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The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in several countries to ascertain the spread of the coronavirus disease 2019 (COVID-19). We consider discrete-time SEIR epidemic model in a closed system which does not account for births or deaths, total population size under consideration is constant. This dynamical system generated by a non-linear evolution operator depending on four parameters. Under some conditions on parameters we reduce the evolution operator to a quadratic stochastic operator (QSO) which maps 3-dimensional simplex to itself. We show that the QSO has uncountable set of fixed points (all laying on the boundary of the simplex). It is shown that all trajectories of the dynamical system (generated by the QSO) of the SEIR model are convergent (i.e. the QSO is regular). Moreover, we discuss the efficiency of the model for Uzbekistan., Comment: 13 pages, 4 figures

We consider a spatial model of cancer in which cells are points on the d-dimensional torus $\mathcal{T}=[0,L]^d$ , and each cell with $k-1$ mutations acquires a kth mutation at rate $\mu_k$ . We assume that the mutation rates $\mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire k mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $k\geq 3$ mutations in Foo et al. (2020), which considered the case in which all of the mutation rates $\mu_k$ are the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.

The search for biosignatures necessitates developing our understanding of life under different conditions. If life can influence the climate evolution of its planet then understanding the behaviour of life-climate feedbacks under extreme conditions is key to determine the ‘edges’ of the habitable zone. Additionally understanding the behaviour of a temperature limited biosphere will help towards formulating biosignature predictions for alien life living under conditions very different to those on Earth. Towards this aim, we extend the ‘ExoGaia Model’ – an abstract model of microbial life living on a highly simplified zero-dimensional planet. Via their metabolisms, microbes influence the atmospheric composition and therefore the temperature of the planet and emergent feedback loops allow microbes to regulate their climate and maintain long-term habitability. Here, we adapt the ExoGaia model to include temperature adaptation of the microbes by allowing different species to have different temperature ‘preferences’. We find that rather than adapting towards the planet’s abiotic conditions the biosphere tends to more strongly influence the climate of its planet, suggesting that the surface temperature of an inhabited planet might be significantly different from that predicted using abiotic models. We find that the success rate for microbial establishment on planets is improved when adaptation is allowed. However, planetary abiotic context is important for determining whether overall survival prospects for life will be improved or degraded. These results indicate the necessity to develop an understanding of life living under different limiting regimes to form predictions for the boundaries of the habitable zone.

Searching for extrasolar biosignatures is important to understand life on Earth and its origin. Astronomical observations of exoplanets may find such signatures, but it is difficult and may be impossible to claim unambiguous detection of life by remote sensing of exoplanet atmospheres. Here, another approach is considered: collecting grains ejected by asteroid impacts from exoplanets in the Milky Way and then traveling to the Solar System. The optimal grain size for this purpose is around 1 $\mu$m, and though uncertainty is large, about $10^5$ such grains are expected to be accreting on Earth every year, which may contain biosignatures of life that existed on their home planets. These grains may be collected by detectors placed in space, or extracted from Antarctic ice or deep-sea sediments, depending on future technological developments., Comment: 5 pages, no figure. Accepted for publication in International Journal of Astrobiology

Genomic selection has increased genetic gain in several livestock species, but due to the complicated genetics and reproduction biology not yet in honey bees. Recently, 2 970 queens were genotyped to gather a reference population. For the application of genomic selection in honey bees, this study analyses the predictive ability and bias of pedigree-based and genomic breeding values for honey yield, three workability traits and two traits for resistance against the parasite Varroa destructor. For breeding value estimation, we use a honey bee-specific model with maternal and direct effects, to account for the contributions of the workers and the queen of a colony to the phenotypes. We conducted a validation for the last generation and a five-fold cross-validation. In the validation for the last generation, the predictive ability of pedigree-based estimated breeding values was 0.06 for honey yield, and ranged from 0.2 to 0.41 for the workability traits. The inclusion of genomic marker data improved these predictive abilities to 0.11 for honey yield, and a range from 0.22 to 0.44 for the workability traits. The inclusion of genomic data did not improve the predictive ability for the disease related traits. Traits with high heritability for maternal effects compared to the heritability for direct effects showed the most promising results. Across all traits, the bias with genomic methods was close to the bias with pedigree-based BLUP. The results show that genomic selection can successfully be applied to honey bees., Comment: 31 pages, 4 figures, submitted to Heredity

As genomic scale datasets motivate research on species tree inference, simulators of the multispecies coalescent (MSC) process are essential for the testing and evaluation of new inference methods. However, the simulators themselves must be tested to ensure they give valid samples from the coalescent process. In this work we develop several statistical tools using summary statistics to evaluate the fit of a simulated gene tree sample to the MSC model. Using these tests on samples from four published simulators, we uncover flaws in several. The tests are implemented as an R package, so that both developers and users will be able to easily check proper performance of future simulators., Comment: 7 pages + 26 pages supplementary materials

This paper proposes a data-driven machine learning framework for parameter estimation and uncertainty quantification in epidemic models based on two key ingredients: (i) prior parameters learning via the cross-entropy method and (ii) update of the model calibration and uncertainty propagation through approximate Bayesian computation. The effectiveness of the new methodology is illustrated with the aid of actual data from COVID-19 epidemic at Rio de Janeiro city in Brazil, employing an ordinary differential equation based model with a generalized SEIR-type mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, which makes the proposed methodology very appealing for use in the context of real-time epidemic modeling.

When searching for inhabited exoplanets, understanding the boundaries of the habitable zone around the parent star is the key. If life can strongly influence its global environment, then we would expect the boundaries of the habitable zone to be influenced by the presence of life. Here, using a simple abstract model of ‘tangled-ecology’ where life can influence a global parameter, labelled as temperature, we investigate the boundaries of the habitable zone of our model system. As with other models of life-climate interactions, the species act to regulate the temperature. However, the system can also experience ‘punctuations’, where the system’s state jumps between different equilibria. Despite this, an ensemble of systems still tends to sustain or even improve conditions for life on average, a feature we call Entropic Gaia. The mechanism behind this is sequential selection with memory which is discussed in detail. With this modelling framework we investigate questions about how Gaia can affect and ultimately extend the habitable zone to what we call the Gaian habitable zone. This generates concrete predictions for the size of the habitable zone around stars, suggests directions for future work on the simulation of exoplanets and provides insight into the Gaian bottleneck hypothesis and the habitability/inhabitance paradox.

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this system is well known. However, nature is usually not deterministic. All ecosystems experience some type of random environmental fluctuations. We incorporate these into a natural framework as follows. Suppose the environment has two possible states. In each of the two environmental states the dynamics is governed by a system of Lotka-Volterra ODE. The randomness comes from spending an exponential amount of time in each environmental state and then switching to the other one. We show how this random switching can create very interesting phenomena. In some cases the randomness can facilitate the coexistence of the three species even though coexistence is impossible in each of the two environmental states. In other cases, even though there is coexistence in each of the two environmental states, switching can lead to the loss of one or more species. We look into how predators and environmental fluctuations can mediate coexistence among competing species., 20 pages, 2 figures

We study two fringe subtree counting statistics, the number of cherries and that of pitchforks for Ford's $\alpha$ model, a one-parameter family of random phylogenetic tree models that includes the uniform and the Yule models, two tree models commonly used in phylogenetics. Based on a nonuniform version of the extended P\'olya urn models in which negative entries are permitted for their replacement matrices, we obtain the strong law of large numbers and the central limit theorem for the joint distribution of these two count statistics for the Ford model. Furthermore, we derive a recursive formula for computing the exact joint distribution of these two statistics. This leads to exact formulas for their means and higher order asymptotic expansions of their second moments, which allows us to identify a critical parameter value for the correlation between these two statistics. That is, when $n$ is sufficiently large, they are negatively correlated for $0\le \alpha \le 1/2$ and positively correlated for $1/2, Comment: 23 pages, 2 figures

Intercity travel is one of the most important parameters for combating a pandemic. The ongoing COVID-19 pandemic has resulted in different computational studies involving intercity connections. In this study, the effects of intercity connections during an epidemic such as COVID-19 are evaluated using a new network model. This model considers the actual geographic neighborhood and population density data. This new model is applied to actual Turkish data by the means of provincial connections and populations. A Monte Carlo algorithm with a hybrid lattice model is applied to a lattice with 8,802 data points. Results show that this model is quantitatively very efficient in modeling real world COVID-19 epidemic data based on populations and geographical intercity connections, by the means of estimating the number of deaths, disease spread, and epidemic termination., 10 pages, 7 figures

The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models. These model ensembles commonly assume stable coexistence of species in the absence of available data. However, existing ensemble-generation methods become computationally inefficient as the size of the ecosystem network increases, preventing larger networks from being studied. We present a novel sequential Monte Carlo sampling approach for ensemble generation that is orders of magnitude faster than existing approaches. We demonstrate that the methods produce equivalent parameter inferences, model predictions, and tightly constrained parameter combinations using a novel sensitivity analysis method. For one case study, we demonstrate a speed-up from 108 days to 6 hours, while maintaining equivalent ensembles. Now, for the first time, larger and more realistic networks can be practically simulated.

While extensive literature exists on the COVID-19 pandemic at regional and national levels, understanding its dynamics and consequences at the city level remains limited. This study investigates the pandemic in Maring\'a, a medium-sized city in Brazil's South Region, using data obtained by actively monitoring the disease from March 2020 to June 2022. Despite prompt and robust interventions, COVID-19 cases increased exponentially during the early spread of COVID-19, with a reproduction number lower than that observed during the initial outbreak in Wuhan. Our research demonstrates the remarkable impact of non-pharmaceutical interventions on both mobility and pandemic indicators, particularly during the onset and the most severe phases of the emergency. However, our results suggest that the city's measures were primarily reactive rather than proactive. Maring\'a faced six waves of cases, with the third and fourth waves being the deadliest, responsible for over two-thirds of all deaths and overwhelming the local healthcare system. Excess mortality during this period exceeded deaths attributed to COVID-19, indicating that the burdened healthcare system may have contributed to increased mortality from other causes. By the end of the fourth wave, nearly three-quarters of the city's population had received two vaccine doses, significantly decreasing deaths despite the surge caused by the Omicron variant. Finally, we compare these findings with the national context and other similarly sized cities, highlighting substantial heterogeneities in the spread and impact of the disease., Comment: 20 pages, 5 figures, supplementary information; accepted for publication in Scientific Reports

The interaction between elephants and their environment has profound implications for both ecology and conservation strategies. This study presents an analytical approach to decipher the intricate patterns of elephant movement in Sub-Saharan Africa, concentrating on key ecological drivers such as seasonal variations and rainfall patterns. Despite the complexities surrounding these influential factors, our analysis provides a holistic view of elephant migratory behavior in the context of the dynamic African landscape. Our comprehensive approach enables us to predict the potential impact of these ecological determinants on elephant migration, a critical step in establishing informed conservation strategies. This projection is particularly crucial given the impacts of global climate change on seasonal and rainfall patterns, which could substantially influence elephant movements in the future. The findings of our work aim to not only advance the understanding of movement ecology but also foster a sustainable coexistence of humans and elephants in Sub-Saharan Africa. By predicting potential elephant routes, our work can inform strategies to minimize human-elephant conflict, effectively manage land use, and enhance anti-poaching efforts. This research underscores the importance of integrating movement ecology and climatic variables for effective wildlife management and conservation planning., 11 pages, 17 figures, Accepted in ACM SIGCAS SIGCHI Conference on Computing and Sustainable Societies (COMPASS 2023)

The concept of sustainable intensification in agriculture necessitates the implementation of management practices that prioritize sustainability without compromising productivity. However, the effects of such practices are known to depend on environmental conditions, and are therefore expected to change as a result of a changing climate. We study the impact of crop diversification on productivity in the context of climate change. We leverage heterogeneous Earth Observation data and contribute a data-driven approach based on causal machine learning for understanding how crop diversification impacts may change in the future. We apply this method to the country of Cyprus throughout a 4-year period. We find that, on average, crop diversification significantly benefited the net primary productivity of crops, increasing it by 2.8%. The effect generally synergized well with higher maximum temperatures and lower soil moistures. In a warmer and more drought-prone climate, we conclude that crop diversification exhibits promising adaptation potential and is thus a sensible policy choice with regards to agricultural productivity for present and future., Accepted for oral presentation at ISPRS Geospatial Week 2023

Phylogenetic networks play an important role in evolutionary biology as, other than phylogenetic trees, they can be used to accommodate reticulate evolutionary events such as horizontal gene transfer and hybridization. Recent research has provided a lot of progress concerning the reconstruction of such networks from data as well as insight into their graph theoretical properties. However, methods and tools to quantify structural properties of networks or differences between them are still very limited. For example, for phylogenetic trees, it is common to use balance indices to draw conclusions concerning the underlying evolutionary model, and more than twenty such indices have been proposed and are used for different purposes. One of the most frequently used balance index for trees is the so-called total cophenetic index, which has several mathematically and biologically desirable properties. For networks, on the other hand, balance indices are to-date still scarce. In this contribution, we introduce the \textit{weighted} total cophenetic index as a generalization of the total cophenetic index for trees to make it applicable to general phylogenetic networks. As we shall see, this index can be determined efficiently and behaves in a mathematical sound way, i.e., it satisfies so-called locality and recursiveness conditions. In addition, we analyze its extremal properties and, in particular, we investigate its maxima and minima as well as the structure of networks that achieve these values within the space of so-called level-$1$ networks. We finally briefly compare this novel index to the two other network balance indices available so-far.

In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [PRL 128, 218301 (2022)] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study, we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. By employing these criteria, we can improve our understanding of the underlying mechanisms driving extinction processes.

In this research, we revisit the paper by Pal et al. [Int. J. Appl. Comput. Math (2017) 3:1833-1845] and comment on the claim that global stability of the interior equilibrium point depends on some key parameters. This is not true, and we have provided detailed proof to this effect. The considered model is a modified Lotka-Volterra model where square root functional response is involved. The square root functional response is non-differentiable at the origin and hence cannot be studied with standard local stability tools. Furthermore, our numerical simulations indicate that we can classify the phase portrait into two modes of behavior where some positive initial conditions converge towards the predator axis in finite time.

Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes the population long-time dynamics, notably by influencing the ability of different strains of microorganisms to coexist. Inspired by the evolution of antimicrobial resistance, we study the dynamics of a community consisting of two competing strains subject to twofold environmental variability. The level of toxin varies in time, favouring the growth of one strain under low levels and the other strain when the toxin level is high. We also model time-changing resource abundance by a randomly switching carrying capacity that drives the fluctuating size of the community. While one strain dominates in a static environment, we show that species coexistence is possible in the presence of environmental variability. By computational and analytical means, we determine the environmental conditions under which long-lived coexistence is possible and when it is almost certain. Notably, we study the circumstances under which environmental and demographic fluctuations promote, or hinder, the strains coexistence. We also determine how the make-up of the coexistence phase and the average abundance of each strain depend on the environmental variability., 15 pages + appendix of 10 pages (Supplementary Material); Figshare resources: https://doi.org/10.6084/m9.figshare.23553066

Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes -- such as environmental carrying capacity or frequency-dependent selection -- entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is amenable to calculations in the context of a phylogenetic birth-death model, and is rich enough to model both carrying capacity and frequency-dependent selection., 30 pages, 1 figure

Compared with mandatory quarantine, voluntary quarantine offers individuals the liberty to decide on whether to isolate themselves or not in case of infection exposure, driven by their own sense of responsibility and concern for public health. To tackle this problem, we perform agent-based simulations to study the coupled dynamics of disease spreading and the adaptive behavior of quarantine. We show that voluntary quarantine can be an effective intervention measure to mitigate the transmission of the disease. Moreover, we discuss the roles played by the level of temptation to refrain from quarantine and the degree of social compassion in reducing the risk of spread and controlling the outbreak. We find that a low level of temptation or a high degree of social compassion not only can lead to the amelioration of the disease impact to some extent but also can result in a complete containment of the epidemic. By shedding light on the intricate interplay between disease spreading and voluntary quarantine, our results provide new insights into the fundamental social dilemma aspect of disease control through nonpharmaceutical interventions including voluntary quarantine., 6 pages, 3 figures

Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems, and their ecosystem, are used to predict their ecological and evolutionary population dynamics. These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful effects of phytoplankton overpopulation on zooplankton - representing a crucial next step in harmful algal bloom (HAB) modeling - and split the nutrient compartment to formulate an NPZD model. We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition, and forward hysteresis, where the bi-stability occurs with multiple attractors. Finally, we extend the threshold analysis to the NPZD model, which displays both forward hysteresis with bi-stability and Hopf bifurcation under different parameter regimes, and examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales., 40 pages, 10 primary figures, 5 supplementary figures, 1 supplementary table

In group foraging situations, the conventional expectation is that increased food availability would enhance consumption, especially when animals prioritize maximizing their food intake. This paper challenges this conventional wisdom by conducting an in-depth game-theoretic analysis of a basic producer-scrounger model, in which animals must choose between intensive food searching as producers or moderate searching while relying on group members as scroungers. Surprisingly, our study reveals that, under certain circumstances, increasing food availability can amplify the inclination to scrounge to such an extent that it paradoxically leads to a reduction in animals' food consumption compared to scenarios with limited food availability. We further illustrate a similar phenomenon in a model capturing free-riding dynamics among workers in a company. We demonstrate that, under certain reward mechanisms, enhancing workers' production capacities can inadvertently trigger a surge in free-riding behavior, leading to both diminished group productivity and reduced individual payoffs. Our findings underscore the significance of contextual factors when comprehending and predicting the impact of resource availability on individual and collective outcomes.

When a fraction of a population becomes immune to an infectious disease, the risk of widespread outbreaks decreases non-linearly as a result of the collective protection known as herd immunity. Typically, immunity to a disease can be acquired through natural infection or vaccination. It has been argued that natural infection in a heterogeneous population may induce a stronger herd immunity effect than homogeneous vaccination, because the early stages of transmission would primarily affect highly interactive individuals, leading to more efficient suppression of subsequent infections. In this study, we provide a comprehensive assessment of the herd immunity effect by analyzing the behavior of the susceptible-infected-recovered (SIR) model on static contact networks. We find that the effectiveness of disease-induced herd immunity is shaped by two competing mechanisms: While it exploits degree heterogeneity in the contact network to efficiently target highly connected individuals for immunity, it also introduces mixing heterogeneity between immune and susceptible individuals, weakening herd immunity. By controlling the degree of spatial embeddedness of the contact network structure, we find that spatial structure generally makes herd immunity stronger and also enhances the advantage of the herd immunity effect induced by random immunization over the disease-induced one in networks with low degree heterogeneity. These findings provide valuable insights into the complexity of herd immunity and have implications for designing effective disease control strategies., 8 pages, 6 figures

We investigate location problems whose optimum lies in the tropical convex hull of the input points. Firstly, we study geodesically star-convex sets under the asymmetric tropical distance and introduce the class of tropically quasiconvex functions whose sub-level sets have this shape. The latter are related to monotonic functions. Then we show that location problems whose distances are measured by tropically quasiconvex functions as before give an optimum in the tropical convex hull of the input points. We also show that a similar result holds if we replace the input points by tropically convex sets. Finally, we focus on applications to phylogenetics presenting properties of consensus methods arising from our class of location problems., 19 pages, 3 figures

A very large class of ODE epidemic models (2.2) discussed in this paper enjoys the property of admitting also an integral renewal formulation, with respect to an "age of infection kernel" a(t) which has a matrix exponential form (3.2). We observe first that a very short proof of this fact is available when there is only one susceptible compartment, and when its associated "new infections" matrix has rank one. In this case, a(t) normalized to have integral 1, is precisely the probabilistic law which governs the time spent in all the "infectious states associated to the susceptible compartment", and the normalization is precisely the basic replacement number. The Laplace transform (LT) of a(t) is a generalization of the basic replacement number, and its structure reflects the laws of the times spent in each infectious state. Subsequently, we show that these facts admit extensions to processes with several susceptible classes, provided that all of them have a new infections matrix of rank one. These results reveal that the ODE epidemic models highlighted below have also interesting probabilistic properties.

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies., 23 pages, 5 figures

The time-varying reproduction number $R(t)$ measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating $R(t)$ from an epidemic time series, is that $R(t)$ has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, $R_A(t)$, the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between $R_A(t)$ and $R(t)$ depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of $R(t)$, and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics.

Field and mesocosm studies repeatedly show that higher tier process reduce the predictive accuracy of toxicity evaluation and consequently their value for pesticide risk assessment. Therefore, understanding the influence of ecological complexity on toxicant effects is crucial to improve realism of aquatic risk assessment. Here we investigate the influence of repeated exposure to ecologically realistic concentrations of esfenvalerate on the similarly sensitive species Daphnia magna and Culex pipiens in a food limited and highly competitive environment. We show that significant perturbations in population development are only present close to the EC50. In contrast, interspecific competition between species is already reduced at concentrations 3-4 orders of magnitude below the acute EC50. We conclude that extremely low, environmentally relevant concentrations can disrupt species interactions. This toxicant mediated alteration of competitive balances in ecological communities may be the underlying mechanism for shifts in species distribution at ultra-low pesticide concentrations. A realistic risk assessment should therefore consider these processes in order to predict potential pesticide effects on the structure of communities.

Comparisons of single-cell RNA sequencing (scRNA-seq) data across species can reveal links between cellular gene expression and the evolution of cell functions, features, and phenotypes. These comparisons invoke evolutionary histories, as depicted with phylogenetic trees, that define relationships between species, genes, and cells. Here we illustrate a tree-based framework for comparing scRNA-seq data, and contrast this framework with existing methods. We describe how we can use trees to identify homologous and comparable groups of genes and cells, based on their predicted relationship to genes and cells present in the common ancestor. We advocate for mapping data to branches of phylogenetic trees to test hypotheses about the evolution of cellular gene expression. We describe the kinds of data that can be compared, and the types of questions that each comparison has the potential to address. Finally, we reconcile species phylogenies, gene phylogenies, cell phylogenies, and cell lineages as different representations of the same concept: the tree of cellular life. By integrating phylogenetic approaches into scRNA-seq analyses, we can overcome challenges for building informed comparisons across species, and robustly test hypotheses about gene and cell evolution., 16 pages, 4 figures

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be common quantitative rules and constraints. However, there are also reasons to believe they should be different. For example, while the environments of trees may be relatively simple, neurons are constructed by a complex iterative program where synapses are made and pruned. This complexity may make neurons less self-similar than trees. Here we test this hypothesis by comparing the features of segmented sub-trees with those of the whole tree. We indeed find more self-similarity within actual trees than neurons. At the same time, we find that many other features are somewhat comparable across the two. Investigation of shapes and behaviors promises new ways of conceptualizing the form-function link.

The COVID-19 pandemic has created unprecedented challenges for governments and healthcare systems worldwide, highlighting the critical importance of understanding the factors that contribute to virus transmission. This study aimed to identify the most influential age groups in COVID-19 infection rates at the US county level using the Modified Morris Method and deep learning for time series. Our approach involved training the state-of-the-art time-series model Temporal Fusion Transformer on different age groups as a static feature and the population vaccination status as the dynamic feature. We analyzed the impact of those age groups on COVID-19 infection rates by perturbing individual input features and ranked them based on their Morris sensitivity scores, which quantify their contribution to COVID-19 transmission rates. The findings are verified using ground truth data from the CDC and US Census, which provide the true infection rates for each age group. The results suggest that young adults were the most influential age group in COVID-19 transmission at the county level between March 1, 2020, and November 27, 2021. Using these results can inform public health policies and interventions, such as targeted vaccination strategies, to better control the spread of the virus. Our approach demonstrates the utility of feature sensitivity analysis in identifying critical factors contributing to COVID-19 transmission and can be applied in other public health domains.

When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and treatment are very helpful for controlling the effects of such infectious diseases. To analyze the impacts of these diseases, we proposed a new compartmental model with a generalized non-linear incidence function, vaccination function, and treatment function, along with time delays in the respective functions, which show how its monotonic features influence the stability of the model. Fundamental properties of a model, such as positivity, boundedness, and the existence of equilibria, are examined in this work. The basic reproduction number has been computed, and correlative studies for local stability in view of the basic reproduction number have been examined at the disease-free and endemic equilibrium points. A delay-independent global stability result has been established, and to be more precise, we explicitly derived the result on global stability by restricting delay parameters within a very specific range. Furthermore, numerical simulations and some examples based on COVID-19 real-time data are pointed out to emphasize the significance of how the disease's dynamical behavior is characterized by various functions for controlling the spread of disease in a population and to justify the mathematical conclusions., 25 pages, 19 figures

The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e., how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the SIR-DDFT model, a combination of the susceptible-infected-recovered (SIR) model from epidemiology with dynamical density functional theory (DDFT) from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak., 15 pages, 2 figures

A core challenge in global change biology is to predict how species will respond to future environmental change and to manage these responses. To make such predictions and management actions robust to novel futures, we need to accurately characterize how organisms experience their environments and the biological mechanisms by which they respond. All organisms are thermodynamically connected to their environments through the exchange of heat and water at fine spatial and temporal scales and this exchange can be captured with biophysical models. Although mechanistic models based on biophysical ecology have a long history of development and application, their use in global change biology remains limited despite their enormous promise and increasingly accessible software. We contend that greater understanding and training in the theory and methods of biophysical ecology is vital to expand their application. Our review shows how biophysical models can be implemented to understand and predict climate change impacts on species' behavior, phenology, survival, distribution, and abundance. It also illustrates the types of outputs that can be generated, and the data inputs required for different implementations. Examples range from simple calculations of body temperature at a particular site and time, to more complex analyses of species' distribution limits based on projected energy and water balances, accounting for behavior and phenology. We outline challenges that currently limit the widespread application of biophysical models relating to data availability, training, and the lack of common software ecosystems. We also discuss progress and future developments that could allow these models to be applied to many species across large spatial extents and timeframes. Finally, we highlight how biophysical models are uniquely suited to solve global change biology problems that involve predicting and interpreting responses to environmental variability and extremes, multiple or shifting constraints, and novel abiotic or biotic environments.

The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\ allele frequencies $p$ are given through a reference database of size $N$, and $q$ is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, $M$ and $N$, on the estimate of $q$. We recall results for the effect of finite $M$, and provide a central limit theorem for the effect of finite $N$, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics., 25 pages, 7 figures

The Coefficient of Parentage (COP) between two individuals is the expected inbreeding of their offspring. Originally exploited by animal breeders, is now a routine calculation among plant breeders as part of crop improvement programs. Here we show that the COP between strains requires a different calculation than the used to calculate the COP between individuals. Failure to do so may result in an overestimation of the amount of inbreeding. Here we provide a simple methodology to calculate the correct coefficient of parentage between strains., The pdf version is 23 pages long, with 6 figures and 5 tables

Epistasis occurs when the effect of a mutation depends on its carrier's genetic background. Despite increasing evidence that epistasis for fitness is common, its role during evolution is contentious. Fitness landscapes, mappings of genotype or phenotype to fitness, capture the full extent and complexity of epistasis. Fitness landscape theory has shown how epistasis affects the course and the outcome of evolution. Moreover, by measuring the competitive fitness of sets of tens to thousands of connected genotypes, empirical fitness landscapes have shown that epistasis is frequent and depends on the fitness measure, the choice of mutations for the landscape, and the environment in which it was measured. Here, I review fitness landscape theory and experiments and their implications for the role of epistasis in adaptation. I discuss theoretical expectations in the light of empirical fitness landscapes and highlight open challenges and future directions towards integrating theory and data, and incorporating ecological factors., 25 pages; submitted to Annual Reviews in Ecology, Evolution, and Systematics

Movements in imagery captivate the human eye and imagination. They are also of interest in variety of scientific disciplines that study spatiotemporal dynamics. Popular methods for quantifying movement in imagery include particle image velocimetry and digital image correlation. Both methods are widely applied in engineering and materials science, but less applied in other disciplines. This paper describes an implementation of a basic digital image correlation algorithm in R open source software as well as an extension designed to quantify persistent movement velocities in sequences of three or more images. Algorithms are applied in the novel arena of landscape ecology to quantify population movement and to produce vector fields for easy visualization of complex movement patterns across space. Functions to facilitate analyses are available in the ICvectorfields software package. These methods and functions are likely to produce novel insights in theoretical and landscape ecology because they facilitate visualization and comparison of theoretical and observed data in complex and heterogeneous environments.

International audience; During the Noachian, Mars' crust may have provided a favourable environment for microbial life1,2. The porous brine-saturated regolith3-5 would have created a physical space sheltered from ultraviolet and cosmic radiation and provided a solvent, whereas the below-ground temperature2 and diffusion6,7 of a dense, reduced atmosphere8,9 may have supported simple microbial organisms that consumed H2 and CO2 as energy and carbon sources and produced methane as a waste. On Earth, hydrogenotrophic methanogenesis was among the earliest metabolisms10,11, but its viability on early Mars has never been quantitatively evaluated. Here we present a probabilistic assessment of Mars' Noachian habitability to H2-based methanogens and quantify their biological feedback on Mars' atmosphere and climate. We find that subsurface habitability was very likely, and limited mainly by the extent of surface ice coverage. Biomass productivity could have been as high as in the early Earth's ocean. However, the predicted atmospheric composition shift caused by methanogenesis would have triggered a global cooling event, ending potential early warm conditions, compromising surface habitability and forcing the biosphere deep into the Martian crust. Spatial projections of our predictions point to lowland sites at low-to-medium latitudes as good candidates to uncover traces of this early life at or near the surface.

The Amazon floodplains represent important surfaces of highly valuable ecosystems, yet they remain neglected from protected areas. While the efficiency of the protected area network of the Amazon basin may be jeopardised by climate change, floodplains are exposed to important consequences of climate change but are omitted from species distribution models and protection gap analyses. We modelled the current and future (2070) distribution of the giant bony-tongue fish Arapaima sp. accounting for climate and habitat requirements, with consideration of dam presence (already existing and planned constructions) and hydroperiod (high- and low-water stages). We further quantified the amount of suitable environment which falls inside and outside the current network of protected areas to identify spatial conservation gaps. We predict climate change to cause the decline of environmental suitability by 16.6% during the high-water stage, and by 19.4% during the low-water stage. We found that about 70% of the suitable environments of Arapaima sp. remain currently unprotected, which is likely to increase by 5% with future climate change effects. Both current and projected dam constructions may hamper population flows between the central and the Bolivian and Peruvian parts of the basin. We highlight protection gaps mostly in the southwestern part of the basin and recommend the extension of the current network of protected areas in the floodplains of the upper Ucayali, Juru\`a and Purus Rivers and their tributaries. This study showed the importance of taking into account hydroperiods and dispersal barriers in forecasting the distribution of freshwater fish species, and stresses the urgent need to integrate floodplains to the protected area networks., Comment: 30 pages, 3 figures + Appendix

Extremophiles have gained prominence by providing an experimental approach to astrobiology. Extremophiles gain equal value by being part of a framework for high-level characterisation of the evolutionary mechanisms that must necessarily restrict or promote their emergence and presence on solar system bodies. Thus, extremophiles exist in extreme environments, and therein lies the paradox: extremophiles can only live in extreme environments but yet are not able to originate in such environments. Therefore, even though the range of extremophile capabilities in extreme environments is wider than that in mesophiles, the range of their emergence possibilities is still equally restricted. Therefore, even if one locates an extreme exoworld where terrestrial extremophiles could live here-and-now, it can be predicted that no extremophile analogues are present anyway. Furthermore, it is possible for a world to be uninhabited, yet be habitable, and therein arises the extreme environment paradox: an extreme environment can sustain chemical evolution as well as arriving non-native life, yet native life cannot be built up in that very environment. Thus, life may exist on an extraterrestrial extreme world (if imported there), and chemical evolution may be present on that world. However, it can be predicted that there is no native life anyway. This situation can be predicted to function as a chemosignature and eventually as a biosignature. However, the fact that a non-native extremopile in principle can exist in extreme environments may demonstrate that the intermediate step between chemical evolution and extremophiles can still occur in the form of a statistical deviation., Comment: 14 pages

Ecological systems are studied using many different approaches and mathematical tools. One approach, based on the Jacobian of Lotka-Volterra type models, has been a staple of mathematical ecology for years, leading to many ideas such as on questions of system stability. Instability in such methods is determined by the presence of an eigenvalue of the community matrix lying in the right half plane. The coefficients of the characteristic polynomial derived from community matrices contain information related to the specific matrix elements that play a greater destabilising role. Yet the destabilising circuits, or cycles, constructed by multiplying these elements together, form only a subset of all the feedback loops comprising a given system. This paper looks at the destabilising feedback loops in predator-prey, mutualistic and competitive systems in terms of sets of the matrix elements to explore how sign structure affects how the elements contribute to instability. This leads to quite rich combinatorial structure among the destabilising cycle sets as set size grows within the coefficients of the characteristic polynomial.

When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper we propose a novel method to infer a missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from our method has at most four Robinson-Foulds (RF) distance from the ground truth and computational experiments with simulated data show our method works well.

Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the initial conditions. We present a efficient numerical method to compute this time-shift distribution for a large class of stochastic models. The method relies on differentiation of certain functional equations, which we show can be effectively automated by deriving rules for different types of model rates that arise commonly when mass-action mixing is assumed. Explicit computation of the time-shift distribution can be used to build a practical tool for the efficient generation of macroscopic trajectories of stochastic population models, without the need for costly stochastic simulations. Full code is provided to implement this and we demonstrate our method on an epidemic model and a model of within-host viral dynamics., 47 pages, 9 figures

Identifying and understanding the large-scale biodiversity patterns in time and space is vital for conservation and addressing fundamental ecological and evolutionary questions. Network-based methods have proven useful for simplifying and highlighting important structures in species distribution data. However, current network-based biogeography approaches cannot exploit the evolutionary information available in phylogenetic data. We introduce a method for incorporating evolutionary relationships into species occurrence networks to produce more biologically informative and robust bioregions. To keep the bipartite network structure where bioregions are grid cells indirectly connected through shared species, we incorporate the phylogenetic tree by connecting ancestral nodes to the grid cells where their descendant species occur. To incorporate the whole tree without destroying the spatial signal of narrowly distributed species or ancestral nodes, we weigh tree nodes by the geographic information they provide. For a more detailed analysis, we enable integration of the evolutionary relationships at a specific time in the tree. By sweeping through the phylogenetic tree in time, our method interpolates between finding bioregions based only on distributional data and finding spatially segregated clades, uncovering evolutionarily distinct bioregions at different time slices. We also introduce a way to segregate the connections between evolutionary branches at a selected time to enable exploration of overlapping evolutionarily distinct regions. We have implemented these methods in Infomap Bioregions, an interactive web application that makes it easy to explore the possibly hierarchical and fuzzy patterns of biodiversity on different scales in time and space.

The framework of iterated Prisoner's Dilemma (IPD) is commonly used to study direct reciprocity and cooperation, with a focus on the assessment of the generosity and reciprocal fairness of an IPD strategy in one-on-one settings. In order to understand the persistence and resilience of reciprocal cooperation, here we study long-term population dynamics of IPD strategies using the Moran process where stochastic dynamics of strategy competition can lead to the rise and fall of cooperation. Although prior work has included a handful of typical IPD strategies in the consideration, it remains largely unclear which type of IPD strategies is pivotal in steering the population away from defection and providing an escape hatch for establishing cooperation. We use a network-based approach to analyze and characterize networks of evolutionary pathways that bridge transient episodes of evolution dominated by depressing defection and ultimately catalyze the evolution of reciprocal cooperation in the long run. We group IPD strategies into three types according to their stationary cooperativity with an unconditional cooperator: the good (fully cooperative), the bad (fully exploitive), and the ugly (in between the former two types). We consider the mutation-selection equilibrium with rare mutations and quantify the impact of the presence versus absence of any given IPD strategy on the resulting population equilibrium. We identify catalysts (certain IPD strategies) as well as bridges (particular evolutionary pathways) that are most crucial for boosting the abundance of good types and suppressing that of bad types or having the highest betweenness centrality. Our work has practical implications and broad applicability to real-world cooperation problems by leveraging catalysts and bridges that are capable of strengthening persistence and resilience., 6 pages, 5 figures

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and a non-genetic (environmental) component and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the trait values of the parents. In previous work, Barton et al.(2017), we showed that when trait values are determined by the sum of a large number of Mendelian factors, each of small effect, one can justify the infinitesimal model as limit of Mendelian inheritance. In this paper, we show that the robustness of the infinitesimal model extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. In this setting, it is natural to decompose trait values, not just into the additive and dominance components, but into a component that is shared by all individuals within the family and an independent `residual' for each offspring, which captures the randomness of Mendelian inheritance. We show that, even if we condition on parental trait values, both the shared component and the residuals within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/\sqrt{M}. We illustrate our results with some numerical examples., 68 pages, 9 figures. To appear in Genetics

For population systems modeled by age-structured hyperbolic partial differential equations (PDEs), we redesign the existing feedback laws, designed under the assumption that the dilution input is directly actuated, to the more realistic case where dilution is governed by actuation dynamics (modeled simply by an integrator). In addition to the standard constraint that the population density must remain positive, the dilution dynamics introduce constraints of not only positivity of dilution, but possibly of given positive lower and upper bounds on dilution. We present several designs, of varying complexity, and with various measurement requirements, which not only ensure global asymptotic (and local exponential) stabilization of a desired positive population density profile from all positive initial conditions, but do so without violating the constraints on the dilution state. To develop the results, we exploit the relation between first-order hyperbolic PDEs and an equivalent representation in which a scalar input-driven mode is decoupled from input-free infinite-dimensional internal dynamics represented by an integral delay system.