Population growth and earth's human carrying capacity

Reconstruction of human dispersal during Aurignacian on pan-European scale

The Aurignacian is the first techno-complex related with certainty to Anatomically Modern Humans in Europe. Studies show that they appeared around 43-42 kyr cal BP and dispersed rapidly in Europe during the Upper Palaeolithic. However, human dispersal is a highly convoluted process which is until today not well understood. Here, we provide a reconstruction of the human dispersal during the Aurignacian on the pan-European scale using a human dispersal model, the Our Way Model, which combines archaeological with paleoclimate data and uses the human existence potential as a unifying driver of human population dynamics. Based on the reconstruction, we identify the different stages of the human dispersal and analyse how human demographic processes are influenced by climate change and topography. A chronology of the Aurignacian human groups in Europe is provided, which is verified for locations where archaeological dating records are available. Insights into highly debated hypotheses, such as human dispersal routes, are provided.

Phase synchronization between culture and climate forcing

Over the history of humankind, cultural innovations have helped improve survival and adaptation to environmental stress. This has led to an overall increase in human population size, which in turn further contributed to cumulative cultural learning. During the Anthropocene, or arguably even earlier, this positive sociodemographic feedback has caused a strong decline in important resources that, coupled with projected future transgression of planetary boundaries, may potentially reverse the long-term trend in population growth. Here, we present a simple consumer/resource model that captures the coupled dynamics of stochastic cultural learning and transmission, population growth and resource depletion in a changing environment. The idealized stochastic mathematical model simulates boom/bust cycles between low-population subsistence, high-density resource exploitation and subsequent population decline. For slow resource recovery time scales and in the absence of climate forcing, the model predicts a long-term global population collapse. Including a simplified periodic climate forcing, we find that cultural innovation and population growth can couple with climatic forcing via nonlinear phase synchronization. We discuss the relevance of this finding in the context of cultural innovation, the anthropological record and long-term future resilience of our own predatory species.

Quintessential Solutions to Existential Problems: How Human Factors and Ergonomics Can and Should Address the Imminent Challenges of Our Times

OBJECTIVE

To examine and evaluate ways in which an understanding of the quintessential element of Human Factors/Ergonomics can address the spectrum of existential threats that confront contemporary civilization.

BACKGROUND

HF/E is dedicated to improving quality of life. Paradoxically, many processes which sustain contemporary civilization act to reduce that overall quality. Some technological developments themselves now even present existential threats to the fragile skein of civilization itself. Many disciplines address these diverse threats, and each may be advised and facilitated by HF/E knowledge and methods. It is a moral imperative of our science to contribute what we can to proposed resolutions.

METHOD

A primary conduit, by the established strengths of HF/E can contribute to potential solutions is identified. The present work advocates for specific, practical interventions using a direct-perception mediated, panopticon principle, that derives from the corpus of our science.

RESULT

Limitations upon a general, social understanding of imminent global concerns, which are largely ignorable when not actually present, are brought to immediate consciousness via an HF/E principle emphasizing the direct-perception of threat. It is argued that this, and allied HF/E insights can generate practical steps toward problem resolution at both macroscopic and localized levels of implementation.

APPLICATIONS

The primary, practical application of the proposed panopticon principle is to use our science to save global civilization. It is postulated that this represents useful employment of the knowledge we have adduced and accumulated across our discipline's existence.

Global population: from Super-Malthus behavior to Doomsday criticality

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r ( t ) or relaxation time τ ( t ) = 1 / r ( t ) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1 ) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ' t / T C - t , whereT C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

The long-term expansion and recession of human populations

Over the last 12,000 y, human populations have expanded and transformed critical earth systems. Yet, a key unresolved question in the environmental and social sciences remains: Why did human populations grow and, sometimes, decline in the first place? Our research builds on 20 y of archaeological research studying the deep time dynamics of human populations to propose an explanation for the long-term growth and stability of human populations. Innovations in the productive capacity of populations fuels exponential-like growth over thousands of years; however, innovations saturate over time and, often, may leave populations vulnerable to large recessions in their well-being and population density. Empirically, we find a trade-off between changes in land use that increase the production and consumption of carbohydrates, driving repeated waves of population growth over thousands of years, and the susceptibility of populations to large recessions due to a lag in the impact of humans on resources. These results shed light on the long-term drivers of human population growth and decline.

Testing the effect of semi-transparent spectrally selective thin film photovoltaics for agrivoltaic application: A multi-experimental and multi-specific approach

The integration of photovoltaic technologies within the agricultural framework, known as agrivoltaics, emerges as a promising and sustainable solution to meet the growing global demands for energy and food production. This innovative technology enables the simultaneous utilization of sunlight for both photovoltaics (PV) and photosynthesis. A key challenge in agrivoltaic research involves identifying technologies applicable to a wide range of plant species and diverse geographic regions. To address this challenge, we adopt a multi-experimental and multi-species approach to assess the viability of semi-transparent, spectrally selective thin-film silicon PV technology. Our findings demonstrate compatibility with crop production in controlled environments for both plants and algae. Notably, selective thin-film PV exhibits the potential to enhance crop yields and serves as a photo-protectant. We observe that plant and algal growth increases beneath the selective PV film when supplemented with appropriate diffuse light in the growth environment. Conversely, in situations where light intensity exceeds optimal levels for plant growth, the selective PV film provides a photo-protective effect. These results suggest potential supplementary benefits of employing this technology in regions characterized by excessive light irradiation, where it can contribute to healthy plant growth.

Our fragile future under the cumulative cultural evolution of two technologies

We derive and analyse a model with unusual features characterizing human activities over the long-run. First, human population dynamics draw heavily on consumer-resource modelling in ecology in that humans must consume biological resources to produce new humans. Second, the model also draws heavily from economic growth theory in that humans do not simply consume biological resources; they also produce the resources they consume. Finally, humans use two types of technology. Consumption technology affects the rate at which humans can extract resources. Production technology controls how effectively humans convert labour into new resources. The dynamics of both types of technology are subject to cumulative cultural evolutionary processes that allow both technological progress and regress. The resulting model exhibits a wide range of dynamical regimes. That said, the system is routinely sensitive to initial conditions, with wildly different outcomes given the same parameter values. Moreover, the system exhibits a basic fragility in the sense that human activities often lead to the endogenous extinction of the human species. This can happen gently, or it can follow periods of explosive human activity with super-exponential growth that ends in collapse. This article is part of the theme issue 'Evolution and sustainability: gathering the strands for an Anthropocene synthesis'.

Positive feedbacks in deep-time transitions of human populations

Abrupt and rapid changes in human societies are among the most exciting population phenomena. Human populations tend to show rapid expansions from low to high population density along with increased social complexity in just a few generations. Such demographic transitions appear as a remarkable feature of Homo sapiens population dynamics, most likely fuelled by the ability to accumulate cultural/technological innovations that actively modify their environment. We are especially interested in establishing if the demographic transitions of pre-historic populations show the same dynamic signature of the Industrial Revolution transition (a positive relationship between population growth rates and size). Our results show that population growth patterns across different pre-historic societies were similar to those observed during the Industrial Revolution in developed western societies. These features, which appear to have been operating during most of our recent demographic history from hunter-gatherers to modern industrial societies, imply that the dynamics of cooperation underlay sudden population transitions in human societies. This article is part of the theme issue 'Evolution and sustainability: gathering the strands for an Anthropocene synthesis'.

A mathematical meta-model for assessing the self-sufficient water resources carrying capacity across different spatial scales in Iran

Hydrological modeling, water accounting assessments, and land evaluations are well-known techniques to carry out water resources carrying capacity (WRCC) assessments at multiple spatial levels. Using the results of an existing process-based model for assessing WRCC from very fine to national spatial scales, we propose a mathematical meta-model, i.e., a set of easily applicable simplified equations to assess WRCC as a function of high-quality agricultural lands for optimistic to realistic scenarios. These equations are based on multi-scale spatial results. Scales include national scale (L0), watersheds (L1), sub-watersheds (L2), and water management hydrological units (L3). Applying the meta-model for different scales could support spatial planning and water management. This method can quantify the effects of individual and collective behavior on self-sufficient WRCC and the level of dependency on external food resources in each area. Carrying capacity can be seen as the inverse of the ecological footprint. Hence, using publicly available data on the ecological footprint in Iran, the results of the proposed method are validated and give an estimation of lower and upper bounds for all biocapacity of the lands. Moreover, the results confirm the law of diminishing returns in the economy for the carrying capacity assessment across spatial scales. The proposed meta-model could be considered a complex manifest of land, water, plants, and human interaction for food production, and it could be used as a powerful tool in spatial planning studies.

Generic catastrophic poverty when selfish investors exploit a degradable common resource

The productivity of a common pool of resources may degrade when overly exploited by a number of selfish investors, a situation known as the tragedy of the commons. Without regulations, agents optimize the size of their individual investments into the commons by balancing incurring costs with the returns received. The resulting Nash equilibrium involves a self-consistency loop between individual investment decisions and the state of the commons. As a consequence, several non-trivial properties emerge. For N investing actors we prove rigorously that typical payoffs do not scale as 1/N, the expected result for cooperating agents, but as (1/N)². Payoffs are hence reduced with regard to the functional dependence on N, a situation denoted catastrophic poverty. We show that catastrophic poverty results from a fine-tuned balance between returns and costs. Additionally, a finite number of oligarchs may be present. Oligarchs are characterized by payoffs that are finite and not decreasing when N increases. Our results hold for generic classes of models, including convex and moderately concave cost functions. For strongly concave cost functions the Nash equilibrium undergoes a collective reorganization, being characterized instead by entry barriers and sudden death forced market exits.

Super-Exponential Growth in Models of a Binary String World

The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a "hockey stick" curve. This equation, initially conceived to describe the growth in time of the number of new types of artifacts, has also been applied to several natural phenomena. A possible drawback is that it may overestimate the number of new artifact types, since it does not take into account the fact that interactions, among existing types, may produce types which have already been previously discovered. We introduce here a Binary String World (BSW) where new string types can be generated by interactions among (at most two) already existing types. We introduce a continuous limit of the TAP equation for the BSW; we solve it analytically and show that it leads to divergence in finite time. We also introduce a criterion to distinguish this type of behavior from the familiar exponential growth, which diverges only as t → ∝. In the BSW, it is possible to directly model the generation of new types, and to check whether the newborns are actually novel types, thus discarding the rediscoveries of already existing types. We show that the type of growth is still TAP-like, rather than exponential, although of course in simulations one never can observes true divergence. We also show that this property is robust with respect to some changes in the model, as long as it deals with types (and not with individuals).

Island carrying capacity for three development types: ecological resource, agricultural production, and urban construction

The evaluation of island carrying capacity is the premise for conducting the island spatial planning and can contributes to guiding island ecological conservation and socioeconomic developments. In this study, the island carrying capacities were evaluated for the three major development types, namely, ecological resource, agricultural production, and urban construction, based on the quantity and quality. The occupancy and vacancy rates of island carrying capacity were measured in different scenarios. Miaodao Archipelago and Dongtou Archipelago in China were selected as the study area to demonstrate the evaluation. The former is constituted all by spatially isolated rocky islands, while the latter is featured by the coexistence of the sandy and rocky islands and the connection with the mainland by bridges. The results indicated the high variances of occupancy and vacancy rates of island carrying capacity at multiple spatial scales. Across the two archipelagos, climate conditions, island composition, and spatial connections with the mainland controlled the spatial variance at this scale. For different types of islands, the sandy island presented distinctly higher occupancy and vacancy rates for agricultural production than the rocky islands. At the single island scale within the same archipelago, the developments of agricultural production and urban construction distinctly increased with the increase in the island area. The dependency of island constructions on the external world in Dongtou Archipelago was higher than that in Miaodao Archipelago. Meanwhile, the difference in traffic conditions between the two archipelagos did not distinctly influence the food dependency on the external world. Then, practical suggestions in terms of quantity control and quality promotion were proposed to improve the island carrying capacity.

Evaluating the Resources and Environmental Carrying Capacity in Laos Using a Three-Dimensional Tetrahedron Model

(1) Background: The quantitative evaluation and comprehensive measurement of resources and environmental carrying capacity (RECC) are key links in the study of RECC from classification to synthesis. Laos, as the only landlocked country of Mainland Southeast Asia (MSEA), is an important economic corridor (i.e., China-MSEA Economic Corridor) of the Belt and Road Initiative (BRI). (2) Methods: Based on the human settlements index (HSI), resource carrying index (RCI), and socio-economic development index (SDI), here, a three-dimensional tetrahedron model for the comprehensive assessment of RECC with equilibrium significance was constructed, including HSI-based suitability classification, RCI-based restrictive classification, and SDI-based adaptability classification. Taking provinces as the basic unit, we quantitatively assessed and comprehensively evaluated RECC in Laos using a three-dimensional tetrahedron model. (3) Results: The human settlement environment in Laos is mainly characterized by the moderate suitable category (85%), while the high suitability area (merely 5%) supports more than 30% of the total population. Laos had over 90% of its area in good condition in resources and environmental carrying status (surplus or balanced state), translating into more than 95% of the population. The social and economic development level is mainly characterized by low-level development (43%), with nearly 30% of the population living in these low-level areas. The comprehensive bearing state of resources and environment is characterized by surplus, and 85% of the population is distributed in the surplus area, which occupies 63% of the land. (4) Conclusions: It is possible to better explore the adaptation strategies and countermeasures for enhancing RECC in Laos and provide a scientific reference for regional sustainable development. We believe that the three-dimensional tetrahedron method can be applied to quantitatively evaluate and comprehensively measure RECC at larger scale, e.g., the BRI regions.

Ecological complexity and the biosphere: the next 30 years

Global warming, habitat loss and overexploitation of limited resources are leading to alarming biodiversity declines. Ecosystems are complex adaptive systems that display multiple alternative states and can shift from one to another in abrupt ways. Some of these tipping points have been identified and predicted by mathematical and computational models. Moreover, multiple scales are involved and potential mitigation or intervention scenarios are tied to particular levels of complexity, from cells to human–environment coupled systems. In dealing with a biosphere where humans are part of a complex, endangered ecological network, novel theoretical and engineering approaches need to be considered. At the centre of most research efforts is biodiversity, which is essential to maintain community resilience and ecosystem services. What can be done to mitigate, counterbalance or prevent tipping points? Using a 30-year window, we explore recent approaches to sense, preserve and restore ecosystem resilience as well as a number of proposed interventions (from afforestation to bioengineering) directed to mitigate or reverse ecosystem collapse. The year 2050 is taken as a representative future horizon that combines a time scale where deep ecological changes will occur and proposed solutions might be effective.

This article is part of the theme issue ‘Ecological complexity and the biosphere: the next 30 years’.

Estimation and Potential Analysis of Land Population Carrying Capacity in Shanghai Metropolis

It is of great practical significance to understand the current situation of urban land carrying capacity, explore its potential space, and continuously improve the economic adaptability and resilience and population carrying capacity of megacities. Based on the guiding principle of territorial spatial division and the concept of moderate-scale resilient cities, combined with GIS technology, this study aims to divide land spaces into three types and construct different index systems to evaluate the land carrying capacity of Shanghai in different spaces. Furthermore, we propose different schemes of estimating subspace land population carrying capacity, and the carrying potential of land population is analysed as well. The acquired results demonstrate three key points. Firstly, the total land population capacity of Shanghai is estimated at 25,476.61–32,047.27 people, with urban land space being the most dominant for the city’s population carrying capacity. Furthermore, the inner suburbs carry the largest population, and the urban centre carries a larger population density than other areas. Secondly, there are significant spatial differences in land population carrying potential. Compared with the demographic data from 2017, Shanghai still has a population carrying potential of 1293.30–7863.97 people and a suitable population carrying potential of 4578.64 people. The population of the urban centre is near the upper limit of the estimated population carrying capacity, and the suburbs, especially the outer suburbs, have large population carrying potential. Thirdly, the estimation method adopted in this study can effectively reveal the spatial differences in population carrying capacity and the potential of different land spaces and different regions in Shanghai, with the estimation results being highly credible. The results will provide references for the improvement of the multi-scenario population planning strategy in Shanghai, as well as enrich the research span and methods currently employed in land carrying capacity.

The edge of the petri dish for a nation: Water resources carrying capacity assessment for Iran

Different methods have been proposed in population dynamics to estimate carrying capacity (K). This study estimates K for Iran, using three novel methods by integrating land and water limits into assessments based on Human Appropriated Net Primary Production (HANPP). The first method uses land suitability as the limiting resource. It gives theoretical estimates for K. The second method which is based on the first method, uses land suitability and water resources availability as limiting resources assuming highly efficient agriculture, also resulting in theoretical estimates for K. The third method is based on the second method assuming a lower, more realistic agricultural efficiency. The third therefore results in more realistic estimates. Four spatial hydrological scale levels were considered to estimate food production. Also, nine scenarios were defined: a reference one reflecting the current situation, five others for the first method, two for the second method, and finally, one scenario for the third method. Results show severe limitations on food production by the availability of suitable land, water availability, and crop productivity for agriculture. We estimated theoretical values for K using land and water limiting resources separately. Two realistic scenarios considering realistic agricultural productivity and water use at national and local levels were assessed, resulting in 35.5 and 20 million people, respectively. These are alarming values compared to the current population of Iran (84 million). Moreover, our conservative estimations are still higher than any assessment when considering social, economic, or political barriers. This research provides a systematic analysis of carrying capacity in Iran, showing the importance of food import on Iranians' lives, relevant to land, water, and food policies.

Cooperation and Lateral Forces: Moving Beyond Bottom-Up and Top-Down Drivers of Animal Population Dynamics

Biologists have long known that animal population dynamics are regulated by a combination of bottom-up (resource availability) and top-down forces (predation). Yet, economists have argued that human population dynamics can also be influenced by intraspecific cooperation. Despite awareness of the role of interspecific cooperation (mutualism) in influencing resource availability and animal population dynamics, the role of intraspecific cooperation (sociality) under different environmental conditions has rarely been considered. Here we examine the role of what we call "lateral forces" that act within populations and interact with external top-down and bottom-up forces in influencing population dynamics using an individual-based model linking environmental quality, intraspecific cooperation, and population size. We find that the proportion of cooperators is higher when the environment is poor and population sizes are greatest under intermediate resources levels due to the contrasting effects of resource availability on behavior and population size. We also show that social populations are more resilient to environmental change than non-social ones because the benefits of intraspecific cooperation can outweigh the effects of constrained resource availability. Our study elucidates the complex relationship between environmental harshness, cooperation, and population dynamics, which is important for understanding the ecological consequences of cooperation.

Greening the Artificial Intelligence for a Sustainable Planet: An Editorial Commentary

Artificial intelligence (AI) is one of the most popular and promising technologies of our time [...]

SARS-CoV-2 mutational cascades and the risk of hyper-exponential growth

The emergence of novel SARS-CoV-2 variants of concern (VOC), in late 2020, with selective transmission advantage and partial immunity escape potential, has been driving further evolution in the pandemic. The timing of mutational evolution and its limits are thus of paramount importance in preparedness planning. Here, we present a model predicting the pattern of epidemic growth including the emergence of variants through mutation. It is based on the SEIR (Susceptible, Exposed, Infected, Removed) model, but its equations are modified according to the transmission parameters of novel variants. Since more transmissible strains will drive a further increase in the number of cases, they will also lead to further novel mutations. As one cannot predict whether there is a viral mutational evolutionary limit, we model a cascade that could lead to hyper-exponential growth (HEG) involving the emergence of even more transmissible mutants that could overwhelm any systematic response. Our results are consistent with the timing, since the beginning of the pandemic, of the concurrent and independent emergence of the VOCs. The current dominance of the Delta variant and the need for additional public health measures indicates some of the risks of a possible HEG. We examine conditions that favor the expected appearance of similar variants, thus enabling better preparedness and more targeted research.

Resources and Environment Carrying Capacity, Social Development and Their Decoupling Relationship: A Case Study of Hubei Province, China

With the rapid urbanization in recent decades, resource shortage and environmental damage have hindered the process of urban sustainable development (SD). As a yardstick of sustainable development, the evaluation of resources and environment carrying capacity (RECC) and its decoupling relationship with social comprehensive development index (SCDI) are of great significance. In this paper, RECC and SCDI are taken as research objects to establish resource and environment system evaluation index system and social comprehensive development level evaluation index system, respectively. Then, the RECC and SCDI of 17 cities in Hubei province during 2009-2018 are calculated by the projection pursuit model based on genetic algorithm, and their spatial-temporal variance characteristics are analyzed. On this basis, the RECC-SCDI Tapio decoupling model is constructed to explore the decoupling relationship between RECC and SCDI. The result shows that: (1) The RECC of Hubei shows a V-shaped development trend during 2009-2018. The SCDI of Hubei rose steadily during 2009-2018. (2) RECC in western and eastern Hubei Province is higher than that in central Hubei Province. SCDI in eastern and central Hubei Province is higher than that in the west. (3) 11 of the 17 cities in Hubei Province have got rid of excessive dependence on resources environment for social development. The study could contribute to scientific and effective policies be formulated by government to promote urban sustainable development.

Revisiting the application and methodological extensions of the planetary boundaries for sustainability assessment

The planetary boundaries (PBs) delineating the safe operating space for human activities have been broadly recognized as a well-grounded framework for global sustainability assessment. This paper provides a comprehensive review of the application and methodological extensions of the PBs by linking with multiscale environmental sustainability assessments. We find that the targeted scales, sharing principles and sustainability perspectives jointly determine the downscaling of the PBs-a complex process that needs to take into account the biophysical, socioeconomic, ethical and cultural dimensions. Despite the varying sharing principles, in general both top-down and bottom-up approaches have been employed to define the environmental boundaries at sub-global scales on which the various PBs highly differ in their threshold behaviors. To clarify the responsibility of different stakeholders for sustainable development, the PB-informed sustainability assessment should refer to a specific perspective (i.e., production-, consumption-, or life cycle-based). Furthermore, the methodological extensions of PBs have the potential to monitor the progress and gaps of the globally consensus-based Sustainable Development Goals (SDGs). To achieve the SDGs within the PBs, there is a great need for a thorough transition of socioeconomic systems towards a prosperous, just and sustainable future.

Conjugate evaluation of sustainable carrying capacity of urban agglomeration and multi-scenario policy regulation

The scientific evaluation of carrying capacity and the formulation of adaptive regulation policies are powerful ways to achieve sustainable development goals. In order to quantitatively and accurately diagnose the sustainable development state of urban agglomeration, this paper responds to the "Future Earth" framework; takes the carrying capacity as the breakthrough point; embeds the conjugate thought; considers the elements of the resources, the environment, the ecology, and the development; and establishes the conjugate evaluation model and the evaluation index system of sustainable carrying capacity. In order to solve the actual bottleneck problem of urban agglomeration, this work identifies the key obstacle factors, constructs the multi-scenario dynamic coupling (MSDC) model, recognizes the sensitivity policies, and proposes the adaptive regulation polices. Taking the urban agglomeration on the northern slope of the Tianshan Mountains (UANSTM) in arid areas as a case study, it was found that from 2007 to 2017, the carrying capacity gradually increased, and the sustainable development showed a benign transformation trend in the UANSTM. It will also be in a transitional stage of growth from now to 2035, and the steady development of the economy and the society and the good maintenance of the resources, the environment and the ecology are equally important. The policies on population intervention and on the management of water resources play a vital role, and the speed of economic development should be controlled throughout the whole process. The study confirms that the effective regulation is necessary for the sustainable development of the urban agglomeration in the future, and the key lies in improving technological progress and governance policy support. It is expected that this new and complete research framework for the conjugate evaluation of the sustainable carrying capacity of urban agglomeration and multi-scenario policy regulation can be applied to other regions or urban agglomerations in developing countries and can make a possible breakthrough in promoting the theoretical exploration and practice of sustainable development.

Ecology of the Anthropocene signals hope for consciously managing the planetary ecosystem

Human populations have grown to such an extent that our species has become a dominant force on the planet, prompting geologists to begin applying the term Anthropocene to recognize the present moment. Many approaches seek to explain the past and future of human population growth, in the form of narratives and models. Some of the most influential models have parameters that cannot be precisely known but are estimated by expert opinion. Here we apply a unified model of ecology to provide a macroscale summary of the net effects of many microscale processes, using a minimal set of parameters that can be known. Our models match estimates of historic and prehistoric global human population numbers and provide predictions that correspond to some of the more complicated current models. In addition to fitting the data well they reveal that, amidst enormous complexity in our human and prehuman past, three key ecological discontinuities have occurred in turn: 1) becoming dominant competitors of large predators rather than their prey, 2) becoming mutualists with food species rather than acting as predators upon them, and 3) changing from a regime of uncontrolled population growth to one of controlled fertility instead. All three processes have been interlinked with cultural evolution and all three ushered in developments of the Anthropocene. Understanding the trajectories that have delivered us to this stage can help guide prudent paths into the future.

Beyond the limit: carrying capacity (K) and the holism/reductionism debate

As the debate about holism and reductionism in ecology has ebbed in the last twenty years, this article aims to reassess the traditional opposition between holistic and reductionist epistemologies during the development of population biology. The history of the notion of carrying capacity, the upper demographic limit of a viable population, will be analyzed as a paradigmatic case of the progressive imposition of reductionist strategies, from both an epistemological and a semantic point of view, since the middle of the twentieth century. Then, Richard Looijen's reduction of the carrying capacity concept to the niche partitioning theory will be assessed and rebuked for both empirical and logical reasons. Eventually, some recent "weak" and "hard" emergent conceptualizations of the notion of carrying capacity, in logistic map models or in coupled niche-population systems, will be presented in order to show how they call into question the nature and the use of the notion of carrying capacity as a predefined ecological limit.

A quantitative analysis of intensification in the ethnographic record

The intensification of food production plays a central role in the evolution of complex human societies. However, it is unclear whether the standard model of intensification is theoretically or empirically justified. This leaves social scientists unable to make reasonable inferences about the relationship between intensification and the evolution of social complexity in past societies. To remedy this problem, I derive a model of intensification from human macroecology, settlement scaling theory, human behavioural ecology, cultural evolutionary theory and niche construction theory. The standard and cultural niche construction models are formalized and their predictions are tested using a comprehensive ethnographic dataset that describes food production in 40 human societies, ranging in complexity from foraging bands to agricultural states. Analysis of the ethnographic record suggests that we reject the standard model and tentatively accept the cultural niche construction model. I attempt to demonstrate the broader utility of the cultural niche construction model as a framework that may help explain the transition from small-scale to large-scale complex societies.

Footprints to singularity: A global population model explains late 20th century slow-down and predicts peak within ten years

Projections of future global human population are traditionally made using birth/death trend extrapolations, but these methods ignore limits. Expressing humanity as a K-selected species whose numbers are limited by the global carrying capacity produces a different outlook. Population data for the second millennium up to the year 1970 was fit to a hyper-exponential growth equation, where the rate constant for growth itself grows exponentially due to growth of life-saving technology. The discrepancies between the projected growth and the actual population data since 1970 are accounted for by a decrease in the global carrying capacity due to ecosystem degradation. A system dynamics model that best fits recent population numbers suggests that the global biocapacity may already have been reduced to one-half of its historical value and global carrying capacity may be at its 1965 level and falling. Simulations suggest that population may soon peak or may have already peaked. Population projections depend strongly on the unknown fragility or robustness of the Earth’s essential ecosystem services that affect agricultural production. Numbers for the 2020 global census were not available for this study.

Diversity lost: COVID-19 as a phenomenon of the total environment

If we want to learn how to deal with the COVID-19 pandemic, we have to embrace the complexity of this global phenomenon and capture interdependencies across scales and contexts. Yet, we still lack systematic approaches that we can use to deal holistically with the pandemic and its effects. In this Discussion, we first introduce a framework that highlights the systemic nature of the COVID-19 pandemic from the perspective of the total environment as a self-regulating and evolving system comprising of three spheres, the Geosphere, the Biosphere, and the Anthroposphere. Then, we use this framework to explore and organize information from the rapidly growing number of scientific papers, preprints, preliminary scientific reports, and journalistic pieces that give insights into the pandemic crisis. With this work, we point out that the pandemic should be understood as the result of preconditions that led to depletion of human, biological, and geochemical diversity as well as of feedback that differentially impacted the three spheres. We contend that protecting and promoting diversity, is necessary to contribute to more effective decision-making processes and policy interventions to face the current and future pandemics.

Regional Land Eco-Security Evaluation for the Mining City of Daye in China Using the GIS-Based Grey TOPSIS Method

Regional ecological security assessment is a significant methodology for environmental protection, land utilisation, and human development. This study aims to reveal the regional constraints of ecological resources to overcome the difficulties and complexities in quantification of current models used in land ecosystems. For this purpose, the technique for order preference by similarity to an ideal solution (TOPSIS) was linked to a grey relational analysis and integrated with a geographic information system. The obtained method was used to construct a land eco-security evaluation on a regional scale for application in a traditional mining city, Daye, in central China. Parameter analysis was introduced to the method to produce a more realistic spatial distribution of eco-security. Subsequently, based on the pressure–state–response framework, the eco-security index was calculated, and the carrying capacity of land resources and population for each sub-region were analysed. The results showed that: (i) very insecure and insecure classes comprised 5.65% and 18.2% of the total area, respectively, highlighting the vulnerable eco-environmental situation; (ii) moderate secure classes areas comprised a large amount of arable land, spanning an area of 494.5 km2; (iii) secure areas were distributed in the northwest, containing mostly water and wetland areas and accounting for 426.3 km2; and (iv) very secure areas were located on the southeastern region, involving traditional woodland with a better vegetation cover and an overall higher eco-environmental quality. In addition, for each sub-region, the extremely low and low ecological security areas were mainly arable and urban lands, which amounted to 305 and 190 km2, respectively. Under the current ecological constraints, sub-region 1 cannot continue supporting the population size in Daye City. The present results demonstrate the accuracy of our methodology, and our method may be used by local managers to make effective decisions for regional environment protection and sustainable use of land resources.

Underestimating the Challenges of Avoiding a Ghastly Future

We report three major and confronting environmental issues that have received little attention and require urgent action. First, we review the evidence that future environmental conditions will be far more dangerous than currently believed. The scale of the threats to the biosphere and all its lifeforms—including humanity—is in fact so great that it is difficult to grasp for even well-informed experts. Second, we ask what political or economic system, or leadership, is prepared to handle the predicted disasters, or even capable of such action. Third, this dire situation places an extraordinary responsibility on scientists to speak out candidly and accurately when engaging with government, business, and the public. We especially draw attention to the lack of appreciation of the enormous challenges to creating a sustainable future. The added stresses to human health, wealth, and well-being will perversely diminish our political capacity to mitigate the erosion of ecosystem services on which society depends. The science underlying these issues is strong, but awareness is weak. Without fully appreciating and broadcasting the scale of the problems and the enormity of the solutions required, society will fail to achieve even modest sustainability goals.

Agricultural land use and the sustainability of social-ecological systems

Agricultural land expansion and intensification, driven by human consumption of agricultural goods, are among the major threats to environmental degradation and biodiversity conservation. Land degradation can ultimately hamper agricultural production through a decrease in ecosystem services. Thus, designing viable land use policies is a key sustainability challenge. We develop a model describing the coupled dynamics of human demography and landscape composition, while imposing a trade-off between agricultural expansion and in-tensification. We model land use strategies spanning from low-intensity agriculture and high land conversion rates per person to high-intensity agriculture and low land conversion rates per person; and explore their consequences on the long-term dynamics of the coupled human-land system. We seek to characterise the strategies' viability in the long run; and understand the mechanisms that potentially lead to large-scale land degradation and population collapse due to resource scarcity. We show that the viability of land use strategies strongly depends on the land's intrinsic recovery rate. We also find that socio-ecological collapses occur when agricultural intensification is not accompanied by a sufficient decrease in land conversion. Based on these findings we stress the dangers of uninformed land use planning and the importance of precautionary behaviour for land use management and land use policy design.

Demographic Resilience in Local Systems: An Empirical Approach with Census Data

This study estimates demographic resilience in local socioeconomic systems of Southern Europe using long-term population dynamics. We assume attractive places with a continuously expanding (resident) population as ‘demographically resilient’, and locations experiencing a persistent decline of population as more fragile to external shocks. Based on these premises, a comprehensive assessment of demographic resilience in more than 1000 municipalities along the urban–rural gradient in Greece, a Mediterranean country with marked regional disparities, was carried out between 1961 and 2011. Municipalities were considered representative of homogeneous local communities, especially in rural areas. The results of non-parametric correlations suggest how basic geographical gradients (coastal–inland and urban–rural) have significantly influenced the demographic resilience of Greek municipalities. These findings outline two contrasting spatial patterns that reflect (i) continuous expansion of peri-urban local communities and (ii) a particularly intense rural shrinkage, linking depopulation to land abandonment and scarce accessibility of inland districts. While long-term population growth in Greece has progressively re-shaped the intrinsic divide in urban and rural areas, the traditional gap in central and peripheral districts is still reflected in the spatial polarization between the ‘demographically resilient’, socially dynamic coastal locations and the ‘demographically fragile’ inland, economically marginal places. These results indicate the persistence of a center–periphery model characterizing long-term settlement expansion in Greece, with spatial patterns delineating ‘resilient’ and ‘fragile’ districts based essentially on infrastructures, accessibility, and amenities.

Population Trends and Urbanization: Simulating Density Effects Using a Local Regression Approach

Density-dependent population growth regulates long-term urban expansion and shapes distinctive socioeconomic trends. Despite a marked heterogeneity in the spatial distribution of the resident population, Mediterranean European countries are considered more homogeneous than countries in other European regions as far as settlement structure and processes of metropolitan growth are concerned. However, rising socioeconomic inequalities among Southern European regions reflect latent demographic and territorial transformations that require further investigation. An integrated assessment of the spatio-temporal distribution of resident populations in more than 1000 municipalities (1961–2011) was carried out in this study to characterize density-dependent processes of metropolitan growth in Greece. Using geographically weighted regressions, the results of our study identified distinctive local relationships between population density and growth rates over time. Our results demonstrate that demographic growth rates were non-linearly correlated with other variables, such as population density, with positive and negative impacts during the first (1961–1971) and the last (2001–2011) observation decade, respectively. These findings outline a progressive shift over time from density-dependent processes of population growth, reflecting a rapid development of large metropolitan regions (Athens, Thessaloniki) in the 1960s, to density-dependent processes more evident in medium-sized cities and accessible rural regions in the 2000s. Density-independent processes of population growth have been detected in the intermediate study period (1971–2001). This work finally discusses how a long-term analysis of demographic growth, testing for density-dependent mechanisms, may clarify the intrinsic role of population concentration and dispersion in different phases of the metropolitan cycle in Mediterranean Europe.

Topography and human pressure in mountain ranges alter expected species responses to climate change

Climate change is leading to widespread elevational shifts thought to increase species extinction risk in mountains. We integrate digital elevation models with a metric of human pressure to examine changes in the amount of intact land area available for species undergoing elevational range shifts in all major mountain ranges globally (n = 1010). Nearly 60% of mountainous area is under intense human pressure, predominantly at low elevations and mountain bases. Consequently, upslope range shifts generally resulted in modeled species at lower elevations expanding into areas of lower human pressure and, due to complex topography, encountering more intact land area relative to their starting position. Such gains were often attenuated at high elevations as land-use constraints diminished and topographic constraints increased. Integrating patterns of topography and human pressure is essential for accurate species vulnerability assessments under climate change, as priorities for protecting, connecting, and restoring mountain landscapes may otherwise be misguided.

It is often assumed that many species will move upslope in mountainous regions as the climate warms. However, the authors show here that as many species move to higher elevations they will enter areas of lower human footprint but potentially more constraining topography.

Dynamics of a birth-death process based on combinatorial innovation

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth-death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters (P, α). This process exhibits a characteristic 'hockey-stick' behaviour: a long period of relatively little growth followed by a relatively sudden 'explosive' increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity.

Population Dynamics and Agglomeration Factors: A Non-Linear Threshold Estimation of Density Effects

Although Southern Europe is relatively homogeneous in terms of settlement characteristics and urban dynamics, spatial heterogeneity in its population distribution is still high, and differences across regions outline specific demographic patterns that require in-depth investigation. In such contexts, density-dependent mechanisms of population growth are a key factor regulating socio-demographic dynamics at various spatial levels. Results of a spatio-temporal analysis of the distribution of the resident population in Greece contributes to identifying latent (density-dependent) processes of metropolitan growth over a sufficiently long time interval (1961-2011). Identification of density-dependent patterns of population growth contributes to the analysis of socioeconomic factors underlying demographic divides, possibly distinguishing between the effects of population concentration and dispersion. Population growth rates were non-linearly correlated with population density, highlighting a positive (or negative) impact of urban concentration on demographic growth when population is lower (or higher) than a fixed threshold (2800 and 1300 inhabitants/km2 in 1961 and 2011, respectively). In a context of low population density (less than 20 inhabitants/km2), the relationship between density and growth was again negative, contrasting with the positive and linear relationship observed in denser contexts. This result evidences a sort of ‘depopulation’ trap that leads to accelerated population decline under a defined density threshold. An improved understanding of density-dependent mechanisms of population growth and decline contributes to rethinking strategies of sustainable development and social policies more adapted to heterogeneous regional contexts.

Evaluation and Forewarning Management of Regional Resources and Environment Carrying Capacity: A Case Study of Hefei City, Anhui Province, China

The evaluation of resources and environment carrying capacity (RECC) is the basis of strategic policy for the development and utilization of regional resources, economic development, and environmental protection. The magnitude of carrying capacity of resources and environment is the result of the balance of multiple aspects including economy, resources, and society. In order to reflect this multi-dimensional vector relationship, a multi-level and multi-targeted evaluation index system needs to be constructed. The paper, adopting the analytic hierarchy process and including PM2.5 (Particulate matter with diameter less than or equal to 2.5 microns in the atmosphere) into the index system, establishes the evaluation system of regional RECC and analyzes the trend of RECC in Hefei city with the index system to put forward the countermeasures of forewarning management. The results are shown as follows: (1) Overall, the RECC in Hefei city presents a declining trend, with a reduction from a middle to lower level during the year 2009 to 2013, of which the year 2010 to 2011 showed the fastest decline and the year 2013 witnessed a slight increase; (2) from the perspective of mutual influence of indexes, the main reason causing the decline of RECC in Hefei city is that the natural resources and environment carrying capacity was in a declining trend from the year 2009 to 2013, respectively declining from middle and high levels to a lower level, while the social economy carrying capacity in Hefei city was in an increasing trend as a whole from the year 2009 to 2013, with an increase from lower level to middle level. From the perspective of the forewarning management of RECC, it focuses on improving the forewarning response system of regional resources and environment carrying capacity, establishes the sharing mechanism of RECC monitoring data and improves the responsibility assigning mechanism of RECC. The study enriches the evaluation index system of RECC and proves that it is reasonable and efficient to build a differentiated index system to scientifically recognize RECC in different regions, having reference value to evaluate similar regional RECC.

Resources and Environmental Pressure, Carrying Capacity, And Governance: A Case Study of Yangtze River Economic Belt

The analysis of the relationship between regional resources and environment and human activities plays an important role in sustainable regional development. This study proposes the pressure–capacity–governance (PCG) model, an analytic framework for the assessment of the resources and environmental pressure (REP), carrying capacity (RECC) and governance (REG) levels over a large watershed scale, with the Yangtze River Economic Belt (YREB) as the study area. A limiting factor analysis is used to recognize the limiting factors of the regional RECC. The coupling analysis of resources and environmental pressure–capacity–governance identifies the regional potential and utilization direction. The research results are as follows. (1) The REP, RECC and REG levels of the YREB exhibit spatial differences. The REPs of the upper reaches are lower than those of the lower reaches, which does not match the RECC but matches the REG levels. (2) The proportions of unused land, water resources, and atmospheric environmental quality are the main limiting factors of the regional RECC. (3) The PCG analysis framework is used as the basis to divide the YREB into several subareas to analyse the resources and environmental potential carrying capacity and utilization direction of different types of region. This research may provide decision-making references for regional sustainable development at the large watershed scale.

Human progress and drought sensitivity behavior

OBJECTIVES

Human progress is the satisfaction of human needs associated with life quality, social and economic justice. Considering that climate had significant effect on socio-economic behavior of Earth populations, the objective of this work was to evaluate the relationship between human progress and drought sensitivity behavior in Minas Gerais State, Brazil.

METHODS

The human progress variable was generated by principal component analysis, considering the factors: Territorial occupation of the population, dependency ratio, urbanization degree, income, habitation, health, education, sanitation, security and human development index. The moisture index product was generated based on map algebra calculation in GIS, using WorldClim precipitation and MODIS evapotranspiration products. Nonlinear least squares method and Levenberg-Marquardt algorithm fit an exponential model to the moisture index (independent) and human progress (dependent) variables. Covariance and crossed-covariance functions were used to characterize the structure and magnitude of spatial dependence between the human progress and the moisture index co-variable.

RESULTS

Couple modeling human progress and moisture index variability generated the human drought sensitivity behavior variable, representing the effects of regional climate in Homo sapiens population. The generated human drought sensitivity behavior values were inverted, i.e. lower and higher human drought sensitivity behavior values indicated higher and lower human sensitivity to drought, respectively. Adaptive management capacity with more capable governments combining economic and engineering solutions to maximize species, habitat, ecosystem survival and resilience, could generate best mitigation solutions to reduce potential impacts of climatic spatial variation in Minas Gerais state, Brazil.

Steering eco-evolutionary game dynamics with manifold control

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Thermal Stress and Resilience of Corals in a Climate-Changing World

Coral reef ecosystems are under the direct threat of increasing atmospheric greenhouse gases, which increase seawater temperatures in the oceans and lead to bleaching events. Global bleaching events are becoming more frequent and stronger, and understanding how corals can tolerate and survive high-temperature stress should be accorded paramount priority. Here, we review evidence of the different mechanisms that corals employ to mitigate thermal stress, which include association with thermally tolerant endosymbionts, acclimatisation, and adaptation processes. These differences highlight the physiological diversity and complexity of symbiotic organisms, such as scleractinian corals, where each species (coral host and microbial endosymbionts) responds differently to thermal stress. We conclude by offering some insights into the future of coral reefs and examining the strategies scientists are leveraging to ensure the survival of this valuable ecosystem. Without a reduction in greenhouse gas emissions and a divergence from our societal dependence on fossil fuels, natural mechanisms possessed by corals might be insufficient towards ensuring the ecological functioning of coral reef ecosystems.

Metapopulation model for a prey-predator system: Nonlinear migration due to the finite capacities of patches

Many species live in spatially separated patches, and individuals can migrate between patches through paths. In real ecosystems, the capacities of patches are finite. If a patch is already occupied by the individuals of some species, then the migration into the patch is impossible. In the present paper, we deal with prey-predator system composed of two patches. Each patch contains a limited number of cells, where the cell is either empty or occupied by an individual of prey or predator. We introduce "swapping migration" defined by the exchange between occupied and empty cells. An individual can migrate, only when there are empty cells in the destination patch. Reaction-migration equations in prey-predator system are presented, where the migration term forms nonlinear function of densities. We numerically solve equilibrium densities, and find that the population dynamics are largely affected by nonlinear migration. Not only extinction points but also the responses to the environmental changes crucially depend on the patch capacities.

Fractal Logistic Equation

In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving fractal differential equations and finding approximate analytical solutions. Fractal differential equations are solved by using the fractal Euler method. Furthermore, fractal logistic equations and functions are given, which are useful in modeling growth of elements in sciences including biology and economics.

Validation of the hypothesis on carrying capacity limits using the water environment carrying capacity

The concept of "carrying capacity" has been widely used in various disciplines in reference to human-environment sustainability. No unified cognition exists regarding carrying capacity limits for humans. As a typical type of carrying capacity, the water environment carrying capacity (WECC) has been researched for human-water environment sustainability. However, most recent research has focused on the assessment of the water environment carrying capacity of a certain region or river basin. The detailed resilience potential of human-water environment systems that could improve the local water environment carrying capacity has not been systematically exploited. The key concerns of the existence of water environment carrying capacity limits and the exact value have not been addressed. This study first distinguished the characteristics of related concepts, such as carrying capacity, planetary boundaries, resilience, limitations, thresholds and tipping points. An analytical framework was then established to exploit the resilience potential from the four dimensions of "scale, structure, pattern and network". The economy scale with full use of the resilience potential is 11,511,880 M yuan under the current technology and development status, which is nearly 37 times that of the current scale of the economy. The analytical framework confirms that the limit on the water environment carrying capacity is a dynamic value, which could be changed from the four dimensions. The socioeconomic scale that the local water environment can support would be nearly unlimited in some extreme ideal situation. The results would provide some enlightenment on the carrying capacity and other similar marked concepts of theoretical research and provide support for human-environment sustainability.

An evolving assessment model for environmental carrying capacity: A case study of coral reef islands

Environmental carrying capacity (ECC) provides an insight into measuring sustainability of the vulnerable coral reef islands. However, an integrated assessment of ECC on the social-ecological system of reef islands is rarely existence. And conventional approaches miss addressing the difference of social development, which would lead to a misinterpretation of sustainable development of reef island system. This study develops an evolving model of RI-ECC which incorporates five specific development phases, and the assessment involves (1) identification and measurement of carrying components, (2) supply/demand surplus analysis of indicators and (3) ECC states determination. A case study is conducted in Zhaoshu Island of China, indicating the efficiency of RI-ECC model and serving as a reference for adaptive management.

Climate change will constrain the rapid urban expansion in drylands: A scenario analysis with the zoned Land Use Scenario Dynamics-urban model

Evaluation of climate change impacts (CCIs) on urban expansion is important to improving the urban sustainability in drylands. Taking the agro-pastoral transitional zone of northern China (APTZNC) as an example, this study evaluates potential CCIs on urban expansion in 2015-2050. First, we set up six climate change scenarios (CCSs) based on the simulated results of global climate model and regional climate model under different representative concentration pathways. Then, we simulate regional urban expansion under the different CCSs using the zoned Land Use Scenario Dynamics-urban (LUSD-urban) model. We find that climate change will be a key factor that affects urban expansion in this region. The urban land affected by climate change in the entire region will increase from 20.24-26.48 km² (2020) to 119.71-339.26 km² (2050), an increase of 4.91-11.81 times. The CCIs on urban expansion will be the most significant in the mid-western region. In 2050, the urban land potentially affected by climate change will be 98.70-213.88 km², which is 42.26%-134.12% of the urban land in the entire region. To improve urban sustainability in the APTZNC, effective measures must be adopted to mitigate and adapt to CCIs on urban expansion.

Estimating recent migration and population-size surfaces

In many species a fundamental feature of genetic diversity is that genetic similarity decays with geographic distance; however, this relationship is often complex, and may vary across space and time. Methods to uncover and visualize such relationships have widespread use for analyses in molecular ecology, conservation genetics, evolutionary genetics, and human genetics. While several frameworks exist, a promising approach is to infer maps of how migration rates vary across geographic space. Such maps could, in principle, be estimated across time to reveal the full complexity of population histories. Here, we take a step in this direction: we present a method to infer maps of population sizes and migration rates associated with different time periods from a matrix of genetic similarity between every pair of individuals. Specifically, genetic similarity is measured by counting the number of long segments of haplotype sharing (also known as identity-by-descent tracts). By varying the length of these segments we obtain parameter estimates associated with different time periods. Using simulations, we show that the method can reveal time-varying migration rates and population sizes, including changes that are not detectable when using a similar method that ignores haplotypic structure. We apply the method to a dataset of contemporary European individuals (POPRES), and provide an integrated analysis of recent population structure and growth over the last ∼3,000 years in Europe.

We introduce a novel statistical method to infer migration rates and population sizes across space in recent time periods. Our approach builds upon the previously developed EEMS method, which infers effective migration rates under a dense lattice. Similarly, we infer demographic parameters under a lattice and use a (Voronoi) prior to regularize parameters of the model. However, our method differs from EEMS in a few key respects. First, we use the coalescent model parameterized by migration rates and population sizes while EEMS uses a resistance model. As another key difference, our method uses haplotype data while EEMS uses the average genetic distance. A consequence of using haplotype data is that our method can separately estimate migration rates and population sizes, which in essence is done by using a recombination rate map to calibrate the decay of haplotypes over time. An additional useful feature of haplotype data is that, by varying the lengths analyzed, we can infer demography associated with different recent time periods. We call our method MAPS for estimating Migration And Population-size Surfaces. To illustrate MAPS on real data, we analyze a genome-wide SNP dataset on 2224 individuals of European ancestry.