Controlling Population Size Research Articles

Genomic reconstruction reveals impact of population management strategies on modern Galápagos dogs.

Free-breeding dogs have occupied the Galápagos Islands at least since the 1830s; however, it was not until the 1900s that dog populations grew substantially, endangering wildlife and spreading disease.1,2,3,4 In 1981, efforts to control the population size of free-roaming dogs began.1 Yet, there exist large free-roaming dog populations on the islands of Isabela and Santa Cruz whose ancestry has never been assessed on a genome-wide scale. We thus performed a complete genomic analysis of the current Galápagos dog population, as well as historical Galápagos dogs sampled between 1969 and 2003, testing for population structure, admixture, and shared ancestry. Our dataset included samples from 187 modern and six historical Galápagos dogs, together with whole-genome sequences from over 2,000 modern purebred and village dogs. Our results indicate that modern Galápagos dogs are recently admixed with purebred dogs but show no evidence of a population bottleneck related to the culling. Additionally, identity-by-descent analyses reveal evidence of shared shepherd-dog ancestry in the historical dogs. Overall, our results demonstrate that the 1980s culling of dogs was ineffective in controlling population size and did little to reduce genetic diversity, instead producing a stable and expanding population with genomic signatures of modern purebred dogs. The insights from this study can be used to improve population control strategies for the Galápagos Islands and other endangered endemic communities.

Spatiotemporal evolution of county level ecological security based on an emergy ecological footprint model: The case of Dingxi, China

Clarifying the spatiotemporal development of regional ecological security can support decision-making related to coordinated, sustainable regional development. This study used an emergy ecological footprint (EEF) model to analyze spatiotemporal changes in ecological security in the Dingxi region, a fragile-environment area in western China. The results indicated that in all counties in Dingxi, the change trends in emergy ecological carrying capacity per capita (eec) were not significant while spatiotemporal differences in emergy ecological footprint per capita (eef) was significant. Overall, the eef in 2019 is 0.2–1.3 times higher than in 2001(except Minxian), respectively. Zhangxian had the highest eef (2.74 ha/cap), followed by An'ding (1.47 ha/cap), while Minxian was the lowest (0.50 ha/cap). During the study, Minxian recorded an ecological surplus, the ecological pressure index showed a decreasing trend, the ecological security level increased, and sustainable development ability was stronger than in the other counties. Other counties are in a state of ecological deficit and have a high ecological pressure index, and regional ecological security is facing great challenges. Moreover, industrial structure, economic level, urbanization, and population size are the main drivers of ecological security in the Dingxi region, while geographic location and climatic factors are the dominant factors leading to its spatial differences. Therefore, controlling population size, reducing the use of nonrenewable resources, developing land resources appropriately, and using resources efficiently can promote the sustainable development of counties. Our findings could serve as a reference for the ecological construction and economic development of the counties.

Groundwater Vulnerability in a Megacity Under Climate and Economic Changes: A Coupled Sociohydrological Analysis

AbstractGroundwater depletion has become increasingly challenging, and many cities worldwide have adopted drastic policies to relieve water stress due to socioeconomic growth. Located on the declining aquifer of the North China Plain, Beijing, for example, has developed plans to limit the size of the city’s population. However, the effect of population displacement under uncertain macroeconomic and climate change remains ambiguous. We adopt a sociohydrological model, with explicit consideration of the dynamics of human‐water interactions, to explore the groundwater vulnerability of Beijing. We investigate how human response might shape the development trajectories of the groundwater‐population‐economy system under different macroscale economic and climate scenarios. Furthermore, we use a machine learning algorithm to identify the decisive factors to be considered for reducing groundwater vulnerability. Our results show that while rapid external economic development or larger annual average precipitation would enable recovery of the groundwater table in the short term, they may slacken human water shortage awareness and result in more acute groundwater depletion in the long run. Strengthening policymaker perceptions of groundwater depletion would prompt timely response policies for controlling population size. Improving the quantity and quality of labor force input to economic development would avoid downturns in the economy due to labor shortages. The outcomes of this study suggest that these strategies would effectively reduce groundwater vulnerability in the long run without causing severe socioeconomic recession. These findings highlight the importance of endogenizing human behavioral dynamics in sustainable urban water management.

Hunting quotas, selectivity and stochastic population dynamics challenge the management of wild reindeer

Wildlife managers adjust harvest quotas based on population changes and specific management goals, like controlling population size and demography or minimizing human-�wildlife interactions. However, establishing quotas that best meet these goals can be challenging due to e.g. population fluctuations, climate change, and bias or variation in harvest effort. High-Arctic Svalbard reindeer Rangifer tarandus platyrhynchus experience strong interannual variation in population size and demographic structure due to environmental stochasticity. Here, we analyzed the demographic and spatial bias of reindeer harvest in relation to quota regulations, hunter preferences, and population dynamics. Despite the protective management goal to avoid demographic impacts, 30 yr of data revealed that the harvest was consistently biased towards yearlings and male adults. This hunting selectivity resulted from both hunter preferences and the coarse license categories separating ‘calf’, ‘yearling or female adult’, and ‘free choice’ licenses. We developed Bayesian multinomial likelihood models to account for hunting selectivity and optimize annual quota distributions among license categories using population monitoring data. Optimized annual quota distributions varied strongly due to demographic fluctuations associated with strong climate variability, whereas simulated harvest offtakes showed that the protective management goal is inherently challenged by the coarse license categories. Although on average, only 7% of the hunted population was harvested annually, we found strong spatial variation in harvest pressure, with potential implications for spatial population dynamics. Our adaptive management approach accounting for hunting selectivity and demographic fluctuations can be of general relevance for harvested species in stochastic environments.

Adaptation of Population Size in Sine Cosine Algorithm

Sine Cosine Algorithm (SCA) is a newly proposed competent population-based metaheuristic, which has gained a multi-disciplinary interest in solving optimization problems. Like other metaheuristics, the performance of SCA is sensitive to the settings of its parameters and one such parameter is Population Size (PS). There is no one population size that fits all; problem uniqueness requires a matching strategy of parameter selection and adaptation. However, in standard SCA and its variants, PS is treated as a user-controlled parameter and no study has explored the effect of PS adaptation on SCA's performance. To fill this research gap, this study investigates and compares the impact of promising strategies for setting and controlling population size, from other metaheuristics, on the performance of the standard SCA and five of its variants in terms of fitness, run-time, and convergence characteristics. Finding the best PS setting for a metaheuristic is a challenging problem since it depends on both the nature of the algorithm used and the problem being solved. Leading PS adaptation techniques considered in this study are linear staircase reduction, iterative halving, reinitialization and incrementation, pulse wave, population diversity, and three parent crossover strategies. A classic set of 23 well-known benchmark functions has been utilized for a fixed number of evaluations to assess the impact of each PS adaptation strategy on the performance of SCA and its variants. Also, non-parametric Wilcoxon's rank sum test is performed to provide a comprehensive view of various PS adaptation strategies' performance with respect to each other in terms of fitness and run-time. Simulation results reveal that proper selection of PS adaptation strategy can further enhance the exploration and exploitation capabilities of SCA and its variants.

Geographical personality gradient in herbivorous animals: Implications for selective culling to reduce crop damage

AbstractTraditional lethal techniques used to mitigate wildlife damage have targeted entire populations through the use of random harvesting. However, recent literature has suggested that controlling population size by random harvesting is not the only mean to mitigate human‐wildlife conflicts. Controlling problem individuals may also be important because individuals with behavioral characteristics such as greater boldness and low neophobia are predicted to cause more damage to crops. Reducing the number of bold individuals may therefore mitigate crop damage, but a method to selectively cull bold individuals has not been determined. Hence, this study aimed to demonstrate their distribution in native habitats because if bold and shy individuals prefer different habitats, selective culling could target areas preferred by bold individuals. To detect differences in neophobia (i.e., shyness/boldness), 17 visible flash and invisible infrared flash sensor cameras were randomly placed in forest areas based on the assumption that neophobic (shy) sika deer (Cervus nippon) would be deterred by visible flash cameras (a novel stimulus). The relationship between camera flash type and the probability of detection (i.e., of being photographed by a camera) was used as an index of shyness/boldness. Geographical information system and regression analyses showed that bold individuals preferred forested areas near farmland. These results indicate that selective lethal control could be conducted in forest areas near farmlands to mitigate crop damage.

Socioeconomic drivers of urban heat island effect: Empirical evidence from major Chinese cities

Does socioeconomic development result in exacerbation of urban thermal environment? The answer to this question is extremely critical for mitigating and adapting urban heat island effect (UHI). However, such question has not yet been fully understood the details. The aim of this study was to measure the magnitudes and marginal effect of socioeconomic drivers on UHI dynamics in major Chinese cities. We utilized generalized additive model (GAM) for modelling non-linear/linear relations between economic output, population, industrial structure, geographical features and UHI at seasonal and climate-zones level. The results demonstrate socioeconomic factors explain 12 %∼20 % of UHI intensity variations. Urban economic scale generally has a higher contribution rate than variables of population and industrial structure. Urban economic growth raised the heat stress in hot summer. Moreover, a negative linear nexus was observed between the UHI intensity and per capita GDP, indicating that the empirical results supported a post-environmental Kuznets curve (EKC) relationship during the sample period. We suggest both controlling population size and increasing per capita GDP may contribute to mitigate the summer UHI in the tropical cities. Our study highlights macro socioeconomic policy design and urban planning should be combined to counteract or mitigate the UHI.

The importance of population control and macroeconomic stability to reducing environmental degradation: An empirical test of the environmental Kuznets curve for developing countries

The main purpose of this study is to provide empirical evidence of the validity of the Environmental Kuznets Curve (EKC) hypothesis for 86 developing countries, over the period 1972–2011. By applying several econometric methods, our robust results confirm the presence of an EKC for developing economies. Moreover, our findings provide evidence that the achievement of greater economic growth in developing economies has had an impact on environmental degradation. By adding other relevant controls (for instance, population size and economic instability), we find a meaningful response by these variables to environmental degradation. We add evidence to the existing literature that controlling population size and ensuring macroeconomic stability could minimize the possibility of an adverse impact by economic development on situations of environmental degradation in the developing world.

Decomposition analysis of energy-related carbon emissions from the transportation sector in Beijing

In the process of rapid development and urbanization in Beijing, identifying the potential factors of carbon emissions in the transportation sector is an important prerequisite to controlling carbon emissions. Based on the expanded Kaya identity, we built a multivariate generalized Fisher index (GFI) decomposition model to measure the influence of the energy structure, energy intensity, output value of per unit traffic turnover, transportation intensity, economic growth and population size on carbon emissions from 1995 to 2012 in the transportation sector of Beijing. Compared to most methods used in previous studies, the GFI model possesses the advantage of eliminating decomposition residuals, which enables it to display better decomposition characteristics (Ang et al., 2004). The results show: (i) The primary positive drivers of carbon emissions in the transportation sector include the economic growth, energy intensity and population size. The cumulative contribution of economic growth to transportation carbon emissions reaches 334.5%. (ii) The negative drivers are the transportation intensity and energy structure, while the transportation intensity is the main factor that restrains transportation carbon emissions. The energy structure displays a certain inhibition effect, but its inhibition is not obvious. (iii) The contribution rate of the output value of per unit traffic turnover on transportation carbon emissions appears as a flat “M”. To suppress the growth of carbon emissions in transportation further, the government of Beijing should take the measures of promoting the development of new energy vehicles, limiting private vehicles’ increase and promoting public transportation, evacuating non-core functions of Beijing and continuingly controlling population size.

An analysis of diet quality, how it controls fatty acid profiles, isotope signatures and stoichiometry in the malaria mosquito Anopheles arabiensis.

BackgroundKnowing the underlying mechanisms of mosquito ecology will ensure effective vector management and contribute to the overall goal of malaria control. Mosquito populations show a high degree of population plasticity in response to environmental variability. However, the principle factors controlling population size and fecundity are for the most part unknown. Larval habitat and diet play a crucial role in subsequent mosquito fitness. Developing the most competitive insects for sterile insect technique programmes requires a “production” orientated perspective, to deduce the most effective larval diet formulation; the information gained from this process offers us some insight into the mechanisms and processes taking place in natural native mosquito habitats.Methodology/Principal FindingsFatty acid profiles and de-novo or direct assimilation pathways, of whole-individual mosquitoes reared on a range of larval diets were determined using pyrolysis gas chromatograph/mass spectrometry. We used elemental analysis and isotope ratio mass spectrometry to measure individual-whole-body carbon, nitrogen and phosphorous values and to assess the impact of dietary quality on subsequent population stoichiometry, size, quality and isotopic signature. Diet had the greatest impact on fatty acid (FA) profiles of the mosquitoes, which exhibited a high degree of dietary routing, characteristic of generalist feeders. De-novo synthesis of a number of important FAs was observed. Mosquito C:N stoichiometry was fixed in the teneral stage. Dietary N content had significant influence on mosquito size, and P was shown to be a flexible pool which limited overall population size.Conclusions/SignificanceDirect routing of FAs was evident but there was ubiquitous de-novo synthesis suggesting mosquito larvae are competent generalist feeders capable of survival on diet with varying characteristics. It was concluded that nitrogen availability in the larval diet controlled teneral mosquito size and that teneral CN ratio is a sex- and species-specific fixed parameter. This finding has significant implications for overall mosquito competitiveness and environmental management.

Analysis of Sino-Singapore Tianjin Eco-city��s Indicator System

Eco-city, trend of future city, aims at realizing the harmonious development among nature, technology and society. Sino-Singapore Tianjin eco-city (SSTE) is an important joint project between China and Singapore governments. To demonstrate the meaning of establishing eco-city under restrained environment is the major aim of it. SSTE has a broad range of indicators to reflect, detect, evaluate, forecast and promote its development. But whether the indicator system and its drawing up meet the development of eco-city, as well as broader part of city is uncertain. The lack of ready-made experience of the establishment of indicator system and planning management leads to inquiring the rationality and coordinate of the system. This paper tries to analyze the indicator system of SSTE, as well as difficulties in meeting indicators, reasons of difficulty arising and solutions of it, discuss effective means to establish eco-city's indicator system and make use of the function of planning. The theory of eco-city, a model of urban development, was presented in 1981 by former Soviet Union urban ecologist O.Yanitsky, which reflects the deepen cognition of the relationship between human and nature.(1) Our country is in high speed development period of urbanization, avoiding repeating errors made in the analogous period in developed countries is an essential task to us. Our country is also a country with fragile environment and scarce resources. The establishment of SSTE can make an example to the sustainable development of eco-city in restrained resources. The eco-city site is located 40 km from the center of Tianjin and 150 km from Beijing. The site is 10 km from the core district of the Tianjin Binhai New Area, with the southern tip of the site only a 10- minute drive from the Tianjin Economic-Technological Development Area. The eco-city is sited on non-arable land. Prior to development, the site of the eco-city is one-third saltpan, one-third deserted beach, and one-third water, including a 270-hectare wastewater pond. SSTE, which is a key area of our country's development, the pattern of its development demonstrates the methods of developing other parts of our country. The building of eco-city is an inevitable trend of society development. The significance of it is high lightened in the course of city development: controlling population size, upgrading the quality of population, carrying out clean production, making up public transport system, setting green parts in urban area, developing ecological agriculture, improving environment, remitting pressure in the centre of city, regulating the density of regional city and fulfilling indicators of analyzing city. The building of eco-city can make nature and city their true color. The general thinking of building SSTE is: Firstly, to build infrastructures in starting parts. Secondly, according to the master plan's quantitative and qualitative indicators, solve various problems via professional view and systematical analyses. Thirdly, build a resource-saving, environment friendly, suitable living city. SSTE puts forward the Three Harmonies and Three Can guidelines: Three Harmonies refers to harmonies between people and people, people and economical activities, people and environment. Three Can refers to can be realized, can be duplicated, and can be popularized. The major contents of eco-city is: site selection under restrained environment, indicator system based on saving energy, spatial pattern following local environment, slow pattern emphasized transport system, recycle of water resource, harmonious community and digitizing infrastructures. SSTE will be ecologically friendly, existing wetlands and biodiversity will be preserved. Green spaces will be interspersed throughout the city. Located in an area of low rainfall, SSTE will draw a

Nudibranch predation and dietary preference for the polyps of Aurelia labiata (Cnidaria: Scyphozoa)

There is concern that jellyfish blooms may be increasing worldwide. Some factors controlling population size, such as temperature and food, often have been studied; however, the importance of predators is poorly known. Aeolid nudibranchs feed on cnidarians, but their predation on the benthic polyps of scyphozoan rarely has been documented. To understand the potential of nudibranchs to consume polyps, we tested several predation preference hypotheses with the generalist feeding nudibranch, Hermissenda crassicornis, and polyps of the common moon jellyfish, Aurelia labiata. Of the six prey species tested during feeding experiments, A. labiata polyps and the tunicate Distaplia occidentalis were significantly preferred. Nudibranch size, diurnal cycle, and ingestive conditioning did not significantly influence prey choice. Nudibranchs showed significant positive chemotaxis toward living polyps, hydroids, and tunicates, but not to sea anemones. Nudibranch chemotaxis was significantly more positive to polar extract of A. labiata than of D. occidentalis. Consumption of polyps was correlated with nudibranch size, with mean consumption by large nudibranchs (>0.92 g) of about 31 polyps h−1. Three other nudibranch species also ate A. labiata polyps. Our results emphasize the potential importance of predation for controlling jellyfish benthic polyp populations and consequent jellyfish blooms.

Population level effects on Vγ2Vδ2 T cell frequencies in healthy adults: a difference in baseline values and resting phenotypes among Caucasian and African American donors (132.16)

Abstract Adult human γδ T cells are dominated by the Vγ2Vδ2 T cell receptor (TCR) which modulates MHC-unrestricted responses to non-peptidic antigens. This subset is so numerous that between 1 in 40 and 1 in 400 circulating CD3+ T cells will respond to stimulation with isoprenoid pyrophosphates. The normal frequency of Vγ2Vδ2+ cells reflects TCR selection and amplification by chronic antigen stimulation, but the regulatory mechanisms controlling population size have not been described. During clinical studies related to Vγ2Vδ2 T cells in cancer and AIDS, we identified a difference in the circulating populations between Caucasian and African American healthy volunteers. When expressed as the percentage of total lymphocytes, Caucasian donors had 5-times higher levels of Vγ2Vδ2 cells compared to African American donors and phenotypes characteristic of mature functional cells were also different among the groups, including CD56 expression that is linked to cytotoxicity. Analysis of the Vg2 repertoire showed a strikingly lower proportion of cells expressing the Vγ2-Jγ1.2 rearrangement. Our data suggest that distinct regulatory mechanisms, in addition to positive selection and chronic amplification, control Vγ2Vδ2 cell levels in blood and that further study of population level effects may uncover unique regulatory mechanisms that control this interesting population.

Gene Flow, Invasiveness, and Ecological Impact of Genetically Modified Crops

The main environmental concerns about genetically modified (GM) crops are the potential weediness or invasiveness in the crop itself or in its wild or weedy relatives as a result of transgene movement. Here we briefly review evidence for pollen- and seed-mediated gene flow from GM crops to non-GM or other GM crops and to wild relatives. The report focuses on the effect of abiotic and biotic stress-tolerance traits on plant fitness and their potential to increase weedy or invasive tendencies. An evaluation of weediness and invasive traits that contribute to the success of agricultural weeds and invasive plants was of limited value in predicting the effect of biotic and abiotic stress-tolerance GM traits, suggesting context-specific evaluation rather than generalizations. Fitness data on herbicide, insect, and disease resistance, as well as cold-, drought-, and salinity-tolerance traits, are reviewed. We describe useful ecological models predicting the effects of gene flow and altered fitness in GM crops and wild/weedy relatives, as well as suitable mitigation measures. A better understanding of factors controlling population size, dynamics, and range limits in weedy volunteer GM crop and related host or target weed populations is necessary before the effect of biotic and abiotic stress-tolerance GM traits can be fully assessed.

Mediative Fuzzy Logic for Controlling Population Size in Evolutionary Algorithms

In this paper we are presenting an intelligent method for controlling population size in evolutionary algorithms. The method uses Mediative Fuzzy Logic for modeling knowledge from experts about what should be the behavior of population size through generations based on the fitness variance and the number of generations that the algorithm is being stuck. Since, it is common that this kind of knowledge expertise can be susceptible to disagreement in a minor or a major part. We selected Mediative Fuzzy Logic (MFL) as a fuzzy method to achieve the inference. MFL is a novelty fuzzy inference method that can handle imperfect knowledge in a broader way than traditional fuzzy logic does.

DEMOGRAPHIC SHIFT AND PROJECTED LABOUR SHORTAGE IN CHINA

As a result of China's family planning policy of ‘raising population quality and controlling population size’ initiated in the late 1970s, China has accomplished a population transition from high birth rate, low mortality rate and high population growth to low birth rate, low mortality rate and low population growth within a remarkably short timeframe. Along with this population transition, however, comes a shift in population age structure, with a rapid increase in the proportion of elderly people. This paper explores the implications of China's demographic shift for labour supply and suggests policy changes to target an emerging labour shortage.

Effects of Culling Fox Populations at the Landscape Scale: A Spatially Explicit Population Modeling Approach

Understanding how culling practices impact target populations is essential in identifying optimum strategies for controlling population size. Red fox (Vulpes vulpes) populations are subject to attempted control throughout much of their range due to their impacts on livestock and game, and disease transmission (e.g., rabies); however, the efficacy of different methods in controlling fox populations is low. For mesomammal species, experimental approaches are often limited by issues of scale. We used an individual-based, spatially explicit population model to investigate the efficacy of different culling practices in artificial landscapes. Model outputs were the number of social groups, the fox population before and after breeding, the extent of successful dispersal within the landscape, and the number of migrants out of the landscape. We investigated 4 different population management strategies using our model: 1) hunting with hounds, 2) winter shooting, 3) culling at the den in spring, and 4) fertility control. Population density in the absence of control was most strongly related to carrying capacity and the extent of immigration from surrounding fox populations. Culling at the den was most successful at suppressing fox populations, while fertility control was least effective, but the effect depended on the carrying capacity of the landscape. We conclude that effective control of populations at landscape scales (e.g., 1,600 km2) is not feasible or practical unless immigration from outside populations is low or can be controlled. These results can be used to inform policy on the management of United Kingdom (UK) fox populations and contribute to the ongoing debate on hunting with hounds as practiced in the UK.

Population dynamics of Leysera gnaphalodes: a statistical modelling approach

Namaqualand is world-renowned for its mass springtime wildflower displays, common in highly disturbed areas. Leysera gnaphalodes is a short-lived perennial shrub that encroaches on these wildflower displays, lessening their aesthetic appeal. For this reason, populations of L. gnaphalodes need to be kept as small as possible. This is usually achieved by tilling the area regularly, but a less disruptive method would be preferable. Alternatives to this approach were explored. An eight-year study was conducted to determine the effects of tilling, grazing and other environmental factors, including rainfall and temperature, on seedbank and population sizes of L. gnaphalodes . Multivariate statistical models were developed to determine the effects of all of these factors on L. gnaphalodes populations. Tilling was confirmed to be effective in reducing population size, but grazing had no effect. Low rainfall was also effective in controlling population size but had the disadvantage of being out of management control and deleterious to desirable wildflowers.

Prediction of Solar Activity Based on Neuro-Fuzzy Modeling

This paper presents an application of the neuro-fuzzy modeling to analyze the time series of solar activity, as measured through the relative Wolf number. The neuro-fuzzy structure is optimized based on the linear adapted genetic algorithm with controlling population size (LAGA-POP). Initially, the dimension of the time series characteristic attractor is obtained based on the smallest regularity criterion (RC) and the neuro-fuzzy model. Then the performance of the proposed approach, in forecasting yearly sunspot numbers, is favorably compared to that of other published methods. Finally, a comparison predictions for the remaining part of the 22nd and the whole 23rd cycle of the solar activity are presented.

A Monte Carlo simulation model for studying evolution in age‐structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity.