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Abstract Natural environments are seldom static and therefore it is important to ask how a population adapts in a changing environment. We consider a finite, diploid population evolving in a periodically changing environment and study how the fixation probability of a rare mutant depends on its dominance coefficient and the rate of environmental change. We find that, in slowly changing environments, the effect of dominance is the same as in the static environment, that is, if a mutant is beneficial (deleterious) when it appears, it is more (less) likely to fix if it is dominant. But, in fast changing environments, the effect of dominance can be different from that in the static environment and is determined by the mutant’s fitness at the time of appearance as well as that in the time-averaged environment. We find that, in a rapidly varying environment that is neutral on average, an initially beneficial (deleterious) mutant that arises while selection is decreasing (increasing) has a fixation probability lower (higher) than that for a neutral mutant as a result of which the recessive (dominant) mutant is favored. If the environment is beneficial (deleterious) on average but the mutant is deleterious (beneficial) when it appears in the population, the dominant (recessive) mutant is favored in a fast changing environment. We also find that, when recurrent mutations occur, dominance does not have a strong influence on evolutionary dynamics.

Organisms often respond to environmental change via phenotypic plasticity, in which an individual modulates its phenotype according to the environment. Highly variable or changing environments can exceed physiological limits and generate maladapted plastic phenotypes, which is termed nonadaptive plasticity. In some cases, selection may reduce the negative or disruptive impacts of environmental stress and produce locally adapted populations. Salt is an increasingly prevalent contaminant of freshwater systems and can induce nonadaptive plastic phenotypes for freshwater organisms like amphibians. Hyla cinerea is a frog species with populations inhabiting brackish, coastal habitats, so we use this species to test whether coastal populations are locally adapted to tolerate saltwater by determining how salt exposure during the embryonic and larval stages alters mortality and plastic developmental and metamorphic phenotypes of coastal and inland populations. Coastal frogs have higher survival, faster growth rates, and metamorphose sooner than inland frogs across salinities. Coastal frogs also metamorphose smaller (likely a consequence of earlier metamorphosis) yet maintain constant size, while higher salinities reduce metamorphic size for inland frogs. Coastal frogs evolved to minimize nonadaptive and disruptive impacts of saltwater during larval development and accelerate the larval period to reduce time spent in a stressful environment.

Performance tradeoffs are ubiquitous in both ecological and evolutionary modeling, yet they are usually postulated and built into fitness and ecological landscapes. However, tradeoffs depend on genetic background and evolutionary history and can themselves evolve.We present a simple model capable of capturing the key feedback loop: evolutionary history shapes tradeoff strength, which, in turn, shapes evolutionary future. One consequence of this feedback is that genomes with identical fitness can have different evolutionary properties shaped by prior environmental exposure. Another is that, generically, the best adaptations to one environment may evolve in another. Our simple framework bridges the gap between the phenotypic Fisher’s Geometric Model and the genotypic properties, such as modularity and evolvability, and can serve as a rich playground for investigating evolution in multiple or changing environments.

Understanding the genetic basis of how species respond to changing environments is essential to the conservation of species. However, the molecular mechanisms of adaptation remain largely unknown for long-lived tree species which always have large population sizes, long generation time, and extensive gene flow. Recent advances in landscape genomics can reveal the signals of adaptive selection linking genetic variations and landscape characteristics and therefore have created novel insights into tree conservation strategies. In this review article, we first summarized the methods of landscape genomics used in tree conservation and elucidated the advantages and disadvantages of these methods. We then highlighted the newly developed method “Risk of Non-adaptedness,” which can predict the genetic offset or genomic vulnerability of species via allele frequency change under multiple scenarios of climate change. Finally, we provided prospects concerning how our introduced approaches of landscape genomics can assist policymaking and improve the existing conservation strategies for tree species under the ongoing global changes.

Water resources variability and availability in a basin affect river flows and sustain river ecosystems. Climate change and human activities disrupt runoff sequences, causing water environmental issues like river channel interruptions. Therefore, determining ecological flow in changing environments is challenging in hydrological research. Based on an analysis of long-term changes in hydrological and meteorological variables and interruption conditions in the semi-arid Liu River Basin (LRB), this study summarizes the controlling factors of river interruption at different temporal and spatial scales and proposes a framework to determine ecological flow under changing environments. Hydrological model and the monthly optimal probability distribution were used to determine the optimal ecological runoff of LRB. The results showed that from 1956 to 2017, precipitation and potential evapotranspiration in the basin showed no significant decreasing trend, but the streamflow significantly decreased, and the downstream interruption worsened, with an average annual interruption duration of 194 days at Xinmin Station from 1988 to 2017. The controlling factors of river interruption are as follows: (1) soil and water conservation measures in the upstream significantly reduce the runoff capacity; (2) the operation mode of the controlling reservoir in the middle reaches changes from “all-year discharge” to “winter storage and spring release” to “combined storage and supply,” severing the hydraulic connection between upstream and downstream; and (3) siltation in the downstream river channel coupled with over-extraction of groundwater increases the seepage capacity of the river. The monthly ecological flow of Naodehai Reservoir was determined by considering the monthly seepage losses after reconstructing the natural runoff using the SWAT model and determining the optimal probability distribution function for monthly runoff. The findings are important for downstream LRB ecological restoration and for determining the ecological flow of other river basins in changing environments.

Global navigation satellite system precise point positioning (PPP) technology can be significantly affected by multipath errors of code and phase observations. Previous studies using multipath hemispherical map (MHM) to mitigate multipath highly rely on stable surrounding environments, and limited work emphasizes multipath mitigation in changing environments (i.e., the surrounding environments are variable but the user maybe static). We propose a new multipath mitigation method using multipath hierarchy (MH) derived from the C/N0 discrepancy in azimuth and elevation grid in changing environments. The main processing procedures using MH in GNSS PPP are given. Two dedicated static datasets are collected to analyze the multipath discrepancy of normal MHM and further conduct the C/N0-based MH. The performance using MH is carefully analyzed in terms of positioning accuracy and residual reduction. Specifically, the normal MHM exhibits multipath discrepancy in changing environments; thus, the C/N0-based MH is of great necessity to further mitigate multipath. Compared to the normal MHM, the MH-corrected positioning errors are improved, especially at the initial epochs. By calculating the three-dimensional positioning accuracy of all epochs, the MH-corrected positioning accuracy can be improved by approximately 6 and 3 cm compared to the uncorrected and MHM-corrected results in centimeter-level PPP, respectively. Also, the standard deviations of MH-corrected code and phase residuals are smaller than MHM-corrected results for each satellite. In this sense, the proposed multipath mitigation method using MH is highly appreciated for the performance of positioning accuracy and residual reduction in changing environments.

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation-limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive-walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.

Drought is one of the most frequent and devastating natural disasters. Based on future climate scenarios and land use/land cover (LULC) patterns, the copula framework was employed to calculate the probabilities of meteorological and hydrological drought risks for the next 30 years (2021–2050) in the Wanquan River Basin, meanwhile, the relationship between hydrological and meteorological droughts was revealed by correlation analysis and cross-wavelet transform (XWT). The results are as follows: (1) In the next 30 years, the risk of intra-seasonal meteorological drought (short-term drought) in the WRB is high at a probability of 40–70%, while the risk of inter-seasonal meteorological drought is relatively small at a probability of close to 30%; (2) compared with meteorological drought, the risk of intra-seasonal hydrological drought is small, but the probability of inter-seasonal hydrological drought (medium- or long-term drought) is 30–50%, and the risk of hydrological drought in the upstream is greater than that in the downstream; (3) the future meteorological and hydrological droughts in the WRB are significantly and positively correlated, and that hydrological drought lags behind meteorological drought.

This paper has two aspects. Mathematically, in the context of global optimization, it provides the existence of an optimum of a perturbed optimization problem that generalizes the celebrated Ekeland variational principle and equivalent formulations (Caristi, Takahashi), whenever the perturbations need not satisfy the triangle inequality. Behaviorally, it is a continuation of the recent variational rationality approach of stay (stop) and change (go) human dynamics. It gives sufficient conditions for the existence of traps in a changing environment. In this way it emphasizes even more the striking correspondence between variational analysis in mathematics and variational rationality in psychology and behavioral sciences.

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.