Alien flora are accumulating steadily in China over the last 80 years.

New alien species are increasingly introduced and established outside their native range. The knowledge of the spatiotemporal dynamics of their accumulation and the factors determining their residence time in the introduced range is critical for proactive management, especially in emerging economies. Based on a comprehensive time series dataset of 721 alien angiosperms in China, we show that new alien flora has been accumulating steadily in China, particularly in the coastal regions, for the last 80 years without saturation. The ability to occupy a large number of habitats facilitates the early introduction of alien flora, whereas a large naturalized range, greater number of uses, and multiple introduction pathways directly contribute to their naturalization and invasion. The temporal pattern is predicted to remain consistent in the foreseeable future. We propose upgrading the country's biosecurity infrastructure based on a standardized risk assessment framework to safeguard the country from ongoing and future invasions.

Abiotic factors and heavy metals defining eco-physiological niche in fish.

Ecosystem dynamics undergoing alterations in structure and function highlights the need to look into the relations between ecological parameters and organismal fitness and tolerance. Ecophysiological studies are used to understand how organisms adapt to and cope up with environmental stress. Current study uses a process-based approach to model physiochemical parameters regarding seven different fish species. Species respond to climatic variations via acclimation or adaptation through physiological plasticity. Four sites are differentiated into two types based on the water quality parameters and metal contamination. Seven fish species are clustered into two groups, each group depicting separate pattern of response in similar habitat. In this manner, biomarkers from three different physiological axes- stress, reproduction, and neurology were taken to determine the organism's ecological niche. Cortisol, Testosterone, Estradiol, and AChE are the signature molecules estimated for the said physiological axes. The ordination technique, nonmetric multidimensional scaling, has been utilized to visualize the differentiated physiological response to changing environmental conditions. Then, Bayesian Model Averaging (BMA) was used to identify the factors that play a key role in refining the stress physiology and determining the niche. Current study confirms different species belonging to similar habitats respond to various environmental and physiological factors in a different manner as various biomarkers respond in a species-specific pattern that induces the choice of habitat preference controlling its ecophysiological niche. In the present study, it is quite apparent that adaptive mechanism of fish to environmental stress is achieved through modification of physiological mechanisms through a panel of biochemical markers. These markers organize a cascade of physiological event at various levels including reproduction.

Instantaneous maturity rate: a novel and compact characterization of biological growth curve models.

Modeling and analysis of biological growth curves are an age-old study area in which much effort has been dedicated to developing new growth equations. Recent efforts focus on identifying the correct model from a large number of equations. The relative growth rate (RGR), developed by Fisher (1921), has largely been used in the statistical inference of biological growth curve models. It is convenient to express growth equations using RGR, where RGR can be expressed as functions of size or time. Even though RGR is model invariant, it has limitations when it comes to identifying actual growth patterns. By proposing interval-specific rate parameters (ISRPs), Pal et al. (2018) appeared to solve this problem. The ISRP is based on the mathematical structure of the growth equations. Therefore, it is not model invariant. The current effort is to develop a measure of growth that is model invariant like RGR and shares the advantages of ISRP. We propose a new measure of growth, which we call instantaneous maturity rate (IMR). IMR is model invariant, which allows it to distinguish growth patterns more clearly than RGR. IMR is also scale-invariant and can take several forms including increasing, decreasing, constant, sigmoidal, bell-shaped, and bathtub. A wide range of possible IMR shapes makes it possible to identify different growth curves. The estimation procedure of IMR under a stochastic setup has been developed. Statistical properties of empirical IMR estimators have also been investigated in detail. In addition to extensive simulation studies, real data sets have been analyzed to prove the utility of IMR.

An occurrence data set for invasive and naturalized alien plants in India.

India has numerous invasive alien plant species (IAPSs), which seriously impact biodiversity, ecosystem services, and economic development. The availability of reliable occurrence records of IAPSs is of great importance for their successful management, prediction of distribution across time and space, and other research and development efforts. Global databases of occurrence data, like the Global Biodiversity Information Facility (GBIF), are often not exhaustive, especially for India, and poorly represent the actual distribution of IAPSs in the country. Our objective in creating this data set was threefold: (1) to compile occurrence data for the invasive and naturalized alien plant species of India, (2) to collect spatial and temporal information associated with occurrence records, and (3) to share the data in an accessible format so every record is traceable to its sources and allow users to submit data to increase the resolution of the data set. To achieve these objectives, we extracted data from 3137 literature records and 357 herbarium sheets. For each occurrence record, we curated information for 20 variables, which were arranged in a table with the Darwin Core (DwC) terms as column names. All data were subjected to technical validation before being included in the database. A total of 12,347 occurrence records were obtained for 362 species (195 invasive aliens and 167 naturalized aliens). The number of collected occurrence records was much higher for the invasive aliens (73.7%) than for the naturalized alien species (26.3%). Our data set will supplement the GBIF data by 60.39%, and occurrence records will be added for 64 invasive and naturalized alien plant species. The data set, as a part of the larger database of the Indian Alien Flora Information (ILORA) database, is made available without any restrictions on use as long as this data paper is properly cited. We have also made provisions for users to submit occurrence-related data following a data standard. The users are encouraged to cite the original reference when using a specific data record. The data set is expected to assist a wide range of stakeholders involved in India's scientific research, policy formulation, and decision-making related to IAPSs.

Different factors influence naturalization and invasion processes - A case study of Indian alien flora provides management insights.

Why do some alien plants become naturalized, and some naturalized become invasive? Do different factors determine successful naturalization and invasion? Most, if not all, studies addressing these questions have focused either on the part of the invasion continuum or a specific group of alien species. In this study, we aimed to answer these questions for alien plant invasion in India by considering 13 variables related to biogeography, introduction pathways, uses, functional traits, and distribution for 715 species belonging to three invasion categories. We deciphered the variables' influence on successful naturalization and invasion through a structural equation modeling framework implemented as path analyses and translated the findings to management implications. Our study revealed that the invasive aliens had significantly higher naturalized range size, a greater number of uses, and higher specific leaf area than the naturalized and casual aliens. Path analyses revealed that the native and naturalized range sizes, number of uses, and growth form had a direct influence on naturalization success, whereas longer minimum residence time (MRT) facilitated overcoming of the dispersal barrier for naturalized species. Invasion success was directly influenced by the MRT and number of uses, which were further influenced by the number of native congeners and the naturalized range size, respectively. Plant growth forms indirectly influenced invasion success, whereas the native range sizes had indirect effects on successful naturalization and invasion by strongly influencing the size of the naturalized range. Our findings suggested considering species biogeography in the formulation of quarantine measures, imposing policies to discourage the uses and spread of alien plants within the country, and implementing early control measures, especially for the naturalized aliens. The curated dataset used in this study would also provide a ready reference for future research and decision-making towards the management of alien plant invasion in the country.

Invasive dynamics for a predator-prey system with Allee effect in both populations and a special emphasis on predator mortality.

We considered a non-linear predator-prey model with an Allee effect on both populations on a two spatial dimension reaction-diffusion setup. Special importance to predator mortality was given as it may be often controlled through human-made harvesting processes. The local dynamics of the model was studied through boundedness, equilibrium, and stability analysis. An extensive numerical stability analysis was performed and found that bi-stability is not possible for the non-spatial model. By analyzing the spatial model, we found the condition for successful invasion and the persistence region of the species based on the predator Allee effect and its mortality parameter. Four different dynamics in this region of the parameter space are mainly explored. First, the Allee effect on both populations leads to various new types of species spread. Second, for a high value of per-capita growth rate, two completely new spreads (e.g., sun surface, colonial) have been found depending on the Allee effect parameter. Third, the Allee coefficient on the predator population leads to spatiotemporal chaos via a patchy spread for both linear and quadratic mortality rates. Finally, a more rigorous analysis is performed to study the chaotic nature of the system within the whole persistence domain. We have studied the possibility of chaos through temporal variation in different invasion regions. Furthermore, the chaotic fluctuation is studied through the sensitivity of initial conditions and by investigating the dominant Lyapunov exponent value.

A Novel Unification Method to Characterize a Broad Class of Growth Curve Models Using Relative Growth Rate.

Growth curve models serve as the mathematical framework for the quantitative studies of growth in many areas of applied science. The evolution of novel growth curves can be categorized in two notable directions, namely generalization and unification. In case of generalization, a modeler starts with a simple mathematical form to describe the behavior of the data and increases the complexity of the equation by incorporating more parameters to obtain a more flexible shape. The unification refers to the process of obtaining a compact representation of a large number of growth equations. An enormous number of growth equations are made available in the literature by means of the generalization of existing growth laws. However, the unification of growth equations has received relatively less attention from the researchers. Two significant unification functions are available in the literature, namely the Box-Cox transformation by Garcia (For Biometry Model Inf Sci 1:63-68, 2005) and generalized logarithmic and exponential functions by Martinez et al. (Phys A 387:5679-5687, 2008; Phys A 388:2922-2930, 2009). Existing unification approaches are found to have limited applications if the growth equation is characterized by the relative growth rate (RGR). RGR has immense practical value in biological growth curve analysis, which has been amplified by the construction of size and time covariate models, in which; RGR is represented either as a function of size or time or both. The present study offers a unification function for the RGR growth curves. The proposed function combines a broad class of the growth curves and possesses a greater generality than the existing unification functions. We also propose the notion of generalized RGR, which is capable of making interrelations among the unifying functions. Our proposed method is expected to enhance the generality of software and may aid in choosing an optimal model from a set of competitor growth equations.

Physiological response of fish under variable acidic conditions: a molecular approach through the assessment of an eco-physiological marker in the brain.

The current study demonstrates oxidative damage and associated neurotoxicity following pH stress in two freshwater carp Labeo rohita and Cirrhinus cirrhosus. Carp (n = 6, 3 replicates) were exposed to four different pH (5.5, 6, 7.5, and 8) against control (pH 6.8 ± 0.05) for 7 days. After completion of treatment, levels of enzymatic (superoxide dismutase [SOD], catalase [CAT], glutathione reductase [GRd]) and non-enzymatic antioxidants (malondialdehyde [MDA], glutathione [GSH]), brain neurological parameters (Na+-K+ATPase, acetylcholinesterase [AcHE], monoamine oxidase [MAO], and nitric oxide [NO]), xanthine oxidase (XO), heat shock proteins (HSP70 and HSP90), and transcription factor NFkB were measured in carp brain. Variation in the pH caused a significant alteration in the glutathione system (glutathione and glutathione reductase), SOD-CAT system, and stress marker malondialdehyde (MDA). Xanthine oxidase was also induced significantly after pH exposure. Brain neurological parameters (MAO, NO, AChE, and Na+-K+ATPase) were significantly reduced at each pH-treated carp group though inhibition was highest at lower acidic pH (5.5). Cirrhinus cirrhosus was more affected than that of Labeo rohita. Molecular chaperon HSP70 expression was induced in all pH-treated groups though such induction was more in acid-stressed fish. HSP90 was found to increase only in acid-stressed carp brain. Expression of NFkB was elevated significantly at each treatment group except for pH 7.5. Finally, both acidic and alkaline pH in the aquatic system was found to disturb oxidative balance in carp brain which ultimately affects the neurological activity in carp. However, acidic environment in the aquatic system was more detrimental than the alkaline system regarding oxidative damage and subsequent neurotoxicity in carp brain.

Evolution of model specific relative growth rate: Its genesis and performance over Fisher's growth rates.

Growth curve models play an instrumental role to quantify the growth of biological processes and have immense practical applications across disciplines. In the modelling approach, the absolute growth rate and relative growth rate (RGR) are two most commonly used measures of growth rates. RGR is empirically estimated by Fisher (1921) assuming exponential growth between two consecutive time points and remains invariant under any choice of the underlying growth model. In this article, we propose a new measure of RGR, called modified RGR, which is sensitive to the choice of underlying growth law. The mathematical form of the growth equations are utilized to develop the formula for model dependent growth rates and can be easily computed for commonly used growth models. We compare the efficiency of Fisher's measure of RGR and modified RGR to infer the true growth profile. To achieve this, we develop a goodness of fit testing procedure using Gompertz model as a test bed. The relative efficiency of the two rate measures is compared by generating power curves of the goodness of fit testing procedure. The asymptotic distributions of the associated test statistics are elaborately studied under Gompertz set up. The simulation experiment shows that the proposed formula has better discriminatory power than the existing one in identifying the true profile. The claim is also verified using existing real data set on fish growth. An algorithm for the model selection mechanism is also proposed based on the modified RGR and is generalized for some commonly used other growth models. The proposed methodology may serve as a valuable tool in growth studies in different research areas.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database.

A host-parasitoid system with predation-driven component Allee effects in host population.

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programmes. In this article, we investigate population dynamics of a discrete-time host-parasitoid system with component Allee effects induced by predation satiation in host to study the synergy effects of Allee effects and parasitism. Our model assumes that parasitism attacks the host after the density dependence of the host. The interactions of component Allee effects and parasitism can lead to extremely rich dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform local and global analysis to study the number of equilibria and their stability; and study the extinction and permanence of our host-parasitoid system. One of the most interesting results shows that the combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their high population density. In addition, component Allee effects may destroy interior equilibrium under different values of parameters' ranges.

A new growth curve model for biological growth: some inferential studies on the growth of Cirrhinus mrigala.

Growth of living organisms is a fundamental biological process. It depicts the physiological development of the species related to the environment. Mathematical development of growth curve models has a long history since its birth. We propose a mathematical model to describe the evolution of relative growth rate as a function of time based on a real life experiment on a major Indian Carp Cirrhinus mrigala. We establish that the proposed model is able to describe the fish growth dynamics more accurately for our experimental data than some existing models e.g. logistic, Gompertz, exponential. Approximate expressions of the points of inflection and the time of achieving the maximum relative growth rate are derived. We study, in detail, the existence of a nonlinear least squares estimator of the model parameters and their consistency properties. Test-statistics is developed to study the equality of points of inflection and equality of the amount of time necessary to achieve the maximum relative growth rate for a species at two different locations. Using the theory of variance stabilizing transformations, we propose a new test statistic to test the effect of the decay parameter for the proposed growth law. The testing procedure is found to be more sensitive in comparison with the test based on nonlinear least squares estimates. Our proposed model provides a general framework to model growth in other disciplines as well.

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach.

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.

An optimal cost effectiveness study on Zimbabwe cholera seasonal data from 2008-2011.

Incidence of cholera outbreak is a serious issue in underdeveloped and developing countries. In Zimbabwe, after the massive outbreak in 2008-09, cholera cases and deaths are reported every year from some provinces. Substantial number of reported cholera cases in some provinces during and after the epidemic in 2008-09 indicates a plausible presence of seasonality in cholera incidence in those regions. We formulate a compartmental mathematical model with periodic slow-fast transmission rate to study such recurrent occurrences and fitted the model to cumulative cholera cases and deaths for different provinces of Zimbabwe from the beginning of cholera outbreak in 2008-09 to June 2011. Daily and weekly reported cholera incidence data were collected from Zimbabwe epidemiological bulletin, Zimbabwe Daily cholera updates and Office for the Coordination of Humanitarian Affairs Zimbabwe (OCHA, Zimbabwe). For each province, the basic reproduction number ([Formula: see text]) in periodic environment is estimated. To the best of our knowledge, this is probably a pioneering attempt to estimate [Formula: see text] in periodic environment using real-life data set of cholera epidemic for Zimbabwe. Our estimates of [Formula: see text] agree with the previous estimate for some provinces but differ significantly for Bulawayo, Mashonaland West, Manicaland, Matabeleland South and Matabeleland North. Seasonal trend in cholera incidence is observed in Harare, Mashonaland West, Mashonaland East, Manicaland and Matabeleland South. Our result suggests that, slow transmission is a dominating factor for cholera transmission in most of these provinces. Our model projects [Formula: see text] cholera cases and [Formula: see text] cholera deaths during the end of the epidemic in 2008-09 to January 1, 2012. We also determine an optimal cost-effective control strategy among the four government undertaken interventions namely promoting hand-hygiene & clean water distribution, vaccination, treatment and sanitation for each province.