Making ecological models adequate

Using neural ordinary differential equations to predict complex ecological dynamics from population density data

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

Spatiotemporal dynamics in butterfly hybrid zones

Evaluating whether hybrid zones are stable or mobile can provide novel insights for evolution and conservation biology. Butterflies exhibit high sensitivity to environmental changes and represent an important model system for the study of hybrid zone origins and maintenance. Here, we review the literature exploring butterfly hybrid zones, with a special focus on their spatiotemporal dynamics and the potential mechanisms that could lead to their movement or stability. We then compare different lines of evidence used to investigate hybrid zone dynamics and discuss the strengths and weaknesses of each approach. Our goal with this review is to reveal general conditions associated with the stability or mobility of butterfly hybrid zones by synthesizing evidence obtained using different types of data sampled across multiple regions and spatial scales. Finally, we discuss spatiotemporal dynamics in the context of a speciation/divergence continuum, the relevance of hybrid zones for conservation biology, and recommend key topics for future investigation.

Ecological threshold of phosphorus load in Baiyangdian Lake based on a PCLake model and ecological network analysis

Ecological thresholds are a useful indicator for implementing ecological management. Many studies determine the thresholds for nutrient loads in lakes based on the maximum allowable concentration of chlorophyll a (Chla), although this neglects the overall performance of the ecosystem. A PCLake model of Baiyangdian (BYD) Lake in northern China was constructed with six ecological network analysis (ENA) indicators that characterized the ecosystem function, system maturity, and food web structure to quantify the overall status of the BYD ecosystem. To my knowledge, this is the first study on the system level responses of the BYD Lake to phosphorus load interference. Different phosphorus load scenarios were designed to simulate the ecological responses of BYD Lake. The simulated results were employed to calculate the ENA indicators. Ecological thresholds were determined through the driving response relationship between the phosphorus load gradient and the ENA indicators. The results show a non-linear transition response of ENA indicator under phosphorus load gradient. As phosphorus load increases, D/H, SOI, and FCI decreases while A/DC, TPP/TR, and TPP/TB increases. This indicates that the overall structure and function of the ecosystem will deteriorate if phosphorus load increases. The phosphorus load thresholds for the overall performance of BYD Lake were 0.50-1.32 mg m-2 d-1, slightly wider than that of Chla (0.53-1.26 mg m-2 d-1). The model results clearly indicate that there is a time-lag phenomenon at the switch points in the response of ENA indicators compared to that of single functional group. In addition, the A/DC, TPP/TR, SOI, and FCI present more time-lag than that of other ENA indicators. These time-lag effects provide a particular opportunity for biodiversity conservation. Therefore, a possible management strategy is proposed to combine system-level and function group-level thresholds, with the ENA-based threshold as the bottom line and the phytoplankton's threshold as the early-warning indicator. This design is expected to be more precise and efficient, by exploiting the advantages of two thresholds, and may benefit for ecological management practices.

Meeting the Growing Need for Land-Water System Modelling to Assess Land Management Actions

Elevated contaminant levels and hydrological alterations resulting from land use are degrading aquatic ecosystems on a global scale. A range of land management actions may be used to reduce or prevent this degradation. To select among alternative management actions, decision makers require predictions of their effectiveness, their economic impacts, estimated uncertainty in the predictions, and estimated time lags between management actions and environmental responses. There are multiple methods for generating these predictions, but the most rigorous and transparent methods involve quantitative modelling. The challenge for modellers is two-fold. First, they must employ models that represent complex land-water systems, including the causal chains linking land use to contaminant loss and water use, catchment processes that alter contaminant loads and flow regimes, and ecological responses in aquatic environments. Second, they must ensure that these models meet the needs of endusers in terms of reliability, usefulness, feasibility and transparency. Integrated modelling using coupled models to represent the land-water system can meet both challenges and has advantages over alternative approaches. The need for integrated land-water system modelling is growing as the extent and intensity of human land use increases, and regulatory agencies seek more effective land management actions to counter the adverse effects. Here we present recommendations for modelling teams, to help them improve current practices and meet the growing need for land-water system models. The recommendations address several aspects of integrated modelling: (1) assembling modelling teams; (2) problem framing and conceptual modelling; (3) developing spatial frameworks; (4) integrating economic and biophysical models; (5) selecting and coupling models.

Models of underlying autotrophic biomass dynamics fit to daily river ecosystem productivity estimates improve understanding of ecosystem disturbance and resilience

Directly observing autotrophic biomass at ecologically relevant frequencies is difficult in many ecosystems, hampering our ability to predict productivity through time. Since disturbances can impart distinct reductions in river productivity through time by modifying underlying standing stocks of biomass, mechanistic models fit to productivity time series can infer underlying biomass dynamics. We incorporated biomass dynamics into a river ecosystem productivity model for six rivers to identify disturbance flow thresholds and understand the resilience of primary producers. The magnitude of flood necessary to disturb biomass and thereby reduce ecosystem productivity was consistently lower than the more commonly used disturbance flow threshold of the flood magnitude necessary to mobilize river bed sediment. The estimated daily maximum percent increase in biomass (a proxy for resilience) ranged from 5% to 42% across rivers. Our latent biomass model improves understanding of disturbance thresholds and recovery patterns of autotrophic biomass within river ecosystems.

Distribution models calibrated with independent field data predict two million ancient and veteran trees in England

Large, citizen-science species databases are powerful resources for predictive species distribution modeling (SDM), yet they are often subject to sampling bias. Many methods have been proposed to correct for this, but there exists little consensus as to which is most effective, not least because the true value of model predictions is hard to evaluate without extensive independent field sampling. We present here a nationwide, independent field validation of distribution models of ancient and veteran trees, a group of organisms of high conservation importance, built using a large and internationally unique citizen-science database: the Ancient Tree Inventory (ATI). This validation exercise presents an opportunity to test the performance of different methods of correcting for sampling bias, in the search for the best possible prediction of ancient and veteran tree distributions in England. We fitted a variety of distribution models of ancient and veteran tree records in England in relation to environmental predictors and applied different bias correction methods, including spatial filtering, background manipulation, the use of bias files, and, finally, zero-inflated (ZI) regression models, a new method with great potential to investigate and remove sampling bias in species data. We then collected new independent field data through systematic surveys of 52 randomly selected 1-km² grid squares across England to obtain abundance estimates of ancient and veteran trees. Calibration of the distribution models against the field data suggests that there are around eight to 10 times as many ancient and veteran trees present in England than the records currently suggest, with estimates ranging from 1.7 to 2.1 million trees compared to the 200,000 currently recorded in the ATI. The most successful bias correction method was systematic sampling of occurrence records, although the ZI models also performed well, significantly predicting field observations and highlighting both likely causes of undersampling and areas of the country in which many unrecorded trees are likely to be found. Our findings provide the first robust nationwide estimate of ancient and veteran tree abundance and demonstrate the enormous potential for distribution modeling based on citizen-science data combined with independent field validation to inform conservation planning.

Simulation applications to support teaching and research in epidemiological dynamics

BACKGROUND

An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP ^Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.

RESULTS

We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R₀, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R₀>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.

CONCLUSION

Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Capturing the dynamics of small populations: A retrospective assessment using long-term data for an island reintroduction

The art of population modelling is to incorporate factors essential for capturing a population's dynamics while otherwise keeping the model as simple as possible. However, it is unclear how optimal model complexity should be assessed, and whether this optimal complexity has been affected by recent advances in modelling methodology. This issue is particularly relevant to small populations because they are subject to complex dynamics but inferences about those dynamics are often constrained by small sample sizes. We fitted Bayesian hierarchical models to long-term data on vital rates (survival and reproduction) for the toutouwai Petroica longipes population reintroduced to Tiritiri Matangi, a 220-ha New Zealand island, and quantified the performance of those models in terms of their likelihood of replicating the observed population dynamics. These dynamics consisted of overall growth from 33 (±0.3) to 160 (±6) birds from 1992-2018, including recoveries following five harvest events for further reintroductions to other sites. We initially included all factors found to affect vital rates, which included inbreeding, post-release effects (PRE), density-dependence, sex, age and random annual variation, then progressively removed these factors. We also compared performance of models where data analysis and simulations were done simultaneously to those produced with the traditional two-step approach, where vital rates are estimated first then fed into a separate simulation model. Parametric uncertainty and demographic stochasticity were incorporated in all projections. The essential factors for replicating the population's dynamics were density-dependence in juvenile survival and PRE, i.e. initial depression of survival and reproduction in translocated birds. Inclusion of other factors reduced the precision of projections, and therefore the likelihood of matching observed dynamics. However, this reduction was modest when the modelling was done in an integrated framework. In contrast, projections were much less precise when done with a two-step modelling approach, and the cost of additional parameters was much higher under the two-step approach. These results suggest that minimization of complexity may be less important than accounting for covariances in parameter estimates, which is facilitated by integrating data analysis and population projections using Bayesian methods.

Plague Exposure in Mammalian Wildlife Across the Western United States

Plague is caused by a bacterial pathogen (Yersinia pestis) that can infect a wide range of mammal species, but its presence in wildlife is often underappreciated. Using a large-scale data set (n = 44,857) that details the extent of Y. pestis exposure in wildlife, we document exposure in 18 wildlife species, including coyotes (Canis latrans), bobcats (Lynx rufus), and black bears (Ursus americanus). Evidence of plague activity is widespread, with seropositive animals detected in every western state in the contiguous United States. Pathogen monitoring systems in wildlife that are both large scale and long-term are rare, yet they open the door for analyses on potential shifts in distribution that have occurred over time because of climate or land use changes. The data generated by these long-term monitoring programs, combined with recent advances in our understanding of pathogen ecology, offer a clearer picture of zoonotic pathogens and the risks they pose.

Host adaptation to novel pathogen introduction: Predicting conditions that promote evolutionary rescue

Novel pathogen introduction can have drastic consequences for naive host populations, and outcomes can be difficult to predict. Evolutionary rescue (ER) provides a foundation for understanding whether hosts are driven to extinction or survive via adaptation. Currently, patterns of host population dynamics alongside evidence of adaptation are used to infer ER. However, the gap between established ER theory and complexity inherent in natural systems makes interpreting empirical patterns difficult because they can be confounded with ecological drivers of survival under current theory. To bridge this gap, we expand ER theory to include biological selective agents, such as pathogens. We find birth processes to be more important than previously theorised in determining ER potential. We employ a novel framework evaluating ER potential within natural systems and gain ability to identify system characteristics that make ER possible. Identifying these characteristics allows a shift from retrospective observation to a predictive mindset, and our findings suggest that ER occurrence may be more limited than previously thought. We use the plague system of Yersinia pestis infecting Cynomys ludovicianus (black-tailed prairie dogs) and Spermophilus beecheyi (California ground squirrels) as a case study.

Towards an ecosystem model of infectious disease

Increasingly intimate associations between human society and the natural environment are driving the emergence of novel pathogens, with devastating consequences for humans and animals alike. Prior to emergence, these pathogens exist within complex ecological systems that are characterized by trophic interactions between parasites, their hosts and the environment. Predicting how disturbance to these ecological systems places people and animals at risk from emerging pathogens-and the best ways to manage this-remains a significant challenge. Predictive systems ecology models are powerful tools for the reconstruction of ecosystem function but have yet to be considered for modelling infectious disease. Part of this stems from a mistaken tendency to forget about the role that pathogens play in structuring the abundance and interactions of the free-living species favoured by systems ecologists. Here, we explore how developing and applying these more complete systems ecology models at a landscape scale would greatly enhance our understanding of the reciprocal interactions between parasites, pathogens and the environment, placing zoonoses in an ecological context, while identifying key variables and simplifying assumptions that underly pathogen host switching and animal-to-human spillover risk. As well as transforming our understanding of disease ecology, this would also allow us to better direct resources in preparation for future pandemics.

Functional biology in its natural context: A search for emergent simplicity

The immeasurable complexity at every level of biological organization creates a daunting task for understanding biological function. Here, we highlight the risks of stripping it away at the outset and discuss a possible path toward arriving at emergent simplicity of understanding while still embracing the ever-changing complexity of biotic interactions that we see in nature.

Building mean field ODE models using the generalized linear chain trick & Markov chain theory

The well known linear chain trick (LCT) allows modellers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these sub-states is the sum of k exponentially distributed random variables, and is thus gamma distributed. The generalized linear chain trick (GLCT) extends this technique to the broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Phase-type distributions are the family of matrix exponential distributions on [0,∞) that represent the absorption time distributions for finite-state, continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build ODE models from underlying stochastic model assumptions. We introduce two novel model families by using the GLCT to generalize the Rosenzweig-MacArthur predator-prey model, and the SEIR model. We illustrate the kinds of complexity that can be captured by such models through multiple examples. We also show the benefits of using a GLCT-based model formulation to speed up the computation of numerical solutions to such models. These results highlight the intuitive nature, and utility, of using the GLCT to derive ODE models from first principles.

Developing Bayesian networks in managing the risk of Legionella colonisation of groundwater aeration systems

An Australian water utility has developed a Legionella High Level Risk Assessment (LHLRA) which provides a semi-qualitative assessment of the risk of Legionella proliferation and human exposure in engineered water systems using a combination of empirical observation and expert knowledge. Expanding on this LHLRA, we propose two iterative Bayesian network (BN) models to reduce uncertainty and allow for a probabilistic representation of the mechanistic interaction of the variables, built using data from 25 groundwater treatment plants. The risk of Legionella exposure in groundwater aeration units was quantified as a function of five critical areas including hydraulic conditions, nutrient availability and growth, water quality, system design (and maintenance), and location and access. First, the mechanistic relationship of the variables was conceptually mapped into a fishbone diagram, parameterised deterministically using an expert elicited weighted scoring system and translated into BN. The "sensitivity to findings" analysis of the BN indicated that system design was the most influential variable while elemental accumulation thresholds were the least influential variable for Legionella exposure. The diagnostic inference was used in high and low-risk scenarios to demonstrate the capabilities of the BNs to examine probable causes for diverse conditions. Subsequently, the causal relationship of Legionella growth and human exposure were improved through a conceptual bowtie representation. Finally, an improved model developed the predictors of Legionella growth and the risk of human exposure through the interaction of operational, water quality monitoring, operational parameters, and asset conditions. The use of BNs modelling based on risk estimation and improved functional decision outputs offer a complementary and more transparent alternative approach to quantitative analysis of uncertainties than the current LHLRA.

"Micropersonality" traits and their implications for behavioral and movement ecology research

Many animal personality traits have implicit movement-based definitions and can directly or indirectly influence ecological and evolutionary processes. It has therefore been proposed that animal movement studies could benefit from acknowledging and studying consistent interindividual differences (personality), and, conversely, animal personality studies could adopt a more quantitative representation of movement patterns.Using high-resolution tracking data of three-spined stickleback fish (Gasterosteus aculeatus), we examined the repeatability of four movement parameters commonly used in the analysis of discrete time series movement data (time stationary, step length, turning angle, burst frequency) and four behavioral parameters commonly used in animal personality studies (distance travelled, space use, time in free water, and time near objects).Fish showed repeatable interindividual differences in both movement and behavioral parameters when observed in a simple environment with two, three, or five shelters present. Moreover, individuals that spent less time stationary, took more direct paths, and less commonly burst travelled (movement parameters), were found to travel farther, explored more of the tank, and spent more time in open water (behavioral parameters).Our case study indicates that the two approaches-quantifying movement and behavioral parameters-are broadly equivalent, and we suggest that movement parameters can be viewed as "micropersonality" traits that give rise to broad-scale consistent interindividual differences in behavior. This finding has implications for both personality and movement ecology research areas. For example, the study of movement parameters may provide a robust way to analyze individual personalities in species that are difficult or impossible to study using standardized behavioral assays.

Predicting the results of competition between two breast cancer lines grown in 3-D spheroid culture

This study develops a novel model of a consumer-resource system with mobility included, in order to explain a novel experiment of competition between two breast cancer cell lines grown in 3D in vitro spheroid culture. The model reproduces observed differences in monoculture, such as overshoot phenomena and final size. It also explains both theoretically and through simulation the inevitable triumph of the same cell line in co-culture, independent of initial conditions. The mobility of one cell line (MDA-MB-231) is required to explain both the success and the rapidity with which that species dominates the population and drives the other species (MCF-7) to extinction. It is shown that mobility directly interferes with the other species and that the cost of that mobility is in resource usage rate.

A versatile web app for identifying the drivers of COVID-19 epidemics

Background

No versatile web app exists that allows epidemiologists and managers around the world to comprehensively analyze the impacts of COVID-19 mitigation. The http://covid-webapp.numerusinc.com/ web app presented here fills this gap.

Methods

Our web app uses a model that explicitly identifies susceptible, contact, latent, asymptomatic, symptomatic and recovered classes of individuals, and a parallel set of response classes, subject to lower pathogen-contact rates. The user inputs a CSV file of incidence and, if of interest, mortality rate data. A default set of parameters is available that can be overwritten through input or online entry, and a user-selected subset of these can be fitted to the model using maximum-likelihood estimation (MLE). Model fitting and forecasting intervals are specifiable and changes to parameters allow counterfactual and forecasting scenarios. Confidence or credible intervals can be generated using stochastic simulations, based on MLE values, or on an inputted CSV file containing Markov chain Monte Carlo (MCMC) estimates of one or more parameters.

Results

We illustrate the use of our web app in extracting social distancing, social relaxation, surveillance or virulence switching functions (i.e., time varying drivers) from the incidence and mortality rates of COVID-19 epidemics in Israel, South Africa, and England. The Israeli outbreak exhibits four distinct phases: initial outbreak, social distancing, social relaxation, and a second wave mitigation phase. An MCMC projection of this latter phase suggests the Israeli epidemic will continue to produce into late November an average of around 1500 new case per day, unless the population practices social-relaxation measures at least 5-fold below the level in August, which itself is 4-fold below the level at the start of July. Our analysis of the relatively late South African outbreak that became the world’s fifth largest COVID-19 epidemic in July revealed that the decline through late July and early August was characterised by a social distancing driver operating at more than twice the per-capita applicable-disease-class (pc-adc) rate of the social relaxation driver. Our analysis of the relatively early English outbreak, identified a more than 2-fold improvement in surveillance over the course of the epidemic. It also identified a pc-adc social distancing rate in early August that, though nearly four times the pc-adc social relaxation rate, appeared to barely contain a second wave that would break out if social distancing was further relaxed.

Conclusion

Our web app provides policy makers and health officers who have no epidemiological modelling or computer coding expertise with an invaluable tool for assessing the impacts of different outbreak mitigation policies and measures. This includes an ability to generate an epidemic-suppression or curve-flattening index that measures the intensity with which behavioural responses suppress or flatten the epidemic curve in the region under consideration.

A New, Catchment-Scale Integrated Water Quality Model of Phosphorus, Dissolved Oxygen, Biochemical Oxygen Demand and Phytoplankton: INCA-Phosphorus Ecology (PEco)

Process-based models are commonly used to design management strategies to reduce excessive algal growth and subsequent hypoxia. However, management targets typically focus on phosphorus control, under the assumption that successful nutrient reduction will solve hypoxia issues. Algal responses to nutrient drivers are not linear and depend on additional biotic and abiotic controls. In order to generate a comprehensive assessment of the effectiveness of nutrient control strategies, independent nutrient, dissolved oxygen (DO), temperature and algal models must be coupled, which can increase overall uncertainty. Here, we extend an existing process-based phosphorus model (INtegrated CAtchment model of Phosphorus dynamics) to include biological oxygen demand (BOD), dissolved oxygen (DO) and algal growth and decay (INCA-PEco). We applied the resultant model in two eutrophied mesoscale catchments with continental and maritime climates. We assessed effects of regional differences in climate and land use on parameter importance during calibration using a generalised sensitivity analysis. We successfully reproduced in-stream total phosphorus (TP), suspended sediment, DO, BOD and chlorophyll-a (chl-a) concentrations across a range of temporal scales, land uses and climate regimes. While INCA-PEco is highly parameterized, model uncertainty can be significantly reduced by focusing calibration and monitoring efforts on just 18 of those parameters. Specifically, calibration time could be optimized by focusing on hydrological parameters (base flow, Manning’s n and river depth). In locations with significant inputs of diffuse nutrients, e.g., in agricultural catchments, detailed data on crop growth and nutrient uptake rates are also important. The remaining parameters provide flexibility to the user, broaden model applicability, and maximize its functionality under a changing climate.

Dispersal in heterogeneous environments drives population dynamics and control of tsetse flies

Spatio-temporally heterogeneous environments may lead to unexpected population dynamics. Knowledge is needed on local properties favouring population resilience at large scale. For pathogen vectors, such as tsetse flies transmitting human and animal African trypanosomosis, this is crucial to target management strategies. We developed a mechanistic spatio-temporal model of the age-structured population dynamics of tsetse flies, parametrized with field and laboratory data. It accounts for density- and temperature-dependence. The studied environment is heterogeneous, fragmented and dispersal is suitability-driven. We confirmed that temperature and adult mortality have a strong impact on tsetse populations. When homogeneously increasing adult mortality, control was less effective and induced faster population recovery in the coldest and temperature-stable locations, creating refuges. To optimally select locations to control, we assessed the potential impact of treating them and their contribution to the whole population. This heterogeneous control induced a similar population decrease, with more dispersed individuals. Control efficacy was no longer related to temperature. Dispersal was responsible for refuges at the interface between controlled and uncontrolled zones, where resurgence after control was very high. The early identification of refuges, which could jeopardize control efforts, is crucial. We recommend baseline data collection to characterize the ecosystem before implementing any measures.

How important is individual foraging specialisation in invasive predators for native-prey population viability?

Predation by invasive species is a major threat to the persistence of naïve prey. Typically, this negative effect is addressed by suppressing the population size of the invasive predator to a point where the predation pressure does not hinder the viability of the prey. However, this type of intervention may not be effective whenever a few specialised predators are the cause of the decline. We investigated the effects of varying levels of specialised invasive stoats (Mustela erminea) abundance on the long-term viability of simulated kiwi (Apteryx spp.) populations. We explored four scenarios with different proportions of highly specialised stoats, which were those that had a ≥ 0.75 probability of predating kiwi eggs and chicks if they were within their home range: (i) a stoat population composed mostly of generalists (mean: 0.5 probability of predation across the population); (ii) 5% of highly specialised stoats and the remaining being generalists; (iii) 10% of highly specialised stoats and the remaining being generalists; and, (iv) half highly specialised stoats and half generalists. We found that stoat home range sizes, rather than stoat density or the density of highly specialised stoats, was the main driver of kiwi population trends. Stoats with large home ranges were more likely to predate kiwi eggs and chicks as these were more likely to fall within a large home range. More broadly, our findings show how the daily individual ranging and foraging behaviour of an invasive predator can scale-up to shape population trends of naïve prey.

Towards Building a Sustainable Future: Positioning Ecological Modelling for Impact in Ecosystems Management

As many ecosystems worldwide are in peril, efforts to manage them sustainably require scientific advice. While numerous researchers around the world use a great variety of models to understand ecological dynamics and their responses to disturbances, only a small fraction of these models are ever used to inform ecosystem management. There seems to be a perception that ecological models are not useful for management, even though mathematical models are indispensable in many other fields. We were curious about this mismatch, its roots, and potential ways to overcome it. We searched the literature on recommendations and best practices for how to make ecological models useful to the management of ecosystems and we searched for 'success stories' from the past. We selected and examined several cases where models were instrumental in ecosystem management. We documented their success and asked whether and to what extent they followed recommended best practices. We found that there is not a unique way to conduct a research project that is useful in management decisions. While research is more likely to have impact when conducted with many stakeholders involved and specific to a situation for which data are available, there are great examples of small groups or individuals conducting highly influential research even in the absence of detailed data. We put the question of modelling for ecosystem management into a socio-economic and national context and give our perspectives on how the discipline could move forward.

Racing against change: understanding dispersal and persistence to improve species' conservation prospects

Climate change is contributing to the widespread redistribution, and increasingly the loss, of species. Geographical range shifts among many species were detected rapidly after predictions of the potential importance of climate change were specified 35 years ago: species are shifting their ranges towards the poles and often to higher elevations in mountainous areas. Early tests of these predictions were largely qualitative, though extraordinarily rapid and broadly based, and statistical tests distinguishing between climate change and other global change drivers provided quantitative evidence that climate change had already begun to cause species’ geographical ranges to shift. I review two mechanisms enabling this process, namely development of approaches for accounting for dispersal that contributes to range expansion, and identification of factors that alter persistence and lead to range loss. Dispersal in the context of range expansion depends on an array of processes, like population growth rates in novel environments, rates of individual species movements to new locations, and how quickly areas of climatically tolerable habitat shift. These factors can be tied together in well-understood mathematical frameworks or modelled statistically, leading to better prediction of extinction risk as climate changes. Yet, species' increasing exposures to novel climate conditions can exceed their tolerances and raise the likelihood of local extinction and consequent range losses. Such losses are the consequence of processes acting on individuals, driven by factors, such as the growing frequency and severity of extreme weather, that contribute local extinction risks for populations and species. Many mechanisms can govern how species respond to climate change, and rapid progress in global change research creates many opportunities to inform policy and improve conservation outcomes in the early stages of the sixth mass extinction.

Mapping validity and validation in modelling for interdisciplinary research

Complex Adaptive Systems (CAS) is an interdisciplinary and dynamic modelling approach for the study of today’s global challenges. It is used for the explanation, description, and prediction of behaviours of system components and the system at large. To understand and assess the quality of research in which CAS models are designed and used, a thorough understanding of the meanings of ‘validity’ from social science research methodology and ‘validation’ from simulation modelling is needed. In this paper, we first describe the modelling process. Then, we analyse the concepts ‘validity’ and ‘validation’ as used in a set of research methodology textbooks and a set of modelling textbooks. We present one single map that integrates validity as characteristic of the model input, the modelling process, model validation, and the validity of the model built. The map is illustrated by means of one example. The terminology proposed in the map allows to describe and distinguish between the validity of primary research used for input in the model, how the quality of the modelling depends on structural and behavioural validation, and, how the assessment of the validity of the model is informed by these types of validation plus research with independent data.

Three questions to ask before using model outputs for decision support

Decision makers must have sufficient confidence in models if they are to influence their decisions. We propose three screening questions to critically evaluate models with respect to their purpose, organization, and evidence. They enable a more transparent, robust, and secure use of model outputs.

The Role of Vector Trait Variation in Vector-Borne Disease Dynamics

Many important endemic and emerging diseases are transmitted by vectors that are biting arthropods. The functional traits of vectors can affect pathogen transmission rates directly and also through their effect on vector population dynamics. Increasing empirical evidence shows that vector traits vary significantly across individuals, populations, and environmental conditions, and at time scales relevant to disease transmission dynamics. Here, we review empirical evidence for variation in vector traits and how this trait variation is currently incorporated into mathematical models of vector-borne disease transmission. We argue that mechanistically incorporating trait variation into these models, by explicitly capturing its effects on vector fitness and abundance, can improve the reliability of their predictions in a changing world. We provide a conceptual framework for incorporating trait variation into vector-borne disease transmission models, and highlight key empirical and theoretical challenges. This framework provides a means to conceptualize how traits can be incorporated in vector borne disease systems, and identifies key areas in which trait variation can be explored. Determining when and to what extent it is important to incorporate trait variation into vector borne disease models remains an important, outstanding question.

Emergency and Urgent Orthopaedic Surgeries in non-covid patients during the COVID 19 pandemic: Perspective from India

Objectives

To Evaluate the results and the protocols of our Institution for 18 Emergency and Urgent Non Covid Surgeries during the Covid 19 Pandemic

Methods

18 patients underwent Emergency and Urgent Orthopaedic Surgeries at institution. The Protocol was Screening, Segregation, Selection, Isolation, theatre modification, and Online Follow.

Results

Two adverse events including, one death and one intensive care admission due to underlying morbidity were recorded. Average Hospital stay was 2.5 days with no patients becoming covid positive at follow up.

Conclusion

Strict Surgical protocols need to be followed for surgery during the Covid19 pandemic.

Including Indigenous and local knowledge in climate research. An assessment of the opinion of Spanish climate change researchers

Researchers have documented that observations of climate change impacts reported by Indigenous Peoples and Local Communities coincide with scientific measurements of such impacts. However, insights from Indigenous and Local Knowledge are not yet completely included in international climate change research and policy fora. In this article, we compare observations of climate change impacts detected by Indigenous Peoples and Local Communities from around the world and collected through a literature review (n=198 case studies), with climate scientists' opinions on the relevance of such information for climate change research. Scientists' opinions were collected through a web survey among climate change researchers from universities and research centres in Spain (n=191). In the survey, we asked about the need to collect local level data regarding 68 different groups of indicators of climate change impacts to improve the current knowledge, and about the feasibility of using Indigenous and local knowledge in climate change studies. Results show consensus on the need to continue collecting local level data from all groups of indicators to get a better understanding of climate change impacts, particularly on impacts on the biological system. However, while scientists of our study considered that Indigenous and local knowledge could mostly contribute to detect climate change impacts on the biological and socioeconomic systems, the literature review shows that information on impacts on these systems is rarely collected; researchers instead have mostly documented the impacts on the climatic and physical systems reported by Indigenous and local knowledge.

Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone

Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks-the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014-2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( N_eff) and initial number of exposed individuals ( E₀) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( t_f/2) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R₀ ≈ 1.7 from country-level data appears to seriously underestimate R₀ ≈ 3.3 - 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate t_f/2 ≈ 22 weeks, compared with 8-10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4-4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Cryptic phenology in plants: Case studies, implications, and recommendations

Plant phenology-the timing of cyclic or recurrent biological events in plants-offers insight into the ecology, evolution, and seasonality of plant-mediated ecosystem processes. Traditionally studied phenologies are readily apparent, such as flowering events, germination timing, and season-initiating budbreak. However, a broad range of phenologies that are fundamental to the ecology and evolution of plants, and to global biogeochemical cycles and climate change predictions, have been neglected because they are "cryptic"-that is, hidden from view (e.g., root production) or difficult to distinguish and interpret based on common measurements at typical scales of examination (e.g., leaf turnover in evergreen forests). We illustrate how capturing cryptic phenology can advance scientific understanding with two case studies: wood phenology in a deciduous forest of the northeastern USA and leaf phenology in tropical evergreen forests of Amazonia. Drawing on these case studies and other literature, we argue that conceptualizing and characterizing cryptic plant phenology is needed for understanding and accurate prediction at many scales from organisms to ecosystems. We recommend avenues of empirical and modeling research to accelerate discovery of cryptic phenological patterns, to understand their causes and consequences, and to represent these processes in terrestrial biosphere models.

The global distribution of Bacillus anthracis and associated anthrax risk to humans, livestock and wildlife

Bacillus anthracis is a spore-forming, Gram-positive bacterium responsible for anthrax, an acute infection that most significantly affects grazing livestock and wild ungulates, but also poses a threat to human health. The geographic extent of B. anthracis is poorly understood, despite multi-decade research on anthrax epizootic and epidemic dynamics; many countries have limited or inadequate surveillance systems, even within known endemic regions. Here, we compile a global occurrence dataset of human, livestock and wildlife anthrax outbreaks. With these records, we use boosted regression trees to produce a map of the global distribution of B. anthracis as a proxy for anthrax risk. We estimate that 1.83 billion people (95% credible interval (CI): 0.59-4.16 billion) live within regions of anthrax risk, but most of that population faces little occupational exposure. More informatively, a global total of 63.8 million poor livestock keepers (95% CI: 17.5-168.6 million) and 1.1 billion livestock (95% CI: 0.4-2.3 billion) live within vulnerable regions. Human and livestock vulnerability are both concentrated in rural rainfed systems throughout arid and temperate land across Eurasia, Africa and North America. We conclude by mapping where anthrax risk could disrupt sensitive conservation efforts for wild ungulates that coincide with anthrax-prone landscapes.

Modeling Connectivity of Non-floodplain Wetlands: Insights, Approaches, and Recommendations

Representing hydrologic connectivity of non-floodplain wetlands (NFWs) to downstream waters in process-based models is an emerging challenge relevant to many research, regulatory, and management activities. We review four case studies that utilize process-based models developed to simulate NFW hydrology. Models range from a simple, lumped parameter model to a highly complex, fully distributed model. Across case studies, we highlight appropriate application of each model, emphasizing spatial scale, computational demands, process representation, and model limitations. We end with a synthesis of recommended "best modeling practices" to guide model application. These recommendations include: (1) clearly articulate modeling objectives, and revisit and adjust those objectives regularly; (2) develop a conceptualization of NFW connectivity using qualitative observations, empirical data, and process-based modeling; (3) select a model to represent NFW connectivity by balancing both modeling objectives and available resources; (4) use innovative techniques and data sources to validate and calibrate NFW connectivity simulations; and (5) clearly articulate the limits of the resulting NFW connectivity representation. Our review and synthesis of these case studies highlights modeling approaches that incorporate NFW connectivity, demonstrates tradeoffs in model selection, and ultimately provides actionable guidance for future model application and development.

A concise guide to developing and using quantitative models in conservation management

Quantitative models are powerful tools for informing conservation management and decision-making. As applied modeling is increasingly used to address conservation problems, guidelines are required to clarify the scope of modeling applications and to facilitate the impact and acceptance of models by practitioners. We identify three key roles for quantitative models in conservation management: (a) to assess the extent of a conservation problem; (b) to provide insights into the dynamics of complex social and ecological systems; and, (c) to evaluate the efficacy of proposed conservation interventions. We describe 10 recommendations to facilitate the acceptance of quantitative models in conservation management, providing a basis for good practice to guide their development and evaluation in conservation applications. We structure these recommendations within four established phases of model construction, enabling their integration within existing workflows: (a) design (two recommendations); (b) specification (two); (c) evaluation (one); and (d) inference (five). Quantitative modeling can support effective conservation management provided that both managers and modelers understand and agree on the place for models in conservation. Our concise review and recommendations will assist conservation managers and modelers to collaborate in the development of quantitative models that are fit-for-purpose, and to trust and use these models appropriately while understanding key drivers of uncertainty.

Global expansion and redistribution of Aedes-borne virus transmission risk with climate change

Forecasting the impacts of climate change on Aedes-borne viruses-especially dengue, chikungunya, and Zika-is a key component of public health preparedness. We apply an empirically parameterized model of viral transmission by the vectors Aedes aegypti and Ae. albopictus, as a function of temperature, to predict cumulative monthly global transmission risk in current climates, and compare them with projected risk in 2050 and 2080 based on general circulation models (GCMs). Our results show that if mosquito range shifts track optimal temperature ranges for transmission (21.3-34.0°C for Ae. aegypti; 19.9-29.4°C for Ae. albopictus), we can expect poleward shifts in Aedes-borne virus distributions. However, the differing thermal niches of the two vectors produce different patterns of shifts under climate change. More severe climate change scenarios produce larger population exposures to transmission by Ae. aegypti, but not by Ae. albopictus in the most extreme cases. Climate-driven risk of transmission from both mosquitoes will increase substantially, even in the short term, for most of Europe. In contrast, significant reductions in climate suitability are expected for Ae. albopictus, most noticeably in southeast Asia and west Africa. Within the next century, nearly a billion people are threatened with new exposure to virus transmission by both Aedes spp. in the worst-case scenario. As major net losses in year-round transmission risk are predicted for Ae. albopictus, we project a global shift towards more seasonal risk across regions. Many other complicating factors (like mosquito range limits and viral evolution) exist, but overall our results indicate that while climate change will lead to increased net and new exposures to Aedes-borne viruses, the most extreme increases in Ae. albopictus transmission are predicted to occur at intermediate climate change scenarios.

New measures for evaluation of environmental perturbations using Before-After-Control-Impact analyses

Before-After-Control-Impact (BACI) designs are powerful tools to derive inferences about environmental perturbations (e.g., hurricanes, restoration programs) when controlled experimental designs are unfeasible. Applications of BACI designs mostly rely on testing for a significant interaction between periods and treatments (so-called BACI contrast) to demonstrate the effects of the perturbation. However, significant interactions can emerge for several reasons, including when changes are larger in control sites, such that additional diagnostics must be performed to determine the full complexity of system changes. We propose two measures that detail the nature of change implied by BACI contrasts, along with its uncertainty. CI-divergence (Control-Impact divergence) quantifies to what extent control and impact sites have diverged between the after and the before period, whereas CI-contribution (Control-Impact contribution) quantifies to what extent the change between periods is stronger in impact sites relative to control sites. To illustrate how these two CI measures can be combined with BACI contrast to gain insights about effects of environmental perturbations, we used count data from the Swedish Breeding Bird Survey to investigate how hurricane Gudrun affected the long-term abundances of four bird species in forested areas of southern Sweden. Before-After-Control-Impact contrasts suggested the hurricane affected all four species. However, the values of the two CI measures strongly differed, even among species showing similar BACI contrasts. Those differences highlight qualitatively distinct population trajectories between periods and treatments requiring different ecological explanations. Overall, we show that BACI contrasts do not provide the full story in assessing the effects of environmental perturbations. The two CI measures can be used to assist ecological interpretations, or to specify detailed hypotheses about effects of restoration actions to allow stronger confirmatory inference about their outcomes. By providing a framework to develop more detailed explanations and hypotheses about ecological changes, the two CI measures can improve conclusions and strengthen evidence of effects of conservation actions and impact assessments under BACI designs.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.