Lyapunov stability for an age-structured population model

This is a short notice on the McKendrick equation that I actually learned from Yu.M. Svirezhev in the 1990s. This McKendrick equation modelling the evolution in time of an age-structured population has received attention recently from mathematicians. The initial and boundary conditions for the McKendrick equation imposed by the population model are not the standard side conditions one sees in PDE theory for an evolution equation. In the simplest case, the problem reduces to a well-known model in demography, the Lotka integral equation.     

Population collapses in the pre-modern period: case study of the Fuping County,Northwest China

The pre-modern history of population change in the Fuping County (Shaanxi Province, China) during the Ming and Qing Dynasties (AD 1368–1911) was reconstructed using historical sources. The Fuping County experienced two major population collapses, i.e. the late Ming Dynasty (1550–1640s) and the 1860–1880s. The first one was caused by the great AD 1556 earthquake and the extreme droughts and warfare in the 1630–1640s. The second one was caused by warfare and extreme droughts. As a whole, natural disasters, including extreme drought and great earthquake, were the key direct causes of population collapse, and climatic cooling would be a potential indirect cause. It is very interesting that population collapses occurred almost synchronously in the Fuping County and whole China, and the trends of population change were also very similar. Climate–population relationship in China would be valid at finer geographic level, and climatic cooling could be a potential indirect cause of population collapse.     

三峡库区农村移民家庭生活安置现状与分析

三峡移民作为迄今为止动迁规模最大、涉及面最广的非自愿性工程移民群体而广受关注。通过2009年大量的抽样调查数据来讨论三峡农村移民家庭的生活安置适应性问题。得到的基本结论：对于三峡库区农村移民家庭适应目前的居住生活,移民家庭的居住条件、医疗保障普遍得到了改善;三峡农村移民家庭的生活也存在生活成本增加和建房费用可能导致的负债隐患,这可能对移民总体的生活安置满意度的选择造成一定的负面影响;三峡农村移民家庭生活安置适应性受到搬迁时间的影响显著。因此,建议关注移民居住生活社会适应一定要与移民生活成本联系紧密;农村移民生活安置工作还要继续完善;移民的适应性与移民的可持续发展还要建立相关体系和指标,做进一步的讨论和研究     

Influence of environmental properties on macrobenthos in the northwest Indian shelf

The paper deals with the standing stock of macrobenthic infauna and associated environmental factors influencing the benthic community in the shelf region of the northwest Indian coast. The data were collected onboard FORV Sagar Sampada during the winter monsoon (January–February, 2003) to understand the community structure and the factors influencing the benthic distribution. The environmental parameters, sediment characteristics and macrobenthic infauna were collected at 26 stations distributed in the depths between 30 and 200 m extending from nobreak{Mormugao} to Porbander. Total benthic abundance was high in lower depths (50–75 m), and low values noticed at 30 m depth contour was peculiar. Polychaetes were the dominant group and were more abundant in shallow and middle depths with moderate organic matter, clay and relatively high dissolved oxygen. On the other hand crustaceans and molluscs were more abundant in deeper areas having sandy sediment and low temperature. High richness and diversity of whole benthic groups observed in deeper depths counter balanced the opposite trend shown by polychaete species. Generally benthos preferred medium grain sized texture with low organic matter and high organic matter had an adverse effect especially on filter feeders. Deposit feeding polychaetes dominated in shallow depths while carnivore species in the middle depths. Ecologically, benthos were controlled by a combination of factors such as temperature, salinity, dissolved oxygen, sand and organic matter and no single factor could be considered as an ecological master factor.     

Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.     

Sperm competition and sexual selection: a meta-analysis of paternity studies of birds

Sperm competition (the competition among the sperm of different males for fertilization of the eggs of a female) has been suggested to be an important component of sexual selection, but no general assessment has been made of this proposition. We used a meta-analytic approach to assess the extensive literature on paternity (the proportion of offspring in a focal nest sired by an attending male) in birds based on allozyme and molecular techniques. The relative variance in male mating success was on average increased by a factor of 4.6 over the variance in apparent male success. Males with more extravagant secondary sexual characters had higher paternity in their own nests than less adorned males. There was a weak effect of male age being positively associated with paternity in own nests. Male body size measured as the length of wing and tarsus was weakly positively associated with paternity in own nests. Male survival prospect was positively associated with paternity in own nests. Polygynous males generally had decreased paternity of their broods compared to monogamous males. Paternity of the resident male decreased with increasing population density and breeding asynchrony. The intensity of paternity guards such as within-pair copulation rate and mate guarding were not significantly related to extra-pair paternity. Sperm competition was thus an important component of sexual selection by increasing the variance in male mating success, and by being associated with the expression of secondary sexual characters, in particular in dense and asynchronously breeding populations of birds. Received: 12 February 1998 / Accepted after revision: 31 May 1998     

A population model for the peach fruit moth, Carposina sasakii Matsumura (Lepidoptera: Carposinidae), in a Korean orchard system

A population model for the peach fruit moth, Carposina sasakii Matsumura, was constructed to understand the population dynamics of this pest species and to develop an effective management strategy for various orchard (apple, peach, apple + peach) systems. The model was structured by the five developmental stages of C. sasakii: egg, larva, pupa, larval-cocoon (overwintering larva), and adult. The model consisted of a series of component models: (1) a bimodal spring adult emergence model, (2) an adult oviposition model, (3) stage emergence models of eggs, larvae, and pupae, (4) a larval survival rate model in fruits, (5) a larval-cocoon formation model, and (6) an insecticide effect model. Simulations using the model described the typical patterns of C. sasakii adult abundance in various orchard systems well, and was specific to the composition of host plants: three adult abundance peaks (first peak, mid-season peak, and last peak) a year with decreased peaks after the first peak in monoculture orchards of late apple, two adult peaks a year with a much higher last peak in monoculture orchards of early peach, and three adult peaks a year with much higher later peaks in mixed orchards of late apple and early peach. The average deviation between model outputs and actual records for first and second adult peak dates was 2.8 and 3.9 d, respectively, in simulations without an insecticide effect. The deviation decreased when insecticide effects were incorporated into the model. We also performed a sensitivity analysis of our model, and suggest possible applications of the model.     

A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.     

The interplay of sex ratio, male success and density-independent mortality affects population dynamics

Environmental constraints can limit a population to a certain size, which is usually called the carrying capacity of a habitat. Besides to this ‘external’ factor, which is mainly determined by the limitation of resources, we investigate here another set of population-intrinsic factors that can limit a population size significantly below the maximum sustainable size. Firstly, density-independent mortality is a prominent factor in all organisms that show age-related and/or accidental death. Secondly, in sexually reproducing organisms the sex ratio and the success of pairing is important for finding reproductive partners. Using a simple model, we demonstrate how sex ratio, mating success and gender-specific mortality can strongly affect the speed of population growth and the maximum population size. In addition, we demonstrate that density-independent mortality, which is often neglected in population models, adds a very important feature to the system: it strongly enhances the negative influence of unbiased sex ratios and inefficient pairing to the maximum sustainable population size. A decrease of the maximum population size significantly affects a population's survival chance in inter-specific competition. Thus, we conclude that the inclusion of density-independent mortality is crucial, especially for models of species that reproduce sexually. We show that density-independent mortality, together with biased sex ratios, can significantly lower the abilities of a population to survive in conditions of strong inter-specific competition and due to the Allee effect. We emphasize that population models should incorporate the sex ratio, male success and density-independent mortality to make plausible predictions of the population dynamics in a gender-structured population. We show that the population size is limited by these intrinsic factors. This is of high ecological significance, because it means that there will always be resources available in any habitat that allows other species (e.g., invaders) to use these resources and settle successfully, if they are sufficiently adapted.