Evaluating Spatial Interaction Models for Regional Mobility in Sub-Saharan Africa

Simple spatial interaction models of human mobility based on physical laws have been used extensively in the social, biological, and physical sciences, and in the study of the human dynamics underlying the spread of disease. Recent analyses of commuting patterns and travel behavior in high-income countries have led to the suggestion that these models are highly generalizable, and as a result, gravity and radiation models have become standard tools for describing population mobility dynamics for infectious disease epidemiology. Communities in Sub-Saharan Africa may not conform to these models, however; physical accessibility, availability of transport, and cost of travel between locations may be variable and severely constrained compared to high-income settings, informal labor movements rather than regular commuting patterns are often the norm, and the rise of mega-cities across the continent has important implications for travel between rural and urban areas. Here, we first review how infectious disease frameworks incorporate human mobility on different spatial scales and use anonymous mobile phone data from nearly 15 million individuals to analyze the spatiotemporal dynamics of the Kenyan population. We find that gravity and radiation models fail in systematic ways to capture human mobility measured by mobile phones; both severely overestimate the spatial spread of travel and perform poorly in rural areas, but each exhibits different characteristic patterns of failure with respect to routes and volumes of travel. Thus, infectious disease frameworks that rely on spatial interaction models are likely to misrepresent population dynamics important for the spread of disease in many African populations.     

Deriving fine-scale models of human mobility from aggregated origin-destination flow data

The spatial dynamics of epidemics are fundamentally affected by patterns of human mobility. Mobile phone call detail records (CDRs) are a rich source of mobility data, and allow semi-mechanistic models of movement to be parameterised even for resource-poor settings. While the gravity model typically reproduces human movement reasonably well at the administrative level spatial scale, past studies suggest that parameter estimates vary with the level of spatial discretisation at which models are fitted. Given that privacy concerns usually preclude public release of very fine-scale movement data, such variation would be problematic for individual-based simulations of epidemic spread parametrised at a fine spatial scale. We therefore present new methods to fit fine-scale mathematical mobility models (here we implement variants of the gravity and radiation models) to spatially aggregated movement data and investigate how model parameter estimates vary with spatial resolution. We use gridded population data at 1km resolution to derive population counts at different spatial scales (down to ∼ 5km grids) and implement mobility models at each scale. Parameters are estimated from administrative-level flow data between overnight locations in Kenya and Namibia derived from CDRs: where the model spatial resolution exceeds that of the mobility data, we compare the flow data between a particular origin and destination with the sum of all model flows between cells that lie within those particular origin and destination administrative units. Clear evidence of over-dispersion supports the use of negative binomial instead of Poisson likelihood for count data with high values. Radiation models use fewer parameters than the gravity model and better predict trips between overnight locations for both considered countries. Results show that estimates for some parameters change between countries and with spatial resolution and highlight how imperfect flow data and spatial population distribution can influence model fit.     

A gravity model for the spread of a pollinator-borne plant pathogen

Many pathogens of plants are transmitted by arthropod vectors whose movement between individual hosts is influenced by foraging behavior. Insect foraging has been shown to depend on both the quality of hosts and the distances between hosts. Given the spatial distribution of host plants and individual variation in quality, vector foraging patterns may therefore produce predictable variation in exposure to pathogens. We develop a "gravity" model to describe the spatial spread of a vector-borne plant pathogen from underlying models of insect foraging in response to host quality using the pollinator-borne smut fungus Microbotryum violaceum as a case study. We fit the model to spatially explicit time series of M. violaceum transmission in replicate experimental plots of the white campion Silene latifolia. The gravity model provides a better fit than a mean field model or a model with only distance-dependent transmission. The results highlight the importance of active vector foraging in generating spatial patterns of disease incidence and for pathogen-mediated selection for floral traits.     

Aerosol bolus dispersion in acinar airways--influence of gravity and airway asymmetry

The aerosol bolus technique can be used to estimate the degree of convective mixing in the lung; however, contributions of different lung compartments to measured dispersion cannot be differentiated unambiguously. To estimate dispersion in the distal lung, we studied the effect of gravity and airway asymmetry on the dispersion of 1 μm-diameter particle boluses in three-dimensional computational models of the lung periphery, ranging from a single alveolar sac to four-generation (g4) structures of bifurcating airways that deformed homogeneously during breathing. Boluses were introduced at the beginning of a 2-s inhalation, immediately followed by a 3-s exhalation. Dispersion was estimated by the half-width of the exhaled bolus. Dispersion was significantly affected by the spatial orientation of the models in normal gravity and was less in zero gravity than in normal gravity. Dispersion was strongly correlated with model volume in both normal and zero gravity. Predicted pulmonary dispersion based on a symmetric g4 acinar model was 391 ml and 238 ml under normal and zero gravity, respectively. These results accounted for a significant amount of dispersion measured experimentally. In zero gravity, predicted dispersion in a highly asymmetric model accounted for ～20% of that obtained in a symmetric model with comparable volume and number of alveolated branches, whereas normal gravity dispersions were comparable in both models. These results suggest that gravitational sedimentation and not geometrical asymmetry is the dominant factor in aerosol dispersion in the lung periphery.     

Scale of dispersal in varying environments and its implications for life histories of marine invertebrates

Summary We present several models concerning the short term consequences of spreading offspring in varying environments. Our goal is to determine what patterns of spatial and temporal variation yield an advantage to increasing scale of dispersal. Of necessity, the models are somewhat artificial but we feel they are a reasonable approximation of and hence generalizable to natural systems. With these models we examine consequences of dispersal arising from environmental variation: increased environmental variance, different degrees of spatial and temporal correlation, some arbitrary spatial patterns of favorability and finally some patterns derived from long-term, large-scale weather data collected along a contiguous stretch of coastline from southern Oregon to northern Washington (USA). We examine the costs and benefits of increasing sclae of dispersal in both density dependent and density independent models.Several conclusions may be drawn from the results of these models. In the absence of any spatial or temporal order to favorability (where favorability is directly proportional to either fitness or carrying capacity) increasing scale of spread produces a higher tate of population increase. At larger scales, though, an asymptote of maximum relative advantage is approached, so each added increment of spread has a smaller contribution to fitness. This asymptote is higher and the approach to it relatively slower with increasing environmental variance. For a given environmental variance, increasing spatial correlation results in a slower approach to the same asymptote. In density independent models, increasing temporal correlation of fitness selects against increased dispersal if expected differences between sites are sufficiently great relative to variation within sites; but in this instance, density dependence yields a somewhat different result: dispersers have a refuge at sites of low carrying capacity or sites lacking non-dispersers. Finally, optimum intermediate scales of dispersal can occur where differences in expected fitness increase with increasing distance from the parental site, such as in a gradient, but where the environmental variation at a given site is fairly large relative to differences in expected fitness between adjacent sites.The foregoing results are extended for the following predictions. When greater longevity in a resistant phase of the life cycle reduces temporal variation in survival and fecundity, increased generation time should decrease the benefits of spreading offspring in an environment that would otherwise favor spread and could either increase or decrease the costs of spreading offspring in an environment selecting against spread. We speculate that if large scale patterns of varying survival and fecundity are similar to the variation in the physical environment which we examined with weather data, there should be little or no short term advantage to large scale spread of offspring (on the order of 50 kilometers or more) because expected differences increase and seldom if ever decrease with increasing distance between sites.This suggests that feeding larvae of benthic invertebrates with their concomitant long planktonic period, receive little if any advantage from increased scale of dispersal, and consequently that the advantages to planktotrophy over lecithotrophy must lie in other life history aspects, such as the ability to produce a greater number of smaller eggs.Order of authorship alphabetical and by increasing age and height     

基于GIS的城市绿地景观引力场研究——以宁波市为例

城市绿地是城市用地的重要组成部分 ,也是城市生态系统的一个子系统。城市绿地景观的评价是城市生态系统研究的重要课题之一。在 GIS技术支持下 ,对城市绿地景观进行了研究。在研究过程中 ,将物理学中“场”的相关理论引入城市绿地景观的研究 ,提出绿地景观引力场的概念及评价方法。绿地景观引力场是城市绿地系统为城市居民提供服务能力的大小或潜力 ,其主要影响因素有绿地景观本身的质量、城市人口分布状况、城市土地利用现状、城市主要交通设施等。在研究中需要建立以下相关模型 :城市阻力的空间分布模型、城市人口的空间分布模型、城市公共绿地的空间分布模型、城市绿地景观引力场的空间分布评价模型。研究结果得出以下结论 :(1)景观引力场用于城市绿地系统的评价 ,能够更好地反映城市绿地的空间分布格局 ;(2 )丰富了城市绿地系统评价的指标内容和评价方法 ;(3)该方法从景观设计上提供了一个可供决策参考的依据 ;(4 )景观引力场还可用于城市其它服务设施的合理性与有效性的评价与研究。     

Pushed to the edge: Spatial sorting can slow down invasions

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.     

Allee effects, aggregation, and invasion success

Understanding the factors that influence successful colonization can help inform ecological theory and aid in the management of invasive species. When founder populations are small, individual fitness may be negatively impacted by component Allee effects through positive density dependence (e.g., mate limitation). Reproductive and survival mechanisms that suffer due to a shortage of conspecifics may scale up to be manifest in a decreased per-capita population growth rate (i.e., a demographic Allee effect). Mean-field population level models are limited in representing how component Allee effects scale up to demographic Allee effects when heterogeneous spatial structure influences conspecific availability. Thus, such models may not adequately characterize the probability of establishment. In order to better assess how individual level processes influence population establishment and spread, we developed a spatially explicit individual-based stochastic simulation of a small founder population. We found that increased aggregation can affect individual fitness and subsequently impact population growth; however, relatively slow dispersal—in addition to initial spatial structure—is required for establishment, ultimately creating a tradeoff between probability of initial establishment and rate of subsequent spread. Since this result is sensitive to the scaling up of component Allee effects, details of individual dispersal and interaction kernels are key factors influencing population level processes. Overall, we demonstrate the importance of considering both spatial structure and individual level traits in assessing the consequences of Allee effects in biological invasions.     

浙江天台山甜槠种群遗传结构的空间自相关分析

采用空间自相关分析方法对浙江天台山亚热带常绿阔叶林优势种甜槠种群全部个体及不同年龄级个体的小尺度空间遗传结构进行了分析,以探讨甜槠种群内遗传变异的分布特征及其形成机制。根据11个ISSR引物所提供的多态位点,经GenAlEx 6软件计算地理坐标和遗传距离矩阵在10个距离等级下的空间自相关系数。在样地内,甜槠种群内个体在空间距离小于10 m时存在显著的正空间遗传结构,其X-轴截矩为9.945。甜槠种群的空间遗传结构与其种子短距离传播和广泛的花粉传播有关。Ⅰ年龄级、Ⅱ年龄级和III年龄级个体在空间距离小于10 m时存在显著的正空间遗传结构,其X-轴截矩分别为11.820、9.746和9.792。当距离等级为5 m时,其空间自相关系数r分别为0.068、0.054和0.070。Ⅳ年龄级个体在所有空间距离等级中均不存在显著的空间遗传结构。甜槠是多年生、长寿命植物,自疏作用是导致IV年龄级个体空间遗传结构消失的主要原因。     

Plant spatial arrangement affects projected invasion speeds of two invasive thistles

The spatial arrangement of plants in a landscape influences wind flow, but the extent that differences in the density of conspecifics and the height of surrounding vegetation influence population spread rates of wind dispersed plants is unknown. Wind speeds were measured at the capitulum level in conspecific arrays of different sizes and densities in high and low surrounding vegetation to determine how these factors affect wind speeds and therefore population spread rates of two invasive thistle species of economic importance, Carduus acanthoides and C. nutans. Only the largest and highest density array reduced wind speeds at a central focal thistle plant. The heights of capitula and surrounding vegetation also had significant effects on wind speed. When population spread rates were projected using integrodifference equations coupling previously published demography data with WALD wind dispersal models, large differences in spread rates resulted from differences in average horizontal wind speeds at capitulum height caused by conspecific density and surrounding vegetation height. This result highlights the importance of spatial structure for the calculation of accurate spread rates. The management implication is that if a manager has time to remove a limited number of thistle plants, an isolated thistle growing in low surrounding vegetation should be targeted rather than a similar sized thistle in a high density population with high surrounding vegetation, if the objective is to reduce spread rates.     

Prediction and error in multi‐stage models for spread of aquatic non‐indigenous species

Aim Predictions of spread of non‐indigenous species allow for greater efficiency in managing invasions by targeting areas for preventative measures. The invasion sequence is a useful concept in predictions of spread, as it allows us to test hypotheses about the transport and establishment of propagules in novel habitats. Our aims are twofold: (1) to develop and validate multi‐stage invasion models for the introduced fishhook waterflea, Cercopagis pengoi, and (2) to assess how variability in the transport patterns of the propagules influences the accuracy and spatial extent for predictions of spread. Location New York State, USA. Methods We developed a two‐stage model for the spread of C. pengoi. First, we developed a stochastic gravity model for dispersal based on surveys of recreational boat traffic in New York State as a proxy for propagule pressure. We then modelled the probability of establishment based on predicted levels of propagule pressure and measures of lakes’ physicochemistry. In addition, we used Monte Carlo simulations based on the gravity model to propagate variability in boater traffic through the establishment model to assess how uncertainty in dispersal influenced predictions of spread. Results The amount recreationalists were willing to spend, lake area and population size of the city nearest to the destination lake were significant factors affecting boater traffic. In turn, boater traffic, lake area, specific conductance and turbidity were significant predictors of establishment. The inclusion of stochastic dispersal reduced the rate of false positives (i.e. incorrect prediction of an invasion) in detecting invasions at the upper 95% prediction interval for the probability of establishment. Main conclusions Combinations of measures of propagule pressure, habitat suitability and stochastic dispersal allow for the most accurate predictions of spread. Further, multi‐stage spread models may overestimate the extent of spread if stochasticity in early stages of the models is not considered.     

Measles on the edge: coastal heterogeneities and infection dynamics

Mathematical models can help elucidate the spatio-temporal dynamics of epidemics as well as the impact of control measures. The gravity model for directly transmitted diseases is currently one of the most parsimonious models for spatial epidemic spread. This model uses distance-weighted, population size-dependent coupling to estimate host movement and disease incidence in metapopulations. The model captures overall measles dynamics in terms of underlying human movement in pre-vaccination England and Wales (previously established). In spatial models, edges often present a special challenge. Therefore, to test the model's robustness, we analyzed gravity model incidence predictions for coastal cities in England and Wales. Results show that, although predictions are accurate for inland towns, they significantly underestimate coastal persistence. We examine incidence, outbreak seasonality, and public transportation records, to show that the model's inaccuracies stem from an underestimation of total contacts per individual along the coast. We rescue this predicted 'edge effect' by increasing coastal contacts to approximate the number of per capita inland contacts. These results illustrate the impact of 'edge effects' on epidemic metapopulations in general and illustrate directions for the refinement of spatiotemporal epidemic models.     

Spatial and temporal invasion dynamics of the 2014–2017 Zika and chikungunya epidemics in Colombia

Zika virus (ZIKV) and chikungunya virus (CHIKV) were recently introduced into the Americas resulting in significant disease burdens. Understanding their spatial and temporal dynamics at the subnational level is key to informing surveillance and preparedness for future epidemics. We analyzed anonymized line list data on approximately 105,000 Zika virus disease and 412,000 chikungunya fever suspected and laboratory-confirmed cases during the 2014–2017 epidemics. We first determined the week of invasion in each city. Out of 1,122, 288 cities met criteria for epidemic invasion by ZIKV and 338 cities by CHIKV. We analyzed risk factors for invasion using linear and logistic regression models. We also estimated that the geographic origin of both epidemics was located in Barranquilla, north Colombia. We assessed the spatial and temporal invasion dynamics of both viruses to analyze transmission between cities using a suite of (i) gravity models, (ii) Stouffer’s rank models, and (iii) radiation models with two types of distance metrics, geographic distance and travel time between cities. Invasion risk was best captured by a gravity model when accounting for geographic distance and intermediate levels of density dependence; Stouffer’s rank model with geographic distance performed similarly well. Although a few long-distance invasion events occurred at the beginning of the epidemics, an estimated distance power of 1.7 (95% CrI: 1.5–2.0) from the gravity models suggests that spatial spread was primarily driven by short-distance transmission. Similarities between the epidemics were highlighted by jointly fitted models, which were preferred over individual models when the transmission intensity was allowed to vary across arboviruses. However, ZIKV spread considerably faster than CHIKV.     

Commuter Mobility and the Spread of Infectious Diseases: Application to Influenza in France

Commuting data is increasingly used to describe population mobility in epidemic models. However, there is little evidence that the spatial spread of observed epidemics agrees with commuting. Here, using data from 25 epidemics for influenza-like illness in France (ILI) as seen by the Sentinelles network, we show that commuting volume is highly correlated with the spread of ILI. Next, we provide a systematic analysis of the spread of epidemics using commuting data in a mathematical model. We extract typical paths in the initial spread, related to the organization of the commuting network. These findings suggest that an alternative geographic distribution of GP accross France to the current one could be proposed. Finally, we show that change in commuting according to age (school or work commuting) impacts epidemic spread, and should be taken into account in realistic models.     

The effect of static and dynamic spatially structured disturbances on a locally dispersing population

Previous models of locally dispersing populations have shown that in the presence of spatially structured fixed habitat heterogeneity, increasing local spatial autocorrelation in habitat generally has a beneficial effect on such populations, increasing equilibrium population density. It has also been shown that with large-scale disturbance events which simultaneously affect contiguous blocks of sites, increasing spatial autocorrelation in the disturbances has a harmful effect, decreasing equilibrium population density. Here, spatial population models are developed which include both of these spatially structured exogenous influences, to determine how they interact with each other and with the endogenously generated spatial structure produced by the population dynamics. The models show that when habitat is fragmented and disturbance occurs at large spatial scales, the population cannot persist no matter how large its birth rate, an effect not seen in previous simpler models of this type. The behavior of the model is also explored when the local autocorrelation of habitat heterogeneity and disturbance events are equal, i.e. the two effects occur at the same spatial scale. When this scale parameter is very small, habitat fragmentation prevents the population from persisting because sites attempting to reproduce will drop most of their offspring on unsuitable sites; when the parameter is very large, large-scale disturbance events drive the population to extinction. Population levels reach their maximum at intermediate values of the scale parameter, and the critical values in the model show that the population will persist most easily at these intermediate scales of spatial influences. The models are investigated via spatially explicit stochastic simulations, traditional (infinite-dispersal) and improved (local-dispersal) mean-field approximations, and pair approximations.     

Modeling the Dynamics of a Non-Limited and a Self-Limited Gene Drive System in Structured Aedes aegypti Populations

Recently there have been significant advances in research on genetic strategies to control populations of disease-vectoring insects. Some of these strategies use the gene drive properties of selfish genetic elements to spread physically linked anti-pathogen genes into local vector populations. Because of the potential of these selfish elements to spread through populations, control approaches based on these strategies must be carefully evaluated to ensure a balance between the desirable spread of the refractoriness-conferring genetic cargo and the avoidance of potentially unwanted outcomes such as spread to non-target populations. There is also a need to develop better estimates of the economics of such releases. We present here an evaluation of two such strategies using a biologically realistic mathematical model that simulates the resident Aedes aegypti mosquito population of Iquitos, Peru. One strategy uses the selfish element Medea, a non-limited element that could permanently spread over a large geographic area; the other strategy relies on Killer-Rescue genetic constructs, and has been predicted to have limited spatial and temporal spread. We simulate various operational approaches for deploying these genetic strategies, and quantify the optimal number of released transgenic mosquitoes needed to achieve definitive spread of Medea-linked genes and/or high frequencies of Killer-Rescue-associated elements. We show that for both strategies the most efficient approach for achieving spread of anti-pathogen genes within three years is generally to release adults of both sexes in multiple releases over time. Even though females in these releases should not transmit disease, there could be public concern over such releases, making the less efficient male-only release more practical. This study provides guidelines for operational approaches to population replacement genetic strategies, as well as illustrates the use of detailed spatial models to assist in safe and efficient implementation of such novel genetic strategies.     

Behavioral states help translate dispersal movements into spatial distribution patterns of floaters

Within the field of spatial ecology, it is important to study animal movements in order to better understand population dynamics. Dispersal is a nonlinear process through which different behavioral mechanisms could affect movement patterns. One of the most common approaches to analyzing the trajectories of organisms within patches is to use random-walk models to describe movement features. These models express individual movements within a specific area in terms of random-walk parameters in an effort to relate movement patterns to the distributions of organisms in space. However, only using the movement trajectories of individuals to predict the spatial spread of animal populations may not fit the complex distribution of individuals across heterogeneous environments. When we empirically tested the results from a random-walk model (a residence index) used to predict the spatial equilibrium distribution of individuals, we found that the index severely underestimated the spatial spread of dispersing individuals. We believe this is because random-walk models only account for the effects of environmental conditions on individual movements, completely overlooking the crucial influence of behavior changes over time. In the future, both aspects should be accounted for when predicting general rules of (meta)population abundance, distribution, and dynamics from patterns of animal movements.     

Clonal and fine-scale genetic structure in populations of a restricted Korean endemic, Hosta jonesii (Liliaceae) and the implications for conservation

BACKGROUND AND AIMS: In plant populations the magnitude of spatial genetic structure of apparent individuals (including clonal ramets) can be different from that of sexual individuals (genets). Thus, distinguishing the effects of clonal versus sexual individuals in population genetic analyses could provide important insights for evolutionary biology and conservation. To investigate the effects of clonal spread on the fine-scale spatial genetic structure within plant populations, Hosta jonesii (Liliaceae), an endemic species to Korea, was chosen as a study species. METHODS: Using allozymes as genetic markers, spatial autocorrelation analysis of ramets and of genets was conducted to quantify the spatial scale of clonal spread and genotype distribution in two populations of H. jonesii. KEY RESULTS: Join-count statistics revealed that most clones are significantly aggregated at < 3-m interplant distance. Spatial autocorrelation analysis of all individuals resulted in significantly higher Moran's I values at 0-3-m interplant distance than analyses of population samples in which clones were excluded. However, significant fine-scale genetic structure was still observed when clones were excluded. CONCLUSIONS: These results suggest that clones enhance the magnitude of spatial autocorrelation due to localized clonal spread. The significant fine-scale genetic structure detected in samples excluding clones is consistent with the biological and ecological traits exhibited by H. jonesii including bee pollination and limited seed dispersal. For conservation purposes, genetic diversity would be maximized in local populations of H. jonesii by collecting or preserving individuals that are spaced at least 5 m apart.     

The gravity of pollination: integrating at‐site features into spatial analysis of contemporary pollen movement

Pollen‐mediated gene flow is a major driver of spatial genetic structure in plant populations. Both individual plant characteristics and site‐specific features of the landscape can modify the perceived attractiveness of plants to their pollinators and thus play an important role in shaping spatial genetic variation. Most studies of landscape‐level genetic connectivity in plants have focused on the effects of interindividual distance using spatial and increasingly ecological separation, yet have not incorporated individual plant characteristics or other at‐site ecological variables. Using spatially explicit simulations, we first tested the extent to which the inclusion of at‐site variables influencing local pollination success improved the statistical characterization of genetic connectivity based upon examination of pollen pool genetic structure. The addition of at‐site characteristics provided better models than those that only considered interindividual spatial distance (e.g. IBD). Models parameterized using conditional genetic covariance (e.g. population graphs) also outperformed those assuming panmixia. In a natural population of Cornus florida L. (Cornaceae), we showed that the addition of at‐site characteristics (clumping of primary canopy opening above each maternal tree and maternal tree floral output) provided significantly better models describing gene flow than models including only between‐site spatial (IBD) and ecological (isolation by resistance) variables. Overall, our results show that including interindividual and local ecological variation greatly aids in characterizing landscape‐level measures of contemporary gene flow.