs) of archaeological radiocar- bon dates to infer demographic changes of food producer human societies and their potential connections to large-scale climatic processes [2–4], as well as to develop and test scenarios for implementing land-use and land-cover changes [5]. In most of these studies, the relationship between human population dynamics and past climate fluctuations is evident. Nevertheless, conceptual and methodological approaches from the theory of population dynamics (TPD) could be used to gain further insights into this phenomenon. Moreover, Electronic supplementary material is available the application of formal methods of modelling provides a context where online at https://doi.org/10.6084/m9.figshare. hypotheses can be tested against empirical evidence. c.5018453. © 2020 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. 2 (a) royalsocietypublishing.org/journal/rspb (c) 0.0015 0.0030 SPD ancient cult birdman cult 0 800 900 1000 1150 1300 1450 1600 1750 1900 elevation (m.asl) 0 50 100 (d ) 150 per-capita growth rates 200 250 1 2 3 0.4 300 350 400 >450 0 genocide hypothesis Proc. R. Soc. B 287: 20200662 −0.4 (b) 800 900 1000 1150 1300 1450 1600 1750 1900 europlan contact year AD humans (e) per-capita growth rates 0.4 3 2 1 1100 1200 1400 1500 1600 1700 1800 0 year AD −0.4 ecocide hypothesis 0 0.0005 0.0010 0.0015 0.0020 0.0025 SPD europlan contact humans 1100 1200 1400 1500 1600 1700 1800 year AD Figure 1. Population data and hypotheses description. (a) Map of Rapa Nui showing the major topographic features of the island. (b) Two hypotheses previously proposed for explaining the socio-ecological trajectory of Rapa Nui. The ecocide hypothesis: human population increased exponentially since its initial colonization. Human populations overshot the carrying capacity to support sustainable crops, and in consequence, the island was severely deforested. Such exhaustion of natural resources led to socio-demographic collapse. The genocide hypothesis: human population grew exponentially since approximately 1150 CE, reached the carrying capacity, but maintained a stable population size and sustainable crops despite deforestation. The collapse occurred after European colonization [14]. (c) Recon- structed SPD for Rapa Nui. Yellow and green vertical bars denote periods of low and exponential population growths, respectively. Orange areas indicate periods with negative population growth rates. The red arrow indicates the arrival of Europeans. (d ) Time-series for per-capita growth rates (blue line) showing the chronology and magnitude of the three demographic collapses (orange bars). (e) R function plotted against the reconstructed SPD (one generation before = 30 years). Orange arrows indicate equilibrium population sizes during the three declines. Departure >0 implies a stronger relationship between SPD values and per-capita growth rates. (Online version in colour.) Since food producer population equilibrium levels are set Here, we apply simple theoretical population dynamic by crop productivity and land area, explanations of climatic models for deciphering the interaction between climatic varia- effects on these societies must rely on formal examinations bility, crop productivity and the long-term dynamics of the of indirect effects that climate changes could exert on the Rapa Nui population from the easternmost fringes of Poly- food production. This is because climate affects the avail- nesia (figure 1a). The Rapa Nui example represents one of ability of limiting resources (food production), and in turn, the most controversial cases for the decline of an ancient farm- it impacts the per-capita resource availability shared between ing society [15], which has been predominantly explained by individuals of a given population [6]. These non-additive invoking an anthropogenically driven ecological catastrophe. effects are expected when the ratio (i.e. population/food pro- This ‘ecocide hypothesis’ assumes a punctuated demographic duction) defines the per-capita share of the resources and the crash caused by the abrupt reduction and replacement of competition strength. Under such scenarios, small changes in native palm forest by grasslands, ultimately driven by a climate factor could have large changes in population unchecked population growth coupled with social instability growth rates due to the coupled interaction between climate, as the per-capita food productivity decreased (figure 1b) [16– food production and population size [6]. Previous studies 18]. Alternatively, a ‘genocide hypothesis’ assumes that the have developed models of human and renewable resource Rapa Nui society did not collapse until European contact in dynamics in order to understand the potential role of overpo- the early eighteenth century (figure 1b) [19]. Past climate fluc- pulation and resource depletion in agrarian societies [7–11], tuations have also been invoked [20], but to date there is no with particular emphasis in the Rapa Nui case [12]. However, evidence showing any direct link between climate change to the best of our knowledge, the role of climate non-additive and societal collapse on Rapa Nui. perturbations on the population dynamic of past food Recent studies [21–23] challenge the predominant causal producer societies has rarely been explored [13]. explanations for large-scale demographic downfall and emphasize the potential roles of climate, anthropogenic press- number of dates per unit area per unit time is greater than or 3 ures and the climate–human relationship. In fact, three main equal to previous studies [3]. For example, at the local scale, a study with a very high number of 14C dates on different royalsocietypublishing.org/journal/rspb societal crises appear to have occurred in Rapa Nui. The first is dated to 1450–1550 CE (coeval to the Little Ice Age—LIA) regions of Britain and Ireland during the mid- and late Holo- and has been attributed to climate–cultural feedbacks and cene showed a range of sampling intensity between 0.13 and synergies. The second crisis is documented by the nineteenth 0.26 dates × 100 yr−1 × 100 km−2 [3], whereas the sampling century due to the introduction of epidemic diseases and the intensity at Rapa Nui is 0.19 dates × 100 yr−1 × 100 km−2. In slave trade. Another, less apparent population decline occurred terms of the ratio number of archaeological sites/geographic between the arrival of the first Europeans in 1722 CE and in area, this study from the British Island and Ireland has a spatial 1774 CE for as yet unknown reasons. By combining indepen- sampling intensity of 1.8 sites × 100 km−2 [3], whereas our dent sources of palaeoclimate, palaeoecological and spatial sampling intensity is 58 sites × 100 km−2. Therefore, palaeodemographic data, we argue that the use of the TPD as both cases are equivalent in both sampling intensity and framework represents an important advance in understanding spatial representativeness, the employment of the SPD the population dynamics of not only Rapa Nui people, but methodological approach is fully justified. Proc. R. Soc. B 287: 20200662 also other prehistoric food producer societies. We have devel- oped and tested explicit population dynamic models (PDMs) that integrate hydroclimatic, demographic and ecological fac- 3. Material and methods tors. By this means, we provide an alternative interpretation for the local population dynamic as well as new insights into (a) Palaeodemographic data the mechanisms underpinning the long-term trajectory of the The human population size proxy is based on the SPD obtained human–environment interaction in the island. from 244 archaeological radiocarbon dates. This proxy assumes that temporal variations in the accumulation of archaeological 14 C dates on a given region reflect human energy consumption/pro- duction [24], which in turn is a function of regional demographic 2. Radiocarbon dates as data of prehistoric patterns [27]. To estimate how Rapa Nui populations fluctuated human population dynamics over time, our SPD is based on 244 radiocarbon dates obtained from 95 archaeological sites (electronic supplementary material, Archaeologists are using large samples of 14C dates to estimate table S4) reported by Mulrooney [28] (n = 218) and Commendador human demographic trends in prehistoric populations [2–4]. et al. [29] (n = 26). We have accepted the quality and reliability con- The use of these data for making inferences about population trol of the chronological determinations presented in [29]. The dynamic patterns is not without methodological challenges resulting palaeodemographic time-series encompasses Class 1 and [5,24]. For example, 14C dates may be biased due to effects of 2 dates compiled by Mulrooney [28], omitting 32 entries that yield the number/distribution of archaeological sites, sample size, modern calibrated ages (less than 125 14C years BP). Although the calibration process, taphonomy and the type of economic or timing for the initial human colonization of Easter Island is still con- ritual activity [24,25]. Radiocarbon dates might be an estimate troversial—with conservative estimates around 1200 CE [15,19]— the oldest cultural date considered here is 1180 ± 230 14C yr BP (on of the quantity of energy consumed by a prehistoric human wood charcoal) from a residential context [28]. Our time-series population [24]. Although both population size and economic thus reproduces palaeodemographic patterns since 890 CE, the ear- complexity have effects on energy consumption, population liest established chronology for the initial peopling based on size explains more of the variability in energy consumption palaeoenvironmental and archaeological evidence [21,22,28]. than economic complexity [24]. In fact, Freeman et al. [24] Terrestrial (n = 214) and marine (n = 4) dates were calibrated at state that ‘The sub-linear scaling of population size with the 2-sigma confidence interval using SHCAL13 and MARINE13 energy consumption suggests that current approaches to inter- curves, respectively. A local reservoir correction of −83 ± 34 years preting date frequencies systematically misestimate population [30] was applied on marine 14C-ages assuming the 100% contri- size over a given interval of time and growth rates.’ Because we bution of marine carbon. Twenty-six radiometric determinations are interested in deciphering the relative, not the absolute, on dentine–collagen samples were calibrated using estimated pro- changes of Rapa Nui population growth rates and population portions (δ13C interpolation end-members) of marine carbon in human diet [29] (electronic supplementary material, table S4). size in a relatively short period, the use of SPD time series is jus- In practice, the SPD of calibrated 14C dates was obtained tified, instead of other statistical approaches such ‘tempo plots’ by implementing the framework proposed by Crema et al. [31] [26] that are aimed to evaluate and constrain the extent in the rcarbon package for R, which can statistically assess and (rhythms) of specific archaeological events (e.g. monumental overcome any methodological biases (oversampling, calibration construction in Rapa Nui [15]). effect and taphonomic loss). To account for the overrepresenta- We have omitted obsidian hydration dates (OHDs) from tion of well-dated sites, normalized calibrated dates from a our analysis. This decision lies with our need for data validated same archaeological site were aggregated into bins of 50 years. as proxies for population levels. More importantly, we aim to Any biases due to calibration were tackled by applying a develop a framework based on a common palaeodemographic 100-year rolling mean to produce the normalized SPD presented proxy to compare fairly dynamics among prehistoric popu- in electronic supplementary material, figure S1. Finally, a linear lations from different cultural contexts or chronological null model was fitted via 1000 Monte Carlo simulations for detecting statistically significant palaeodemographic fluctuations phases. Unlike 14C dates, the availability of OHDs is case- from the obtained normalized and smoothed SPD curve. By this specific as it depends on the preservation/recovery of certain means, magenta (blue) vertical bars in electronic supplementary artefacts (lithic artefacts) from the archaeological record material, figure S1 represent significant positive (negative) devi- and is subject to spatio-temporal variations in technologies, ations from the critical 95% confidence area for the null model, subsistence strategies or cultural behaviours. and in turn, genuine population rises (falls) that cannot be Although the absolute number of radiocarbon dates from explained by taphonomic loss and/or the overall trend of Rapa Nui would be relatively small (244 14C dates), the increasing population growth observed for Rapa Nui over the past 800 years (figure 1c). Before the implementation of PDMs, logistic equation [6], 4 the normalized and smoothed SPD time-series was sectioned into time-step intervals of 30 years in order to only capture Nt ¼ Nt1  erN [1ðNt1 =KÞ] , ð3:1Þ royalsocietypublishing.org/journal/rspb large population trends and avoid high-frequency noise source where Nt denotes the human population size at time t, rN is a of variability. Then, our models were fitted with SPD data positive constant representing the maximum per-capita repro- taken at these regular intervals since 890 CE onwards. ductive rate and K is a constant for competition intensity and resource depletion represented by the availability of crop land and productivity (i.e. equilibrium population size) [6]. We assume that palm forest cover is a proxy for the potential (b) Palaeoclimate data agriculture area available for food production and food pro- Precipitation at Rapa Nui depends on the westerlies winds cross- ductivity; this assumption is consistent with the general pattern ing the island, which in turn are controlled by the interplay of of association between palm forest clearance and the increase the South Pacific Anticyclone (SPA), the South Pacific Convergence in charcoal influx and soil erosion in Polynesian islands [42,43] Zone (SPCZ) and the westerly storm tracks [32]. The interaction and in the particular case of Rapa Nui [23,37,41,44]. This between these three large systems determines the climate on the dynamic can be described by a generalized exponential discrete island. Seasonally, the weakening and northward migration of Proc. R. Soc. B 287: 20200662 logistic model for the human (N) population [6,45], SPA during fall and winter causes an increase in precipitation during the April–June period, allowing the storm fronts associated Nt ¼ Nt1  erN ½1ðNt1 =KðFt1 ÞÞ , ð3:2Þ with the westerlies winds pass over the island. During the sum- mers, SPA is displaced southwards blocking the westerly storm where rN is a positive constant for maximum per-capita repro- fronts north of 34° S [33] and areas such as the Rapa Nui Island ductive rates and K(Ft−1) is a function of the palm forest cover receive minimum precipitation [32]. Additionally, a relevant com- used as a proxy of resource availability (e.g. land use, ecosystem ponent of annual precipitation has been attributed to land–sea services and crop yields) [6]. breeze convection storms [34]. Meanwhile, under a human population dynamic driven by the The role of ENSO in driving short-term Holocene climate interaction between climate and crop production, the growth rate variations in Rapa Nui has been hotly debated as model depends on the combined effect of recurrent droughts and anthro- simulations, and raw statistical analyses on observational data pogenic pressures imposed by large human populations. Under suggest inconclusive or non-significant correlations at interannual this hypothesis, the human population (N) is described with the and centennial scales [34,35]. Recent reanalysis data assimilation following model: for the period 1960–2014 CE [36], however, indicates that ENSO Nt ¼ Nt1  erN ½1ðNt1 =KðCt1 ÞÞ , ð3:3Þ could provoke local precipitation and temperature anomalies brought about by perturbations on the main atmospheric where Nt and rN are the same parameters as in equation (3.2), and circulation structures that modulate interannual and seasonal K(Ct−1) is function of climate variability [6]. A detailed description variability over the Southern Pacific Ocean. ENSO modifies the of model parameters is depicted in electronic supplementary position of SPA, SPCZ and Subtropical Jetstream (STJ). During material, table S1. El Niño (La Niña) events, the SPCZ experiences a northeast (south- Our starting point is to use the R function [45] as a central west) displacement that leads to increased (decreased) convective element for connecting models and quantitative palaeodemo- activity and rainfall amounts over Rapa Nui [36]. This warm graphic, vegetational and palaeoclimate data. The realized (cold) phase also results in increased (suppressed) frontal population per-capita rate of change for a given interval of time, precipitations facilitated by the weakening (intensification) R, is defined as the value over the same time interval estimated and northward (southward) migration of the Pacific High, by subtracting the logarithmic count at the first sampling date as well as through the equatorward (poleward) incursion of from that at the second. For human populations, this is R = loge mid-latitude westerlies. Here, we performed correlation analyses Nt−loge Nt−1, where Nt is the human population size (SPD between the Southern Oscillation Index (SOI) and 54-year time- data) at time t. In this study, the time interval used for human series of mean annual rainfall in Rapa Nui (1961–2015 CE). Our population analyses was 30 years, which represents a reasonable results point to a major influence of La Niña episodes on the generational time for food producer populations [46]. For analyti- local hydroclimate. A weak but significant negative correlation cal convenience, we write equations (3.2) and (3.3) in terms of the exists between rainfall and the SOI (r = −0.34, p = 0.016, d.f. = 49, per-capita rate of ‘population’ change: t = 2.50), indicating that positive SOI values (La Niña) are associ-    ated with decreased rainfall. This implies that Rapa Nui Nt1 Rt ¼ r N 1  : ð3:4Þ hydroclimate is sensitive only to cold ENSO phases, probably K(Ft1 , Ct1 ) due to its influence on the position of the SPA, the SPCZ and STJ, as previously suggested in [32,37,38]. The chronologically well-constrained record of pollen per- These circulation patterns can operate at several time scales— centages of palm from Raraku lake sediments [21] provides a from annual to millennial [36,38]—and imply that reconstruc- time-series for local vegetation dynamics since 800 CE (electronic tions for past changes in ENSO activity can serve as a proxy supplementary material, table S5). Thus, we defined a standar- for local hydroclimate conditions in Rapa Nui. Our selected dized measure of vegetation cover over time obtained from the proxy for ENSO-driven changes in the local hydroclimate is perceptual representativeness of pollen types between consecutive 14 the 2000-year reconstruction for the SOI index by Yan et al. [39] C dates. This response variable was used in simple regression (electronic supplementary material, table S5). linear models for fitting explanatory variables of local palm forest cover dynamics. Thus, F ¼ a þ b  N þ g  C þ v  (N  C) þ 1, ð3:5Þ (c) Model conceptualization for hypotheses where F denotes the palm tree pollen %, N is the SPD mean values The basic dynamic model (equation (3.1)) predicts that after the of the previous 30 years, C is the reconstructed SOI index and the initial colonization around 1100–1280 CE [15,28] population term N*C represents the interaction between human population grew exponentially until equilibrium population size, which is and climatic conditions. The interaction term assumes that determined by land area and food productivity [37,40,41]. human deforestation rates increase/decrease during periods of The starting point is the exponential version of the general harsh/favourable climatic conditions for crop productivity. Equation (3.4) was fitted through nonlinear least squares CE ( phase 1, figure 1d), followed by accelerated population 5 using the nls (nonlinear least squares) library in the R platform, growth from 1100 to 1400 CE ( phase 2, figure 1d). These assuming (i) a constant carrying capacity, (ii) a linear effect of royalsocietypublishing.org/journal/rspb two phases encompass the statistically significant period of the interpolated palm pollen percentage, (iii) a linear effect of high density in 14C dates observed between 1250 CE and reconstructed SOI index and (iv) both effects combined (elec- 1530 CE ( phase 3, electronic supplementary material, figure tronic supplementary material, table S2), and equation (3.5) S1). The third phase characterizes three decrease–increase was fitted using simple linear regression models. We compared cycles (figure 1d,e). Two of these cycles (1430–1550 CE and the goodness of fit between models by measuring the Akaike information criterion corrected for low sample size, AICc. 1640–1700 CE) occurred before European contact (cycles 3a Models with lowest AICc values were selected. Simulations pro- and 3b; figure 1d,e). Compared with the null model, the vided the mean for evaluating the capacity of models for first pre-European decline represents a significant negative describing the observed dynamic of the SPD trends. Simulations deviation associated with a high amplitude negative trend were fitted considering the first observed value of the time-series, that characterizes such peak in the SPD by approximately and then, running the algorithm using each model with their 1420 CE (electronic supplementary material, figure S1). estimated parameters to obtain the simulated values. Uncertainty While the remaining two declines extend throughout the Proc. R. Soc. B 287: 20200662 on SPD estimates were incorporated by resampling a joint multi- overall low-density phase, they occur against a backdrop variate normal distribution of the estimated parameters of significant negative deviation since 1660 CE onwards considering the asymptotic distribution of maximum-likelihood (electronic supplementary material, figure S1). estimates. The 95% of the confidence intervals (CIs) of SPD Per-capita growth rates are inversely related to SPD trends time-series were obtained using the percentile method based on 10 000 iterations. In addition, values of the coefficient of pre- (figure 1e), suggesting the action of negative feedback pro- diction between observed and predicted values of each model cesses in the dynamics of past Rapa Nui populations. This were calculated to evaluate the predictive performance of the relationship is unclear, however, for the period 800–1100 CE models using the following equation: R 2 = 1 − ∑(Y – X )2/ due to the noisy nature of the palaeodemographic data (i.e. ∑(X – mean (X ))2, where Y is the predicted value of the model low-chronological resolution), which is probably associated and X is the observed value [47]. with an actual later colonization of the island [19]. We vetted PDMs have a long history in ecological theory and modelling these inconsistent SPD values, as well as data from after Euro- and provide a simple general framework for analysing and inter- pean contact (greater than 1760 CE) from our subsequent preting human population growth data. The PDMs developed analyses (figure 1e). here (equations (3.1)–(3.5)) are used to evaluate the expected pre- The coefficient of prediction between the basic model dictions from the alternative ecological scenarios. The genocide trajectories and data explains 61% of the observed variation hypothesis will be supported by a basic model of population growth without feedback between people and the limiting (electronic supplementary material, table S2). In contrast, a island resources, a simple logistic model with a stable population model that includes lateral perturbation effects on carrying size before the European contact (equation (3.1)). Under the ‘eco- capacity [6] using palm tree pollen (model 2, electronic cide’ hypothesis, the human population dynamics would be supplementary material, table S2) or the SOI reconstructed function of forest palm cover as a proxy of the available land variability impacts (model 3, electronic supplementary for agriculture, and the change in palm pollen percentage will material, table S2) significantly improves the prediction coef- be negatively affected by human population size. On the other ficients to 90% as well as model plausibility (Akaike weights; hand, if long-term climatic variability affected crop productivity electronic supplementary material, table S2). Palaeoecologi- and land use, the proper model structure is one where climatic cal data indicate that from 1100 to 1760 CE, there was a variability and palm forest cover are proxies of limiting resources clear and accelerated decrease in palm tree cover on the for human dynamics, while both human population size and cli- island, and palaeoclimate records show a coeval increasing mate will influence the palm pollen percentage decrease during the studied period. These testable models were fed with the trend towards positive SOI values (i.e. a ‘La Niña-like’ con- 660-year palaeodemographic time series previously described ditions) (figure 2a,b). Model simulations fed explicitly by as well as with time series for local vegetation dynamics and available palaeoenvironmental information thus provide ENSO-induced hydroclimate anomalies (electronic supplementary strong empirical support for a logistic population growth material, tables S5 and S6). with a variable carrying capacity driven by land-use and hydroclimate to explain observed patterns from 1130 to 1760 CE. In fact, when SPD data are expressed as ratios of either palm pollen percentage (figure 2c) or SOI (figure 2d), 4. Results we find a common negative linear R function, which provides The SPD values obtained for Rapa Nui suggest that human additional evidence for the feedback relationship between energy consumption was very low from 800 to 1100 CE land use, demography and climate in driving Rapa Nui (figure 1c), which is indicative of a stationary phase with population dynamics. Both models show that lateral pertur- reduced demographic pressures on the island or even no bation effects either by palm tree cover, SOI or both can stable human colonization. This phase appears as a statisti- better predict population dynamics compared with models cally significant negative deviation against the lineal null that do not account for such exogenous effects (figure 3a–d). model (electronic supplementary material, figure S1). In con- Furthermore, palm tree pollen % dynamics in Rapa Nui are trast, 14C-dated densities increased quickly at 1150 CE, and best explained by the negative effect of the human population, different peaks and troughs of values are recognizable in supporting the idea that pressure for farming land was the the SPD curve from 1300 CE onwards (figure 1d; electronic main driver of the deforestation process [23,41,44,48] (elec- supplementary material, figure S1). The resulting per-capita tronic supplementary material, table S3). Stone mulching growth rate time series shows three different phases in the farming and other agriculture features to assure food con- SPD dynamic of the Rapa Nui population over the last 800 sumption prevented further soil and plant erosion because of years. First, a slow growth rate during the period 800–1100 wind and rain action [49–52]. (a) 80 (b) 2 6 royalsocietypublishing.org/journal/rspb 60 1 SOI pr pollen % 40 0 20 –1 0 –2 1100 1300 1500 1700 1900 1100 1300 1500 1700 1900 year (AD) year (AD) (c) (d) Proc. R. Soc. B 287: 20200662 per-capita growth rates per-capita growth rates 0.4 0.4 0.2 0.2 0 0 –0.2 –0.2 0 0.00010 0.00020 0 0.002 0.004 0.006 SPD/palm pollen% SPD*SOI Figure 2. Palaeoenvironmental data. (a) Time series for the percentage of palm pollen (green line and dots) from the Raraku lacustrine record covering the period 1100–1960 CE [21]. (b) SOI reconstruction (SOIpr), annually resolved (red thin line) and smoothed time series [39]. (c) Relationship between per-capita growth rates and the SPD per unit of palm pollen % for the same period (line fitted by linear regression; y = 0.44 – 2935x, F1,20 = 97.23, p < 0.0001, r 2 = 0.82). (d ) Relation- ship between per-capita growth rates and the SPD by the unit of the Southern Index Oscillation for the same period (line fitted by linear regression; y = 0.49– 96.25x, F1,20 = 126.3, p < 0.0001, r2 = 0.86). (Online version in colour.) (a) (b) 0.0020 0.0020 SPD 0.0010 0.0010 0.0000 0.0000 1200 1400 1600 1200 1400 1600 (c) (d) 0.0020 0.0020 SPD 0.0010 0.0010 0.0000 0.0000 1200 1400 1600 1200 1400 1600 years AD years AD Figure 3. Comparisons between model-predicted trajectories (lines) and observed SPD data ( points) at Rapa Nui. Estimated (black dots) and predicted (red line) SPD values for the period 1130–1760 CE. Grey shaded area shows 95% confidence intervals of model predictions based on Ricker logistic population models: (a) model 1, (b) model 2 ( palm cover effects), (c) model 3 (climatic effects; SOI) and (d) model 4 (SOI and palm cover effects). See electronic supplementary material, tables S1 and S2 for details. (d ) These models support the hypothesis that the Rapa Nui experienced major demographic changes well before the arrival of European colo- nizers. More importantly, this trajectory was represented by a very simple population model where carrying capacity is a function of either palm tree cover and climate, and offers an alternative to the simple dichotomy of ‘ecological self-destruction’ versus the ‘idyllic equilibrium’ with nature. (Online version in colour.) (a) (b) 7 per-capita growth rates 0.4 royalsocietypublishing.org/journal/rspb 0.0020 SPD 0 0.0010 moai cult birdman cult –0.4 0 1100 1250 1400 1550 1700 0 0.0010 0.0020 year AD SPD (c) Proc. R. Soc. B 287: 20200662 + K1 R 0 K2 – Rapa Nui colonization 1000–1200 AD N La Niña El Niña – crop production + + deforestation – Figure 4. Graphical representations for the best model. (a) The observed population dynamic pattern from SPD data. (b) The effect of lateral perturbations caused by decreased crop production (or available land) either from palm tree cover or ENSO-induced hydroclimate anomalies. K represents the first equilibrium population size, and orange arrows denote reconstructed consecutive population declines. Solid and dotted lines are the graphical representations of the lateral perturbation effect. (c) Gradual changes in the island carrying capacity caused by a lateral perturbation process. The population trajectory of the Rapa Nui population in terms of the relationship between per-capita growth rates (R) and population size (N ). The green solid curve represents the population logistic model with the carrying capacity K1 at the initial colonization (1100–1200 CE). The gradual deterioration of the carrying capacity (dotted brown lines) is driven by negative hydroclimatic changes that lead to low crop productivity, intense land use and deforestation and in turn a lower equilibrium population size, K2. Solid and dashed arrows illustrate demographic trajectories since the colonization (black arrows positive growth rates) to the collapses (red arrows negative growth rates). (Online version in colour.) Rapa Nui was the long-term forcing effect of climate on the 5. Discussion island’s per-capita resource base. In summary, climatic Population analysis of the prehistoric Rapa Nui time series change interacts with the effects of human population size suggests that long-term climatic variability (e.g. SOI) and on land use. palm tree cover are proxies of the island’s carrying capacity. Conversely, observed population boom and bust In fact, a simple model appears to describe the dynamics of dynamics in Rapa Nui can be interpreted as the consequence the human population in Rapa Nui quite well and is able of non-additive long-term effects of climate variability and to explain the increasing trend as well as population decline palm tree cover on the limiting resources (land and food pro- episodes that impacted during several generations, which ductivity) on human population dynamics, since equilibrium we think can be defined as demographic collapses (sensu population size is set by which resource is in short supply [53]). [45] (figure 4a–d). This mechanism has been used for explain- Our results contradict recent work by DiNapoli et al. [15], ing the observed population collapses in Europe as a direct which argues against pre-contact collapses in the island. The link between long-term climate change and carrying capacity tempo-activity curve for the construction of megalithic struc- [13]. In our results, demographic collapses of the Rapa Nui tures reconstructed by DiNapoli et al. (fig. 5 in [15]) based on population resulted from the long-term effects of exogenous independent datasets is essentially—and paradoxically— factors on the island’s carrying capacity and in turn on the equivalent to our normalized and smoothed SPD (figure 4a; ‘per-capita food supply’. This implies that the palm tree electronic supplementary material, figure S1). These authors cover and climate may represent different proxies of the verify an exponential increase in the rate of construction same limiting factors that control crop production in Rapa since about 1300 CE, peaking at 1450 CE, and then this rate Nui. Human population size and energy consumption at experiences a sustained slowdown since 1550 CE. We think the Rapa Nui society would be limited by food production, that DiNapoli et al. [15] precluded collapses in the island by which depends on two processes: crop productivity and considering evidence for a totally different phenomenon: land availability. Our analyses are consistent with the the ‘continuities/discontinuities’ in a given cultural tradition hypothesis that climate variability influences crop pro- (i.e. the ‘ahu moai’ tradition), not a demographic process. Our ductivity, whereas palm tree cover is a proxy of land use analyses support a demographic expansion and collapse, as linked to the total cultivated area. Thus, the combination of predicted by the ‘ecocide’ hypothesis [16–18] and consu- positive population growth rates and a gradual increasing mer-resource models [12]. We think that the key driver in long-term trend in La Niña conditions (which causes understanding the demographic and landscape changes in droughts on the island) [37,54] could explain the extensive deforestation as agriculture production increased the demand organization and religion [48,64]. In fact, demographic and 8 for farming lands, linked also to soil erosion and exhaustion. social collapses seem to be the rule across different farming royalsocietypublishing.org/journal/rspb Intensified agricultural activities accelerated palm forest cultures in the Pacific Islands [65]. Intense pressures on the degradation further after 1200 CE [21]. Establishing causal island ecosystem services were required by the high-energy links between climate and demographic change is always labour invested in the building and maintenance of the old complex, and the effects of past hydroclimate variability on socio-cultural system, materialized in the monumental archi- the island ecosystems have been widely debated [34,55]. tectural tradition of ancient ahu moai cult. Around 1500 CE, Severe droughts during the second half of the Little Ice Age this ancient system shifted to a much simpler hierarchical have been identified as the main driver of the demographic political system and cult which required less energy and and cultural changes [56]. Indeed, the population crashes resource investment for its building and maintenance [63]. shown here were coeval with a positive trend of the SOI Although we do not test the relative role of high-energy index during the period 1250–1700 CE on inter-decadal perturbation events (e.g. volcano eruptions and tsunamis) time scales, which have been recorded across the ENSO- in our analyses, these might have exerted positive synergistic sensitive regions in the Eastern Pacific [54]. Independently impacts as documented for other Polynesian societies. For Proc. R. Soc. B 287: 20200662 of the intensity/magnitude of any given environmental instance, the Kuwae eruption (1453 CE) matches with the change (e.g. droughts), PDMs predict that the impact of major population crash detected in Rapa Nui (figure 4a), exogenous variables on limiting factors is modulated by and it also is coeval to the interruption of the traditional population size (non-additive effects), particularly through Vanuatu–Tonga trade [66]. Palaeoenvironmental and docu- a per-capita resource share [6]. This means that even small mentary records suggest that deforestation and agricultural perturbations in climate can trigger disproportionately large activities ceased by this period [21,67]. Whether the Kawae demographic responses when population sizes are near eruption played a role in driving a population collapse equilibrium, but much less so when such populations are in remains to be tested. their exponential growth phase (figure 4c). Our results Understanding the relationship between human popu- imply that climate effects should not be evaluated indepen- lation dynamics and climate change is one of the major dently of population size when attempting to explain challenges for addressing the present environmental crisis demographic changes. and the possibility of a sustainable future [68]. Here, we The notion that forest degradation may have had a negli- demonstrate how the classical TPD is a useful framework gible impact on the crop production in the inherently for testing predictions of explanations for population changes nutrient-poor soils of Rapa Nui [14] has been challenged as it in the Rapa Nui society. Finally, our results support the ignores concomitant soil erosion and loss of key ecosystem hypothesis that Rapa Nui experienced a long-term climatic services (i.e. freshwater and nutrient cycling) [17,21,37,41]. trend towards drier conditions since the initial colonization Existing evidence suggests that forest clearance created wide- of the island. This, concomitant with a gradual decrease in spread soil erosion between 1200 CE and 1650 CE [37,41]. rainfall and island productivity, explains the process of More importantly, land use varied considerably after 1240 CE, expansion and demographic collapse experienced by the driven by environmental constraints and variation in agricul- Rapa Nui society (figure 4c). tural production [23]. The introduction of stone gardens after Population dynamic theory can thus be successfully 1300 CE for agricultural production additionally helped to applied to understand and explain population changes stop soil erosion [49–51]. These technologies lasted for less in prehistoric food producer societies. In particular, we high- than 600 years until population density lowered to its minimum light the use of the logistic model as it can take apart [50]. Precisely, SPD curves derived from OHD data reproduce the simple dichotomy between the extremes of ‘ecological consistent variations in land use for food production, with an self-destruction’ versus ‘idyllic equilibrium’ with nature. overall expansion in intensity starting at 1240 CE and spatially Conversely, by undertaking profound adaptive socio-cultural heterogeneous slowdowns at approximately 1380–1430 CE and practices, the Rapa Nui peoples were resilient for more than then since approximately 1660 CE [23]. 1000 years on a tiny volcanic island in the middle of the Our results suggest that deforestation of the original Pacific Ocean, despite resource scarcity, overpopulation and palm forest of Rapa Nui is a consequence of the population climate change. Overpopulation and ongoing climate change pressure for stone farming land (rock gardens) [49,52] are serious problems facing modern societies, and the historical and not a cause in itself of population collapse. In fact, defores- trajectory described here for the Rapa Nui provides important tation after the arrival of humans is a common phenomenon in insights regarding food security and ecological resilience for the colonization of Polynesia [57] and elsewhere [58–61]. More- such populations. over, the patterns of an increase in charcoal influx values for the period 1400–1700 CE, probably associated with an intensifica- Data accessibility. The data is available from the Dryad Digital Reposi- tory: https://doi.org/10.5061/dryad.bk3j9kd7j [69]. tion of fire disturbance by humans [21], combined with the Authors’ contributions. Conceptualization: M.L., E.M.G., S.A.E., C.L. and evidence of changes in the intensity of land use previous to N.C.S. Data curation: E.M.G., N.C.-B., O.M., S.G., A.S. and S.P.-R. the European contact [23], are consistent with the increase/ Formal analysis: M.L., S.A.E. and E.M.G. Investigation: M.L., decrease SPD dynamic. E.M.G., S.A.E., C.L., C.M.S., N.C.-B., O.M., S.G., A.S., S.P.-R. and The population decline from 1430 to 1550 CE (involving N.C.S. Methodology: M.L., S.A.E., N.C.-B. and E.M.G. Validation: approximately four generations) could be in the origin of M.L., E.M.G. and S.A.E. Visualization: M.L. and S.A.E. Writing— original draft: M.L., E.M.G., S.A.E., C.L., C.M.S. and N.C.S. Writ- the posterior major socio-cultural changes in the island, ing—review and editing: M.L., E.M.G., S.A.E., C.L., S.G., A.S., O.M. such as from the moai cult to the birdman cult [62] (figure 4a), and S.P.-R. initiated around 1600 CE [63]. These changes show important Competing interests. We declare we have no competing interests. investments in civil works for agriculture and water manage- Funding. 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