Medium-Term Review: 1991-1996, No. 4 June 1991

Our medium-term forecast for the period 1991-96 is for a pattern of resumed, steady growth in GNP, after a temporary slow-down this year. The average rate of growth should be in the region of 3.5% per annum, a slower growth than was anticipated prior to the downward revisions of the prospects for the world economy made over the last two years. In particular, the rise in German interest rates, consequent on unification, has reduced the prospective Irish growth rate in the medium-term by 0.5%

Quantifying evolutionary constraints on B cell affinity maturation

The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B cell sequence data, and then apply them to a very deep short-read data set of B cell receptors. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on B cell receptors using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which provides a more nuanced view of the constraints on framework and variable regions.Comment: Previously entitled "Substitution and site-specific selection driving B cell affinity maturation is consistent across individuals

Bounding mean orders of sub-kk-trees of kk-trees

For a $k$-tree $T$, we prove that the maximum local mean order is attained in a $k$-clique of degree $1$ and that it is not more than twice the global mean order. We also bound the global mean order if $T$ has no $k$-cliques of degree $2$ and prove that for large order, the $k$-star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees.Comment: 20 Pages, 6 Figure

Recovery of critically endangered Nassau grouper (Epinephelus striatus) in the Cayman Islands following targeted conservation actions.

Many large-bodied marine fishes that form spawning aggregations, such as the Nassau grouper (Epinephelus striatus), have suffered regional overfishing due to exploitation during spawning. In response, marine resource managers in many locations have established marine protected areas or seasonal closures to recover these overfished stocks. The challenge in assessing management effectiveness lies largely in the development of accurate estimates to track stock size through time. For the past 15 y, the Cayman Islands government has taken a series of management actions aimed at recovering collapsed stocks of Nassau grouper. Importantly, the government also partnered with academic and nonprofit organizations to establish a research and monitoring program (Grouper Moon) aimed at documenting the impacts of conservation action. Here, we develop an integrated population model of 2 Cayman Nassau grouper stocks based on both diver-collected mark-resight observations and video censuses. Using both data types across multiple years, we fit parameters for a state-space model for population growth. We show that over the last 15 y the Nassau grouper population on Little Cayman has more than tripled in response to conservation efforts. Census data from Cayman Brac, while more sparse, show a similar pattern. These findings demonstrate that spatial and seasonal closures aimed at rebuilding aggregation-based fisheries can foster conservation success

Trees maximizing the number of almost-perfect matchings

We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings missing only one or two leaves. We also determine the trees that minimize the number of maximal matchings. We apply these results to extremal problems on the weighted Hosoya index for several choices of vertex-degree-based weight function.Comment: 21 pages, 8 figure

From Curves to Words and Back Again: Geometric Computation of Minimum-Area Homotopy

Let $\gamma$ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if $\gamma$ is self-overlapping by geometrically constructing a combinatorial word from $\gamma$. More recently, Zipei Nie, in an unpublished manuscript, computed the minimum homotopy area of $\gamma$ by constructing a combinatorial word algebraically. We provide a unified framework for working with both words and determine the settings under which Blank's word and Nie's word are equivalent. Using this equivalence, we give a new geometric proof for the correctness of Nie's algorithm. Unlike previous work, our proof is constructive which allows us to naturally compute the actual homotopy that realizes the minimum area. Furthermore, we contribute to the theory of self-overlapping curves by providing the first polynomial-time algorithm to compute a self-overlapping decomposition of any closed curve $\gamma$ with minimum area.Comment: 27 pages, 16 figure

Migratory behavior of aggregating male Tiger Grouper (Mycteroperca tigris) in Little Cayman, Cayman Islands

Tiger Grouper (Mycteroperca tigris) form fish spawning aggregations (FSAs) around the winter full moons (typically January through April) in the Caribbean. Males defend territories to attract mates in a lek-like reproductive strategy. Prior studies have documented rapid declines in populations with FSA-associated fisheries. This study examines the migratory behavior of adult male Tiger Grouper in Little Cayman, Cayman Islands, to better understand the impacts of aggregation fishing. As part of the Grouper Moon Project, we acoustically tagged ten spawning male Tiger Grouper at the western end of Little Cayman in February 2015. Using a hydrophone array surrounding the island, we tracked the movements of the tagged fish for 13 months. We observed 3 migratory strategies: resident fish (n = 2) that live at the FSA site, neighboring fish (n = 5) that live within 4 km of the site, and commuter fish (n = 3) that travel over 4 km for spawning. Fish began aggregating 2 days before the full moon and left 10–12 days after the full moon, from January to May. Regardless of migratory strategy, all tagged fish that aggregated after February 2015 returned to the west end FSA. However, in January 2016, one fish appeared to attend a different FSA closer to its presumed home territory. Tiger Grouper may establish multiple FSAs around Little Cayman, and males appear to attend FSAs near their home territories. Protracted spawning seasons, FSA site infidelity, and putative FSA catchments should all be considered to ensure sustainable fisheries management for this important species.publishedVersio

Use of nuclear spin noise spectroscopy to monitor slow magnetization buildup at millikelvin temperatures

At ultralow temperatures, longitudinal nuclear magnetic relaxation times become exceedingly long and spectral lines are very broad. These facts pose particular challenges for the measurement of NMR spectra and spin relaxation phenomena. Nuclear spin noise spectroscopy is used to monitor proton spin polarization buildup to thermal equilibrium of a mixture of glycerol, water, and copper oxide nanoparticles at 17.5 mK in a static magnetic field of 2.5 T. Relaxation times determined in such a way are essentially free from perturbations caused by excitation radiofrequency pulses, radiation damping, and insufficient excitation bandwidth. The experimental spin-lattice relaxation times determined on resonance by saturation recovery with spin noise detection are consistently longer than those determined by using pulse excitation. These longer values are in better accordance with the expected field dependence trend than those obtained by on-resonance experiments with pulsed excitation

Protected fish spawning aggregations as self-replenishing reservoirs for regional recovery

Dispersal of eggs and larvae from spawning sites is critical to the population dynamics and conservation of marine fishes. For overfished species like critically endangered Nassau grouper (Epinephelus striatus), recovery depends on the fate of eggs spawned at the few remaining aggregation sites. Biophysical models can predict larval dispersal, yet these rely on assumed values of key parameters, such as diffusion and mortality rates, which have historically been difficult or impossible to estimate. We used in situ imaging to record three-dimensional positions of individual eggs and larvae in proximity to oceanographic drifters released into egg plumes from the largest known Nassau grouper spawning aggregation. We then estimated a diffusion–mortality model and applied it to previous years' drifter tracks to evaluate the possibility of retention versus export to nearby sites within 5 days of spawning. Results indicate that larvae were retained locally in 2011 and 2017, with 2011 recruitment being a substantial driver of population recovery on Little Cayman. Export to a nearby island with a depleted population occurred in 2016. After two decades of protection, the population appears to be self-replenishing but also capable of seeding recruitment in the region, supporting calls to incorporate spawning aggregation protections into fisheries management.publishedVersio