arXiv subjects

Mark A. Lewis

Publications and source records attributed to Mark A. Lewis.

At least 19 recordsLinked to original sources

arXiv2025

A phylogeny of biological patterns formed by nonlocal advection

From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly recognised as powerful tools for capturing such phenomena. However, most research has focused on one-dimensional domains, leaving their two-dimensional behaviour largely unexplored. Here, we present a detailed numerical study of the patterns formed by these systems on 2D domains. Depending on the underlying mechanisms, a wide variety of spatial patterns can emerge - including segregated clusters, stripes, volcanos, and polygonal mosaics - many of which have been observed in natural systems. By systematically varying model parameters, we classify the links between emergent patterns and their underlying movement mechanisms. In comparing these patterns with empirical observations, we show how this modelling framework can help reveal possible mechanisms of self-organisation in various situations within the life sciences, from ecology and developmental biology to cancer research.

q-bio.PE↗

arXiv2025

Website visits can predict angler presence using machine learning

Understanding and predicting recreational angler effort is important for sustainable fisheries management. However, conventional methods of measuring angler effort, such as surveys, can be costly and limited in both time and spatial extent. Models that predict angler effort based on environmental or economic factors typically rely on historical data, which often limits their spatial and temporal generalizability due to data scarcity. In this study, high-resolution data from an online fishing platform and easily accessible auxiliary data were tested to predict daily boat presence and aerial counts of boats at almost 200 lakes over five years in Ontario, Canada. Lake-information website visits alone enabled predicting daily angler boat presence with 78% accuracy. While incorporating additional environmental, socio-ecological, weather and angler-reported features into machine learning models did not remarkably improve prediction performance of boat presence, they were substantial for the prediction of boat counts. Models achieved an R2 of up to 0.77 at known lakes included in the model training, but they performed poorly for unknown lakes (R2 = 0.21). The results demonstrate the value of integrating data from online fishing platforms into predictive models and highlight the potential of machine learning models to enhance fisheries management.

physics.soc-ph↗

arXiv2025

Analyzing recreational fishing effort -- Gender differences and the impact of Covid-19

Recreational fishing is an important economic driver and provides multiple social benefits. To predict fishing activity, identifying variables related to variation, such as gender or Covid-19, is helpful. We conducted a Canada-wide email survey of users of an online fishing platform and analyzed responses focusing on gender, the impact of Covid-19, and variables directly related to fishing effort. Genders (90% men and 10% women) significantly differed in demographics, socioeconomic status, and fishing skills but showed similar fishing preferences, fishing effort in terms of trip frequency, and travel distance. Covid-19 altered trip frequency for almost half of fishers, with changes varying by gender and activity level. A Bayesian network revealed travel distance as the main determinant of trip frequency, negatively impacting fishing activity for 61% of fishers, with fishing expertise also playing a role. The results suggest that among active fishers, socio-economic differences between genders do not drive fishing effort, but responses to Covid-19 were gender-specific. Recognizing these patterns is critical for equitable policy-making and accurate socio-ecological models, thereby improving resource management and sustainability.

physics.soc-ph↗

arXiv2025

Biological barriers to forest pest invasions: A novel host tree slows mountain pine beetle range expansion

Following widespread outbreaks across western North America, mountain pine beetle recently expanded its range from British Columbia into Alberta. However, mountain pine beetle's eastward expansion across Canada has stalled unexpectedly, defying predictions of rapid spread through jack pine, a novel host tree. This study investigates the underlying causes of this deceleration using an integrative approach combining statistical modeling, simulations, and experimental data. We find that the slow spread is primarily due to mountain pine beetle's difficulty in finding and successfully attacking jack pine trees, rather than issues with reproduction or larval development. The underlying mechanism impeding beetle range expansion has been hypothesized to be lower pine volumes in eastern forests, which are primarily a consequence of lower stem density. However, our analysis suggests that jack pine's phenotype itself is the primary impediment. We propose that jack pine's smaller size, thinner phloem, and lower monoterpene concentrations result in weaker chemical cues during the host-finding and mass-attack stages of MPB's life cycle, ultimately leading to fewer successful attacks. These findings suggest a reduced risk of further eastward spread, but should be interpreted cautiously due to enormous policy implications and the inherent limitations of ecological forecasting.

q-bio.PE↗

arXiv2025

An assessment of Alberta's strategy for controlling mountain pine beetle outbreaks

The Canadian province of Alberta spent over 500 million dollars on controlling mountain pine beetle populations, but did it work? Using a statistical modeling framework coupled with long-term field data, we examined how direct control measures, severe winters, and host-tree depletion shaped the trajectory of Alberta's mountain pine beetle outbreak between 2009 and 2020. Simulations suggest that control efforts reduced total tree mortality by 79% (95% predictive interval: 58--89%) and prevented 1.8 (0.91--4.1) trees per hectare from being killed from 2010--2020. Although cold winters had little effect on overall damage, they acted synergistically with control to end the outbreak, causing population collapse circa 2020. This synergy supports a "wait it out" strategy of mountain pine beetle management, where moderate control effort is applied until an extreme weather event delivers the final blow. Any effects of host-tree depletion via beetle attack were negligible. From an economic perspective, removing one infestation tree -- at an approximate cost of 320 CAD -- prevented the loss of roughly six (2.6--15) trees, demonstrating the potential for long-term cost-effectiveness. Our results further indicate that future outbreaks may vary widely in severity due to environmental stochasticity, with potential damage in a no-control scenario ranging from 0.41 to 9.7 trees per hectare killed (over a hypothetical 11-year period). An alternative model predicts an even wider range of outcomes: 1--40 trees per hectare. These findings highlight not only the potential of sustained control efforts in mitigating forest pest outbreaks, but also the inherent uncertainty in long-term ecological forecasting.

q-bio.PE↗

arXiv2025

Webpage Views as a Proxy for Angler Pressure and Effort: Insights from Bayesian Networks

Reliable angler activity data inform fisheries management. Traditionally, such data are gathered through surveys, but an innovative cost-effective approach involves utilizing online platforms and smartphone applications. These citizen-sourced data were reported to correlate with conventional survey information. However, the nature of this correlation--whether direct or mediated by intermediate variables--remains unclear. We applied BNs to data from conventional surveys, the Angler's Atlas website, the MyCatch smartphone application, and environmental data across Alberta and Ontario, Canada, to detect probabilistic dependencies. Using Bayesian model averaging, we quantified the strength of connections between variables. Waterbody webpage views were directly related to daily and weekly-aggregated boat counts in Ontario (51\% and 100\% probability) and to weekly-aggregated creel survey-reported fishing duration in Alberta (100\%). This highlights the value of citizen-sourced data in providing unique insights beyond meteorological factors, with online interest serving as a potentially reliable proxy for angler pressure and effort.

physics.soc-ph↗

arXiv2025

Deep Learning for Disease Outbreak Prediction: A Robust Early Warning Signal for Transcritical Bifurcations

Early Warning Signals (EWSs) are vital for implementing preventive measures before a disease turns into a pandemic. While new diseases exhibit unique behaviors, they often share fundamental characteristics from a dynamical systems perspective. Moreover, measurements during disease outbreaks are often corrupted by different noise sources, posing challenges for Time Series Classification (TSC) tasks. In this study, we address the problem of having a robust EWS for disease outbreak prediction using a best-performing deep learning model in the domain of TSC. We employed two simulated datasets to train the model: one representing generated dynamical systems with randomly selected polynomial terms to model new disease behaviors, and another simulating noise-induced disease dynamics to account for noisy measurements. The model's performance was analyzed using both simulated data from different disease models and real-world data, including influenza and COVID-19. Results demonstrate that the proposed model outperforms previous models, effectively providing EWSs of impending outbreaks across various scenarios. This study bridges advancements in deep learning with the ability to provide robust early warning signals in noisy environments, making it highly applicable to real-world crises involving emerging disease outbreaks.

cs.LG↗

arXiv2024

Explaining excitable population dynamics in bark beetles: From life history to large, episodic outbreaks

Bark beetles are significant forest pests, with some species capable of causing widespread tree mortality. Among these, the mountain pine beetle (MPB) stands out for its exceptionally destructive outbreak in the 2000s. We use MPB as a case study to explore the concept of =excitable dynamics, where ephemeral perturbations produce large excursions from equilibrium. Our empirically-calibrated model of reveals five features of MPB biology: stand density-dependent dispersal, an Allee effect, time-scale separation between beetle and tree life cycles, tree size-dependent fecundity, and a large-tree preference. The first three features explain MPB's characteristic boom-bust dynamics, while the latter two explain outbreak magnitude. Other bark beetles lack one or more of these traits, partially explaining their generally lower impact. However, predicting bark beetle impact requires consideration of both life history and landscape factors: total damage increases linearly with host-tree biomass, but this relationship holds only for irruptive (i.e., excitable) beetle species. We distill our findings into a minimal mechanistic model that captures the essence of irruptive bark beetle dynamics. This model firmly establishes MPB as one of the first empirical examples of excitable dynamics in ecology.

q-bio.PE↗

arXiv2024

Identifiability analysis of vaccination decision-making dynamics

Variations in individuals' perceptions of vaccination and decision-making processes can give rise to poor vaccination coverage. The future vaccination promotion programs will benefit from understanding this heterogeneity amongst groups within a population and, accordingly, tailoring the communication strategies. Motivated by this, we developed a mechanistic model consisting of a system of ordinary differential equations that categorizes individuals based on two factors: (i) perceived payoff gains for vaccination and (ii} decision-making strategies where we assumed that individuals may behave as either myopic rationalists, going for a dose of vaccine if doing so maximizes their perceived payoff gain, or success-based learners, waiting to observe feedback on vaccination before deciding. We then investigated the global identifiability of group proportions and perceived payoff gains, that is, the possibility of globally retrieving these parameters by observing the error-free cumulative proportion of vaccinated individuals over time. To do so, for each group, we assumed a piecewise constant payoff gain and, for each time interval, obtained the so-called generalized input-output equation. We then proved the global identifiability of these parameters under certain conditions. Global identifiability opens the door to reliable estimations of the group proportions and their perceived payoffs.

q-bio.QM↗

arXiv2024

Stratified dispersal explains mountain pine beetle's range expansion in Alberta

The mountain pine beetle (MPB), a destructive pest native to Western North America, has recently extended its range into Alberta, Canada. Predicting the dispersal of MPB is challenging due to their small size and complex dispersal behavior. Because of these challenges, estimates of MPB's typical dispersal distances have varied widely, ranging from 10 meters to 18 kilometers. Here, we use high-quality data from helicopter and field-crew surveys to parameterize a large number of dispersal kernels. We find that fat-tailed kernels -- those which allow for a small number of long-distance dispersal events -- consistently provide the best fit to the data. Specifically, the radially-symmetric Student's t-distribution with parameters ν = 0.012 and ρ = 1.45 stands out as parsimonious and user-friendly; this model predicts a median dispersal distance of 60 meters, but with the 95th percentile of dispersers travelling nearly 5 kilometers. The best-fitting mathematical models have biological interpretations. The Student's t-distribution, derivable as a mixture of diffusive processes with varying settling times, is consistent with observations that most beetles fly short distances while few travel far; early-emerging beetles fly farther; and larger beetles from larger trees exhibit greater variance in flight distance. Finally, we explain why other studies have found such a wide variation in the length scale in MPB dispersal, and we demonstrate that long-distance dispersal events are critical for modelling MPB range expansion.

q-bio.PE↗

arXiv2024

Early detection of disease outbreaks and non-outbreaks using incidence data

Forecasting the occurrence and absence of novel disease outbreaks is essential for disease management. Here, we develop a general model, with no real-world training data, that accurately forecasts outbreaks and non-outbreaks. We propose a novel framework, using a feature-based time series classification method to forecast outbreaks and non-outbreaks. We tested our methods on synthetic data from a Susceptible-Infected-Recovered model for slowly changing, noisy disease dynamics. Outbreak sequences give a transcritical bifurcation within a specified future time window, whereas non-outbreak (null bifurcation) sequences do not. We identified incipient differences in time series of infectives leading to future outbreaks and non-outbreaks. These differences are reflected in 22 statistical features and 5 early warning signal indicators. Classifier performance, given by the area under the receiver-operating curve, ranged from 0.99 for large expanding windows of training data to 0.7 for small rolling windows. Real-world performances of classifiers were tested on two empirical datasets, COVID-19 data from Singapore and SARS data from Hong Kong, with two classifiers exhibiting high accuracy. In summary, we showed that there are statistical features that distinguish outbreak and non-outbreak sequences long before outbreaks occur. We could detect these differences in synthetic and real-world data sets, well before potential outbreaks occur.

cs.LG↗

arXiv2024

An early warning indicator trained on stochastic disease-spreading models with different noises

The timely detection of disease outbreaks through reliable early warning signals (EWSs) is indispensable for effective public health mitigation strategies. Nevertheless, the intricate dynamics of real-world disease spread, often influenced by diverse sources of noise and limited data in the early stages of outbreaks, pose a significant challenge in developing reliable EWSs, as the performance of existing indicators varies with extrinsic and intrinsic noises. Here, we address the challenge of modeling disease when the measurements are corrupted by additive white noise, multiplicative environmental noise, and demographic noise into a standard epidemic mathematical model. To navigate the complexities introduced by these noise sources, we employ a deep learning algorithm that provides EWS in infectious disease outbreak by training on noise-induced disease-spreading models. The indicator's effectiveness is demonstrated through its application to real-world COVID-19 cases in Edmonton and simulated time series derived from diverse disease spread models affected by noise. Notably, the indicator captures an impending transition in a time series of disease outbreaks and outperforms existing indicators. This study contributes to advancing early warning capabilities by addressing the intricate dynamics inherent in real-world disease spread, presenting a promising avenue for enhancing public health preparedness and response efforts.

cs.LG↗

arXiv2024

Can machine learning predict citizen-reported angler behavior?

Prediction of angler behaviors, such as catch rates and angler pressure, is essential to maintaining fish populations and ensuring angler satisfaction. Angler behavior can partly be tracked by online platforms and mobile phone applications that provide fishing activities reported by recreational anglers. Moreover, angler behavior is known to be driven by local site attributes. Here, the prediction of citizen-reported angler behavior was investigated by machine-learning methods using auxiliary data on the environment, socioeconomics, fisheries management objectives, and events at a freshwater body. The goal was to determine whether auxiliary data alone could predict the reported behavior. Different spatial and temporal extents and temporal resolutions were considered. Accuracy scores averaged 88% for monthly predictions at single water bodies and 86% for spatial predictions on a day in a specific region across Canada. At other resolutions and scales, the models only achieved low prediction accuracy of around 60%. The study represents a first attempt at predicting angler behavior in time and space at a large scale and establishes a foundation for potential future expansions in various directions.

physics.soc-ph↗

arXiv2023

Revealing the unseen: Likely half of the Americans relied on others' experience when deciding on taking the COVID-19 vaccine

Efficient coverage for newly developed vaccines requires knowing which groups of individuals will accept the vaccine immediately and which will take longer to accept or never accept. Of those who may eventually accept the vaccine, there are two main types: success-based learners, basing their decisions on others' satisfaction, and myopic rationalists, attending to their own immediate perceived benefit. We used COVID-19 vaccination data to fit a mechanistic model capturing the distinct effects of the two types on the vaccination progress. We estimated that 47 percent of Americans behaved as myopic rationalist with a high variations across the jurisdictions, from 31 percent in Mississippi to 76 percent in Vermont. The proportion was correlated with the vaccination coverage, proportion of votes in favor of Democrats in 2020 presidential election, and education score.

q-bio.PE↗

arXiv2023

Weakly nonlinear analysis of a two-species non-local advection-diffusion system

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a Ginzburg-Landau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the Ginzburg-Landau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimisers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions.

math.AP↗

arXiv2022

Boosting propagule transport models with individual-specific data from mobile apps

Management of invasive species and pathogens requires information about the traffic of potential vectors. Such information is often taken from vector traffic models fitted to survey data. Here, user-specific data collected via mobile apps offer new opportunities to obtain more accurate estimates and to analyze how vectors' individual preferences affect propagule flows. However, data voluntarily reported via apps may lack some trip records, adding a significant layer of uncertainty. We show how the benefits of app-based data can be exploited despite this drawback. Based on data collected via an angler app, we built a stochastic model for angler traffic in the Canadian province Alberta. There, anglers facilitate the spread of whirling disease, a parasite-induced fish disease. The model is temporally and spatially explicit and accounts for individual preferences and repeating behaviour of anglers, helping to address the problem of missing trip records. We obtained estimates of angler traffic between all subbasins in Alberta. The model's accuracy exceeds that of direct empirical estimates even when fewer data were used to fit the model. The results indicate that anglers' local preferences and their tendency to revisit previous destinations reduce the number of long inter-waterbody trips potentially dispersing whirling disease. According to our model, anglers revisit their previous destination in 64% of their trips, making these trips irrelevant for the spread of whirling disease. Furthermore, 54% of fishing trips end in individual-specific spatially contained areas with mean radius of 54.7km. Finally, although the fraction of trips that anglers report was unknown, we were able to estimate the total yearly number of fishing trips in Alberta, matching an independent empirical estimate.

q-bio.QM↗

arXiv2022

Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species

Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy states of a broad class of multi-species nonlocal advection-diffusion models, recently proposed for modelling the spatial structure of ecosystems. We show that when each pair of species respond to one another in a symmetric fashion (i.e. via mutual avoidance or mutual attraction, with equal strength), the system admits an energy functional that decreases in time and is bounded below. This suggests that the system will eventually reach a local minimum energy steady state, rather than fluctuating in perpetuity. We leverage this energy functional to develop tools, including a novel application of computational algebraic geometry, for making conjectures about the number and qualitative structure of local minimum energy solutions. These conjectures give a guide as to where to look for numerical steady state solutions, which we verify through numerical analysis. Our technique shows that even with two species, multi-stability with up to four classes of local minimum energy state can emerge. The associated dynamics include spatial sorting via aggregation and repulsion both within and between species. The emerging spatial patterns include a mixture of territory-like segregation as well as narrow spike-type solutions. Overall, our study reveals a general picture of rich multi-stability in systems of moving and interacting species.

math.AP↗

arXiv2022

Simulating how animals learn: a new modelling framework applied to the process of optimal foraging

Animal learning has interested ecologists and psychologists for over a century. Mathematical models that explain how animals store and recall information have gained attention recently. Central to this work is statistical decision theory (SDT), which relates information uptake in animals to Bayesian inference. SDT effectively explains many learning tasks in animals, but extending this theory to predict how animals will learn in changing environments still poses a challenge for ecologists. We addressed this shortcoming with a novel implementation of Bayesian Markov Chain Monte Carlo (MCMC) sampling to simulate how animals sample environmental information and learn as a result. We applied our framework to an individual-based model simulating complex foraging tasks encountered by wild animals. Simulated ``animals" learned behavioral strategies that optimized foraging returns simply by following the principles of an MCMC sampler. In these simulations, behavioral plasticity was most conducive to efficient foraging in unpredictable and uncertain environments. Our model suggests that animals prioritize highly concentrated resources even when these resources are less available overall, in line with existing knowledge on optimal foraging and ideal free distribution theory. Our innovative computational modelling framework can be applied more widely to simulate the learning of many other tasks in animals and humans.

q-bio.QM↗