In this paper, we study the existence of travelling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct suitable sub/super-solutions and to prove the regularity of travelling wave solutions.

Aging is the subject of various studies by the scientific community and monitoring by responsible institutions. The intensity of aging and the proportion of age groups among various communities differ due to different socio-economic conditions and characteristics. This article researches the impact of the war in Croatia 1991–1995 and postwar living conditions on the divergence of population aging in the ethnically heterogeneous Banija region. The first postwar census in 2001 recorded a population decline of 44.9% compared to the 1991 census. We analyze the effects of the war on changes in ethnic and age structure, as well as their interrelations. The quantitative and qualitative magnitude of these demographic changes in the inter-census period had a decisive influence on the correlation of age and ethnic structure. The article examines whether the relative share of Serbs or Croats in the total population of a settlement affects the average age of the settlement. The results confirmed that the Serbs are older than the Croats, and are in the phase of the most advanced demographic age. These changes raise the question of the demographic future and the biological viability of the Serbs, who were the majority in the region before the war.

The recovery of species’ populations is one of the most challenging tasks in conservation, which is why species recovery is most likely to be successful if it involves as many stakeholders as possible. Podocarpus angustifolius, a tree endemic to Cuba, is potentially threatened by overexploitation, deforestation and expansion of exotic species. In December of 2017, in two protected areas containing the only known subpopulations of this species, we recorded the geographical position, height, and diameter at breast height of each individual, and calculated the extent of occurrence (EOO) and area of occupancy (AOO). We recorded a total of 575 individuals, 174 of which were adult (defined as ≥ 6 m height on the basis of the occurrence of reproductive structures), and most of which occurred in Lomas de Banao Ecological Reserve. The EOO and AOO were 125.8 km2 and 6.0 km2, respectively. All P. angustifolius that remain in the wild are within two protected areas, either in rainforest relicts or in coffee plantations. The size structure indicates a growing population. Based on our findings we recommend that P. angustifolius should be recategorized from Vulnerable (on the IUCN Red List) and Critically Endangered (on the national Red List) to Endangered, based on criterion D (small population size). We recommend the continued reinforcement of the population at Topes de Collantes Natural Protected Landscape and the continued engagement of local stakeholders for the long-term conservation of this species.

This paper studies the periodic trajectories of a novel age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion. To begin with, the system is turned into an abstract non-densely defined Cauchy problem, and a time-lag effect in their interaction is investigated. Next, we acquire that this system appears a periodic orbit near the positive steady state by employing the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, which is also the main result of this article. Finally, in order to illustrate our theoretical analysis more vividly, we make some numerical simulations and give some discussions.

In this paper, we study the principal spectral theory of age-structured models with random diffusion. First, we provide an equivalent characteristic for the principal eigenvalue, the strong maximum principle and a positive strict super-solution. Then, we use the result to investigate the effects of diffusion rate on the principal eigenvalue. Finally, we study how the principal eigenvalue affects the global dynamics of the KPP model and verify that the principal eigenvalue being zero is a critical value.

Each species is subject to various biotic and abiotic factors during growth. This paper formulates a deterministic model with the consideration of various factors regulating population growth such as age-dependent birth and death rates, spatial movements, seasonal variations, intra-specific competition and time-varying maturation simultaneously. The model takes the form of two coupled reaction–diffusion equations with time-dependent delays, which bring novel challenges to the theoretical analysis. Then, the model is analysed when competition among immatures is neglected, in which situation one equation for the adult population density is decoupled. The basic reproduction number $\mathcal{R}_0$ is defined and shown to determine the global attractivity of either the zero equilibrium (when $\mathcal{R}_0\leq 1$ ) or a positive periodic solution ( $\mathcal{R}_0\gt1$ ) by using the dynamical system approach on an appropriate phase space. When the immature intra-specific competition is included and the immature diffusion rate is neglected, the model is neither cooperative nor reducible to a single equation. In this case, the threshold dynamics about the population extinction and uniform persistence are established by using the newly defined basic reproduction number $\widetilde{\mathcal{R}}_0$ as a threshold index. Furthermore, numerical simulations are implemented on the population growth of two different species for two different cases to validate the analytic results.

Chinese tallowtree [Triadica sebifera (L.) Small] has reached unprecedented prevalence in coastal landscapes in the Gulf of Mexico, especially along edge habitat with low competition and abundant resource (e.g., light) availability. This study investigated the spatiotemporal patterns and mechanisms of T. sebifera spread along roadways and fire lines. Triadica sebifera individuals and landscape and community features were surveyed in equally spaced, spatially mapped plots. All T. sebifera individuals were felled to determine tree age and status (seed trees or non-seed bearing trees), and T. sebifera seed and seedling (≤2 yr old) densities and community and landscape features (over- and understory conditions, distance to seed trees) were measured. A zero-inflated negative binomial model was used to evaluate factors affecting T. sebifera seed dispersal and seedling recruitment contributing to the observed spatiotemporal patterns. Introduced into the Grand Bay National Wildlife Refuge around 30 yr ago, T. sebifera trees distribute in clustered patterns along roadways and fire lines and exhibit an exponential growth in density. High T. sebifera seed and seedling densities mainly occurred in sites that are ≤250 m from seed trees or have sparse overstory and high understory grass/herb coverage. With respect to the avian seed dispersal mechanism, the spatiotemporal patterns of T. sebifera spread along roadways and fire lines could be simply characterized by using landscape and community features that influence avian behaviors, including distance to seed trees, overstory tree density, and ground grass/herb coverage.

We analyzed the recent (< 25 yr) spread in New Hampshire, USA, of the exotic tree Kalopanax septemlobus, native to Asia. The invasion was likely initiated by a single tree planted ca. 1972. Our objective was to assess the viability of the invasion, especially in light of the small propagule size. We tallied, mapped, aged, and measured the height and growth of K. septemlobus individuals at two sites, the University of New Hampshire campus (UC) and Thompson Farm (TF), both in Durham. We found over 3,800 plants at UC and 270 at TF in < 120 ha (296 ac) total area. Plant age ranged from 0 to 22 yr, and UC plants were as far as 775 m (2,543 ft) from the purported parent tree. Annual height growth was comparable to midtolerant native trees. Plants occurred in both open and forested habitats, and the mean level of photosynthetically active radiation incident on understory plants was 4 to 6% of full sun. The large population size, shade tolerance, rapid height growth, and ability to sprout from damaged stems suggest potential for K. septemlobus to invade and persist in forests, the most common natural ecosystem in the northeastern United States. We further suggest that small propagule size, likely a single tree, has not prevented K. septemlobus from initiating a spatially extensive and vigorous population. Kalopanax septemlobus has been planted as an ornamental in the northeastern United States, and prevention of region-wide invasion might depend on removal of these trees, even when they occur as single individuals.

To investigate the relative importance of long-distance dispersal vs. diffusion in the invasion of a nonnative plant, we used age structure to infer the contribution to recruitment of external propagule rain vs. within-population reproduction. We quantified the age structure of 14 populations of Amur honeysuckle in a landscape where it recently invaded, in Darke County, OH. We sampled the largest honeysuckle individuals in each population (woodlots), and aged these by counting annual rings in stem cross sections. Individuals in the oldest four 1-yr age classes are assumed to be from external recruitment, given the minimum age at which shrubs reproduce. We used these recruitment rates to model external recruitment over the next 5 yr and used observed age structures to estimate total recruitment. We used the difference between total and external recruitment to infer the rate of internal recruitment. Our findings indicate that recruitment from within the population is of about the same magnitude as immigration in the fifth to seventh year after population establishment, but by years 8 to 9 internal recruitment dominates. At the landscape scale, the temporal-spatial pattern of population establishment supports a stratified dispersal model, with the earliest populations establishing in widely spaced woodlots, about 4 km from existing populations, and these serving as “nascent foci” for diffusion to nearby woodlots. Understanding the relative importance of long-distance dispersal vs. diffusion will inform management, e.g., whether it is more effective to scout for isolated shrubs or remove reproducing shrubs at the edge of invaded areas.

Subsistence hunting can change the demographic structure of wild mammal populations, increasing the proportion of young animals, inducing females to reproduce early and increasing litter sizes. We examined the relationship between hunting pressure and age structure in the Vulnerable white-lipped peccary Tayassu pecari, analysing the distribution of age classes at seven sites in the region Terra do Meio in the Brazilian Amazon. These sites differ in the number of human inhabitants and hence were subject to differing hunting pressures. We completed semi-structured interviews with local people to assess the importance of hunting and of the white-lipped peccary as food. We also estimated the age of hunted white-lipped peccaries by assessing tooth eruption and tooth wear in skulls of hunted individuals. Our results indicated that the white-lipped peccary was the most frequently hunted terrestrial animal in the region. Fishing, followed by hunting, provided the main sources of animal protein. Our data suggest there is no relationship between age structure and hunting at the study sites. The social structure and mobility of white-lipped peccaries seem to minimize the effects of hunting on age structure. Our results, similar to previous studies, show that the age structure of the white-lipped peccary is robust to hunting impacts. Other factors may have stronger effects on age structure than subsistence hunting. We suggest that deforestation may explain the prevalence of older individuals in peccary populations to the north of our study sites.

A general framework for age-structured predator-prey systems is introduced. Individualsare distinguished into two classes, juveniles and adults, and several possibleinteractions are considered. The initial system of partial differential equations isreduced to a system of (neutral) delay differential equations with one or two delays.Thanks to this approach, physically correct models for predator-prey with delay areprovided. Previous models are considered and analysed in view of the above results. ARosenzweig-MacArthur model with delay is presented as an example.

The first UK epizootic of highly pathogenic (HP) H5N1 influenza in wild birds occurred in 2008, in a population of mute swans that had been the subject of ornithological study for decades. Here we use an innovative combination of ornithological, phylogenetic and immunological approaches to investigate the ecology and age structure of HP H5N1 in nature. We screened samples from swans and waterbirds using PCR and sequenced HP H5N1-positive samples. The outbreak's origin was investigated by linking bird count data with a molecular clock analysis of sampled virus sequences. We used ringing records to reconstruct the age-structure of outbreak mortality, and we estimated the age distribution of prior exposure to avian influenza. Outbreak mortality was low and all HP H5N1-positive mute swans in the affected population were <3 years old. Only the youngest age classes contained an appreciable number of individuals with no detectable antibody responses to viral nucleoprotein. Phylogenetic analysis indicated that the outbreak strain circulated locally for ∼1 month before detection and arrived when the immigration rate of migrant waterbirds was highest. Our data are consistent with the hypothesis that HP H5N1 epizootics in wild swans exhibit limited mortality due to immune protection arising from previous exposure. Our study population may represent a valuable resource for investigating the natural ecology and epidemiology of avian influenza.

Dependence of individual reproduction upon the size of the whole population is studied in a general branching process context. The particular feature under scrutiny is that of reproduction changing from supercritical in small populations to subcritical in large populations. The transition occurs when the population size passes a critical threshold, known in ecology as the carrying capacity. We show that populations either die out directly, never coming close to the carrying capacity, or grow quickly towards the carrying capacity, subsequently lingering around it for a time that is expected to be exponentially long in terms of a carrying capacity tending to infinity.

Asiatic lions Panthera leo persica, once confined to the 1,883 km2 Gir Protected Area in Gujarat, India, have in the past 2 decades colonized the adjacent Girnar forest, coastal scrub and agro-pastoral areas covering c. 10,000 km2. In May 2008 the Government of Gujarat declared 180 km2 of the sacred Girnar forests a Wildlife Sanctuary. We obtained data on location, age, gender and group composition of lions in Girnar Wildlife Sanctuary from opportunistic sightings during March–May 2008 and from systematic surveys in April 2008 (six surveys of 3–4 days each), totalling 81 lions on 40 occasions. Of the 81 sightings 43% were in the recruitment age group. Adult sex ratio was 0.87 males : 1 female. In the systematic survey we made 26 sightings of nine individuals, identified from their vibrissae patterns and permanent body markings, and used these for population estimation using a capture–recapture analysis. The population estimate using the best fit null model Mo was 10 ± SE 1.2 giving an adult lion density of 5.6 ± SE 0.7 per 100 km2. Population viability analysis emphasized the importance of immigrants for the persistence of this small population. One immigrant in 2 years reduced the probability of extinction by 16%. Conservation of the habitat matrix to the south-east of the Sanctuary, used as a corridor for movement between Girnar and Gir, by declaring it an eco-sensitive zone would facilitate the long-term survival of the Girnar lion population.