Caribbean connectivity: implications for Marine Protected Area Management. Proceedings of a Special Symposium, 9-11 November 2006, 59th Annual Meeting of the Gulf and Caribbean Fisheries Institute, Belize City, Belize

Executive Summary: Tropical marine ecosystems in the Caribbean region are inextricably linked through the movement of pollutants, nutrients, diseases, and other stressors, which threaten to further degrade coral reef communities. The magnitude of change that is occurring within the region is considerable, and solutions will require investigating pros and cons of networks of marine protected areas (MPAs), cooperation of neighboring countries, improved understanding of how external stressors degrade local marine resources, and ameliorating those stressors. Connectivity can be broadly defined as the exchange of materials (e.g., nutrients and pollutants), organisms, and genes and can be divided into: 1) genetic or evolutionary connectivity that concerns the exchange of organisms and genes, 2) demographic connectivity, which is the exchange of individuals among local groups, and 3) oceanographic connectivity, which includes flow of materials and circulation patterns and variability that underpin much of all these exchanges. Presently, we understand little about connectivity at specific locations beyond model outputs, and yet we must manage MPAs with connectivity in mind. A key to successful MPA management is how to most effectively work with scientists to acquire the information managers need. Oceanography connectivity is poorly understood, and even less is known about the shape of the dispersal curve for most species. Dispersal kernels differ for various systems, species, and life histories and are likely highly variable in space and time. Furthermore, the implications of different dispersal kernels on population dynamics and management of species is unknown. However, small dispersal kernels are the norm - not the exception. Linking patterns of dispersal to management options is difficult given the present state of knowledge. The behavioral component of larval dispersal has a major impact on where larvae settle. Individual larval behavior and life history details are required to produce meaningful simulations of population connectivity. Biological inputs are critical determinants of dispersal outcomes beyond what can be gleaned from models of passive dispersal. There is considerable temporal and spatial variation to connectivity patterns. New models are increasingly being developed, but these must be validated to understand upstream-downstream neighborhoods, dispersal corridors, stepping stones, and source/sink dynamics. At present, models are mainly useful for providing generalities and generating hypotheses. Low-technology approaches such as drifter vials and oceanographic drogues are useful, affordable options for understanding local connectivity. The “silver bullet” approach to MPA design may not be possible for several reasons. Genetic connectivity studies reveal divergent population genetic structures despite similar larval life histories. Historical stochasticity in reproduction and/or recruitment likely has important, longlasting consequences on present day genetic structure. (PDF has 200 pages.)

Connectivity: Science, people and policy in the Florida Keys National Marine Sanctuary

Executive Summary: The Connectivity Colloquium evolved from an exhortation by Dan Basta, Director of the National Marine Sanctuary Program, to come together and assess what we know about the condition of our natural resources, identify information gaps and how to fill them, and transform science and management from an emphasis on documentation to a nexus for action. This purpose in some ways reflects the initiation of the Florida Keys National Marine Sanctuary itself, which was designated by an act of the U.S. Congress in 1990 in the aftermath of the 1989 Exxon Valdez oil spill in Alaska and three major ship groundings of the Florida Reef Tract in late 1989. Over the next seven years NOAA worked with federal, state, and local partners to develop a comprehensive management plan for the Sanctuary implemented under a co-trustee partnership between NOAA and the State of Florida. (PDF contains 270 pages; 14Mb)

Resilient internet connectivity at Myerscough College

Myerscough College, a land-based further and higher education college in the north west, is one of the approximately 160 further education colleges in England to take additional connections to Jisc’s Janet network. Ian Brown, director of IT and MIS at the college, talks to us about why they’ve taken an extra four connections.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Connectivity and Function of the Primate Insula

The insula is a mammalian cortical structure that has been implicated in a wide range of low- and high-level functions governing one’s sensory, emotional, and cognitive experiences. One particular role of this region is considered to be processing of olfactory stimuli. The ability to detect and evaluate odors has significant effects on an organism’s eating behavior and survival and, in case of humans, on complex decision making. Despite such importance of this function, the mechanism in which olfactory information is processed in the insula has not been thoroughly studied. Moreover, due to the structure’s close spatial relationship with the neighboring claustrum, it is not entirely clear whether the connectivity and olfactory functions attributed to the insula are truly those of the insula, rather than of the claustrum. My graduate work, consisting of two studies, seeks to help fill these gaps. In the first, the structural connectivity patterns of the insula and the claustrum in a non-human primate brain is assayed using an ultra-high-quality diffusion magnetic resonance image, and the results suggest dissociation of connectivity — and hence function — between the two structures. In the second study, a functional neuroimaging experiment investigates the insular activity during odor evaluation tasks in humans, and uncovers a potential spatial organization within the anterior portion of the insula for processing different aspects of odor characteristics.

Structural Integration of Tellurium Oxide into Mixed-Network-Former Glasses: Connectivity Distribution in the System NaPO3–TeO2

FSodium phosphate tellurite glasses in the system (NaPO3)(x)(TeO2)(1-x) were prepared and structurally characterized by thermal analysis, vibrational spectroscopy, X-ray photoelectron spectroscopy (XPS) and a variety of complementary solid-state nuclear magnetic resonance (NMR) techniques. Unlike the situation in other mixed-network-former glasses, the interaction between the two network formers tellurium oxide and phosphorus oxide produces no new structural units, and no sharing of the network modifier Na2O takes place. The glass structure can be regarded as a network of interlinked metaphosphate-type P(2) tetrahedral and TeO4/2 antiprismotic units. The combined interpretation of the O 1s XPS data and the P-31 solid-state NMR spectra presents clear quantitative evidence for a nonstatistical connectivity distribution. Rather the formation of homootomic P-O-P and Te-O-Te linkages is favored over mixed P-O-Te connectivities. As a consequence of this chemical segregation effect, the spatial sodium distribution is not random, as also indicated by a detailed analysis of P-31/No-23 rotational echo double-resonance (REDOR) experiments. ACHTUNGTRENUNG(TeO2)1 x were prepared and structurally characterized by thermal analysis,vibrat ional spectroscopy,X-ray photoelectron spectroscopy (XPS) and a variety of complementary solid-state nuclear magnetic resonance (NMR) techniques. Unlike the situation in other mixed-network-former glasses,the interaction between the two network formers tellurium oxide and phosphorus oxide produces no new structural units,and no sharing of the network modifier Na2O takes place. The glass structure can be regarded as a network of interlinked metaphosphate-type P(2) tetrahedral and TeO4/2 antiprismatic units. The combined interpretation of the O 1s XPS data and the 31P solid-state NMR spectra presents clear quantitative evidence for a nonstatistical connectivity distribution. Rather,the formation of homoatomic P O P and Te O Te linkages is favored over mixed P O Te connectivities. As a consequence of this chemical segregation effect,the spatial sodium distribution is not random,as also indicated by a detailed analysis of 31P/23Na rotational echo double-resonance (REDOR) experiments.

Population structure, long-term connectivity, and effective size of mutton snapper (Lutjanus analis) in the Caribbean Sea and Florida Keys

Genetic structure and average long-term connectivity and effective size of mutton snapper (Lutjanus analis) sampled from offshore localities in the U.S. Caribbean and the Florida Keys were assessed by using nuclear-encoded microsatellites and a fragment of mitochondrial DNA. No significant differences in allele, genotype (microsatellites), or haplotype (mtDNA) distributions were detected; tests of selective neutrality (mtDNA) were nonsignificant after Bonferroni correction. Heuristic estimates of average long-term rate of migration (proportion of migrant individuals/generation) between geographically adjacent localities varied from 0.0033 to 0.0054, indicating that local subpopulations could respond independently of environmental perturbations. Estimates of average longterm effective population sizes varied from 341 to 1066 and differed significantly among several of the localities. These results indicate that over time larval drift and interregional adult movement may not be sufficient to maintain population sustainability across the region and that there may be different demographic stocks at some of the localities studied. The estimate of long-term effective population size at the locality offshore of St. Croix was below the minimum threshold size considered necessary to maintain the equilibrium between the loss of adaptive genetic variance from genetic drift and its replacement by mutation. Genetic variability in mutton snapper likely is maintained at the intraregional level by aggregate spawning and random mating of local populations. This feature is perhaps ironic in that aggregate spawning also renders mutton snapper especially vulnerable to overexploitation.

Population connectivity among Dry Tortugas, Florida, and Caribbean populations of mutton snapper (Lutjanus analis), inferred from multiple microsatellite loci

Determining patterns of population connectivity is critical to the evaluation of marine reserves as recruitment sources for harvested populations. Mutton snapper (Lutjanus analis) is a good test case because the last known major spawning aggregation in U.S. waters was granted no-take status in the Tortugas South Ecological Reserve (TSER) in 2001. To evaluate the TSER population as a recruitment source, we genotyped mutton snapper from the Dry Tortugas, southeast Florida, and from three locations across the Caribbean at eight microsatellite loci. Both Fstatistics and individual-based Bayesian analyses indicated that genetic substructure was absent across the five populations. Genetic homogeneity of mutton snapper populations is consistent with its pelagic larval duration of 27 to 37 days and adult behavior of annual migrations to large spawning aggregations. Statistical power of future genetic assessments of mutton snapper population connectivity may benefit from more comprehensive geographic sampling, and perhaps from the development of less polymorphic DNA microsatellite loci. Research where alternative methods are used, such as the transgenerational marking of embryonic otoliths with barium stable isotopes, is also needed on this and other species with diverse life history characteristics to further evaluate the TSER as a recruitment source and to define corridors of population connectivity across the Caribbean and Florida.