Using singular perturbations to reduce an epidemiological model: application to bovine viral diarrhoea virus within-herd spread

Studying the spread of a pathogen in a managed metapopulation such as cattle herds in a geographical region often requires to take into account both the within- and between-herd transmission dynamics. This can lead to high-dimensional metapopulation systems resulting from the coupling of several within-herd transmission models. To tackle this problem, we aim in this paper at reducing the dimension of a tractable but realistic dynamical system reproducing the within-herd spread. The context chosen to illustrate our purpose is bovine viral diarrhoea virus (BVDV) transmission in a cattle herd structured in two age classes and several epidemiological states, including two infectious states (transiently and persistently infected). Different time scales, corresponding to the epidemiological and demographic processes, are identified which allow to build a reduced model. Singular perturbation technique is used to prove that, under some non-restrictive conditions on parameter values, the behaviour of the original system is quite accurately approximated by that of the reduced system. Simulations are also performed to corroborate the approximation quality. Our study illustrates the methodological interest of using singular perturbations to reduce model complexity. It also rigorously proves the biologically intuitive assumption that transiently infected individuals can be neglected in a homogeneous population, when capturing the global dynamics of BVDV spread.     

Discovery of a novel type of body scale in the marine dinoflagellate,Amphidinium cupulatisquama sp. nov. (Dinophyceae)

A new species of Amphidinium, A. cupulatisquama Tamura et Horiguchi, from sand samples from Ikei Island, Okinawa Prefecture in subtropical Japan, is described based on light, scanning and transmission electron microscopy and the partial sequencing of the large subunit rDNA gene. The species has a typical morphology for the genus, but is distinguished from previously described species by having a combination of the following characteristics: (i) a relatively large cell (over 30 µm in length); (ii) possessing an eyespot on the dorsal side of the cingulum; (iii) the longitudinal flagellum emerging from a point close to the cingulum; (iv) cell division taking place in the motile phase; and (v) possessing body scales. This is the third species of this genus to possess body scales. The body scales of A. cupulatisquama are uniform and cup‐shaped in side view and elliptical in face view. Their dimensions are 136.4 nm by 91.0 nm by 81.8 nm high. In side view, the scale is seen to have a thick lower half and a thin upper half. This scale type is very different from those of previously reported Amphidinium species (HG114 and HG115). The molecular tree indicated that A. cupulatisquama and the two other strains of body scale‐bearing Amphidinium are distantly related within the Amphidinium clade.     

HIV-1 dynamics at different time scales under antiretroviral therapy

We exploit a model that considers three compartments: blood plasma (BP), lymphoid tissue-interstitial spaces (LT-IS), and follicular dendritic cells (FDC), for the HIV-1 dynamics under the application of highly active antiretroviral therapy (HAART) which allowed us to unravel distinct viral dynamics occurring in short- (2 days), middle- (21 days), and long-term (183 days) time scales. The different time scales are determined by the viral clearance rate, the ratio of productively infected CD4⁺ T cells to chronically infected cells, and the dissociation rate of HIV-1 complexes from FDC. This generates a scenario in which, after an initial transient stage, the viral BP dynamics decouples and becomes governed by the lymphoid tissue (LT) dynamics; in a later stage, a new decoupling occurs in which the LT-IS dynamics is slaved to that of the FDC dynamics. We observed an initial increase in the viremia after HAART in a patient who did not receive protease inhibitors (PI). By means of the above-mentioned model we were able to highlight the relevant parameters which need to be estimated at three different time scales after HAART.     

Multi-scale analysis on species diversity within a 40-ha old-growth temperate forest

In order to better explore the maintenance mechanisms of biodiversity,data collected from a 40-ha undisturbed Pinus forest were applied to the Individual SpecieseArea Relationship model (ISAR) to determine distribution patterns for species richness.The ecological processes influencing species abundance distribution patterns were assessed by applying the same data set to five models:a LogNormal Model (LNM),a Broken Stick Model (BSM),a Zipf Model (ZM),a Niche Preemption Model (NPM),and a Neutral Model (NM).Each of the five models was used at six different sampling scales (10 m×10 m,20 m×20 m,40 m×40 m,60 m×60 m,80 m×80 m,and 100 m×100 m).Model outputs showed that:(1) Accumulators and neutral species strongly influenced species diversity,but the relative importance of the two types of species varied across spatial scales.(2) Distribution patterns of species abundance were best explained by the NPM at small scales (10 me20 m),whereas the NM was the best fit model at large spatial scales.(3) Species richness and abundance distribution patterns appeared to be driven by similar ecological processes.At small scales,the niche theory could be applied to describe species richness and abundance,while at larger scales the neutral theory was more applicable.     

Genetic diversity of upper Lake Constance whitefish Coregonus spp. under the influence of fisheries: a DNA study based on archived scale samples from 1932, 1975 and 2006

This investigation examined changes in the genetic diversity of pelagic upper Lake Constance (ULC) whitefish Coregonus wartmanni population before and after the alteration of fishery methods and management from 1932 to 2006. The study spans a period of pronounced changes in trophic status of the lake and transitions from traditional relatively unselective pelagic seine (Klusgarn) fishing to highly size‐selective nylon gillnet techniques. In addition, supportive breeding and stocking became most popular during the phase of eutrophication in the 1970s. The main hypothesis is that size‐selective fisheries and breeding lead to an overall decrease in genetic variability over time. A total of 215 archived C. wartmanni scale samples from 1932, 1975 and 2006 were analysed by genotyping 11 microsatellite loci. A comparison of population genetic parameters, including allelic richness, observed and expected heterozygosities, and estimates of effective population sizes, suggests that the genetic diversity of C. wartmanni population has not decreased. The appearance of new alleles in the gene pool in 1975 and 2006 may be indicative of admixture with other forms in the lake or with stocked allochthonous forms. Overall, the fisheries management practice in ULC, including the effects of size‐selective fisheries, supportive breeding and stocking, have not significantly altered the genetic diversity of Coregonus spp. over an 80 year period.     

A protocol for in vitro mass propagation of asiatic hybrids of lily through liquid stationary culture

Summary A simple, rapid and cost-effective in vitro scheme has been proposed for mass propagating two cultivars of Asiatic lily hybrids. An average of seven bulblets was formed after 17 d when 1×1 cm² bulb scale segments (explants) were cultured on Murashige and Skoog (MS) medium with 3% sucrose and 0.5 μM α-naphthaleneacetic acid (NAA). On MS medium containing 0.5 μM NAA and 6 or 9% sucrose, depending on the cultivar, large numbers of bulblets of increased size (3.5–5.0 cm in circumference) were formed under a 16/8 h photoperiod. A continuous system of mass propagation of bulblets was achieved through in vitro scale formation (secondary explants) on MS medium supplemented with 23 μM kinetin and 0.5 μM NAA, as well as scale proliferation on MS basal liquid stationary medium. Upon transplantation all bulblets sprouted, of which 40% flowered in the first season. Under ideal conditions, ca. 9.68×10⁵ bulblets can be produced from a single scale segment in 1 yr by following the systematic propagation steps proposed here.     

桂西北典型喀斯特区生态服务价值的环境响应及其空间尺度特征

Study on ecosystem service values (ESVs) is the bridge of understanding ecosystem and economic decision-making. To investigate the response of ESVs to ambient environment and their spatial scales is an urgent work in the process of ecological restoration and sustainable development in southwest China. Based on the previous research results, the remote images, and weather data of 31 years (1975-2005), the response of ESVs to ambient environment and their spatial scales in a typical karst area of northwest Guangxi, China were evaluated with the method of empirical mode decomposition (EMD) in this paper. The results showed that ESVs had obvious variations with changes in elevation, rocky types and soil types, and had corresponding characteristics of spatial scales. The ESVs in middle and low elevation areas were higher, but they decreased due to human activities such as deforestation. The ESVs in peak-cluster depression areas were lower, and they would increase as influenced by policies such as returning farmland to forestland. The ESVs were influenced by rocky types, showing lower values but an increasing trend in the typical karst regions while higher values but a decreasing trend in non-karst regions. The average ESVs in the west part of the study region, which is not only the main nature reserve for rare wildlife species in Guangxi, but also one of the best preserved natural vegetation regions in China, were more than 15,000 RMB Yuan ha-1,. Comparatively, the ESVs were less than 10,000 Yuan ha-1 in the middle part of the region attributed to low vegetation coverage, serious peak-cluster depression and karst rocky desertification. After about 20 years, that is from 1985 to 2005, the ecosystem conditions had been improved and the ESVs had increased in the middle and eastern part of this study region. On the contrary, in most western part, which was dominated by subtropical evergreen broad-leaved forest, they had been worsened, and the balance values of ESVs were negative. As for the relationships of ESVs with rocky types and soil types, lime soil and red soil were the two main soil types that contributed to ESVs (The total contribution was above 60%, and it is 63.77%,64.37%,64.56%,64.91% respectively in the four years of 1985, 1990, 2000 and 2005.). The variance contribution of intrinsic mode function (IMF) and trend (R) showed that there were obvious special sales for ESVs in this study area, and the main spatial scales were about 2.7 km, 5.5 km, and 11.6 km. The variance contribution ratio was 12.29%, 11.26%, 11.49% respectively, and the trend (R) was high (17.74%). In conclusion, this study indicated that ecosystem conditions in the typical karst area were improved owing to the application of rocky desertification control policies, such as ecological migration and returning farmland to forestland. Besides, the main spatial scales of ESVs in the study area were the interactions of terrain, physiognomy, land use / land cover and human activities.     

Relationship between Riparian Vegetation and Stream Benthic Communities at Three Spatial Scales

We examined the influence of riparian vegetation on macroinvertebrate community structure in streams of the Upper Thames River watershed in southwestern Ontario. Thirty-three μ-basins (129–1458 ha) were used to identify land cover variables that influenced stream macroinvertebrates. Micro-basins represented the entire drainage area of study streams and were similar in stream order (first, second) and land cover (agricultural or forest; no urban). We described the structure and composition of riparian vegetation and benthic macroinvertebrate communities at the outflow reach. The nature of the land cover was quantified for the stream network buffer (30 m) and the whole μ-basin. The objective of this study was to measure the magnitude and nature of the relationship between the riparian vegetation and benthic macroinvertebrate community at the outflow reach, stream network buffer, and whole μ-basin scales. Taxon richness (including total number of Ephemeroptera, Plecoptera, and Trichoptera taxa) and Simpson’s diversity of the macroinvertebrate community all increased with increased tree cover in the riparian zone at the outflow reach scale. Simpson’s equitability was lower with greater agricultural land cover in the stream network buffer. No relationship between the macroinvertebrate community and land cover was found at the whole μ-basin scale. Analysis of the influence of land cover on stream communities within a spatial hierarchy is important for understanding the interactions of stream ecosystems with their adjacent landscapes.