In India, undernutrition among children has been extremely critical for the last few decades. Most analyses of undernutrition among Indian children have used the administrative boundaries of a state or a district level as a unit of analysis. This paper departs from such a practice and focuses instead on the political boundaries of a parliamentary constituency (PC) as the unit of analysis. The PC is a critical geopolitical unit where political parties and party candidates make election promises and implement programmes to improve the socio-economic condition of their electorate. A focus on child undernutrition at this level has the potential for greater policy and political traction and could lead to a paradigm shift in the strategy to tackle the problem by creating a demand for political accountability. Different dimensions and new approaches are also required to evaluate the socio-economic status and generate concrete evidence to find solutions to the problem. Given the significance of advanced analytical methods and models embedded into geographic information system (GIS), the current study, for the first time, uses GIS tools and techniques at the PC level, conducting in-depth analysis of undernutrition and its predictors. Hence, this paper examines the spatial heterogeneity in undernutrition across PCs by using geospatial techniques such as univariate and bivariate local indicator of spatial association and spatial regression models. The analysis highlights the high–low burden areas in terms of local hotspots and identifies the potential spatial risk factors of undernutrition across the constituencies. Striking variations in the prevalence of undernutrition across the constituencies were observed. Most of these constituencies that performed poorly both in terms of child nutrition and socio-economic indicators were located in the northern, western, and eastern parts of India. A statistically significant association of biological, socio-economic, and environmental factors such as women’s body mass index, anaemia in children, poverty, household sanitation facilities, and institutional births was established. The results highlight the need to bring in a mechanism of political accountability that directly connects elected representatives to maternal and child health outcomes. The spatial variability and pattern of undernutrition indicators and their correlates indicate that priority setting in research may also be greatly influenced by the neighbourhood association.

The intrinsic complexity, variety of concepts and numerous ways to quantify landscape heterogeneity (LH) may hamper a better understanding of how its components relate to ecological phenomena. Our study is the first to synthesize understanding of this concept and to provide the state of the art on the subject based on a comprehensive systematic literature review of 661 articles published between 1982 and 2019. Definitions, terminologies and measurements of LH were diverse and conflicting. Most articles (534 out of 661) did not provide any definition for LH, and we found great variation among the studies that did. According to our review, only 10 studies measured the effects of different land-cover types on biotic or abiotic processes (functional LH). The remaining 651 studies measured physical attributes of the landscape without mentioning that different land-cover types may impact biotic and abiotic processes differently (structural LH). The metrics most frequently used to represent LH were the Shannon diversity index and proportion of land-cover type. Most metrics used as proxies of LH also coincided with those used to represent non-heterogeneity metrics, such as fragmentation and connectivity. We identify knowledge gaps, indicate future perspectives and propose guidelines that should be addressed when researching LH.

This corrigendum corrects a result in [1].

In conventional pollen analysis, usually one sediment core per basin is analyzed to reconstruct past environmental conditions. This approach does not consider spatial heterogeneity of pollen assemblages, and assumes that one analyzed location is representative of the whole basin. To improve the spatial resolution of fossil pollen studies, further knowledge of the factors influencing variations in pollen assemblages throughout a basin is needed. We examined the spatial heterogeneity of pollen assemblages from 45 lacustrine surface samples from a lake with relatively simple hydrology and compared this dense network of surface pollen samples with the Lithuanian State Forest Service arboreal vegetation database. Calculations of pollen productivity at different locations across the lake revealed variations in the behavior of a pollen-vegetation relationship model in different parts of the basin. Our findings suggest that the model underestimated pollen contributions from the lakeshore vegetation. We demonstrate that detailed investigations of surface pollen as a step prior to fossil pollen investigations can provide useful insights, including understanding the influence of sedimentation rate on modelling results and spatial variations in pollen composition, thus providing guidance for site selection for fossil pollen studies.

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent λ* for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of λ* It is shown that the disease-free almost periodic solution is globally attractive if λ* < 0, while the disease is persistent if λ* > 0. By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

In aquatic microbial systems, high-magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance (“apparent disappearance”), are relatively common. We suggest that in order for this to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind or external factors of any other nature. Instead, such variations can be caused by internal factors and, in particular, by bacteria–phage interaction. Specifically, we suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, we consider a reasonably simple mathematical model of bacteria–phage interaction based on the model suggested by Beretta and Kuang, which assumes neither periodic forcing nor action of other external factors. The model admits a loss of stability via Andronov–Hopf bifurcation and exhibits dynamics which explains the phenomenon. These properties of the model are especially distinctive for spatially nonhomogeneous biosystems as well as biosystems with some sort of cooperation or community effects.

This is the second part of our study on the spatially heterogeneous predator–prey model where the interaction is governed by a Crowley–Martin type functional response. In part I, we have proved that when the predator competition is strong (i.e. k is large), the model has at most one positive steady-state solution for any $\mu \in \mathbb {R}$, moreover it is globally asymptotically stable for any $\mu >0$. This part is denoted to study the effect of saturation. Our result shows that the large saturation coefficient (i.e. large m) can not only lead to the uniqueness of positive solutions, but also lead to the multiplicity of positive solutions, moreover the stability of the corresponding positive solutions is also completely obtained. This work can be regarded as a supplement of Ref. [10].

Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017–18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018–19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017–18 (1.33 with 95% CI 1.29–1.37) was significantly higher than those for 2016–17 (1.23 with 95% CI: (1.22, 1.24)) and 2018–19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%–1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.

Large-scale control of invasive plants can benefit strongly from reliable assessment of spatial variation in plant invasibility. With this knowledge, limited management resources can be concentrated in areas of high invasion risk. We assessed the influence of spatial environments and proximity to roads on the invasibility of African mustard (Brassica tournefortii Gouan) over the 280,000-ha Barry M. Goldwater Range West in southwestern Arizona, USA. We used presence/absence data of B. tournefortii acquired from a vegetation classification project, in which lands were mapped to the level of vegetation subassociations. Logistic regression models suggested that spatial environments represented by the subassociations, not proximity to roads, represented the only factor significantly explaining B. tournefortii presence. We then used the best model to predict B. tournefortii invasibility in each subassociation. This prediction indicates management strategy should differ between the western part and the central to eastern part of the range. The western range is a large spatial continuum with intermediate to high invasion risk, vulnerable to an untethered spread of B. tournefortii. Controlling efforts should focus on preventing existing local populations from further expansion. The central and eastern ranges are a mosaic varying strongly in invasion risk. Control efforts can take advantage of natural invasion barriers and further reduce connectivity through removal of source populations connected with other high-risk locations via roads and other dispersal corridors. We suggest our approach as one effective way to combine vegetation classification and plant invasion assessment to manage complex landscapes over large ranges, especially when this approach is used through an iterative prediction–validation process to achieve adaptive management of invasive plants.

Bottlenose dolphins (Tursiops truncatus) are abundant in many coastal ecosystems, including the coastal Everglades. Understanding spatial and temporal variation in their abundance and group sizes is important for estimating their potential ecological importance and predicting how environmental changes (e.g. ecosystem restoration) might impact their populations. From August 2010 to June 2012, we completed a total of 67 belt transects covering a total of 2650 linear km and an area of 1232 km2. Dolphin densities varied spatially and temporally. The highest densities of dolphins were found in coastal oceans and inland bays and were lowest in rivers. Use of rivers, however, increased during the dry season while densities in other habitats remained similar across seasons. Dolphins appeared to prefer portions of bays close to mangrove-covered islands over open waters. A resighting rate of 63.6% of individuals across the 2-year study suggests that at least a portion of the population is probably resident within study regions over long time periods. The largest groups (mean 6.28, range 1–31) were found in open waters and bays despite apparently low predation pressure. Indeed, shark bite scars – likely the result of unsuccessful predation attempts – were conclusively observed on only 1% of individuals. Although further studies are warranted, the high densities of dolphins suggest that they are an important upper trophic level predator in the coastal Everglades, but their ecological importance probably varies in space and time.

Site properties and weed species abundance are known to vary spatially across fields. The extent to which they covary is not well understood. The objective of this research was to assess how canonical correlation analysis could be used to identify associations among site properties and weed species abundance within an agricultural field. A farmer-managed field rotated between Zea mays and Glycine max in Boone County, IA, was grid-sampled for site properties in 1992 and for weed species abundance between 1994 and 1997. Twelve site properties were considered in relation to five weed species that were identified and counted after all weed control operations were completed. Site properties such as total nitrogen, Bray-1 P, percent organic carbon, and texture were spatially variable. Weed species abundance was also spatially variable such that most weeds were found in patches and much of the field was weed-free. Canonical correlation analysis identified one to four significant correlations between linear combinations of site properties and weed species abundance. The first and second pairs of linear combinations explained the majority of variation in the data and were used to identify associations among site properties and weed species abundance. In years with Z. mays, the first pair of linear combinations described an association between herbicide activity and weed presence, and the second described topography and soil texture associations with weed presence. In years with G. max, the single observed association described a link between soil texture and presence of Setaria species and Polygonum coccineum. Several consistent associations were identified across years, indicating that site properties can influence weed abundance. However, annual variation in the associations may be attributed to differences in agronomic and weed management practices for each crop, as well as temporal weather variation influencing weed abundance from year to year. This multivariate technique is an important tool to identify associations between site properties and weed abundance that could help explain observed patchy patterns of weed abundance. These associations are an important first step in the generation of hypotheses to be tested at the whole field scale.

The temporal dynamics of spatial heterogeneity was studied for the weed communities in a seashore paspalum turf with the use of a power-law model. Surveys were conducted in January, March, May, July, September, and November in 2007. In every survey, we set 100 quadrats (50 by 50 cm) referred to as L quadrats on a 50-m line transect at the same position in the turf. Each L quadrat was then divided into four S quadrats (25 by 25 cm) and all plant species occurring in each of these S quadrats were identified and recorded. These data were summarized into frequency distributions and the percentage of S quadrats containing a given species, and the variance of each species was estimated. The power law was used to evaluate the spatial heterogeneity (δ) and frequency of occurrence (p) for each species in the weed communities in six survey months. The results showed that weeds emerged more frequently in the summer–spring season than in winter–autumn, and the spatial heterogeneity was much higher in summer–spring than winter–autumn, especially in summer. The Shannon–Wiener diversity indexes (H') from large to small were July (5.9202) > May (5.6775) > September (5.6631) > March (5.5727) > January (5.1742) > November (4.9668). Likewise, the spatial heterogeneity index (δc ) of the whole community was also different in different months. The biggest δc (0.2790) was in July, and the smallest (0.1811) in November. Meanwhile, manilagrass had a high p (= 1.0), indicating that it occurred in all S quadrats in every weed community of every month. However, the turfgrass, seashore paspalum, only emerged in March, May, July, and November, and possessed a low p, indicating the seashore paspalum turf has been naturally replaced by manilagrass.

Identification of associations between site properties and weed species abundance led to the generation of hypotheses as to why weed populations occur where they do, or do not, in agricultural fields. The objective of this research was to use a multivariate statistical technique, canonical correlation analysis, to identify the associations. Two continuous Zea mays production fields under center-pivot irrigation in the central Platte River Valley of Nebraska were grid-sampled between 1994 and 1997 for nine site properties and six to seven weed species. Weed species were identified and counted just prior to postemergence weed control in two adjacent quadrats (1 by 0.38 m) at each grid sampling point. These quadrats represented untreated weed populations emerging between crop rows and treated populations that survived preemergence herbicide banded within the crop row. Canonical correlation analysis identified one to five significant correlations between linear combinations of site properties and weed species abundance depending on field site, years, and between- vs. on-crop row weed populations. The first pair of linear combinations consistently described an association that separated weed species across a gradient of topography and soil type. The second pair of linear combinations described associations between weed species and soil fertility. In all cases, it was hypothesized that management practices strongly interacted with site properties to create the observed associations with weed populations. Other hypothesized mechanisms for weed patchiness include patchiness in available soil moisture that would influence weed seed germination, emergence, and seedling growth. Additional variation in plant-available preemergence herbicide concentration across the field site would vary weed control efficacy. Another mechanism would be variation in soil fertility that affects the growth, reproduction, and competitive ability of both the crop and the weed.

A two-stage multinomial logit selection model is used to model the relationship between demographic characteristics and housing density across Tennessee's six metropolitan statistical areas. The study finds that there is both spatial correlation and heterogeneity in the spatial distribution of housing both within and across the six areas. For example, Memphis, the most densely populated area, has the least amount of spatial correlation among housing density at the neighborhood level, while Johnson City, which has the lowest overall housing density, has the highest degree of spatial correlation.

We study a susceptible–infected–susceptible reaction–diffusion model with spatially heterogeneous disease transmission and recovery rates. A basic reproduction number is defined for the model. We first prove that there exists a unique endemic equilibrium if . We then consider the global attractivity of the disease-free equilibrium and the endemic equilibrium for two cases. If the disease transmission and recovery rates are constants or the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infected individuals, we show that the disease-free equilibrium is globally attractive if , while the endemic equilibrium is globally attractive if .

Protected areas are one of the main tools for biological conservation worldwide. Although they have contributed to an increase in fish abundance and alleviated the impacts of fishing on marine ecosystems, the impacts of fishing and of protected areas in freshwater ecosystems are less well known. We compared fishing productivity and fish assemblage descriptors of two distinct protected areas designated for sustainable use of natural resources and an unprotected area in the Tapajós River, in the Brazilian Amazon. Two hypotheses were tested: (1) fishers from protected areas have higher catch per unit effort than those from unprotected areas; and (2) fish assemblages in protected areas have higher biomass, abundance, presence of target species, species richness, fish size and mean trophic level than those in unprotected areas. A total of 2,013 fish landings were recorded and two surveys were undertaken to sample fishes. Eleven environmental parameters were quantified to distinguish between effects of environmental heterogeneity and protected areas. The catch per unit effort of fishers was higher within protected areas than in unprotected areas, suggesting that protected areas reduce the levels of fishing pressure and increase fishing productivity. However, the fish assemblage descriptors were correlated more with environmental variables than with protected areas, indicating a relatively weak effect of protected areas on fish communities in lakes. The results highlight the importance of considering the influence of environmental heterogeneity in fish conservation programmes, and the positive effect of protected areas on fishing productivity in freshwater environments.

Although sponges constitute the dominant animal group in marine caves globally, few studies have investigated quantitatively their diversity patterns in this habitat. Regarding Mediterranean marine caves, data describing the structure and diversity gradients of sponge assemblages are available for the north-western basin, while information for the eastern Mediterranean is almost inexistent. In this study, the sponge assemblages in two Aegean marine caves (eastern Mediterranean Sea) with different topography were examined using a non-destructive method. In each cave, three quadrats (25 × 25 cm) were photographed at 5 m intervals, along three transects: one along the ceiling and two along the opposite walls. Per cent coverage for each sponge species was calculated using advanced image processing software. Our analyses revealed a rich sponge assemblage, which consisted of 50 species assigned to eight growth forms. Resemblance analysis for the surveyed caves revealed two major groups of samples corresponding to the shadowy outer and the darker internal cave sectors. However, differences in species composition as well as divergent spatial patterns of species richness, Shannon–Wiener diversity and morphological diversity were found not only between the caves but also between different transects within each cave. Sponge morphological diversity presented significant positive correlation with species richness and Shannon–Wiener diversity in both caves, suggesting that it could possibly be used as a surrogate measure for describing sponge diversity gradients in Mediterranean caves. Cave topography was found to have a significant effect on the observed diversity patterns and assemblage structure, highlighting the high level of individuality in these unique habitats.

Environmental complexity and spatial heterogeneity are important factors influencing the structure of ant species assemblages. This paper documents the effect of different vegetation and environmental factors on ant community structure and functional group composition in different habitat patches. Ants were sampled at 16 sites distributed across five habitat types in the Kuldiha Wildlife Sanctuary. Sampling was performed 10 times over a 2-y period using pitfall traps. A total of 100 species belonging to 41 genera were collected during the study. Ant species richness was best explained by a combination of percentage grass cover, percentage litter cover and number of saplings whereas percentage litter cover and soil nitrogen concentration significantly explained the variation in ant species abundance. Dominant Dolichoderinae were present only at forest edge and were found to be associated positively with percentage bare ground cover and negatively with percentage litter cover. Generalized Myrmicinae, subordinate Camponotini and tropical climate specialists were prevalent in shaded forest habitats whereas opportunists were more common in two types of open habitat. Our study underpins the influence of vegetational complexity, litter and soil chemical properties on the structure and composition of ant species assemblages and various functional groups across forested habitats in this little-studied region.