Single-species Model Research Articles

Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control

In this paper, a single-species logistic model with both fear effect-type feedback control and additive Allee effect is developed and investigated using the new coronavirus as a feedback control variable. When the system introduces additive Allee effect and fear effect-type feedback control, more complicated dynamical behavior is obtained. The system can undergo transcritical bifurcation, saddle-node bifurcation, degenerate Hopf bifurcation and Bogdanov–Takens bifurcation. By numerical simulations, the system exhibits homoclinic bifurcation and saddle-node bifurcation of limit cycles as parameters are altered. Remarkably, it is the first time that two limit cycles have been discovered in a single-species logistic model with the Allee effect. Further, stronger Allee effect or stronger fear effect can lead to the extinction of the species population.

Preliminary Insights on Moisture Content Measurement in Square Timbers Using GPR Signals and 1D-CNN Models

Accurately measuring the moisture content (MC) of square timber is crucial for ensuring the quality and performance of wood products in wood processing. Traditional MC detection methods have certain limitations. Therefore, this study developed a one-dimensional convolutional neural network (1D-CNN) model based on the first 8 nanoseconds of ground-penetrating radar (GPR) signals to predict the MC of square timber. The study found that the mixed-species model exhibited effective predictive performance (R2 = 0.9864, RMSE = 0.0393) across the tree species red spruce, Dahurian larch, European white birch, and Manchurian ash (MC range 0%–133.1%), while single-species models showed even higher accuracy (R2 ≥ 0.9876, RMSE ≤ 0.0358). Additionally, the 1D-CNN model outperformed other algorithms in automatically capturing complex patterns in GPR full-waveform amplitude data. Moreover, the algorithms based on full-waveform amplitude data demonstrated significant advantages in detecting wood MC compared to those based on a traditional time–frequency feature parameter. These results indicate that the 1D-CNN model can be used to optimize the drying process and detect the MC of load-bearing timber in construction and bridge engineering. Future work will focus on expanding the dataset, further optimizing the algorithm, and validating the models in industrial applications to enhance their reliability and applicability.

Evolutionary stable strategies of a single species model with carry-over effects due to fear

Evolutionary stable strategies of a single species model with carry-over effects due to fear

Systematic Review of Multi-Species Models in Fisheries: Key Features and Current Trends

In the context of ecosystem-based fisheries management (EBFM), multi-species models offer a potential alternative to traditional single-species models for managing key species, particularly in mixed-fishery settings. These models account for interactions between different species, providing a more holistic approach to fisheries compared to traditional single-species management. There is currently no comprehensive list or recent analysis of the diverse methods used to account for species interactions in fisheries worldwide. We conducted a systematic review to objectively present the current multi-species models used in fisheries. The systematic search identified 86 multi-species models, which were then evaluated to assess their similarities. Employing a clustering analysis, three distinct groups were identified: extensions of single-species/dynamic multi-species models, aggregated ecosystem models, and end-to-end/coupled and hybrid models. The first group was among the most diverse, owing to their ability to integrate biological components, while maintaining an intermediate level of complexity. The second group, primarily defined by the EwE method, features an aggregated biomass pool structure incorporating biological components and environmental effects. The third cluster featured the most complex models, which included a comprehensive representation of size and age structure, the ability to incorporate biological components and environmental effects, as well as spatial representation. The application of these methods is primarily concentrated on small pelagic and demersal species from North America and Europe. This analysis provides a comprehensive guide for stakeholders on the development and use of multi-species models, considering data constraints and regional contexts.

On the stability of a single-species model with a generic delay distribution kernel

The delayed logistic equation, also known as Hutchinson’s equation, is a simple and elegant model commonly used to capture critical features of complex phenomena in biology, medicine, and economics. This paper studies the stability of a single-species logistic model with a general delay distribution and a constant inflow of nutritional resources. We provide conditions for the linear stability of the positive equilibrium and the occurrence of Hopf bifurcation. The findings complement existing literature and are applied to specific delay distributions: Uniform, Dirac-delta, and gamma distributions. Without resource inflow, we find that the positive equilibrium is stable for short delays but loses stability through Hopf bifurcation as the mean delay increases. The model’s dynamics vary with resource inflow based on the delay distribution: in uniform and Dirac-delta distributions, the dynamics are similar to the no-inflow case, whereas for the gamma distribution, stability depends on the delay order p=1,2,3.

Derivation and dynamics of discrete population models with distributed delay in reproduction

We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least τ and at most τ+τM breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, τ˜c. For given delay kernel length τM, if each individual takes at least τ˜c time units to reach maturity, then the population is predicted to go extinct. We show that the positive equilibrium is decreasing in both τ and τM. In the case of a constant reproductive rate, we provide an equation to determine τ˜c for fixed τM, and similarly, provide a lower bound on the kernel length, τ˜M for fixed τ such that the population goes extinct if τM≥τ˜M. We compare these critical thresholds for different maturation distributions and show that if all else is the same, to avoid extinction it is best if all individuals in the population have the shortest delay possible. We apply the model derivation to a Beverton–Holt model and discuss its global dynamics. For this model with kernels that share the same mean delay, we show that populations with the largest variance in the time required to reach maturity have higher population levels and lower chances of extinction.

Demographic but not competitive time lags can transiently amplify climate-induced changes in vegetation carbon storage.

How terrestrial ecosystems will accumulate carbon as the climate continues to change is a major source of uncertainty in projections of future climate. Under growth-stimulating environmental change, time lags inherent in population and community dynamic processes have been posed to dampen, or alternatively amplify, short-term carbon gain in terrestrial vegetation, but these outcomes can be difficult to predict. To theoretically frame this problem, we developed a simple model of vegetation dynamics that identifies the stage-structured demographic and competitive processes that could govern the timescales of carbon storage and loss. We show that demographic lags associated with growth-stimulating environmental change can allow a rapid increase in population-level carbon storage that is lost back to the atmosphere in later years. However, this transient carbon storage only emerges when environmental change increases the transition of adult individuals into a larger size class that suffers markedly higher mortality. Otherwise, demographic lags simply slow carbon accumulation. Counterintuitively, an analogous tradeoff between maximum adult size and survivorship in two-species models, coupled with environmental change-driven replacement, does not generate the transient carbon gain seen in the single-species models. Instead lags in competitive replacement slow the approach to the eventual carbon trajectory. Together, our results suggest that time lags inherent in demographic and compositional turnover tend to slow carbon accumulation in systems responding to growth-stimulating environmental change. Only under specific conditions will lagged demographic processes in such systems drive transient carbon accumulation, conditions that investigators can examine in nature to help project future carbon trajectories.

Novel organizational patterns of stability phases in a single-species population model: chiral tree, spikes adding-doubling complexification cascade

Novel organizational patterns of stability phases in a single-species population model: chiral tree, spikes adding-doubling complexification cascade

Quantification of tree growth change under climate change using National Forest Inventory of Korea

To achieve carbon neutrality in the face of climate change, accurately estimating forest carbon uptake is crucial. Environmental changes, such as temperature increases or precipitation fluctuations caused by climate change, can alter the growth responses of each species and act as a driver for changes in forest productivity. In particular, using a single-species growth model increases uncertainty in predicting stand growth, given the high species diversity in temperate forests in East Asia. Therefore, in this study, we identified the growth curve of 17 species-specific distributed in Korean temperate forest as well as the growth trend over the last 30 years (1976–2005). For this purpose, the species distribution and growth characteristics of 17 major Korean species of trees were analyzed using 13,808 tree-ring series from the 5th National Forest Inventory, which was conducted between 2006 and 2010. The growth characteristics of each species were analyzed using the average growth curve specific to each species, and the yearly growth trend was examined through residual analysis of the average growth curve. The distribution range of the 17 major tree species varied by species, as did the growth rate, ranging from 7 cm² · year⁻¹ to 17 cm² · year⁻¹ for the 30-year-old average basal area increment (BAI). Over time, fast-growing tree species exhibited initially high BAI, followed by a sharp decline from the 2000s. In contrast, broadleaf trees showed a continuous increase. Furthermore, a comparison of the total volume of individual trees and the volume of the yield table revealed that accurately estimating the actual forest volume was challenging. This study contributes to improving the accuracy of productivity predictions for temperate forests, underscoring the necessity to investigate the interaction between climate and forest succession in the future.

A note on the application of the RVT method to general classes of single-species population models formulated by random differential equations

The Random Variable Transformation (RVT) technique has been applied in recent years to analyze a wide variety of dynamic models formulated via random differential equations. The applicability of this technique has usually been focused on problems where an explicit solution of the underlying deterministic problem is available. This fact limits the usefulness of the RVT method. This note aims to point out that the RVT technique can be successfully applied without this requirement by showing a wider range of potential applications including very general classes of single-species models.

Some Progress on Single Species Models with Nonlocal Dispersal Strategies in Heterogeneous Environments

Some Progress on Single Species Models with Nonlocal Dispersal Strategies in Heterogeneous Environments

Evaluating the effectiveness of joint species distribution modeling for freshwater fish communities within large watersheds

Accurately predicting species’ distributions is critical for the management and conservation of fish and wildlife populations. Joint species distribution models (JSDMs) account for dependencies between species often ignored by traditional species distribution models. We evaluated how a JSDM approach could improve predictive strength for stream fish communities within large watersheds (the Chesapeake Bay Watershed, USA), using a cross-validation study of JSDMs fit to data from over 50 species. Our results suggest that conditional predictions from JSDMs have the potential to make large improvements in predictive accuracy for many species, particularly for more generalist species where single species models may not perform well. For some species there was no added explanatory effect from conditional information, most of which already exhibited strong marginal predictive ability. For several rare species there were significant improvements in occurrence predictions, while the results for two invasive species considered did not show the same improvements. Overall, the optimal number of species to condition upon, as well as the effects of conditioning upon an increasing number of species, varied widely among species.

On the selection and effectiveness of pseudo-absences for species distribution modeling with deep learning

Species distribution modeling is a highly versatile tool for understanding the intricate relationship between environmental conditions and species occurrences. However, the available data often lacks information on confirmed species absence and is limited to opportunistically sampled, presence-only observations. To overcome this limitation, a common approach is to employ pseudo-absences, which are specific geographic locations designated as negative samples. While pseudo-absences are well-established for single-species distribution models, their application in the context of multi-species neural networks remains underexplored. Notably, the significant class imbalance between species presences and pseudo-absences is often left unaddressed. Moreover, the existence of different types of pseudo-absences (e.g., random and target-group background points) adds complexity to the selection process. Determining the optimal combination of pseudo-absences types is difficult and depends on the characteristics of the data, particularly considering that certain types of pseudo-absences can be used to mitigate geographic biases. In this paper, we demonstrate that these challenges can be effectively tackled by integrating pseudo-absences in the training of multi-species neural networks through modifications to the loss function. This adjustment involves assigning different weights to the distinct terms of the loss function, thereby addressing both the class imbalance and the choice of pseudo-absence types. Additionally, we propose a strategy to set these loss weights using spatial block cross-validation with presence-only data. We evaluate our approach using a benchmark dataset containing independent presence-absence data from six different regions and report improved results when compared to competing approaches.

Even low levels of cannibalism can bias population estimates for Pacific hake

Abstract By incorporating trophic interactions and temperature-dependent bioenergetics, multi-species models such as CEATTLE (climate-enhanced age-based model with temperature-specific trophic linkages and energetics) are a step towards ecosystem-based stock assessment and management of high-value commercial species such as Pacific hake (Merluccius productus). Hake are generalist predators and previous studies in the California Current Ecosystem have determined that their diet consists of ∼30% cannibalism. We used CEATTLE to include cannibalism in a model of hake population dynamics and re-examined hake diet data to determine the proportion by age that can attributed to cannibalism. The proportion was highly variable, ranging between 0 and 80% of stomach contents by weight. When included in the CEATTLE model, the estimated spawning biomass, total biomass, and recruitment increased by 15, 23, and 58%, on average, relative to the single-species model, due to the estimation of time- and age-varying predation mortality, primarily for age-1 hake. The effects of cannibalism varied over time, with further increases in total biomass and recruitment resulting from the age structure of the population following large cohorts in 1980 and 1984. Results from the cannibalism model could be used to inform the estimation of time- and age-varying mortality in the single-species assessment and as a pathway for including ecosystem information in management through environmental and trophic drivers of variability in mortality.

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling.

Bifurcations of a single species model with spatial memory environment

This paper reports on the bifurcations of a single-species model with spatial memory environment. The occurrence conditions of the Hopf bifurcation and Turing bifurcation are given with/without the spatial memory effect. Especially, we show that the positive equilibrium enjoys the stability switches with spatial memory effect.

Body mass mediates spatio-temporal responses of mammals to human frequentation across Italian protected areas.

Protected area (PA) networks are a pivotal tool to fight biodiversity loss, yet they often need to balance the mission of nature conservation with the socio-economic need of giving opportunity for outdoor recreation. Recreation in natural areas is important for human health in an urbanized society, but can prompt behavioural modifications in wild animals. Rarely, however, have these responses being studied across multiple PAs and using standardized methods. We deployed a systematic camera trapping protocol at over 200 sites to sample medium and large mammals in four PAs within the European Natura 2000 network to assess their spatio-temporal responses to human frequentation, proximity to towns, amount of open habitat and topographical variables. By applying multi-species and single-species models for the number of diurnal, crepuscular and nocturnal detections and a multi-species model for nocturnality index, we estimated both species-specific- and meta-community-level effects, finding that increased nocturnality appeared the main strategy that the mammal meta-community used to cope with human disturbance. However, responses in the diurnal, crepuscular and nocturnal site use were mediated by species' body mass, with larger species exhibiting avoidance of humans and smaller species more opportunistic behaviours. Our results show the effectiveness of standardized sampling and provide insights for planning the expansion of PA networks as foreseen by the Kunming-Montreal biodiversity agreement.

Antimicrobial Effect of Dental Adhesive on Cariogenic Multi-Species Biofilm

Dental caries, or tooth decay, is one of the most widespread chronic and multifactorial diseases affecting people worldwide. It is described as the localized destruction of tooth structure by acids produced from bacteria fermentation of edible carbohydrates. The disease process begins within the bacterial biofilm on the surfaces of the teeth. Streptococcus sanguinis, Sreptococcusgordonii, and Streptococcus mutans are the main organisms in the biofilm associated with health or disease conditions in the oral cavity. Streptococcus mutans is believed to be the primary cause of enamel demineralization and the development of dental caries. S. gordonii and S. sanguinis belong to a group of streptococci considered health-related commensal oral bacteria, crucial for forming a biofilm on oral hard tissues. Several types of materials with multipurpose characteristics have been incorporated into dental adhesives. Recently, the calcium salt of an acidic monomer (calcium salt of 4-methacryloxyethyl trimellitic acid, or CMET) has been included in dental adhesive and demonstrated to suppress cariogenic biofilm formation of S. mutans. However, using a single-species model may not mimic the intricate antagonistic and synergistic relations that occur in oral biofilms. Therefore, the effect on cariogenic multi-species biofilm was assessed in this study. Dental adhesive consisting of CMET and 10-methacryloyloxydecyl dihydrogen calcium phosphate (MDCP) (Bio-Coat CA) was spread over the flat-bottom surface of the 96-well plate and LED light-cured. Then it was coated with sterile saliva at 37 °C for 45 min to form an acquired pellicle for microbial attachment. The multi-species bacterial suspension containing Streptococcus mutans ATCC 25715, Streptococcus sanguinis ATCC 10556, and Streptococcus gordonii ATCC 10558 was prepared and added to the saliva-coated well. Then, the plate was incubated at 37°C in a 5% CO2 atmosphere for 24 h, 48 h, and 72 h to support the biofilm formation. The number of vital bacteria in the biofilm was determined with the WST-8 Microbial Cell Counting Kit (Dojindo Molecular Technologies, USA). All tests were done in triplicate and repeated three times. For statistical analysis, Kruskal-Wallis and Dunn’s tests were employed. The results showed that at 24 h, 48 h, and 72 h, dental adhesive with CMET could inhibit the biofilm formation of multi-species bacteria significantly compared with controls. The percentages of biofilm inhibition were 29.1%, 34.7%, and 33.2% at 24 h, 48 h, and 72 h, respectively. Dental adhesive containing CMET displayed favorable multi-species biofilm-inhibiting effects up to 72 h of biofilm growth. It is a promising adhesive for use to prevent secondary caries at the sites of restorations.

Quasi-stationary distribution of a single species model under demographic stochasticity and Allee effects

In this paper, we utilize an absorbed diffusion process to model the dynamics of a single species under the influence of demographic stochasticity and component Allee effects. The trajectories of stochastic solutions exhibits multi-scale dynamics distinct from those of the corresponding mean-field model. The primary focus is on analyzing transient dynamics before extinction, which is described by the quasi-stationary distribution. The paper provides results on the existence, uniqueness, and exponential convergence to the quasi-stationary distribution for initial distributions with compact support. Due to the singularity of the noise at 0, we employ the idea of changing variables to transfer the model into one-dimensional Kolmogorov diffusions with a drift possibly exploding at 0, to prove the main results.

Modeling and CFD simulation of photocatalytic removal of tetracycline by ZnO/PbBiO2Cl nanocomposite catalyst

In this work, the photocatalytic degradation process under visible light in a batch photoreactor was investigated using computational fluid dynamics (CFD). The removal of tetracycline (TC) by the ZnO/PbBiO2Cl photocatalyst was modeled using the single organic species model based on Langmuir-Hinshelwood kinetics. In addition, the hydrodynamic behavior of the two-phase flow inside the photoreactor was simulated using the Eulerian-Lagrangian approach. In this study, the kinetic of the degradation reaction, velocity field of suspension, and concentration of TC were investigated. Based on the CFD results, it has been determined that a rotational velocity of 250 rpm in the reactor is the optimal speed that leads to the highest homogeneity (approximately 95 %) in suspension. Therefore, more light is absorbed by performing experiments in high-quality mixing, and maximum degradation can be achieved. The kinetic study showed that the degradation rate follows pseudo-first-order kinetics. The effect of different weight percentages of PbBiO2Cl and various loading of ZnO/PbBO2Cl on the degradation rate was also examined. The results showed that the 0.5 g/l of ZnO/PbBO2Cl (40 %) is the optimal amount. The degradation reaction kinetic constant was also calculated about 200 × 10−4 min−1. Finally, the obtained modeling results demonstrate excellent agreement with the experimental data.