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Motivated by recent advances in mapping mesoscale eddy tracer mixing in the ocean we evaluate the sensitivity of a coarse‐resolution global ocean model to a spatially variable neutral diffusion coefficient κn(x, y, z). We gradually introduce physically motivated models for the horizontal (mixing length theory) and vertical (surface mode theory) structure of κn along with suppression of mixing by mean flows. Each structural feature influences the ocean's hydrography and circulation to varying extents, with the suppression of mixing by mean flows being the most important factor and the vertical structure being relatively unimportant. When utilizing the full theory (experiment “FULL”) the interhemispheric overturning cell is strengthened by 2 Sv at 26°N (a ∼20% increase), bringing it into better agreement with observations. Zonal mean tracer biases are also reduced in FULL. Neutral diffusion impacts circulation through surface temperature‐induced changes in surface buoyancy fluxes and nonlinear equation of state effects. Surface buoyancy forcing anomalies are largest in the Southern Ocean where a decreased neutral diffusivity in FULL leads to surface cooling and enhanced dense‐to‐light surface water mass transformation, reinforced by reductions in cabbeling and thermobaricity. The increased water mass transformation leads to enhanced midlatitude stratification and interhemispheric overturning. The spatial structure for κn in FULL is important as it enhances the interhemispheric cell without degrading the Antarctic bottom water cell, unlike a spatially uniform reduction in κn. These results highlight the sensitivity of modeled circulation to κn and motivate the use of physics‐based models for its structure. Plain Language Summary The diffusion of tracers such as temperature and salinity along surfaces of constant density by the action of mesoscale eddy mixing, known as neutral diffusion, is an important transport process in the ocean which impacts heat, carbon, and nutrient budgets as well as climate variability. However, most global ocean circulation models used for climate studies have a horizontal grid resolution that is too coarse to resolve mesoscale eddies. Thus, the effects of eddy‐driven neutral diffusion must be parameterized through the inclusion of a neutral diffusivity parameter κn. While the strength of neutral diffusion is known to vary spatially within the ocean, most models still make simple choices for κn; a constant, or scaled according to the grid resolution. In this study, we examine the sensitivity of a coarse‐resolution global ocean model to the spatial structure of κn using a recently developed and physically motivated three‐dimensional mapping of mesoscale mixing. Our results show that the modeled meridional overturning circulation and tracer structure are sensitive to both the magnitude and the spatial structure of κn, suggesting that more attention should be paid to this parameter in future model development. Key Points A new spatially variable parameterization for mesoscale neutral diffusion is tested in a 1‐degree ocean model Both hydrography and circulation are sensitive to the magnitude and spatial structure of the neutral diffusivity A 2 Sv enhancement in interhemispheric overturning stems from suppression of neutral diffusion by mean flows

Hybrid zones are geographic regions where differentiated taxa meet and potentially exchange genes. Increasingly, genomic analyses have demonstrated that many hybrid zones are semipermeable boundaries across which introgression is highly variable. In some cases, certain alleles penetrate across the hybrid zone in only one direction, recombining into the alternate genome. We investigated this phenomenon using genomic (genotyping-by-sequencing) and morphological (plumage reflectance spectrophotometry) analyses of the hybrid zone between two subspecies of the red-backed fairy-wren (Malurus melanocephalus) that differ conspicuously in a sexual signal, male back plumage color. Geographic cline analyses revealed a highly variable pattern of differential introgression, with many narrow coincident clines combined with several significantly wider clines, suggesting that the hybrid zone is a semipermeable tension zone. The plumage cline was shifted significantly into the genomic background of the orange subspecies, consistent with sexual selection driving asymmetrical introgression of red plumage alleles across the hybrid zone. This interpretation is supported by previous experimental work demonstrating an extra-pair mating advantage for red males, but the role of genetic dominance in driving this pattern remains unclear. This study highlights the potential for sexual selection to erode taxonomic boundaries and promote gene flow, particularly at an intermediate stage of divergence.

Functional traits mediate ecological responses of organisms to the environment, determining community structure. Community-weighted trait means (CWM) are often used to characterize communities by combining information on species traits and distribution. Relating CWM variation to environmental gradients allows for evaluating species sorting across the metacommunity, either based on correlation tests or ordinary least squares (OLS) models. Yet, it is not clear if phylogenetic signal in both traits and species distribution affect those analyses. On one hand, phylogenetic signal might indicate niche conservatism along clade evolution, reinforcing the environmental signal in trait assembly patterns. On the other hand, it might introduce phylogenetic autocorrelation to mean trait variation among communities. Under this latter scenario, phylogenetic signal might inflate type I error in analysis relating CWM variation to environmental gradients. We explore multiple ways phylogenetic history may influence analysis relating CWM to environmental gradients. We propose the concept of neutral trait diffusion, which predicts that for a functional trait x, CWM variation among local communities does not deviate from the expectation that x evolved according to a neutral evolutionary process. Based on this framework we introduce a graphical tool called neutral trait diffusion representation (NTDR) that allows for the evaluation of whether it is necessary to carry out phylogenetic correction in the trait prior to analyzing the association between CWM and environmental gradients. We illustrate the NTDR approach using simulated traits, phylogenies and metacommunities. We show that even under moderate phylogenetic signal in both the trait used to define CWM and species distribution across communities, OLS models relating CWM variation to environmental gradients lead to inflated type I error when testing the null hypothesis of no association between CWM and environmental gradient. To overcome this issue, we propose a phylogenetic correction for OLS models and evaluate its statistical performance (type I error and power). Phylogeny-corrected OLS models successfully control for type I error in analysis relating CWM variation to environmental gradients but may show decreased power. Combining the exploratory tool of NTDR and phylogenetic correction in traits, when necessary, guarantees more precise inferences about the environmental forces driving trait-mediated species sorting across metacommunities.

This paper deals with Galerkin finite element (GFE) approximation to the initial-boundary value problems (IBVPs) of neutral reaction-diffusion equations with piecewise continuous arguments. For solving this kind of IBVPs, we first present a semi-discrete GFE scheme and give its error estimates in L 2 - and H 1 -norm. Then, we further construct a class of one-parameter fully discrete GFE methods with parameter θ ( 0 ≤ θ ≤ 1 ) and analyze their unique solvability and L 2 - and H 1 -error. The result of error analysis shows that, under the suitable conditions and sense of L 2 -norm (resp. H 1 -norm), the one-parameter fully discrete GFE methods are convergent of order r (resp. r - 1 ) in space and order one (resp. two) in time when θ ≠ 1 2 (resp. θ = 1 2 ), where r - 1 ( r ≥ 2 ) denotes the degree of the piecewise polynomial in finite element space. In the end, some numerical experiments are performed to verify the computational effectiveness and theoretical accuracy of the methods.

In this note, the stability of neutral delay reaction–diffusion systems (NDRDS) was concerned by applying the matrix pencil and the Kronecker product. A new computing method for the distribution of imaginary axis eigenvalues on general n ‐dimensional NDRDS will be introduced. A practical, checkable criterion for the asymptotic stability will be derived. The main contribution of this paper is that we provide a computational method for determining imaginary axis eigenvalues and minimal delay margin on general NDRDS.

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments. First, for the analytical solutions of the equations, we derive their expressions and asymptotical stability criteria. Second, for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations, we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable. Finally, with a typical example with numerical experiments, we illustrate the applicability of the obtained theoretical results.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

In the present paper, we firstly improve the results on traveling wave solution that were established in (Liu and Weng in J. Differ. Equ. 258:3688–3741, 2015) for a neutral reaction–diffusion equation with quasi-monotone reaction. Secondly, by constructing two auxiliary equations and using Schauder’s Fixed Point Theorem, we further establish the existence and the asymptotic properties of the traveling wave solution for the equation with non-monotone reaction. Two examples are also given as the application of our results.

This article described the basic concepts of the permeable boundary (PB) and impermeable boundary (IPB) conditions between electrode and electrolyte that are essential in studying diffusion and migration of ions through the electrode for electrochemical devices. The transmission line models (TLMs) were introduced to explain the boundary conditions at the electrode/electrolyte interfaces. The impedance data were simulated based upon the TLMs for PB and IPB conditions, giving attention to the different behaviors of low-frequency impedance. In addition, this article explained that the electrodes used for fuel cells and batteries can be classified according to the PB and IPB conditions.

Let S be a compact metric space, let θ ≥ 0, and let ν0be a Borel probability measure on S. An explicit formula is found for the transition function of the Fleming-Viot process with type space S and mutation operator (Af)(x) = (1/2)θ∫S(f(ξ) - f(x))ν0(dξ).