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Abstract Estimates of home range sizes for marine fishes are essential for designing and assessing the effects of spatial wildlife conservation policies and management interventions. However, in situ studies of marine species movement are challenging and often expensive, resulting in a paucity of data on the home range size of the vast majority of marine fishes. Here, we develop a set of new datasets, which we have collectively named Marine Fish Movement, that synthesises published empirically evaluated home ranges reported for adult marine fishes that interact with fisheries and leverage these data to estimate home range sizes for unstudied species. The empirical data contain estimated home range sizes (km2) for 193 species across 63 family groups from 179 studies published between 1971 and 2022. We use a random forest regression model to estimate home range sizes (km2) for 664 fished marine species currently lacking home range estimates. Marine Fish Movement can inform spatial interventions including the design and management of marine protected areas and dynamic fisheries management to meet sustainability goals.

We study the Schr\"odinger equation $\left(\mathrm{Q}_{\varepsilon}\right)$: $- \varepsilon^{2(p-1)} \Delta_p v + V(x)\, |v|^{p-2} v - |v|^{q-1}v = 0$, $x \in \mathbb{R}^N$, with $v(x) \rightarrow 0$ as $|x| \rightarrow+\infty$, for the infinite case, as given by Byeon and Wang for a situation of critical frequency, $\displaystyle \{x\in \mathbb{R}^N \, / \: V(x) = \inf V = 0\} \neq \emptyset$. In the semiclassical limit, $\varepsilon \rightarrow 0$, the corresponding limit problem is $\left(\mathrm{P}\right)$: $\Delta_p w+|w|^{q-1} w=0$, $x \in \Omega$, with $w(x)=0, x \in \partial \Omega$, where $\Omega \subseteq \mathbb{R}^N$ is a smooth bounded strictly star-shaped region related to the potential $V$. We prove that for $\left(\mathrm{Q}_{\varepsilon}\right)$ there exists a non-trivial solution with any prescribed $\mathrm{L}^{q+1}$-mass.Applying a Ljusternik-Schnirelman scheme, shows that $\left(\mathrm{Q}_{\varepsilon}\right)$ and $\left(\mathrm{P}\right)$ have infinitely many pairs of solutions. Fixed a topological level $k \in \mathbb{N}$, we show that a solution of $\left(\mathrm{Q}_{\varepsilon}\right)$, $v_{k, \varepsilon}$, sub converges, in $\mathrm{W}^{1,p}(\mathbb{R}^N)$ and up to scaling, to a corresponding solution of $\left(\mathrm{P}\right)$. We also prove that the energy of each solution, $v_{k,\eps}$ converges to the corresponding energy of the limit problem $\left(\mathrm{P}\right)$ so that the critical values of the functionals associated, respectively, to $\left(\mathrm{Q}_{\varepsilon}\right)$ and $\left(\mathrm{P}\right)$ are topologically equivalent.

Marine protected areas (MPAs) are a key tool for achieving goals for biodiversity conservation and human well-being, including improving climate resilience and equitable access to nature. At a national level, they are central components in the U.S. commitment to conserve at least 30% of U.S. waters by 2030. By definition, the primary goal of an MPA is the long-term conservation of nature; however, not all MPAs provide the same ecological and social benefits. A U.S. system of MPAs that is equitable, well-managed, representative and connected, and includes areas at a level of protection that can deliver desired outcomes is best positioned to support national goals. We used a new MPA framework, The MPA Guide, to assess the level of protection and stage of establishment of the 50 largest U.S. MPAs, which make up 99.7% of the total U.S. MPA area (3.19 million km2). Over 96% of this area, including 99% of that which is fully or highly protected against extractive or destructive human activities, is in the central Pacific ocean. Total MPA area in other regions is sparse – only 1.9% of the U.S. ocean excluding the central Pacific is protected in any kind of MPA (120,976 km2). Over three quarters of the non-central Pacific MPA area is lightly or minimally protected against extractive or destructive human activities. These results highlight an urgent need to improve the quality, quantity, and representativeness of MPA protection in U.S. waters to bring benefits to human and marine communities. We identify and review the state of the science, including focal areas for achieving desired MPA outcomes and lessons learned from places where sound ecological and social design principles come together in MPAs that are set up to achieve national goals for equity, climate resilience, and biodiversity conservation. We recommend key opportunities for action specific to the U.S. context, including increasing funding, research, equity, and protection level for new and existing U.S. MPAs.