The ladybird Eriopis connexa (Germar, 1824), a voracious aphid predator, faces challenges from insecticide applications, compromising biological control. As a result, the number of studies analysing the resistance and susceptibility of ladybirds has increased. Some studies have found that resistant populations differ in predation and foraging behaviour from susceptible ones. This study modelled the population dynamics of resistant and susceptible E. connexa preying on Aphis gossypii Glover, 1877 and Myzus persicae (Sulzer, 1776). A logistic model with density dependence and type II functional response was constructed to analyse predation dynamics, incorporating bifurcation analysis of predation parameters (attack rate and handling time) and the mortality rate of susceptible ladybirds. This model was used to simulate scenarios that included or excluded insecticide application and aphid resistance. To simulate the effects of insecticide applications, the parameters related to the aphids’ intrinsic growth rate ( r 1 and r 2 ) were changed to reflect the responses of susceptible and resistant populations. The same approach was used for the mortality rate of ladybirds ( d 2 and d 3 ). The results demonstrated that mortality, attack rate, and handling time were critical in shaping predator–prey interactions. Temporal simulations revealed fluctuating abundances, highlighting the fragility of these interactions under insecticide stress. This study contributed to understanding the ecological implications of insecticides, which disrupt natural predation dynamics, and showed how changes in the rates of behaviours can impact prey control. This research demonstrated the importance of integrated strategies that balance insecticide applications with preserving natural enemies and causing sustainable agricultural practices. • A pest-biocontrol model with insecticide-resistant and susceptible strains was constructed. • Coexistence of susceptible/resistant predators aids biocontrol under insecticide stress. • Insecticides disrupt aphid-ladybird dynamics by reducing the abundance of the biocontrol agent. • Abrupt changes might occur if parameters are near bifurcation points. • The results collectively show the importance of integrated pest management for aphids.

Organisms acclimate to environmental temperatures to maintain physiological homeostasis. Acclimation can alter demographic rates, thereby affecting population dynamics. Previous research has demonstrated that acclimation can have positive or negative effects on population growth rates in variable thermal environments, depending on the amount of time acclimation takes. A clear picture of the timescale of acclimation may help identify the consequences of various frequencies of thermal fluctuations for population dynamics. However, the progression of population-level effects of acclimation over time has not been explored. We used experimental microcosms to test the effects of acclimation on population dynamics of the ciliated protist Colpidium striatum in various thermal regimes. We also observed the progression of these effects over the course of acclimation. Prior acclimation to cooler conditions increased intrinsic growth rates in warm trial conditions relative to the growth rates of warm-acclimated populations. In contrast, prior acclimation to warm conditions decreased intrinsic growth rates in cool trial conditions relative to the growth rates of cold-acclimated populations. These results are consistent with an overcompensatory acclimation response and either the "colder is better" or "optimal acclimation temperature" hypothesis, though we cannot distinguish between these two possibilities without an intermediate acclimation temperature treatment. The observed patterns may be due to resource uptake dynamics and/or increased stress at high temperatures with increased exposure duration. The progression of these effects over the course of acclimation also differed in trajectory, and perhaps duration, for populations acclimating to warmer versus cooler conditions. Differences in the effects and progress of thermal acclimation depending on the direction of thermal change suggest that different physiological mechanisms may be driving acclimation to warmer versus cooler conditions.

Microbial respiration is a key biotic driver of climate change. Warming boosts microbial population growth, which increases biomass and respiration, potentially leading to more warming. This feedback might be disrupted by adaptation in thermal performance curves (TPCs) -whose shape describes how temperature drives growth. In this study, we uncover substantial genetic variation (G) in the intrinsic population growth rates (r) of the protist Tetrahymena thermophila, demonstrate a causal link between heritable variation in r and heritable variation in TPC shape, and show how this variation constrains predicted r-TPC shape evolution along specific evolutionary paths across temperatures. We also uncover Gene-by-Environment (G × E) variation in r, which results in specific signatures in TPC shape and predictable temperature-dependent TPC evolution that can erode heritable variation, thus reducing future evolutionary potential. Overall, we show how temperature-dependent evolution in microbial TPC shape-a linchpin of global ecosystem function-is determined by a combination of heritable and non-heritable variation in intrinsic growth rates.

Abstract In this study, we investigate the invasion dynamics of a predator-prey system, focusing on the spread of prey in the predator's occupied region and vice-versa. The model assumes that both species disperse locally through diffusion and that the invading population initially occupies a compact spatial region, while the resident population is distributed at its equilibrium density. To rigorously study the invasion speeds, we use the comparison principle and assume that the predator population experience either positive or negative intrinsic growth in the absence of prey. As a result, a positive intrinsic growth rate of predator promotes prey invasion, and for the case of negative intrinsic growth rate, predator invasion is found. For each scenario, invasion speed of both species is determined analytically and numerically. Numerical sensitivity experiments are presented to find the most sensitive parameter that causes the invasion speed in either case.

This study constructs a discrete-time model featuring the Holling type II functional response to investigate how the Allee effect drives the appearance of both periodic and chaotic behaviors. Through rigorous algebraic analysis, it is demonstrated that Neimark-Sacker (NS) bifurcations occur when varying the Allee parameter n and the prey's intrinsic growth rate r within the positive quadrant. By applying the center manifold theorem and core results from bifurcation theory, a solid theoretical framework is established to track these qualitative changes. Extensive numerical simulations validate that the system undergoes a subcritical NS bifurcation as n and r change, marking a shift from stable equilibria into chaotic oscillations with increasing Allee intensity. Moreover, the model reveals the coexistence of periodic attractors of periods 11 and 34 over certain (n,r) pairs, underscoring how initial population levels critically shape long-term outcomes. A parallel analysis contrasts this Holling II formulation with its Holling type I analog. By varying the Allee threshold n, it becomes apparent that the type I system collapses at a lower Allee value than the type II system. This disparity suggests that predation saturation-a hallmark of Holling II-confers greater resilience under strong Allee effects. Finally, a comparative evaluation of both functional responses' advantages and limitations highlights the need for adaptive management strategies to preserve biodiversity and maintain ecological stability.

Theory predicts that indirect interactions in ecological networks sustain species diversity through oscillatory dynamics. However, a framework linking interaction structure to the presence, type, and complexity of these cycles is lacking. Here, we develop an analytical toolbox combining invasion graphs with a mathematical decomposition of interaction matrices into symmetric and antisymmetric components. We find that invasion cycles-closed loops of species invasions-are suppressed when symmetric interactions dominate, reflecting strong self-limitation. Conversely, antisymmetric dominance, indicating competitive asymmetries, leads to the well-known cycles of single-species invasion such as rock-paper-scissors as well as novel multispecies invasion patterns, in which several species simultaneously invade each transition of the cycle. As asymmetries increase, more complex cycles involving both sequential and simultaneous invasions emerge. Yet this potential for cycles is suppressed as variability in intrinsic growth rates increases. Our work clarifies when interactions drive cycles and introduces a simple ratio that assesses symmetric versus antisymmetric contributions in the interaction matrix, constraining cycle emergence and the number of species they can sustain.

Stochastic dynamics at the back of a gene drive eradication wave.

ABSTRACT The Bigeye grunt (Brachydeuterus auritus) and Lesser African threadfin (Galeoides decadactylus) underpin food security and livelihoods in the Eastern Central Atlantic Ocean, yet robust stock assessments remain scarce for the northern stock (NS) region delineated by the Committee for the Eastern Central Atlantic Fisheries (CECAF). This study applied the Bayesian Catch-Maximum Sustainable Yield (CMSY++) catch-only model to Food and Agriculture Organization FishStatJ catch data (2001–2021) for Guinea-Bissau, Guinea, Sierra Leone, and Liberia. The study aimed to (1) assess the predictive accuracy of CMSY++ under four biomass-prior (b/k) scenarios, and (2) estimate the status of both stocks. From the results, the expert-informed prior yielded the most reliable estimates: Bigeye grunt exhibited sustainable biomass above the Maximum Sustainable Yield (i.e., B/BMSY >1.0), fishing mortality below the Maximum Sustainable Yield threshold (i.e., F/FMSY< 1.0), and a high intrinsic growth rate (i.e., r ≈ 0.6 per year). Conversely, Lesser African threadfin was overexploited and depleted (B/BMSY ≈ 0.6, F/FMSY ≈ 2.6, r ≈ 0.4). These findings affirm CMSY++ as a valuable tool for data-limited fisheries, contingent on expert-informed priors, and underscore the urgent need for precautionary management of Lesser African threadfin to promote stock rebuilding and long-term sustainability.

Stability and bifurcation analysis of a discrete-time plant-herbivore model with chaotic dynamics under weak Allee effect on plant

Context: Understanding crop–crop and crop–weed interactions is essential for designing overyielding and weed-suppressive intercropping systems. Measurements of canopy cover over time can provide insights into these interactions, but are labour-intensive to collect. Machine learning methods, specifically convolutional neural networks (CNNs), could automatically analyse cover of individual species from canopy cover photos, yet the quality of the cover assessment that is needed to study species interaction remains unclear. Objective: This study aimed to quantify competitive dynamics in cereal–faba bean intercrops based on canopy cover and assess CNN performance required for reliable analysis. Methods: We collected RGB images from cereal–faba bean intercrops varying in cereal species (barley, rye, triticale, wheat), triticale:faba bean mixing ratios (1:1, 1:3, 3:1), and spatial design (row or mixed). Canopy cover was manually annotated for 397 images, identifying cereal, faba bean, and weed classes. Four CNN models of varying complexity were trained, the simplest of which were used off-the-shelf. We compared qualitative patterns and Lotka–Volterra competition parameters between ground-truth and CNN-segmented data. Results: Ground-truth data revealed that rye was the most competitive cereal, and wheat the least, reflected in Lotka-Volterra intrinsic growth rate parameters. Separating cereals and legumes into rows and reducing the cereal proportion in intercrops decreased cereal competitiveness relative to faba bean, resulting in more even canopy cover and more symmetrical competition parameters between species. All CNN models achieved high accuracy (Intersection over Union (IoU) = 0.900–0.926). While CNN-based segmentations matched ground-truth patterns visually, only our most complex model came close to the ground-truth parameter estimates, whereas the other three produced values too uncertain or biased to support the same conclusions. Conclusion: We conclude that moderate-complexity CNN models are sufficient to qualitatively interpret cover trends, but for more refined ecological analysis more complex CNNs are needed. Sensitivity analysis could aid in quantifying the performance needed before training such a complex CNN.

Effect of group size on life table parameters of the two-spotted spider mite, Tetranychus urticae Koch (Acari: Tetranychidae) was assessed using an age-stage, two-sex life table analysis. One (single), 2 (double), 4 (quadruple), and 6 (sextuple) individuals were placed on leaf discs, under controlled conditions like 25℃, 60-80% RH and a 16L: 8D photoperiod. Leaf discs of varying sizes, e.g., of 8, 11, 16, and 20 mm were used to maintain approximately equal mite densities, allowing us to evaluate the impact of conspecific presence on mite behavior without confounding effects related to density. Both male and female T. urticae successfully completed development under all rearing conditions, confirming that the experimental setup was suitable for subsequent evaluation of density effects on life-history traits and life table parameters. Rearing density significantly affected several life-history traits of T. urticae. The average pre-oviposition period decreased from 2.29 days in singly reared females to 1.66 days in the sextuple group, while oviposition duration increased from 8.29 to 13.62 days. Female longevity and fecundity were highest in the sextuple treatment, with females producing 82.00 eggs compared with 34.45 eggs in the single treatment. Demographic parameters were also significantly influenced by rearing density. The net reproductive rate (R₀) increased from 15.71 in singly reared mites to 45.88 in the sextuple group, and the intrinsic rate of increase (r) rose from 0.1340 to 0.1858 day⁻¹. Similarly, the finite rate of increase (λ) increased from 1.1434 to 1.2042 day⁻¹, indicating enhanced population growth at higher rearing densities. These results demonstrate that rearing density strongly influences life-history traits and population growth parameters of T. urticae, with single rearing producing significantly lower reproductive output and intrinsic growth rates compared with group-rearing conditions. This study underscores the significance of group size on the life parameters of T. urticae, which has potential implications for better pest management.

Thermal stress precludes the multigenerational build-up of carbamate tolerance in Daphnia magna by offsetting increased antioxidant defenses.

This study investigates a two-species chemotaxis system incorporating Lotka–Volterra competitive kinetics within a bounded domain with smooth boundaries. Unlike prior works, we relax the regularity assumptions on the initial data to (u0, v0, w0, z0) ∈ L2(Ω) × W1,2(Ω) × L2(Ω) × W1,2(Ω). We establish the existence of global weak solutions for the system in arbitrary dimensions. Additionally, in three-dimensional settings, we prove that these weak solutions evolve into classical solutions after some finite waiting time, provided that the condition riminμi,μi32+ω&amp;lt;ξ with some ξ = ξ(ω) &amp;gt; 0, whenever ω &amp;gt; 0. This result demonstrates that the eventual smoothness of weak solutions is achieved when either intrinsic growth rates ri is sufficiently small or the self-limitation effects μi is sufficiently large. To the best of our knowledge, our findings not only significantly generalize existing results on global weak solutions for such systems but also provide the first known result on the eventual smoothness of solutions in three dimensions.

&lt;p&gt;In this paper, we extend the classical logistic law by incorporating &lt;span&gt;autonomously evolving, time-dependent coefficients&lt;/span&gt; that allow both the intrinsic growth rate &lt;span class="math inline"&gt;\(\gamma(t)\)&lt;/span&gt; and the carrying capacity &lt;span class="math inline"&gt;\(K(t)\)&lt;/span&gt; to vary over time according to logistic modulated dynamics. In particular, the carrying capacity is modeled as a logistic process with intrinsic growth rate &lt;span class="math inline"&gt;\(\alpha\)&lt;/span&gt; and saturation parameter &lt;span class="math inline"&gt;\(\beta\)&lt;/span&gt;, yielding an asymptotic level of &lt;span class="math inline"&gt;\(\frac{\alpha}{\beta}\)&lt;/span&gt;. The objective is to investigate how temporal variability in the governing coefficients influences both transient and asymptotic regimes of the population dynamics and to assess the extent to which the system behavior can be controlled through a reduced set of key parameters. &lt;span&gt;Analytical results are derived in closed form, expressed in terms of hypergeometric functions, and compared with numerical integrations for validation purposes.&lt;/span&gt; It is shown that the model admits a long-term equilibrium determined by the ratio &lt;span class="math inline"&gt;\(\frac{\alpha}{\beta}\)&lt;/span&gt;, independently of the initial population size &lt;span class="math inline"&gt;\(S_0\)&lt;/span&gt;, while short- and medium-term dynamics are strongly shaped by the interplay between &lt;span class="math inline"&gt;\(S_0\)&lt;/span&gt; and the &lt;span&gt;non-autonomous logistic evolution&lt;/span&gt; of the carrying capacity &lt;span class="math inline"&gt;\(K(t)\)&lt;/span&gt;. These results illustrate how analytically tractable &lt;span&gt;non-autonomous logistic models with internally generated coefficient trajectories&lt;/span&gt; can enhance the qualitative understanding of population dynamics and provide reliable benchmarks for numerical simulations, with potential applications in sustainable resource management, aquaculture, and ecological modeling.&lt;/p&gt;

In this paper, we investigate the existence of forced waves for an asymptotic KPP equation with anisotropic nonlocal dispersal in a shifting habitat. Without requiring the sign of intrinsic growth rate at negative infinity, we prove the existence of zero-valued forced waves at + ∞ or − ∞ for s in different ranges. The main method is based on the construction of suitable upper and lower solutions combined with the monotone iteration principle and Schauder's fixed point theorem. Furthermore, we investigate the asymptotic behavior of forced waves via contracting rectangles. Finally, to illustrate our results, we consider forced waves in three classical models.

In this paper, we consider the following discrete periodic Ricker model x n + 1 = x n exp ⁡ [ r n ( 1 − x n k n ) ] , n = 0 , 1 , 2 , … , where intrinsic growth rate { r n } and carrying capacity { k n } are two given sequences of positive numbers with a common period ω. We obtain new sufficient conditions for the model to have a unique positive ω-periodic solution, which is stable and attracts all positive solutions. Our results are suitable for the case when the magnitude of the series { k n } is large and partly fill a gap in the existing literature. For the special case of ω = 2 , we show the model has at most three 2-periodic solutions, and give sufficient conditions for the existence of a unique, two and three 2-periodic solutions, respectively. We also discuss and present some results regarding the minimal period of the periodic solution of the model when ω is a composite number.

Characterizing biological parameters of Myzus persicae biotypes and diagnosing R81T linked neonicotinoids resistance.

Understanding how information spreads through online social networks is a fundamental problem in computational social science. Classical diffusion models, such as the Diffusive Logistic (DL) model, account for time and spatial dynamics, but typically assume a structurally homogeneous network. This assumption neglects the impact of network topology on diffusion patterns, which can lead to oversimplified predictions in complex social environments. In this work, we introduce (WDL) Wiener-Based Diffusive Logistic model, a topology-aware extension of the classical DL model. Our approach incorporates a structural metric known as the small Wiener index w(s,G), which quantifies the cumulative distance from a given node s to the rest of the network G. By modulating the intrinsic growth rate based on this topological centrality measure, the WDL model better captures how structural positioning influences diffusion speed and reach. We apply our model to the Higgs Twitter retweet network (SNAP dataset), extracting a subgraph around a central node and computing w(s,G) for each distance layer. Numerical simulations show that the WDL model produces heterogeneous diffusion curves: nodes closer to the center receive and propagate information faster than peripheral ones, consistent with real-world observations. These findings highlight the potential of incorporating topological indices, such as the small Wiener index, into PDE-based diffusion models to generate more realistic and adaptive predictions of information propagation in complex networks.

In this paper, we will study the Holling-Tanner predator-prey model with a prey refuge, considering that the intrinsic growth rate of the predator is much lower than that of the prey. We first discuss the dynamic behavior of the system in the presence of positive equilibrium. Using geometric singular perturbation theory and the slow-fast normal form, we show that the system exhibits a singular Hopf bifurcation near the fold point. This bifurcation is accompanied by a canard explosion, validated through Melnikov integral analysis. Then, we prove the existence of canard limit cycles near the canard point using slow divergence integral methods, and the existence of relaxation oscillations via entry-exit function analysis. Our proof shows that the introduction of the prey refuge significantly enhances the global stability of the system. The refuge can balance the predation pressure through the buffer effect, which plays an important role in regulating the sustainability of the ecosystem.

We study the May-Leonard asymmetric model in \(\mathbb{R}^3\) which was introduced in[3,8]. It is the celebrated classical May-Leonard model incorporating asymmetric competitive effects instead of requiring equal intrinsic growth rates for each competing population. We study this system when it has an invariant of Darboux type and for these values of the parameters we shall describe its global dynamics in the compactification of the sphere, adding its infinity. In particular, we study the dynamics of that system on the invariant planes and we complete the study describing the dynamics at infinity. We also prove that the system is completely integrable and describe the \(\alpha\) and \(\omega\) limits of all the orbits of the system. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/115/abstr.html