Critical thresholds for eventual extinction in randomly disturbed population growth models

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.

Timing and magnitude of climatic extremes differentially elevate mortality but enhance recovery in a fish population

The countervailing effects of disturbances (e.g., high mortality and enhanced recovery) on population dynamics can occur through demographic processes under rapidly increasing climatic extremes. Across an extreme-event gradient, we mechanistically demonstrated how dramatic changes in streamflow have affected the population persistence of endangered salmon in monsoonal Taiwan over a three-decade period. Our modeling indicated that the dynamics of the age-structured population were attributed to demographic processes, in which extensive mortality was characterized as a function of climatic extremes and vulnerability in the young stage of fish. In the stochastic simulations, we found that the extensive mortality and high proportion of large fish resulted from extreme flooding, which caused high values of postimpact population recovery. Our empirical evidence suggests that the magnitudes and timing of disturbance can explain the population persistence when facing climatic extremes and thereby challenges the understanding of the mechanistic drivers of these countervailing phenomena under changing environmental conditions.

Two-species competing population dynamics with the population-dependent environmental capacities under random disturbance

We propose and analyze a stochastic competing two-species population dynamics model subject to jump and continuous correlated noises. Competing benthic algae population dynamics in river environment, which is an important engineering problem, motivates this new model. The model is a system of stochastic differential equations having a characteristic that the two populations are competing with each other through the environmental capacities; an increase in one population decreases the other's environmental capacity. Unique existence of the uniformly bounded strong solution is proven, and attractors of the solutions are identified depending on the parameter values. The Kolmogorov's backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. A novel uncertain correlation case is also analyzed in the framework of viscosity solutions. Numerical computation results using a finite difference scheme and a Monte-Carlo method are presented to deeper analyze the model. Our analysis results can be utilized for establishment of a foundation for modeling, analysis and control of the competing population dynamics.

Management guidelines in disturbance-Prone populations: The importance of the intervention time

The use of conservation and management practices to buffer possible damages after disturbance events is growing to become popular worldwide. However, little is known about their efficacy in real-life situations. To fill this gap, we will derive management guidelines in disturbance-prone populations regarding the external introduction of individuals and the ecological restoration. We will also discuss the efficacy of these practices in the population dynamics of three species (a fast life-cycle mayfly, a slow life-cycle dragonfly and an ostracod) when their habitat suffers from periodic controlled flooding. One of the main messages of this paper is that the interplay between the inherited parameters of the population and disturbance events is a source of rich and unexpected behaviours. More importantly, intervention time plays a critical role in the performance of some management strategies.

Genetic and genomic analysis of the seed-filling process in maize based on a logistic model

Seed filling is a dynamic process that determines seed size and nutritional quality. This time-dependent trait follows a logistic (S-shaped) growth curve that can be described by a logistic function, with parameters of biological relevance. When compared between genotypes, the filling dynamics variations are explained by the differences of parameter values; as such, the parameter estimates can be considered as “traits” for genetic analysis to identify loci that are associated with the seed-filling process. We carried out genetic and genomic analysis of the seed-filling process in maize, using a recombinant inbred line (RIL) population derived from the two inbred lines with contrasting seed-filling dynamics. We recorded seed dry weight at 14 time points after pollination, spanning the early filling phases to the late maturation stages. Fitting these data to a logistic model allowed for estimating 12 characteristic parameters that can be used to meaningfully describe the seed-filling process. Quantitative trait locus (QTL) mapping of these parameters identified a total of 90 nonredundant loci. Using bulked segregant RNA-sequencing (BSR-seq) analysis, we identified eight genes that showed differential gene expression patterns at multiple time points between the extreme pools, and these genes co-localize with the mapped QTL regions. Two of the eight genes, GRMZM2G391936 and GRMZM2G008263, are implicated in starch and sucrose metabolism, and biosynthesis of secondary metabolites that are well known for playing a vital role in seed filling. This study suggests that the logistic model-based approach can efficiently identify genetic loci that regulate dynamic developing traits.