Reproduction Number Research Articles

The low-lethal concentrations of rotenone and pyrethrins suppress the population growth of Rhopalosiphum padi

As an important pest on winter wheat, Rhopalosiphum padi (L.) causes damage to the wheat yield by sucking plant nutrients, transmitting plant viruses and producing mildew. R. padi has been reported to develop resistance to pyrethroids and neonicotinoids. To explore potential alternative approaches for R. padi control, the activity of 10 botanical insecticides was evaluated. Results suggested that the toxicity of rotenone and pyrethrins to R. padi were the highest and near to the commonly used chemical insecticides. When exposed to the low-lethal concentrations (LC10, LC30) of rotenone or pyrethrins for 24 h, the lifespan and fecundity of adults in F0 generation decreased significantly compared to control. The negative effect could also be observed in the F1 generation, including the decreased average offspring, longevity of adult, and prolonged nymph period. The population parameters in F1 generation of R. padi were also inhibited by exposing to the low-lethal concentrations of rotenone or pyrethrins, including the decreased net reproductive rate, intrinsic rate of natural increase, finite rate of population increase, and gross reproduction rate. Co-toxocity factor results showed that mixtures of rotenone and thiamethoxam, pyrethrins and thiamethoxam showed synergistic effect. Our work suggested that rotenone and pyrethrins showed negative effect on the population growth under low-lethal concentrations. They are suitable for R. padi control as foliar spraying without causing population resurgence.

Improving students’ problem-solving abilities through answering questions in metaverse games: taking GOXR software as an example

In computer-based dialogue learning, students’ willingness to communicate and ability to interact is one of the important factors. Few studies have examined the testing of mobile metaverse teaching material systems built for interactive communication and learning courses. This study developed and designed course content for a virtual classroom, which is suitable for mobile learning on Android or iOS systems and can provide metaverse space for students to discuss homework using their mobile phones, as well as a system for online self-learning and testing. Students can participate in classes without time or space restrictions. In addition, questions related to life math knowledge and leveling up are included, such as the basic reproduction number of COVID-19, influenza, and enterovirus. There were 100 valid responses from two schools, which recognized the convenience and benefit of the virtual digital technology of the mobile self-learning system in the metaverse space as an auxiliary tool for learning, as it provides a more flexible and diversified educational learning mode. This system can be used for course teaching, after-class review, and testing to facilitate self-testing of learning results.

Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator

COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease’s status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.

Jointly estimating epidemiological dynamics of Covid-19 from case and wastewater data in Aotearoa New Zealand

BackgroundTimely and informed public health responses to infectious diseases such as COVID-19 necessitate reliable information about infection dynamics. The case ascertainment rate (CAR), the proportion of infections that are reported as cases, is typically much less than one and varies with testing practices and behaviours, making reported cases unreliable as the sole source of data. The concentration of viral RNA in wastewater samples provides an alternate measure of infection prevalence that is not affected by clinical testing, healthcare-seeking behaviour or access to care.MethodsWe construct a state-space model with observed data of levels of SARS-CoV-2 in wastewater and reported case incidence and estimate the hidden states of the effective reproduction number, R, and CAR using sequential Monte Carlo methods.ResultsWe analyse data from 1 January 2022 to 31 March 2023 from Aotearoa New Zealand. Our model estimates that R peaks at 2.76 (95% CrI 2.20, 3.83) around 18 February 2022 and the CAR peaks around 12 March 2022. We calculate that New Zealand’s second Omicron wave in July 2022 is similar in size to the first, despite fewer reported cases. We estimate that the CAR in the BA.5 Omicron wave in July 2022 is approximately 50% lower than in the BA.1/BA.2 Omicron wave in March 2022.ConclusionsEstimating R, CAR, and cumulative number of infections provides useful information for planning public health responses and understanding the state of immunity in the population. This model is a useful disease surveillance tool, improving situational awareness of infectious disease dynamics in real-time.

Identifying numerical bifurcation structures of codimensions 1 and 2 in interacting species system

The present study has focused on the examination of a Holling type III nonlinear mathematical model that incorporates the influence of fear and Michaelis–Menten‐type predator harvesting. The incorporation of fear with respect to the prey species has been observed to result in a reduction in the survival probability of the prey population and a concurrent reduction in the reproduction rate of the prey species. The existence and stability of ecologically significant equilibria have been ascertained through mathematical analysis. Emphasis within the proposed model primarily centers on numerical bifurcations of codimensions 1 and 2. Numerical validation has been performed on all simulated outcomes within the feasible range of parametric values. Dynamical characteristics of the model have subsequently undergone investigation through a series of numerical simulations, successfully revealing various forms of local and global bifurcations. In addition to the identification of saddle‐node, Hopf, Bogdanov–Takens, transcritical, cusp, homoclinic, and limit point cycle (LPC) bifurcations, the model has also demonstrated bistability and global asymptotic stability. These bifurcation phenomena serve as illustrative examples of the intricate dynamical behavior inherent to the model. Numerical validation through graphical representations has been utilized to elucidate the effects of factors such as fear, nonlinear predator harvesting, and predation rate on the dynamics of the interacting species under different parametric conditions.

Deterministic modelling of asymptomatic spread and disease stage progression in vaccine preventable infectious diseases

AbstractThis study introduces a deterministic formulation for modelling the asymptotic spread of a vaccine preventable disease as well as the different stages for the progression of the disease. We derive the formula for the associated basic reproduction number. To illustrate the proposed model, we use data from the 2017–2018 diphtheria outbreak in Yemen and fit the parameters of the model. A sensitivity analysis of the basic reproduction number, with respect to the model parameters, show that this number increases with an increase of the transmission rate while this number decreases when vaccination rate increases.

Dynamics of a delayed nonlocal reaction–diffusion heroin epidemic model in a heterogenous environment

To study the consumption of heroin in a heterogeneous environment, we propose and analyze a spatiotemporal model with a distributed delay. Using the spectral theory, we determine the basic reproduction number , which serves a threshold role. If , then the addiction‐free steady state is globally asymptotically stable while if , then there is at least one addictive steady state. Moreover, when , if one of the dispersal coefficients is zero, then there is only one addictive steady state, and it is globally asymptotically stable; if both diffusions of susceptible and addicted individuals are present, we cannot identify the temporal behavior of solutions, and hence, we study the asymptotic profile of addictive steady states when one of the dispersal coefficients tend to zero.

Multi-generation effects of lead (Pb) on two Daphnia species.

Two monophyletic Daphnia species (Daphnia magna and D. similis) were exposed to a sub-lethal concentration of Pb (50 µg/L) for nine generations under two food regimes (usual and restricted) and analyzed for acetylcholinesterase (AChE) activity, first reproduction delay, lifespan, and net reproductive rate (R0) at the subcellular, individual, and population levels, respectively. In the sixth generation, Pb-acclimated neonates were moved to clean media for three more generations to check for recovery. The net reproductive rate (R0) of D. magna was not affected by Pb. However, Pb stimulated reproduction, reduced lifespan, and decreased AChE activity. First reproduction delay and lifespan did not improve during the recovery process, suggesting a possible genetic adaptation. Food restriction reduced R0, lifespan, delayed hatching, and increased AChE activity; the opposite outcomes were observed for D. similis. The full recovery shown by R0 suggests the physiological acclimation of D. similis. Under food restriction, the animals exhibited a reduction of R0 and lifespan, delayed first reproduction, and increased AChE activity; however, there was no effect of Pb. The recovery process under food restriction showed that D. similis might not cope with Pb exposure, indicating a failed recovery. Such outcomes indicate that one model species' sensitivity may not represent another's sensitivity.

Early mutational signatures and transmissibility of SARS-CoV-2 Gamma and Lambda variants in Chile

Genomic surveillance (GS) programmes were crucial in identifying and quantifying the mutating patterns of SARS-CoV-2 during the COVID-19 pandemic. In this work, we develop a Bayesian framework to quantify the relative transmissibility of different variants tailored for regions with limited GS. We use it to study the relative transmissibility of SARS-CoV-2 variants in Chile. Among the 3443 SARS-CoV-2 genomes collected between January and June 2021, where sampling was designed to be representative, the Gamma (P.1), Lambda (C.37), Alpha (B.1.1.7), B.1.1.348, and B.1.1 lineages were predominant. We found that Lambda and Gamma variants’ reproduction numbers were 5% (95% CI: [1%, 14%]) and 16% (95% CI: [11%, 21%]) larger than Alpha’s, respectively. Besides, we observed a systematic mutation enrichment in the Spike gene for all circulating variants, which strongly correlated with variants’ transmissibility during the studied period (r = 0.93, p-value = 0.025). We also characterised the mutational signatures of local samples and their evolution over time and with the progress of vaccination, comparing them with those of samples collected in other regions worldwide. Altogether, our work provides a reliable method for quantifying variant transmissibility under subsampling and emphasises the importance of continuous genomic surveillance.

Drivers of epidemic dynamics in real time from daily digital COVID-19 measurements.

Understanding the drivers of respiratory pathogen spread is challenging, particularly in a timely manner during an ongoing epidemic. Here we present insights obtained using daily data from the NHS COVID-19 app for England and Wales and shared with health authorities in almost real time. Our indicator of the reproduction number R(t) was available days earlier than other estimates, with a novel capability to decompose R(t) into contact rates and probabilities of infection. When Omicron arrived, the main epidemic driver switched from contacts to transmissibility. We separate contacts and transmissions by day of exposure and setting, finding pronounced variability over days of the week and during Christmas holidays and events. As an example, during the Euro football tournament in 2021, days with England matches showed sharp spikes in exposures and transmissibility. Digital contact tracing technologies can help control epidemics not only by directly preventing transmissions but also by enabling rapid analysis at scale and with unprecedented resolution.

Cytotoxicity and Genotoxicity Effects of a Magnetic Zeolite Composite in Daphnia magna (Straus, 1820)

Zeolite type 5A combined with the magnetic properties of maghemite nanoparticles facilitate the rapid absorption of heavy metals, which makes them an interesting proposal for the remediation of water contaminated with lead and arsenic. However, the physicochemical analysis related to concentration and size for the use of this magnetic zeolite composite (MZ0) in water bodies and the possible toxicological effects on aquatic fauna has not yet been carried out. The main objective of the research work is to determine lethal concentrations that cause damage to Daphnia magna based on LC50 tests, morphology, reproductive rate, and quantification of the expression of three genes closely involved in the morphological development of vital structures (Glass, NinaE, Pph13). To achieve this objective, populations of neonates and young individuals were used, and results showed that the LC50 for neonates was 11,314 mg L−1, while for young individuals, it was 0.0310 mg L−1. Damage to morphological development was evidenced by a decrease in eye size in neonates, an increase in eye size in young individuals, variations in the size of the caudal spine for both age groups, and slight increases in the heart size, body, and antenna for both age groups. The reproductive rate of neonates was not affected by the lower concentrations of MZ0, while in young individuals, the reproductive rate decreased by more than 50% from the minimum exposure concentration of MZ0. And for both ages, Glass gene expression levels decreased as the MZ0 concentration increased. Also, the MZ0 evidenced its affinity for the exoskeleton of D. magna, which was observed using both light microscopy and electron microscopy. It is concluded that MZ0 did not generate significant damage in the mortality, morphology, reproductive rate, or gene expression in D. magna at lower concentrations, demonstrating the importance of evaluating the possible impacts on different life stages of the cladoceran.

Cytotoxicity and Genotoxicity Effects of a Magnetic Zeolite Composite in Daphnia magna (Straus, 1820)

Zeolite type 5A combined with the magnetic properties of maghemite nanoparticles facilitate the rapid absorption of heavy metals, which makes them an interesting proposal for the remediation of water contaminated with lead and arsenic. However, the physicochemical analysis related to concentration and size for the use of this magnetic zeolite composite (MZ0) in water bodies and the possible toxicological effects on aquatic fauna has not yet been carried out. The main objective of the research work is to determine lethal concentrations that cause damage to Daphnia magna based on LC50 tests, morphology, reproductive rate, and quantification of the expression of three genes closely involved in the morphological development of vital structures (Glass, NinaE, Pph13). To achieve this objective, populations of neonates and young individuals were used, and results showed that the LC50 for neonates was 11,314 mg L−1, while for young individuals, it was 0.0310 mg L−1. Damage to morphological development was evidenced by a decrease in eye size in neonates, an increase in eye size in young individuals, variations in the size of the caudal spine for both age groups, and slight increases in the heart size, body, and antenna for both age groups. The reproductive rate of neonates was not affected by the lower concentrations of MZ0, while in young individuals, the reproductive rate decreased by more than 50% from the minimum exposure concentration of MZ0. And for both ages, Glass gene expression levels decreased as the MZ0 concentration increased. Also, the MZ0 evidenced its affinity for the exoskeleton of D. magna, which was observed using both light microscopy and electron microscopy. It is concluded that MZ0 did not generate significant damage in the mortality, morphology, reproductive rate, or gene expression in D. magna at lower concentrations, demonstrating the importance of evaluating the possible impacts on different life stages of the cladoceran.

The impact of impaired intrauterine growth on male fertility: A systematic review and meta-analysis.

Adverse intrauterine environment was believed to have deleterious effects on the gonadal function. However, the association between impaired intrauterine growth and fertility in adult males has not been established. To compare the reproductive rates of males born small for gestational age (SGA), with low birth weight (LBW) or very low birth weight (VLBW) with control groups. The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) statement was followed to search PubMed, Web of Science, Cochrane Library, and Embase databases from inception to June 16, 2023. Cohort studies investigating the reproductive rates of males born SGA, with LBW or VLBW were included. A random or fixed effects model was used for different exposures. A total of 10 studies out of 3,801 records were included. Males born SGA showed a higher risk of infertility than the control group (odds ratio, OR=0.91, 95% confidence interval, 95% CI 0.89-0.93, p=0.000). The reproductive rates of individuals born with LBW or VLBW were lower than the control group (OR=0.86, 95% CI 0.78-0.94, p=0.001; OR=0.57, 95% CI 0.40-0.81, p=0.002, respectively). Participants were further divided into two age groups of 18-35 and 35-45 years. In both subgroups, the reproductive rates were lower in males born SGA, with LBW or VLBW compared with controls. Sensitivity analysis showed the robustness of the pooled estimates among LBW and VLBW. In summary, SGA, LBW, and VLBW were associated with a higher risk of male infertility in both early and middle adulthood. Achieving optimal intrauterine growth would be helpful to prevent male infertility.

Indirect effect of earthworms on wheat-aphid interactions

Studies on interactions between plants and belowground organisms, or between plants and aboveground organisms, are numerous and highlight their importance in understanding ecosystem functioning. However, these two compartments are rarely studied together, despite the direct link formed by the plant itself. Soil organisms can influence interactions between plants and herbivores by changes in plant growth and chemistry. Under controlled conditions the influence of earthworms and aphids on wheat was investigated. The effect of earthworms on aphid reproduction was also investigated, to demonstrate the indirect plant-trait-mediated effects. We showed a significant effect of both above and belowground organisms on wheat. Interestingly, nitrogen content was higher in the presence of aphids (1.63 ± 0.07 %,) or earthworms alone (1.58 ± 0.04 %) and even higher in presence of both (2.07 ± 0.07 %). Moreover, we showed a strong effect of earthworms on aphid reproduction rates which are almost twice as high as in the absence of earthworms where we observed a reproduction rate of 32 individuals per day compared with 57 in the presence of earthworms. The presence of aphids led to a 16 % reduction in above-ground biomass compared with the control (1.83 ± 0.08 g vs 2.19 ± 0.09 g for the control), while the presence of earthworms led to an 46 % increase (3.20 ± 0.12 g vs 2.19 ± 0.09 g), and the presence of both organisms had no significant effect on the above-ground biomass of wheat compared with the control (2.39 ± 0.08 g vs 2.19 ± 0.09 g). These results could have implications for pest management, as they indicate that the presence of earthworms compensate the negative effect of aphids on plant biomass, probably by acting on nutrient uptake and plant defensive traits. By addressing the effects of earthworms on both the pest performances and plant traits, we highlight the need for further research on the indirect effects of below-ground compartments on pest performance. This study builds towards a better understanding of the interaction between soil, plant and pests and highlights the importance to study the pest management with a holistic view of agroecosystems.

Indirect effect of earthworms on wheat-aphid interactions

Studies on interactions between plants and belowground organisms, or between plants and aboveground organisms, are numerous and highlight their importance in understanding ecosystem functioning. However, these two compartments are rarely studied together, despite the direct link formed by the plant itself. Soil organisms can influence interactions between plants and herbivores by changes in plant growth and chemistry. Under controlled conditions the influence of earthworms and aphids on wheat was investigated. The effect of earthworms on aphid reproduction was also investigated, to demonstrate the indirect plant-trait-mediated effects. We showed a significant effect of both above and belowground organisms on wheat. Interestingly, nitrogen content was higher in the presence of aphids (1.63 ± 0.07 %,) or earthworms alone (1.58 ± 0.04 %) and even higher in presence of both (2.07 ± 0.07 %). Moreover, we showed a strong effect of earthworms on aphid reproduction rates which are almost twice as high as in the absence of earthworms where we observed a reproduction rate of 32 individuals per day compared with 57 in the presence of earthworms. The presence of aphids led to a 16 % reduction in above-ground biomass compared with the control (1.83 ± 0.08 g vs 2.19 ± 0.09 g for the control), while the presence of earthworms led to an 46 % increase (3.20 ± 0.12 g vs 2.19 ± 0.09 g), and the presence of both organisms had no significant effect on the above-ground biomass of wheat compared with the control (2.39 ± 0.08 g vs 2.19 ± 0.09 g). These results could have implications for pest management, as they indicate that the presence of earthworms compensate the negative effect of aphids on plant biomass, probably by acting on nutrient uptake and plant defensive traits. By addressing the effects of earthworms on both the pest performances and plant traits, we highlight the need for further research on the indirect effects of below-ground compartments on pest performance. This study builds towards a better understanding of the interaction between soil, plant and pests and highlights the importance to study the pest management with a holistic view of agroecosystems.

Source-Sink Dynamics in a Two-Patch SI Epidemic Model with Life Stages and No Recovery from Infection.

This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by real-world ecological crises like the decline of amphibian populations due to chytridiomycosis and sea star populations due to Sea Star Wasting Disease, aims to understand the conditions under which a sink host population can present ecological rescue from a healthier, source population. Mathematical and numerical analyses reveal the critical roles of the basic reproductive numbers of the source and sink populations, the maturation rate, and the dispersal rate of juveniles in determining population outcomes. The study identifies basic reproduction numbers for each of the patches, and conditions for the basic reproduction numbers to produce a receiving patch under which its population. These findings provide insights into managing natural populations affected by disease, with implications for conservation strategies, such as the importance of maintaining reproductively viable refuge populations and considering the effects of dispersal and maturation rates on population recovery. The research underscores the complexity of host-pathogen dynamics in spatially structured environments and highlights the need for multi-faceted approaches to biodiversity conservation in the face of emerging diseases.

Source-Sink Dynamics in a Two-Patch SI Epidemic Model with Life Stages and No Recovery from Infection.

This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by real-world ecological crises like the decline of amphibian populations due to chytridiomycosis and sea star populations due to Sea Star Wasting Disease, aims to understand the conditions under which a sink host population can present ecological rescue from a healthier, source population. Mathematical and numerical analyses reveal the critical roles of the basic reproductive numbers of the source and sink populations, the maturation rate, and the dispersal rate of juveniles in determining population outcomes. The study identifies basic reproduction numbers for each of the patches, and conditions for the basic reproduction numbers to produce a receiving patch under which its population. These findings provide insights into managing natural populations affected by disease, with implications for conservation strategies, such as the importance of maintaining reproductively viable refuge populations and considering the effects of dispersal and maturation rates on population recovery. The research underscores the complexity of host-pathogen dynamics in spatially structured environments and highlights the need for multi-faceted approaches to biodiversity conservation in the face of emerging diseases.

Effect of fear with saturated fear cost and harvesting on aquatic food chain model (plankton–fish model) in the presence of nanoparticles

Studying the interplay of phytoplankton–zooplankton–fish (PP–ZP–F) in an aquatic system is crucial for better understanding of nutrient cycling, assessing ecosystem health, predicting and mitigating harmful algal blooms, and managing fisheries in the water bodies. In order to investigate the effectiveness of nanoparticles (NPs), fear, and harvesting, this paper focuses on exploring the dynamics of a food chain model among PP–ZP–F species. We consider the fear of fish on zooplankton species (which reduces the reproduction rate of ZPs) with saturated fear cost in the presence of nanoparticles (NPs) and harvesting in fish. The system dynamics are studied from the viewpoint of proving positivity, boundedness, and uniqueness, followed by analysing the existence and local stability of biologically feasible equilibria. Conditions for the global stability of the interior equilibrium point are also found. Furthermore, we established the transversality conditions for the occurrence of Hopf, transcritical, and saddle–node bifurcations. To validate our theoretical results, we made numerous phase portraits, time-series graphs, tables showing the extinction of species, and bifurcation diagrams. It is numerically observed that increasing the contact rate of NPs with PPs makes the system stable from chaos, and further increase of contact rate may lead to extinction. Chaos at a low contact rate can also be managed by increasing the fear level, and the chaotic behaviour at a low fear level can again be controlled by enhancing the harvesting of fish species. Over-exploitation may result in the extinction of fish, whereas fear may promote coexistence, stability, and long-term survival of the species. Increased saturated fear cost can make the system chaotic from stable dynamics. Therefore, the theoretical as well as numerical findings of our paper may be of great interest in estimating the behaviour of aquatic systems biologically and practically.

The dynamics of evolutionary branching in an ecological model

AbstractEco-evolutionary modelling involves the coupling of ecological equations to evolutionary ones. The interaction between ecological dynamics and evolutionary processes is essential to simulating evolutionary branching, a precursor to speciation. The creation and maintenance of biodiversity in models depends upon their ability to capture the dynamics of evolutionary branching. Understanding these systems requires low-dimension models that are amenable to analysis. The rapid reproduction rates of marine plankton ecosystems and their importance in determining the fluxes of climatically important gases between the ocean and atmosphere suggest that the next generation of global climate models needs to incorporate eco-evolutionary models in the ocean. This requires simple population-level models, that can represent such eco-evolutionary processes with orders of magnitude fewer equations than models that follow the dynamics of individual phenotypes. We present a general framework for developing eco-evolutionary models and consider its general properties. This framework defines a fitness function and assumes a beta distribution of phenotype abundances within each population. It simulates the change in total population size, the mean trait value, and the trait differentiation, from which the variance of trait values in the population may be calculated. We test the efficacy of the eco-evolutionary modelling framework by comparing the dynamics of evolutionary branching in a six-equation eco-evolutionary model that has evolutionary branching, with that of an equivalent one-hundred equation model that simulates the dynamics of every phenotype in the population. The latter model does not involve a population fitness function, nor does it assume a distribution of phenotype abundance across trait values. The eco-evolutionary population model and the phenotype model produce similar evolutionary branching, both qualitatively and quantitatively, in both symmetric and asymmetric fitness landscapes. In order to better understand the six-equation model, we develop a heuristic three-equation eco-evolutionary model. We use the density-independent mortality parameter as a convenient bifurcation parameter, so that differences in evolutionary branching dynamics in symmetric and asymmetric fitness landscapes may be investigated. This model shows that evolutionary branching of a stable population is flagged by a zero in the local trait curvature; the trait curvature then changes sign from negative to positive and back to negative, along the solution. It suggests that evolutionary branching points may be generated differently, with different dynamical properties, depending upon, in this case, the symmetry of the system. It also suggests that a changing environment, that may change attributes such as mortality, could have profound effects on an ecosystem’s ability to adapt. Our results suggest that the properties of the three-dimensional model can provide useful insights into the properties of the higher-dimension models. In particular, the bifurcation properties of the simple model predict the processes by which the more complicated models produce evolutionary branching points. The corresponding bifurcation properties of the phenotype and population models, evident in the dynamics of the phenotype distributions they predict, suggest that our eco-evolutionary modelling framework captures the essential properties that underlie the evolution of phenotypes in populations.

Dietary restriction promote sperm remodeling in aged roosters based on transcriptome analysis

BackgroundThe breeder rooster has played a pivotal role in poultry production by providing high-quality semen. Typically, fertility peaks between 30 and 40 weeks of age and then declines rapidly from 45 to 55 weeks of age. Research into improving fertility in aging roosters is essential to extend their productive life. While progress has been made, enhancing fertility in aging roosters remains a significant challenge.MethodsTo identify the genes related to promoting sperm remodeling in aged Houdan roosters, we combined changes in testis and semen quality with transcriptome sequencing (RNA-seq) to analyze the synchrony of semen quality and testis development. In this study, 350-day-old Houdan breeder roosters were selected for RNA-seq analysis in testis tissues from induced molting roosters (D group) and non-induced molting roosters (47DG group). All analyses of differentially expressed genes (DEGs) and functional enrichment were performed. Finally, we selected six DEGs to verify the accuracy of the sequencing by qPCR.ResultsCompared with the 47DG group, sperm motility (P < 0.05), sperm density (P < 0.01), and testis weight (P < 0.05) were significantly increased in roosters in the D group. Further RNA-seq analysis of the testis between the D group and 47DG group identified 61 DEGs, with 21 up-regulated and 40 down-regulated. Functional enrichment analysis showed that the DEGs were primarily enriched in the cytokine-cytokine receptor interaction, Wnt signaling pathway, MAPK signaling pathway, TGF-β signaling pathway, and focal adhesion pathway. The qRT-PCR results showed that the expression trend of these genes was consistent with the sequencing results. WNT5A, FGFR3, AGTR2, TGFβ2, ROMO1, and SLC26A7 may play a role in testis development and spermatogenesis. This study provides fundamental data to enhance the reproductive value of aging roosters.