How optimal allocation of limited testing capacity changes epidemic dynamics.

Insufficient testing capacity has been a critical bottleneck in the worldwide fight against COVID-19. Optimizing the deployment of limited testing resources has therefore emerged as a keystone problem in pandemic response planning. Here, we use a modified SEIR model to optimize testing strategies under a constraint of limited testing capacity. We define pre-symptomatic, asymptomatic, and symptomatic infected classes, and assume that positively tested individuals are immediately moved into quarantine. We further define two types of testing. Clinical testing focuses only on the symptomatic class. Non-clinical testing detects pre- and asymptomatic individuals from the general population, and a concentration parameter governs the degree to which such testing can be focused on high infection risk individuals. We then solve for the optimal mix of clinical and non-clinical testing as a function of both testing capacity and the concentration parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. At high but empirically observed testing capacities, a mix of clinical testing and non-clinical testing, even if extremely unfocused, becomes optimal. We further highlight the advantages of early implementation of testing programs, and of combining optimized testing with contact reduction interventions such as lockdowns, social distancing, and masking.

How range residency and long-range perception change encounter rates.

Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home-range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can lead to systematic, non-negligible biases in encounter-rate predictions.

A framework for modelling range shifts and migrations: asking when, whither, whether and will it return.

Many animals undertake movements that are longer scaled and more directed than their typical home ranging behaviour. These movements include seasonal migrations (e.g. between breeding and feeding grounds), natal dispersal, nomadic range shifts and responses to local environmental disruptions. While various heuristic tools exist for identifying range shifts and migrations, none explicitly model the movement of the animals within a statistical framework that facilitates quantitative comparisons. We present the mechanistic range shift analysis (MRSA), a method to estimate a suite of range shift parameters: times of initiation, duration of transitions, centroids and areas of respective ranges. The method can take the autocorrelation and irregular sampling that is characteristic of much movement data into account. The mechanistic parameters suggest an intuitive measure, the range shift index, for the extent of a range shift. The likelihood based estimation further allows for statistical tests of several relevant hypotheses, including a range shift test, a stopover test and a site fidelity test. The analysis tools are provided in an R package (marcher). We applied the MRSA to a population of GPS tracked roe deer (Capreolus capreolus) in the Italian Alps between 2005 and 2008. With respect to seasonal migration, this population is extremely variable and difficult to classify. Using the MRSA, we were able to quantify the behaviours across the population and among individuals across years, identifying extents, durations and locations of seasonal range shifts, including cases that would have been ambiguous to detect using existing tools. The strongest patterns were differences across years: many animals simply did not perform a seasonal migration to wintering grounds during the mild winter of 2006-2007, even though some of these same animals did move extensively in other, harsher winters. For seasonal migrants, however, site fidelity across years was extremely high, even after skipping an entire seasonal migration. These results suggest that for roe deer behavioural plasticity and tactical responses to immediate environmental cues are reflected in the decision of whether rather than where to migrate. The MRSA also revealed a trade-off between the probability of migrating and the size of a home range.

Epidemiology of La Crosse Virus Emergence, Appalachia Region, United States.

La Crosse encephalitis is a viral disease that has emerged in new locations across the Appalachian region of the United States. Conventional wisdom suggests that ongoing emergence of La Crosse virus (LACV) could stem from the invasive Asian tiger (Aedes albopictus) mosquito. Efforts to prove this, however, are complicated by the numerous transmission routes and species interactions involved in LACV dynamics. To analyze LACV transmission by Asian tiger mosquitoes, we constructed epidemiologic models. These models accurately predict empirical infection rates. They do not, however, support the hypothesis that Asian tiger mosquitoes are responsible for the recent emergence of LACV at new foci. Consequently, we conclude that other factors, including different invasive mosquitoes, changes in climate variables, or changes in wildlife densities, should be considered as alternative explanations for recent increases in La Crosse encephalitis.

How far to go? Determinants of migration distance in land mammals.

Animal migration is a global phenomenon, but few studies have examined the substantial within- and between-species variation in migration distances. We built a global database of 94 land migrations of large mammalian herbivore populations ranging from 10 to 1638 km. We examined how resource availability, spatial scale of resource variability and body size affect migration distance among populations. Resource availability measured as normalised difference vegetation index had a strong negative effect, predicting a tenfold difference in migration distances between low- and high-resource areas and explaining 23% of the variation in migration distances. We found a weak, positive effect of the spatial scale of resource variability but no effect of body size. Resource-poor environments are known to increase the size of mammalian home ranges and territories. Here, we demonstrate that for migratory populations as well, animals living in resource-poor environments travel farther to fulfil their resource needs.

From fine-scale foraging to home ranges: a semivariance approach to identifying movement modes across spatiotemporal scales.

Understanding animal movement is a key challenge in ecology and conservation biology. Relocation data often represent a complex mixture of different movement behaviors, and reliably decomposing this mix into its component parts is an unresolved problem in movement ecology. Traditional approaches, such as composite random walk models, require that the timescales characterizing the movement are all similar to the usually arbitrary data-sampling rate. Movement behaviors such as long-distance searching and fine-scale foraging, however, are often intermixed but operate on vastly different spatial and temporal scales. An approach that integrates the full sweep of movement behaviors across scales is currently lacking. Here we show how the semivariance function (SVF) of a stochastic movement process can both identify multiple movement modes and solve the sampling rate problem. We express a broad range of continuous-space, continuous-time stochastic movement models in terms of their SVFs, connect them to relocation data via variogram regression, and compare them using standard model selection techniques. We illustrate our approach using Mongolian gazelle relocation data and show that gazelle movement is characterized by ballistic foraging movements on a 6-h timescale, fast diffusive searching with a 10-week timescale, and asymptotic diffusion over longer timescales.

Optimizing the search for resources by sharing information: Mongolian gazelles as a case study.

We investigate the relationship between communication and search efficiency in a biological context by proposing a model of Brownian searchers with long-range pairwise interactions. After a general study of the properties of the model, we show an application to the particular case of acoustic communication among Mongolian gazelles, for which data are available, searching for good habitat areas. Using Monte Carlo simulations and density equations, our results point out that the search is optimal (i.e., the mean first hitting time among searchers is minimum) at intermediate scales of communication, showing that both an excess and a lack of information may worsen it.

Spatial patterns in mesic savannas: the local facilitation limit and the role of demographic stochasticity.

We propose a model equation for the dynamics of tree density in mesic savannas which considers long-range competition among trees and the effect of fire indirectly acting as a local facilitation mechanism. Despite the fact that we take short-range facilitation to the local-range limit, the standard full spectrum of spatial structures already obtained in self-organization models of vegetation is recovered. Nonlocal competition, in the limit of infinitesimally short facilitation, promotes the clustering of trees. The long time coexistence between trees and grass, and how fires affect the survival of trees as well as the maintenance of the patterns is studied. The influence of demographic noise is analyzed. The stochastic system, under the parameter constraints typical of mesic savannas, shows non-homogeneous patterns characteristic of realistic situations. The coexistence of trees and grass still remains at reasonable noise intensities.

Personnel Scheduling during the COVID-19 Pandemic: A Probabilistic Graph-Based Approach.

Effective personnel scheduling is crucial for organizations to match workload demands. However, staff scheduling is sometimes affected by unexpected events, such as the COVID-19 pandemic, that disrupt regular operations. Limiting the number of on-site staff in the workplace together with regular testing is an effective strategy to minimize the spread of infectious diseases like COVID-19 because they spread mostly through close contact with people. Therefore, choosing the best scheduling and testing plan that satisfies the goals of the organization and prevents the virus's spread is essential during disease outbreaks. In this paper, we formulate these challenges in the framework of two Mixed Integer Non-linear Programming (MINLP) models. The first model aims to derive optimal staff occupancy and testing strategies to minimize the risk of infection among employees, while the second is aimed only at optimal staff occupancy under a random testing strategy. To solve the problems expressed in the models, we propose a canonical genetic algorithm as well as two commercial solvers. Using both real and synthetic contact networks of employees, our results show that following the recommended occupancy and testing strategy reduces the risk of infection 25-60% under different scenarios. The minimum risk of infection can be achieved when the employees follow a planned testing strategy. Further, vaccination status and interaction rate of employees are important factors in developing scheduling strategies that minimize the risk of infection.

Species invasiveness and community invasibility of North American freshwater fish fauna revealed via trait-based analysis.

While biological invasions are recognized as a major threat to global biodiversity, determining non-native species' abilities to establish in new areas (species invasiveness) and the vulnerability of those areas to invasions (community invasibility) is challenging. Here, we use trait-based analysis to profile invasive species and quantify the community invasibility for >1,800 North American freshwater fish communities. We show that, in addition to effects attributed to propagule pressure caused by human intervention, species with higher fecundity, longer lifespan and larger size tend to be more invasive. Community invasibility peaks when the functional distance among native species was high, leaving unoccupied functional space for the establishment of potential invaders. Our findings illustrate how the functional traits of non-native species determining their invasiveness, and the functional characteristics of the invaded community determining its invasibility, may be identified. Considering those two determinants together will enable better predictions of invasions.

Fine-scale variation in the effect of national border on COVID-19 spread: A case study of the Saxon-Czech border region.

The global extent and temporally asynchronous pattern of COVID-19 spread have repeatedly highlighted the role of international borders in the fight against the pandemic. Additionally, the deluge of high resolution, spatially referenced epidemiological data generated by the pandemic provides new opportunities to study disease transmission at heretofore inaccessible scales. Existing studies of cross-border infection fluxes, for both COVID-19 and other diseases, have largely focused on characterizing overall border effects. Here, we couple fine-scale incidence data with localized regression models to quantify spatial variation in the inhibitory effect of an international border. We take as a case study the border region between the German state of Saxony and the neighboring regions in northwestern Czechia, where municipality-level COVID-19 incidence data are available on both sides of the border. Consistent with past studies, we find an overall inhibitory effect of the border, but with a clear asymmetry, where the inhibitory effect is stronger from Saxony to Czechia than vice versa. Furthermore, we identify marked spatial variation along the border in the degree to which disease spread was inhibited. In particular, the area around Löbau in Saxony appears to have been a hotspot for cross-border disease transmission. The ability to identify infection flux hotspots along international borders may help to tailor monitoring programs and response measures to more effectively limit disease spread.

A network-based approach to identifying correlations between phylogeny, morphological traits and occurrence of fish species in US river basins.

The complex network framework has been successfully used to model interactions between entities in Complex Systems in the Biological Sciences such as Proteomics, Genomics, Neuroscience, and Ecology. Networks of organisms at different spatial scales and in different ecosystems have provided insights into community assembly patterns and emergent properties of ecological systems. In the present work, we investigate two questions pertaining to fish species assembly rules in US river basins, a) if morphologically similar fish species also tend to be phylogenetically closer, and b) to what extent are co-occurring species that are phylogenetically close also morphologically similar? For the first question, we construct a network of Hydrologic Unit Code 8 (HUC8) regions as nodes with interaction strengths (edges) governed by the number of common species. For each of the modules of this network, which are found to be geographically separated, there is differential yet significant evidence that phylogenetic distance predicts morphological distance. For the second question, we construct and analyze nearest neighbor directed networks of species based on their morphological distances and phylogenetic distances. Through module detection on these networks and comparing the module-level mean phylogenetic distance and mean morphological distance with the number of basins of common occurrence of species in modules, we find that both phylogeny and morphology of species have significant roles in governing species co-occurrence, i.e. phylogenetically and morphologically distant species tend to co-exist more. In addition, between the two quantities (morphological distance and phylogentic distance), we find that morphological distance is a stronger determinant of species co-occurrences.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19.

The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supply-constrained resource allocation strategies for controlling novel disease epidemics. To address the challenge of constrained resource optimization for managing diseases with complications like pre- and asymptomatic transmission, we develop an integro partial differential equation compartmental disease model which incorporates realistic latent, incubation, and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals. Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission. To analyze the influence of these realistic features on disease controllability, we find optimal strategies for reducing total infection sizes that allocate limited testing resources between 'clinical' testing, which targets symptomatic individuals, and 'non-clinical' testing, which targets non-symptomatic individuals. We apply our model not only to the original, delta, and omicron COVID-19 variants, but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions, which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness. We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies, while the relationship between incubation-latent mismatch, controllability, and optimal strategies is complicated. In particular, though greater degrees of presymptomatic transmission reduce disease controllability, they may increase or decrease the role of non-clinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length. Importantly, our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.

Behavioral responses of terrestrial mammals to COVID-19 lockdowns.

COVID-19 lockdowns in early 2020 reduced human mobility, providing an opportunity to disentangle its effects on animals from those of landscape modifications. Using GPS data, we compared movements and road avoidance of 2300 terrestrial mammals (43 species) during the lockdowns to the same period in 2019. Individual responses were variable with no change in average movements or road avoidance behavior, likely due to variable lockdown conditions. However, under strict lockdowns 10-day 95th percentile displacements increased by 73%, suggesting increased landscape permeability. Animals' 1-hour 95th percentile displacements declined by 12% and animals were 36% closer to roads in areas of high human footprint, indicating reduced avoidance during lockdowns. Overall, lockdowns rapidly altered some spatial behaviors, highlighting variable but substantial impacts of human mobility on wildlife worldwide.

Statistical inference for stochastic simulation models--theory and application.

Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well-established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern-Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.

Data driven high resolution modeling and spatial analyses of the COVID-19 pandemic in Germany.

The SARS-CoV-2 virus has spread around the world with over 100 million infections to date, and currently many countries are fighting the second wave of infections. With neither sufficient vaccination capacity nor effective medication, non-pharmaceutical interventions (NPIs) remain the measure of choice. However, NPIs place a great burden on society, the mental health of individuals, and economics. Therefore the cost/benefit ratio must be carefully balanced and a target-oriented small-scale implementation of these NPIs could help achieve this balance. To this end, we introduce a modified SEIRD-class compartment model and parametrize it locally for all 412 districts of Germany. The NPIs are modeled at district level by time varying contact rates. This high spatial resolution makes it possible to apply geostatistical methods to analyse the spatial patterns of the pandemic in Germany and to compare the results of different spatial resolutions. We find that the modified SEIRD model can successfully be fitted to the COVID-19 cases in German districts, states, and also nationwide. We propose the correlation length as a further measure, besides the weekly incidence rates, to describe the current situation of the epidemic.

Resource selection of a nomadic ungulate in a dynamic landscape.

Nomadic movements are often a consequence of unpredictable resource dynamics. However, how nomadic ungulates select dynamic resources is still understudied. Here we examined resource selection of nomadic Mongolian gazelles (Procapra gutturosa) in the Eastern Steppe of Mongolia. We used daily GPS locations of 33 gazelles tracked up to 3.5 years. We examined selection for forage during the growing season using the Normalized Difference Vegetation Index (NDVI). In winter we examined selection for snow cover which mediates access to forage and drinking water. We studied selection at the population level using resource selection functions (RSFs) as well as on the individual level using step-selection functions (SSFs) at varying spatio-temporal scales from 1 to 10 days. Results from the population and the individual level analyses differed. At the population level we found selection for higher than average NDVI during the growing season. This may indicate selection for areas with more forage cover within the arid steppe landscape. In winter, gazelles selected for intermediate snow cover, which may indicate preference for areas which offer some snow for hydration but not so much as to hinder movement. At the individual level, in both seasons and across scales, we were not able to detect selection in the majority of individuals, but selection was similar to that seen in the RSFs for those individuals showing selection. Difficulty in finding selection with SSFs may indicate that Mongolian gazelles are using a random search strategy to find forage in a landscape with large, homogeneous areas of vegetation. The combination of random searches and landscape characteristics could therefore obscure results at the fine scale of SSFs. The significant results on the broader scale used for the population level RSF highlight that, although individuals show uncoordinated movement trajectories, they ultimately select for similar vegetation and snow cover.

Reproductive asynchrony in spatial population models: how mating behavior can modulate allee effects arising from isolation in both space and time.

Mate finding, which is essential to both population growth and gene exchange, involves both spatial and temporal components. From a population dynamics perspective, spatial mate-finding problems are well studied, and decreased mate-finding efficiency at low population densities is a well-recognized mechanism for the Allee effect. Temporal aspects of mate finding have been rarely considered, but reproductive asynchrony may engender an Allee effect in which some females go mateless by virtue of temporal isolation. Here we develop and explore a model that unifies previously disparate theoretical considerations of spatial and temporal aspects of mate finding. Specifically, we develop a two-sex reaction-diffusion system to examine the interplay between reproductive asynchrony and the dispersal of individuals out of a patch. We also consider additional behavioral complications, including several alternative functional forms for mating efficiency and advective movements in which males actively seek out females. By calculating the fraction of females expected to go mateless as a joint function of reproductive asynchrony and patch size, we find that the population-level reproductive rates necessary to offset female matelessness may be quite high. These results suggest that Allee effects engendered by reproductive asynchrony will be greatly exacerbated in spatially isolated populations.

The independent and interactive effects of tree-tree establishment competition and fire on savanna structure and dynamics.

Savanna ecosystems are widespread and economically important and harbor considerable biodiversity. Despite extensive study, the mechanisms regulating savanna tree populations are not well understood. Recent empirical work suggests that both tree-tree competition and fire are key factors in semiarid to mesic savannas, but the potential for competition to structure savannas, particularly in interaction with fire, has received little theoretical attention. We develop a minimalistic and analytically tractable stochastic cellular automaton to study the individual and combined effects of these two factors on savannas. We find that while competition often substantially depresses tree density, fire generally has little effect but can drive tree extinction in extreme scenarios. When combined, competition and fire interact nonlinearly with strong negative consequences for tree density. This novel result may help explain observed variability among apparently similar savannas in their response to fire. Paradoxically, this interaction could also render the presence of competition more difficult to detect in empirical studies because fire can override the characteristic regular spacing driven by competition and lead instead to clustering.

Dynamical phase coexistence: a simple solution to the "savanna problem".

We introduce the concept of dynamical phase coexistence to provide a simple solution for a long-standing problem in theoretical ecology, the so-called "savanna problem". The challenge is to understand why in savanna ecosystems trees and grasses coexist in a robust way with large spatiotemporal variability. We propose a simple model, a variant of the contact process (CP), which includes two key extra features: varying external (environmental/rainfall) conditions and tree age. The system fluctuates locally between a woodland and a grassland phase, corresponding to the active and absorbing phases of the underlying pure contact process. This leads to a highly variable stable phase characterized by patches of the woodland and grassland phases coexisting dynamically. We show that the mean time to tree extinction under this model increases as a power-law of system size and can be of the order of 10,000,000 years in even moderately sized savannas. Finally, we demonstrate that while local interactions among trees may influence tree spatial distribution and the order of the transition between woodland and grassland phases, they do not affect dynamical coexistence. We expect dynamical coexistence to be relevant in other contexts in physics, biology or the social sciences.