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1. As management tools, freshwater reserves are under-represented in protected area networks for fisheries conservation and enhancement. This is surprising considering that freshwater ecosystems, and the biodiversity they support, are among the most threatened worldwide.2. We compared freshwater reserve types established to prevent overexploitation of migratory galaxiids (mostly īnanga Galaxias maculatus) from fishing and evaluated their performance as reproductive reservoirs. We studied 10 streams classified into three a priori types: (a) closed, (b) partially closed and (c) open streams.3. Closed streams had greater abundances, biomasses and egg production of G. maculatus despite having a greater proportion of smaller fish compared to partially closed and open streams. Community-level analyses indicated differences in fish assemblages between closure types. Large, native, predatory fish (longfin eel Anguilla dieffenbachii, shortfin eel Anguilla australis and giant kōkopu Galaxias argenteus) were more common in closed streams. 4. Overall, there were notable reserve effects related to closed streams. There was slight evidence that partially closed streams conferred some fisheries benefits compared to streams open to fishing. While the limited number of reserve streams warrants some caution in conclusions, partial closures may still be worthwhile as a management tool where complete closure to fishing is not feasible.5. Closures can be effective in increasing fish numbers, albeit at a cost of smaller sized individuals, most likely because of density-dependent processes relating to food and habitat. Despite clear benefits in total egg production of populations in closed streams, it remains unclear how these benefits may translate across the full life history of the annual G. maculatus.6. Synthesis and applications. We demonstrate that freshwater reserves have many of the 'reserve effects' observed in more common marine reserves, but there are also important differences. Stream closure should be considered as one potential management tool that is unlikely to be effective unless stream habitats are returned to more pristine states. Our effort to evaluate the explicit effects of different reserve types across different spatial scales is the first we know of for migratory freshwater fishes, providing useful insights for adjusting the current reserve network and establishing new reserves.

The Wittrick-Williams (WW) algorithm was developed over 30 years ago and has been applied with increasing sophistication to problems in structural mechanics ever since. Much wider applications, to any field requiring eigenvalues of self-adjoint systems of differential equations, are possible based on a theorem due to Balakrishnan that underpins the algorithm. These can be calculated to machine accuracy and none are missed. Here the value of the algorithm in mathematics is illustrated by studying in depth Sturm-Liouville equations on large homogeneous trees. These typically involve 10 13 equations and eigenvalues, which often coincide to form high multiplicity ones. Computation is quick (e.g. 1 s) and numerically stable because the multi-level subsysteming corollary of the theorem underpinning the WW algorithm is used.Our numerical results confirm the recent theoretical bounds of Sobolev & Solomyak on the bands into which the spectrum is divided by gaps split by one very high multiplicity eigenvalue. Additionally, an analogy based on structural mechanics and confirmed by numerical results gives exact equations for the high multiplicities of the gap eigenvalue and of those in the band. These cover any b and n, the branching number and number of levels of the tree. When these equations are divided by the number of eigenvalues in one band-gap interval, dimensionless results are obtained which become exact for n → ∞. Finally, the fragmentation of multiple eigenvalues caused by introducing a potential is studied numerically and interpreted using the structural mechanics analogy.

Energy efficiency in biomass production is a major challenge for a future transition to sustainable food and energy provision. This study uses methodologically consistent data on agroecosystem energy flows and different metrics of energetic efficiency from seven regional case studies in North America (USA and Canada) and Europe (Spain and Austria) to investigate energy transitions in Western agroecosystems from the late nineteenth to the late twentieth centuries. We quantify indicators such as external final energy return on investment (EFEROI, i.e., final produce per unit of external energy input), internal final EROI (IFEROI, final produce per unit of biomass reused locally), and final EROI (FEROI, final produce per unit of total inputs consumed). The transition is characterized by increasing final produce accompanied by increasing external energy inputs and stable local biomass reused. External inputs did not replace internal biomass reinvestments, but added to them. The results were declining EFEROI, stable or increasing IFEROI, and diverging trends in FEROI. The factors shaping agroecosystem energy profiles changed in the course of the transition: Under advanced organic and frontier agriculture of the late nineteenth and early twentieth centuries, population density and biogeographic conditions explained both agroecosystem productivity and energy inputs. In industrialized agroecosystems, biogeographic conditions and specific socio-economic factors influenced trends towards increased agroecosystem specialization. The share of livestock products in a region's final produce was the most important factor determining energy returns on investment.Keywords Agroecosystem energy transition . Long-term socio-ecological research . Energy return on investment . Energy efficiency Electronic supplementary material The online version of this article (https://doi

Analytical theories are developed for post-local buckling-driven delamination in bilayer composite beams. The total energy release rate (ERR) is obtained more accurately by including an axial strain energy contribution from the intact part of the beam and by developing a more accurate expression for the post-buckling mode shape than that in the work by Chai et al. (1981) and Hutchinson and Suo (1992). The total ERR is partitioned by using partition theories based on the Euler beam, Timoshenko beam and 2D-elasticity theories. Independent experimental tests by show that, in general, the analytical partitions based on the Euler beam theory predicts the propagation behaviour very well and much better than the partitions based on the Timoshenko beam and 2D-elasticity theories.