Canadian Lynx Research Articles

Accounting for age: uncovering the nuanced drivers of mammal body-size responses to climate change.

Shifts in mean body size coinciding with environmental change are well documented across animal species and populations, serving as a widespread and complex indicator of climate-change response. In mammal research, identifying and disentangling the potential drivers of these trends (e.g., thermoregulation, resource availability) is hindered by treating adult size as fixed, ignoring morphological changes that occur throughout life in many species. However, observed population-level size trends may reflect underlying shifts in age structure (i.e., change in the proportion of older, potentially larger individuals in the population). Here, we assessed the role of age structure by explicitly evaluating age as a contributor to temporal variation in skull size (a proxy for body size) in 2 carnivorans, Canadian Lynx (Lynx canadensis) and American Marten (Martes americana). Using a series of linear and nonlinear models, we tested age in years (determined by cementum-layer analysis) as a predictor of skull size alongside other factors previously proposed to be important drivers of body-size trends, including population density for lynx and growing season conditions for martens. In both species, age was a significant predictor of skull size indicating a rapid year-to-year increase in young adult size that diminished in later adulthood. However, temporal shifts in age structure alone did not explain the observed changes in size over time, indicating that age structure acts in concert with other as-yet unidentified factors to drive body-size change. By explicitly evaluating the role of age, we can both refine models of temporal body-size trends and gain insights into size change as a signal of underlying demographic shifts-such as age-specific survivorship-providing a more holistic understanding of how mammals are responding to climate change.

Analysis of the Canadian Lynx Data Under Two Different Transformations

Analysis of the Canadian Lynx Data Under Two Different Transformations

Stability Analysis of Deep Belief Network: Based SD-AR Model for Nonlinear Time Series

As for nonlinear time series prediction, many different kinds of varying-coefficient models have been proposed and analysised in recent years. A kind of varying functional-coefficient autoregressive model, called the deep belief network-based state-dependent autoregressive (DBN-AR) model is considered in this paper. The stability conditions and existing conditions of limit cycle of the DBN-AR model are also studied. An especial designed parameter estimation method is used to identify the DBN-AR model. The DBN-AR model is used to predict the famous Canadian lynx data and Henon chaotic series, the prediction capability of the DBN-AR model is compared with other prediction models, the experimental results show that the DBN-AR model obtains better prediction accuracy.

Forecasting Implementation of Hybrid Time Series and Artificial Neural Network Models

This study implemented AR, SARIMA, and SETAR models and their hybrid with ANN using the Canadian lynx data. Implementing a SETAR-ANN has been shown to be successful in generating up to 10-step forecasts. The forecasting capability of AR-ANN and SARIMA-ANN applied to the same data are also investigated. The study shows that implementing hybridization does not guarantee better forecasting performance and accuracy, except for the case of SETAR-ANN. Despite results showing that the efficiency of the hybrid models may be worse than its components models, this study exhibits the promising predictive capability of time series, ANN, and its hybrid models.

SARS-CoV-2 Infection Dynamics in the Pittsburgh Zoo Wild Felids with Two Viral Variants (Delta and Alpha) during the 2021-2022 Pandemic in the United States.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been reported in multiple animal species besides humans. The goal of this study was to report clinical signs, infection progression, virus detection and antibody response in a group of wild felids housed in adjacent but neighboring areas at the Pittsburgh Zoo. Initially, five African lions (Panthera leo krugeri) housed together exhibited respiratory clinical signs with viral shedding in their feces in March of 2021 coinciding with infection of an animal keeper. During the second infection wave in December 2021, four Amur tigers (Panthera tigris altaica) and a Canadian lynx (Lynx canadensis) showed clinical signs and tested positive for viral RNA in feces. In infected animals, viral shedding in feces was variable lasting up to 5 weeks and clinical signs were observed for up to 4 weeks. Despite mounting an antibody response to initial exposure, lions exhibited respiratory clinical signs during the second infection wave, but none shed the virus in their feces. The lions were positive for alpha variant (B.1.1.7 lineage) during the first wave and the tiger and lynx were positive for delta variant (AY.25.1. lineage) during the second wave. The viruses recovered from felids were closely related to variants circulating in human populations at the time of the infection. Cheetahs (Acinonyx jubatus) in the park did not show either the clinical signs or the antibody response.

Klasik Kanada Lynx Verileri İçin Önceden Bulunmuş Zaman Serisi Modellerinin K-Means Küme Yöntemi ve BDS Testi ile İncelenmesi

Canadian lynx data are widely used and modeled in the literature. Although many different models have been made so far, no model-based classification studies have been carried out in terms of residuals to investigate the similarities or differences between these models. This study reviewed previously obtained models for the Canadian lynx time series. The starting point of the current study is residuals, and some statistical data analysis tools are used for this. The residual series of the models are clustered with the K-means cluster method. Besides, a new model is proposed for this time series, and the model is included in the data analysis together with other models in the literature. In addition, chaos analysis was performed for all residual time series of the models.

Recognition of recombinant interferon-gamma from Felidae species by anti-cat antibodies

Mycobacterial infections cause a reasonable burden of morbidity and mortality in global feline populations, many of which are ‘Vulnerable’ or ‘Endangered’. Identifying these infections may facilitate efforts to protect these animals. An interferon-gamma (IFNγ) release assay (IGRA) to diagnose mycobacteriosis in domestic cats has been adapted for use in lions; however, the development of species-specific antibodies may be laborious. Therefore, we investigated whether anti-cat IFNγ antibodies can bind to recombinant IFNγ (rIFNγ) from other Felidae species, permitting use of the feline IGRA in a wider range of felids. Unique Felidae IFNγ protein sequences and their corresponding coding nucleotide sequence were identified from online databases; plasmids with an IFNγ-gene insert were synthesised to transform E. coli-DH5α and subsequently transfect HEK 293 T cells to secrete rIFNγ. Enzyme-linked immunosorbent assay using a commercial anti-cat IFNγ kit was performed to detect rIFNγ from Felidae, the domestic dog and cattle. Five unique rIFNγ Felidae proteins were synthesised; anti-cat IFNγ antibodies were able to bind to all five proteins, while cross-reactivity with canine and bovine rIFNγ was negligible. This suggests that anti-cat IFNγ antibodies are sufficient for detection of IFNγ across other Felidae species, namely the lion, tiger, cheetah, cougar, Iberian lynx and the Canadian lynx.

Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares

The Bayesian statistical inversion method is implemented to obtain the parameter estimations for fractional LotkaVolterra models, including the derivative orders, based on analytical solutions obtained by the multi-step homotopy method. For the posterior distributions of the parameter of interest, we used Markov Chain Monte Carlo method through the JAGS package within R software. The posterior predictive model–checking method is implemented to select the best model for a real data set.

Revisiting the Canadian Lynx Time Series Analysis Through TARMA Models

The class of threshold autoregressive models has been proven to be a powerful and appropriate tool to describe many dynamical phenomena in different fields. In this work, we deploy the threshold autoregressive moving-average framework to revisit the analysis of the benchmark Canadian lynx time series. This data set has attracted great attention among non-linear time series analysts due to its asymmetric cycle that makes the investigation very challenging. We compare some of the best threshold autoregressive models (TAR) proposed in literature with a selection of thresholdautoregressive moving-average models (TARMA). The models are compared under different prospectives: (i) goodness-of-fit through information criteria, (ii) their ability to reproduce characteristic cycles, (iv) their capability to capture multimodality and (iii) forecasting performance. We found TARMAmodels that perform better than TAR models with respect to all these aspects.

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

We applied n-variable conserving nonlinear differential equations (n-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... n-variable conserving nonlinear interactions (n-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as a standard rhythm of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem.

Weighted MLP-ARIMA series hybrid model for time series forecasting

With the increasing importance of forecasting with the utmost degree of accuracy, utilizing hybrid frameworks become a must for obtaining more accurate and more reliable forecasting results. Series hybrid methodology is one of the most widely-used hybrid approaches that has encountered a great amount of popularity in the literature of time series forecasting and has been applied successfully in a wide variety of domains. In such hybrid methods is assumed that there is an additive relationship among different components of time series. Thus, based on this assumption, various individual models can apply separately on decomposed components, and the final forecast can be obtained. However, developed series hybrid models in the literature are constructed based on the decomposing time series into linear and nonlinear parts and generating linear-nonlinear modeling order for decomposed parts. Another assumption considered in the traditional series model is assigning equal weights to each model used for modeling linear and nonlinear components. Thus, contrary to traditional series hybrid models, to improve the performance of series hybrid models, these two basic assumptions have been violated in this paper. This study aims to propose a novel weighted MLP-ARIMA model filling the gap of series hybrid models by changing the order of sequence modeling and assigning weight for each component. Firstly, the modeling order is changed to nonlinear-linear, and then Multi-Layer Perceptron Neural Network (MLPNN) -Auto-Regressive Integrated Moving Average(ARIMA) models are employed to model and process nonlinear and linear components respectively. Secondly, each model's weights are computed by the Ordinary Least Square (OLS) weighting algorithm. Thus, in this paper, a novel improved weighted MLP-ARIMA series hybrid model is proposed for time series forecasting. The real-world benchmark data sets, including Wolf's sunspot data, the Canadian lynx data, and the British pound/US dollar exchange rate data, are elected to verify the effectiveness of the proposed weighted MLP-ARIMA series hybrid model. The simulation results revealed that the weighted MLP-ARIMA model could obtain superior performance compared to ARIMA-MLP, MLP-ARIMA, as well as the ARIMA and MLPNN individual models. The proposed hybrid model can be an effective alternative to improve forecasting accuracy obtained by traditional series hybrid methods.

Sequence in Hybridization of Statistical and Intelligent Models in Time Series Forecasting

With the importance of forecasting with a high degree of accuracy, the increasing attention has been evolved to combine individual models, especially statistical and intelligent ones. The main aim of such that hybrid models is to extract unique modeling strengths in linear and nonlinear pattern recognition, respectively. Therefore, different hybridization methods are proposed in recent literature for time series forecasting. One of the most widely-used combination strategies applied for numerous forecasting problems to yield more accurate results is the series hybrid strategy. In this hybridization methodology, components of a time series are separated and then modeled sequentially by choosing appropriate single models. However, the most accurate series hybrid model developed by determining the proper arrangement of single models. Thus, one of the critical issues in constructing series hybrid models is how to choose the appropriate sequence of individual models in a sequential modeling procedure. Although it is critically affecting on obtaining more accurate forecasting results, it has not been appropriately discussed in the literature of time series forecasting. Thus, in this paper, the performance of two possible sequence modeling procedures, including linear–nonlinear and nonlinear–linear, are evaluated. For this purpose, autoregressive integrated moving average (ARIMA), support vector machines (SVM), and multilayer perceptrons (MLP) models are chosen due to the popularity of these approaches for developing statistical/intelligent series hybrid models. Five well-known real data sets, e.g., Wolf’s Sunspot, Canadian Lynx, British pound/US dollar exchange rate, Nikkei 225 stock price, and the Colorado wind speed, are considered to distinguish better sequences. In this way, the main objective of this paper is to response this unanswered question in the literature that which sequence of single models can lead to obtain much better accuracy in constructing bi-component series hybrid models. Empirical results indicate that choosing the nonlinear intelligent model as first component in sequential modeling procedure can lead to yield more accurate results. Both SVM–ARIMA and MLP–ARIMA models can improve the performance of the ARIMA–SVM and ARIMA–MLP, respectively. Therefore, it can be concluded that the nonlinear–linear series hybrid models may produce more accurate results than linear–nonlinear hybrid models for time series forecasting.

Importance of spatio–temporal connectivity to maintain species experiencing range shifts

Climate change can affect the habitat resources available to species by changing habitat quantity, suitability and spatial configuration, which largely determine population persistence in the landscape. In this context, dispersal is a central process for species to track their niche. Assessments of the amount of reachable habitat (ARH) using static snap‐shots do not account, however, for the temporal overlap of habitat patches that may enhance stepping‐stone effects. Here, we quantified the impacts of climate change on the ARH using a spatio–temporal connectivity model. We first explored the importance of spatio–temporal connectivity relative to purely spatial connectivity in a changing climate by generating virtual species distributions and analyzed the relative effects of changes in habitat quantity, suitability and configuration. Then, we studied the importance of spatio–temporal connectivity in three vertebrate species with divergent responses to climate change in North America (grey wolf, Canadian lynx and white‐tailed deer). We found that the spatio–temporal connectivity could enhance the stepping‐stone effect for species predicted to experience range contractions, and the relative importance of the spatio–temporal connectivity increased with the reduction in habitat quantity and suitability. Conversely, for species that are likely to expand their ranges, spatio–temporal connectivity had no additional contribution to improve the ARH. We also found that changes in habitat amount (quantity and suitability) were more influential than changes in habitat configuration in determining the relative importance of spatio–temporal connectivity. We conclude that spatio–temporal connectivity may provide less biased and more realistic estimates of habitat connectivity than purely spatial connectivity.

Improvement of time forecasting models using a novel hybridization of bootstrap and double bootstrap artificial neural networks

Hybrid models such as the Artificial Neural Network-Autoregressive Integrated Moving Average (ANN–ARIMA) model are widely used in forecasting. However, inaccuracies and inefficiency remain in evidence. To yield the ANN–ARIMA with a higher degree of accuracy, efficiency and precision, the bootstrap and the double bootstrap methods are commonly used as alternative methods through the reconstruction of an ANN–ARIMA standard error. Unfortunately, these methods have not been applied in time series-based forecasting models. The aims of this study are twofold. First, is to propose the hybridization of bootstrap model and that of double bootstrap mode called Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (B-ANN–ARIMA) and Double Bootstrap Artificial Neural Network-Autoregressive Integrated Moving Average (DB-ANN–ARIMA), respectively. Second, is to investigate the performance of these proposed models by comparing them with ARIMA, ANN and ANN–ARIMA. Our investigation is based on three well-known real datasets, i.e., Wolf’s sunspot data, Canadian lynx data and, Malaysia ringgit/United States dollar exchange rate data. Statistical analysis on SSE, MSE, RMSE, MAE, MAPE and VAF is then conducted to verify that the proposed models are better than previous ARIMA, ANN and ANN–ARIMA models. The empirical results show that, compared with ARIMA, ANNs and ANN–ARIMA models, the proposed models generate smaller values of SSE, MSE, RMSE, MAE, MAPE and VAF for both training and testing datasets. In other words, the proposed models are better than those that we compare with. Their forecasting values are closer to the actual values. Thus, we conclude that the proposed models can be used to generate better forecasting values with higher degree of accuracy, efficiency and, precision in forecasting time series results becomes a priority.

An Ensemble Model of Arima and Ann with Restricted Boltzmann Machine Based on Decomposition of Discrete Wavelet Transform for Time Series Forecasting

Time series forecasting research area mainly focuses on developing effective forecasting models to improve prediction accuracy. An ensemble model composed of autoregressive integrated moving average (ARIMA), artificial neural network (ANN), restricted Boltzmann machines (RBM), and discrete wavelet transform (DWT) is presented in this paper. In the proposed model, DWT first decomposes time series into approximation and detail. Then Khashei and Bijari’s model, which is an ensemble model of ARIMA and ANN, is applied to the approximation and detail to extract their both linear and nonlinear components and fit the relationship between the components as a function instead of additive relationship. Furthermore, RBM is used to perform pre-training for generating initial weights and biases based on inputs feature for ANN. Finally, the forecasted approximation and detail are combined to obtain final forecasting. The forecasting capability of the proposed model is tested with three well-known time series: sunspot, Canadian lynx, exchange rate time series. The prediction performance is compared to the other six forecasting models. The results indicate that the proposed model gives the best performance in all three data sets and all three measures (i.e. MSE, MAE and MAPE).

A Hybridized Forecasting Method Based on Weight Adjustment of Neural Network Using Generalized Type-2 Fuzzy Set

This paper proposes a hybridized forecasting method on weight adjustment of neural networks with back-propagation learning using general type-2 fuzzy sets. Initialization of weights and their adjustment in neural network are important areas of research as it increases the computation speed to get the optimized result. Higher order fuzzy logic systems are able to deal with the high levels of uncertainties present in the majority of real-world problems. Here, the concept of interval-based zSlices has been used to obtain the general type-2 fuzzy weights for the neural network architecture. We implement this proposed methodology on benchmark Mackey–Glass time series data (for $$\tau =17$$ ) and present a comparison of the results obtained with our approach and those of the existing approaches. The method is also applied on enrollment data of University of Alabama, closing price index of Shenzhen stock exchange, closing price index of Shanghai stock exchange, Canadian lynx data, and the results are presented.

An Inverse Problem: Trappers Drove Hares to Eat Lynx.

The Canadian lynx and snowshoe hare pelt data by the Hudson Bay Company did not fit the classical predator-prey theory. Rather than following the peak density of the hare, that of the lynx leads it, creating the hares-eat-lynx (HEL) paradox. Although trappers were suspected to play a role, no mathematical model has ever demonstrated the HEL effect. Here we show that the long-held assumption that the pelt number is a proxy of the wild populations is false and that when the data are modeled by the harvest rates by the trappers, the problem is finally resolved: both the HEL paradox and the classical theory are unified in our mechanistic hare-lynx-competitor-trapper (HLCT) model where competitor stands for all predators of the hares other than the lynx. The result is obtained by systematically fitting the data to various models using Newton's inverse problem method. Main findings of this study include: the prey-eats-predator paradox in kills by an intraguild top-predator can occur if the top-predator prefers the predator to the prey; the benchmark HLCT model is more sensitive to all lynx-trapper interactions than to the respective hare-trapper interactions; the Hudson Bay Company's hare pelt number maybe under-reported; and, the most intriguing of all, the trappers did not interfere in each other's trapping activities.

Changes in future potential distributions of apex predator and mesopredator mammals in North America

Climate change has determined shifts in distributions of species and changing climates are likely to continue to affect species in the future. In this study, we used Maxent, an ecological niche modeling algorithm, to estimate the potential future distributions of apex predator and mesopredator mammals in boreal forest and tundra biomes of North America. We projected the climatic niche models of apex predators and mesopredators on future climate datasets based on three global circulation models (Beijing Climate Center Climate System Model, Hadley Global Environment Model, and Model for Interdisciplinary Research on Climate Earth System Model) and four greenhouse gas emission scenarios (RCP2.6, RCP4.5, RCP6, and RCP8.5). Under future climate projections, the potential distributions of most of the predators studied increased by 2050 and 2070. The potential distributions of two apex predators (brown bear, Ursus arctos, and polar bear, U. maritimus) and two mesopredator species (Canadian lynx, Lynx canadensis, and Arctic fox, Vulpes lagopus) were predicted to decline under all emission scenarios, by 2050 and 2070. The only apex predator that was predicted to increase its distribution under all greenhouse gas emission scenarios was U. americanus (American black bear). Similarly, distributions of mesopredators like Mephitis mephitis (striped skunk), and Procyon lotor (raccoon) were predicted to increase greatly under future climate conditions of all four emission scenarios. Predicted expansions of distribution ranges of most mesopredators and contractions of distribution ranges of apex predators included in this study may result in changes of species interactions in North American boreal forests and tundras in the future.

Education

The SIAM Review Education section has many objectives. One of them is to bring contemporary applications to mathematics courses that would otherwise be outside of the mainstream curriculum. Another is to present topics in applied mathematics in new ways that provide a pedagogical advantage. In this issue, we feature an article that does both. In “Population Interactions in Ecology: A Rule-Based Approach to Modeling Ecosystems in a Mass-Conserving Framework,” authors Cropp and Norbury take a comprehensive and modern look at population modeling. In many differential equations and dynamics textbooks, population dynamics begins and ends with the famous Lotka--Volterra model with perhaps some mild variations as exercises. Presented as an application of the analysis of systems of differential equations, this approach leaves the student and instructor with the sense that the deep questions of ecology can be answered with attractors and limit cycles. Unfortunately, those in the life sciences community do not accept the model as relevant. Indeed, if this is the only exposure mathematics students have to population models, it may leave students with an overly simplistic perspective on ecology. On the other side of the disciplinary divide, courses for nonmathematics majors tend to present population ecology in a “just in time” fashion where solutions to the Verhulst equation are presented as formulae without much explanation. These students will be left without the necessary modeling and analytical skills to quantitatively study ecological systems. This Education section feature takes on the problem directly through what they call the “conservative normal” (CN) framework. While the approach is a theoretical basis for understanding ecological systems, it has considerable merit as a way for students to construct and understand models of populations in a food web. The CN framework is a system of rules that maps ecological principles to mathematical structures and formulae. For instance, the first rule is that one should measure a population by the limiting nutrient it contains (e.g., do not model the number of plankton cells, model the mass of nitrogen in the living population). It is both a modeling approach and a unified way for students to think about many interacting species. Other rules include mechanisms for change in populations, resource constraints, and other essential processes that govern ecological systems. The authors then apply CN to a variety of small but interesting problems. These include ecological systems of autotrophs where multiple species compete for a single resource, and systems of mixotrophs such as phytoplankton that can switch between growing inefficiently via photosynthesis and grazing on other phytoplankton. Given that phytoplankton consume a significant fraction of the carbon dioxide produced from burning fossil fuels, one could argue that it may be more relevant for nonmathematicians to learn about these mixotrophic systems before dwelling on cycles in the Canadian Lynx and the Snowshoe Hare populations. The CN framework puts whole categories of ecological systems on equal footing for students to explore. In summary, this article is a notable contribution that spans a disciplinary divide between the mathematics and life sciences communities. As such, the CN framework may be a valuable resource in classes for mathematicians as well as classes for nonmathematicians. On one hand, it presents classic applications of differential equations in an exciting new way, and on the other, it links biological principles to mathematical structures in a way that will appeal to nonmathematicians. While the examples in this article are aimed at the undergraduate curriculum, the CN framework is useful in many broad contexts, including systems with spatial dependence that would likely end up in a graduate curriculum or more specialized course. Most importantly, for the relatively low cost of introducing the framework, this approach gives students a broader perspective on ecological systems and the modeling process in general than what is typically provided in differential equations and dynamical systems texts.

Error modeling approach to improve time series forecasters

In time series forecasting exercises it has been usual to suppose that the error series generated by the forecasters have a white noise behavior. However, it is possible that such supposition is violated in practice due to model misspecification or disturbances of the phenomenon not captured by the predictive models. It may lead to statistically biased and/or inefficient predictors. The present paper introduces an approach to correct predetermined forecasters by recursively modeling their remaining residuals. Two formalisms are used to illustrate the recursive approach: the well-known (linear) autoregressive integrated moving average (ARIMA) and the (non-linear) Artificial Neural Network (ANN). These models are recursively adjusted to the remaining residuals of a given forecaster until a white noise behavior is achieved. Applications involving ARIMA and ANN forecasters for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, Nasdaq Index, Wolf׳s Sunspot, and Canadian Lynx data series indicate the usefulness of the proposed framework.