Modeling the Pre-Industrial Roots of Modern Super-Exponential Population Growth

To Malthus, rapid human population growth—so evident in 18th Century Europe—was obviously unsustainable. In his Essay on the Principle of Population, Malthus cogently argued that environmental and socioeconomic constraints on population rise were inevitable. Yet, he penned his essay on the eve of the global census size reaching one billion, as nearly two centuries of super-exponential increase were taking off. Introducing a novel extension of J. E. Cohen''s hallmark coupled difference equation model of human population dynamics and carrying capacity, this article examines just how elastic population growth limits may be in response to demographic change. The revised model involves a simple formalization of how consumption costs influence carrying capacity elasticity over time. Recognizing that complex social resource-extraction networks support ongoing consumption-based investment in family formation and intergenerational resource transfers, it is important to consider how consumption has impacted the human environment and demography—especially as global population has become very large. Sensitivity analysis of the consumption-cost model''s fit to historical population estimates, modern census data, and 21^st Century demographic projections supports a critical conclusion. The recent population explosion was systemically determined by long-term, distinctly pre-industrial cultural evolution. It is suggested that modern globalizing transitions in technology, susceptibility to infectious disease, information flows and accumulation, and economic complexity were endogenous products of much earlier biocultural evolution of family formation''s embeddedness in larger, hierarchically self-organizing cultural systems, which could potentially support high population elasticity of carrying capacity. Modern super-exponential population growth cannot be considered separately from long-term change in the multi-scalar political economy that connects family formation and intergenerational resource transfers to wider institutions and social networks.     

Deforestation and land farming as regulators of population size and climate

This work reveals that deforestation and farming of the cleared land may be considered as regulators of the size of world population and climate. When the green matter is cleared, it decomposes, oxidizes, and releases to the climate the heat of carbon conversion to carbon dioxide. The farmed land provides carrying capacity that sustains population growth. As world population grows, energy consumption increases. Most of this energy has been fossil fuel based, and the heat released is gained by the climate. Warming of the surface and population growth are thus processes that depend on land clearing and conversion into farmland. If deforestation increases, the size of the farmland increases, population size increases, and the surface accumulates heat and vice versa. Therefore, analyses of the correlation between deforestation, population growth, and climate change may have merit for research and society. Through 1990, deforestation has contributed at least 36% of the total heat added to the surface. Therefore, deforestation contribution to climate change is substantial. At the current rate of deforestation, the world population may approach 14.5 billion by the year 2100. Should deforestation decrease and approach zero by then, the world population may steady at nearly 10.3 billion instead.     

People, species richness and human population growth

Aim To investigate how the magnitude of conservation conflicts arising from positive relationships between human population size and species richness is altered during a period of marked human population growth (2% year^?1). Location South Africa. Methods Anuran and avian species richness were calculated from atlas distribution maps, and human population was measured in 1996 and 2001, all at a quarter‐degree resolution. We investigated the relationships between human population size in, and its change during, these two periods and environmental energy availability. We then investigated the nature of relationships between species richness and human population size in both time periods, and its change during them; these analyses were conducted both with and without taking environmental energy availability into account. Finally, we investigated the nature of the relationships between human population size, and its change, and the proportion of protected land. Analyses were conducted both without and with taking spatial autocorrelation into account; the latter was achieved using mixed models that fitted a spatial covariance structure to the data. Results Change in human population size between 1996 and 2001 exhibited marked spatial variation, with both large increases and decreases, but was poorly correlated with environmental energy availability. The nature of the relationship between human population size and environmental energy availability did not, however, exhibit statistically significant differences regardless of whether the former was measured in 1996 or 2001. Similarly, relationships between species richness and human population size did not exhibit significant differences between the two periods. The strengths of the species–human relationships were markedly reduced when energy availability was taken into account. Change in human population size was poorly correlated with species richness. The proportion of protected land was negatively, albeit rather weakly, correlated with human population size in 1996 and 2001, and with its change between these two periods. Main conclusions Positive species–human relationships arise largely, but not entirely, because both species richness and human population size exhibit similar responses to environmental energy availability. During a period of rapid human population growth, and marked changes in the spatial variation in human population size, positive correlations remained between human population size and both anuran and avian species richness. The slope of these correlations did not, however, alter, and the most species‐rich areas are not those with the largest increases in human population. Despite marked population growth, the magnitude of conservation conflicts arising from positive species–human relationships thus appears to have remained largely unchanged.     

Population size dependent incidence in models for diseases without immunity

Epidemiological models of SIS type are analyzed to determine the thresholds, equilibria, and stability. The incidence term in these models has a contact rate which depends on the total population size. The demographic structures considered are recruitment-death, generalized logistic, decay and growth. The persistence of the disease combined with disease-related deaths and reduced reproduction of infectives can greatly affect the population dynamics. For example, it can cause the population size to decrease to zero or to a new size below its carrying capacity or it can decrease the exponential growth rate constant of the population.     

Characterization of the acclimation period before anaerobic dehalogenation of halobenzoates

The acclimation periods prior to detectable dehalogenation of halogenated benzoates in anaerobic lake sediments ranged from 3 weeks to 6 months. These acclimation periods were reproducible over time and among sampling sites and were characteristic of the chemical tested. The lengthy acclimation period appears to represent an induction phase in which little or no aryl dehalogenation is observed, followed by an exponential increase in activity typical of an enrichment response. Continuous growth from the time of the first exposure to the chemical is inconsistent with the extremely low per-cell activities estimated for the early days of the acclimation period and the fact that the dehalogenation yields no carbon to support microbial growth. The finding of a characteristic acclimation time for each chemical argues against nutritional deficiency, inhibition, or predation as an explanation for this phase of metabolism, while the reproducibility of the findings with time and space and among replicates argues against genetic changes as the explanation. The acclimation times did correlate with the eventual dehalogenation rates. This may reflect the general energy limitations in the anaerobic communities and suggests that those chemicals with faster dehalogenation rates provide more energy for the induction and growth phases of the active population.     

Characterization of the acclimation period before anaerobic dehalogenation of halobenzoates.

The acclimation periods prior to detectable dehalogenation of halogenated benzoates in anaerobic lake sediments ranged from 3 weeks to 6 months. These acclimation periods were reproducible over time and among sampling sites and were characteristic of the chemical tested. The lengthy acclimation period appears to represent an induction phase in which little or no aryl dehalogenation is observed, followed by an exponential increase in activity typical of an enrichment response. Continuous growth from the time of the first exposure to the chemical is inconsistent with the extremely low per-cell activities estimated for the early days of the acclimation period and the fact that the dehalogenation yields no carbon to support microbial growth. The finding of a characteristic acclimation time for each chemical argues against nutritional deficiency, inhibition, or predation as an explanation for this phase of metabolism, while the reproducibility of the findings with time and space and among replicates argues against genetic changes as the explanation. The acclimation times did correlate with the eventual dehalogenation rates. This may reflect the general energy limitations in the anaerobic communities and suggests that those chemicals with faster dehalogenation rates provide more energy for the induction and growth phases of the active population.     

Effects of body size and temperature on population growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.     

Climate change and large‐scale human population collapses in the pre‐industrial era

Aim It has long been assumed that deteriorating climate (cooling and warming above the norm) could shrink the carrying capacity of agrarian lands, depriving the human population of sufficient food. Population collapses (i.e. negative population growth) follow. However, this human–ecological relationship has rarely been verified scientifically, and evidence of warming‐caused disaster has never been found. This research sought to explore quantitatively the temporal pattern, spatial pattern and triggers of population collapses in relation to climate change at the global scale over 1100 years. Location Various countries/regions in the Northern Hemisphere (NH) during the pre‐industrial era. Methods We performed time‐series analysis to examine the association between temperature change and country‐wide/region‐wide population collapses in different climatic zones. All of the known population collapse incidents in the NH in the period ce 800–1900 were included in our data analysis. Results Nearly 90% of population collapses in various NH countries/regions occurred during periods of climate deterioration characterized by shrinking carrying capacity of the land. In addition, we found that cooling dampened the human ecosystem and brought about 80% of the collapses in warmer humid, cooler humid and dry zones, while warming adversely affected the ecosystems in dry and tropical humid zones. All of the population collapses and growth declines in periods of warm climate occurred in dry and tropical humid zones. Malthusian checks (famines, wars and epidemics) were the dominant triggers of population collapses, which peaked dramatically when climate deteriorated. Main conclusions Global demographic catastrophes and most population collapse incidents occurred in periods with great climate change, owing to overpopulation caused by diminished carrying capacity of the land and the resultant outbreak of Malthusian checks. Impacts of cooling or warming on land carrying capacity varied geographically, as a result of the diversified ecosystems in different parts of the Earth. The observed climate–population synchrony challenges Malthusian theory and demonstrates that it is not population growth alone but climate‐induced subsistence shortage and population growth working synergistically, that cause large‐scale human population collapses on the long‐term scale.     

Dynamic models of infectious diseases as regulators of population sizes

Five SIRS epidemiological models for populations of varying size are considered. The incidences of infection are given by mass action terms involving the number of infectives and either the number of susceptibles or the fraction of the population which is susceptible. When the population dynamics are immigration and deaths, thresholds are found which determine whether the disease dies out or approaches an endemic equilibrium. When the population dynamics are unbalanced births and deaths proportional to the population size, thresholds are found which determine whether the disease dies out or remains endemic and whether the population declines to zero, remains finite or grows exponentially. In these models the persistence of the disease and disease-related deaths can reduce the asymptotic population size or change the asymptotic behavior from exponential growth to exponential decay or approach to an equilibrium population size.Research supported by Centers for Disease Control contract 200-87-0515. Support services provided at the University of Iowa Center for Advanced Studies     

Process and measurement errors of population size: their mutual effects on precision and bias of estimates for demographic parameters

Knowing the parameters of population growth and regulation is fundamental for answering many ecological questions and the successful implementation of conservation strategies. Moreover, detecting a population trend is often a legal obligation. Yet, inherent process and measurement errors aggravate the ability to estimate these parameters from population time-series. We use numerical simulations to explore how the lengths of the time-series, process and measurement error influence estimates of demographic parameters. We first generate time-series of population sizes with given demographic parameters for density-dependent stochastic population growth, but assume that these population sizes are estimated with measurement errors. We then fit parameters for population growth, habitat capacity, total error and long-term trends to the ‘measured’ time-series data using non-linear regression. The length of the time-series and measurement error introduce a substantial bias in the estimates for population growth rate and to a lesser degree on estimates for habitat capacity, while process error has little effect on parameter bias. The total error term of the statistical model is dominated by process error as long as the latter is larger than the measurement error. A decline in population size is difficult to document as soon as either error becomes moderate, trends are not very pronounced, and time-series are short (<10–15 seasons). Detecting an annual decline of 1% within 6-year reporting periods, as required for the European Union for the species of Community Interest, appears unachievable.     

Fission yeast cells grow approximately exponentially

How the rate of cell growth is influenced by cell size is a fundamental question of cell biology. The simple model that cell growth is proportional to cell size, based on the proposition that larger cells have proportionally greater synthetic capacity than smaller cells, leads to the prediction that the rate of cell growth increases exponentially with cell size. However, other modes of cell growth, including bilinear growth, have been reported. The distinction between exponential and bilinear growth has been explored in particular detail in the fission yeast Schizosaccharomyces pombe. We have revisited the mode of fission yeast cell growth using high-resolution time-lapse microscopy and find, as previously reported, that these two growth models are difficult to distinguish both because of the similarity in shapes between exponential and bilinear curves over the two-fold change in length of a normal cell cycle and because of the substantial biological and experimental noise inherent to these experiments. Therefore, we contrived to have cells grow more than twofold, by holding them in G2 for up to 8 h. Over this extended growth period, in which cells grow up to 5.5-fold, the two growth models diverge to the point that we can confidently exclude bilinear growth as a general model for fission yeast growth. Although the growth we observe is clearly more complicated than predicted by simple exponential growth, we find that exponential growth is a robust approximation of fission yeast growth, both during an unperturbed cell cycle and during extended periods of growth.     

Clutch size variation and morphology in a cyclomorphic Bosmina population

Clutch size, cyclomorphosis and allometric growth were analysedin a population of the humpbacked Bosmina (E.) coregoni gibbera.This species shows cyclomorphosis in antennule length and bodyheight, traits that may reduce predation risk from Leptodorakindtii. Individuals with long antennule and extreme body heightmay pay a cost in terms of decreased reproductive capacity.On the other hand, increasing the body height may be a way toincrease the brood chamber volume during periods of good foodconditions. We tested these hypotheses by comparing the seasonalvariation in clutch size with the seasonal variation in morphology.Antennule length and body height increased from mid-May to Augustand showed usually positive allometry at times with high populationdensities of the predatory cladoceran Leptodora kindtii. Clutchsize decreased from spring to late summer contrary to the hypothesisthat cyclomorphosis in height is caused by a seasonal variationin reproductive demand. However, within-dates antennule lengthwas negatively related and body height was positively relatedto clutch size. We conclude that the long antennule may imposea cost that reduces the reproductive capacity. The hypothesisthat carapace cyclomorphosis is driven by seasonally varyingclutch sizes was rejected.     

Estimating population growth rates from stochastic Leslie matrices

Stochastic versions of exponential growth models predict that even when r or λ values calculated from mean vital statistics indicate exponential growth, most of the individual populations may become extinct. Several recent papers have considered this problem and some misunderstanding has arisen due to the difference between mathematical expectation of population size and most likely course of population growth. We replicated Boyce's (1977, 1979) simulations of population growth with age structure and a single randomly varying vital statistic, and reconciled some of these differences. Mean number can be projected using the dominant eigenvalue of the mean Leslie matrix, but the modal number may be considerably lower. We compared several measures of the rate of growth of the geometric mean or median of numbers and conclude that Tuljapurkar's α is an acceptable measure.     

Home range size and population dynamic

A relationship between home range size and population density is developed. Dynamics of the adjustment of home range size to equilibrium are considered for two cases. When the equilibrial size is constant, actual home range size approaches the equilibrial value in an exponential fashion. When the equilibrial size is a variable determined jointly by many physical and biotic factors, home range size dynamics become complex. The dynamics are treated in the simplified case in which all factors affecting the equilibrial home range size are constant except population density. Equilibrial home range size as determined by population density is defined as the sum of the area available per animal and the per animal overlap of home ranges, with a quadratic function relating overlap to population density. During exponential population growth, home range size becomes constant as the population expands infinitely or contracts toward zero. Actually, home ranges might be disrupted at extreme high or low densities. With logistic growth, home range approaches a stable size between its maximal and minimal values if the carrying capacity lies in the range of population sizes for which the equilibrial home range size is variable.     

Survival of small populations under demographic stochasticity.

We estimate the mean time to extinction of small populations in an environment with constant carrying capacity but under stochastic demography. In particular, we investigate the interaction of stochastic variation in fecundity and sex ratio under several different schemes of density dependent population growth regimes. The methods used include Markov chain theory, Monte Carlo simulations, and numerical simulations based on Markov chain theory. We find a strongly enhanced extinction risk if stochasticity in sex ratio and fluctuating population size act simultaneously as compared to the case where each mechanism acts alone. The distribution of extinction times deviates slightly from a geometric one, in particular for short extinction times. We also find that whether maximization of intrinsic growth rate decreases the risk of extinction or not depends strongly on the population regulation mechanism. If the population growth regime reduces populations above the carrying capacity to a size below the carrying capacity for large r (overshooting) then the extinction risk increases if the growth rate deviates from an optimal r-value.     

From Experiment to Theory: What Can We Learn from Growth Curves?

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic–exponential, exponential–linear, exponential–linear–saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.     

Spare capacity and phenotypic flexibility in the digestive system of a migratory bird: defining the limits of animal design

Flexible phenotypes enable animals to live in environments that change over space and time, and knowing the limits to and the required time scale for this flexibility provides insights into constraints on energy and nutrient intake, diet diversity and niche width. We quantified the level of immediate and ultimate spare capacity, and thus the extent of phenotypic flexibility, in the digestive system of a migratory bird in response to increased energy demand, and identified the digestive constraints responsible for the limits on sustained energy intake. Immediate spare capacity decreased from approximately 50% for birds acclimated to relatively benign temperatures to less than 20% as birds approached their maximum sustainable energy intake. Ultimate spare capacity enabled an increase in feeding rate of approximately 126% as measured in birds acclimated for weeks at −29°C compared with +21°C. Increased gut size and not tissue-specific differences in nutrient uptake or changes in digestive efficiency or retention time were primarily responsible for this increase in capacity with energy demand, and this change required more than 1–2 days. Thus, the pace of change in digestive organ size may often constrain energy intake and, for birds, retard the pace of their migration.     

Widespread rapid reductions in body size of adult salamanders in response to climate change

Reduction in body size is a major response to climate change, yet evidence in globally imperiled amphibians is lacking. Shifts in average population body size could indicate either plasticity in the growth response to changing climates through changes in allocation and energetics, or through selection for decreased size where energy is limiting. We compared historic and contemporary size measurements in 15 Plethodon species from 102 populations (9450 individuals) and found that six species exhibited significant reductions in body size over 55 years. Biophysical models, accounting for actual changes in moisture and air temperature over that period, showed a 7.1–7.9% increase in metabolic expenditure at three latitudes but showed no change in annual duration of activity. Reduced size was greatest at southern latitudes in regions experiencing the greatest drying and warming. Our results are consistent with a plastic response of body size to climate change through reductions in body size as mediated through increased metabolism. These rapid reductions in body size over the past few decades have significance for the susceptibility of amphibians to environmental change, and relevance for whether adaptation can keep pace with climate change in the future.     

Growth autocorrelation and animal size variation

It has long been recognized that variability in animal size is affected by how individual growth rate is autocorrelated in time. Earlier studies have attributed the mechanism generating the autocorrelation primarily to size‐dependent growth rate and autocorrelation in resource abundance. All of these studies have shown that positive autocorrelation in individual growth rate always translates into increased variability in size. We show that energy reserves in individuals induce growth autocorrelation by acting like a low pass filter between the resource and the internal energy that is available for metabolism, growth and reproduction. However, the reserve also reduces the variance in growth rate. Consequently, reserve‐induced growth autocorrelation has relatively little effect on size variability in the population, contradicting existing ideas about the relationship between the growth autocorrelation and size variability.     

Dynamics of an age‐structured population drawn from a random numbers table

I constructed age‐structured populations by drawing numbers from a random numbers table, the constraints being that within a cohort each number be smaller than the preceding number (indicating that some individuals died between one year and the next) and that the first two‐digit number following 00 or 01 ending one cohort’s life be the number born into the next cohort. Populations constructed in this way showed prolonged existence with total population numbers fluctuating about a mean size and with long‐term growth rate (r) ≈ 0. The populations’ birth rates and growth rates and the females’ per capita fecundity decreased significantly with population size, whereas the death rates showed no significant relationship to population size. These results indicate that age‐structured populations can persist for long periods of time with long‐term growth rates of zero in the absence of negative‐feedback loops between a population’s present or prior density and its birth rate, growth rate, and fecundity, contrary to the assumption of density‐dependent regulation hypotheses. Thus, a long‐term growth rate of zero found in natural populations need not indicate that a population’s numbers are regulated by density‐dependent factors.