On global location-domination in graphs

A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\overline{G}$. The global location-domination number $\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between locating-dominating sets and the location-domination number in a graph and its complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference

Moduli spaces of toric manifolds

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version, 19 pages, 6 figure

Extremal Graph Theory for Metric Dimension and Diameter

A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}_{\beta,D}$ be the set of graphs with metric dimension $\beta$ and diameter $D$. It is well-known that the minimum order of a graph in $\mathcal{G}_{\beta,D}$ is exactly $\beta+D$. The first contribution of this paper is to characterise the graphs in $\mathcal{G}_{\beta,D}$ with order $\beta+D$ for all values of $\beta$ and $D$. Such a characterisation was previously only known for $D\leq2$ or $\beta\leq1$. The second contribution is to determine the maximum order of a graph in $\mathcal{G}_{\beta,D}$ for all values of $D$ and $\beta$. Only a weak upper bound was previously known

Nordhaus-Gaddum bounds for locating domination

A dominating set S of graph G is called metric-locating-dominating if it is also locating, that is, if every vertex v is uniquely determined by its vector of distances to the vertices in S. If moreover, every vertex v not in S is also uniquely determined by the set of neighbors of v belonging to S, then it is said to be locating-dominating. Locating, metric-locating-dominating and locating-dominating sets of minimum cardinality are called b-codes, e-codes and l-codes, respectively. A Nordhaus-Gaddum bound is a tight lower or upper bound on the sum or product of a parameter of a graph G and its complement G. In this paper, we present some Nordhaus-Gaddum bounds for the location number b, the metric-location-number e and the location-domination number l. Moreover, in each case, the graph family attaining the corresponding bound is characterized.Comment: 7 pages, 2 figure

Assessment of methods for estimating wild rabbit population abundance in agricultural landscapes

Various methods have been used to estimate rabbit abundance, but comparisons of standard methods are still lacking, and thus, results remain roughly comparable across studies. Ideally, a method should be applicable over a wide range of situations, such as differing abundances or habitat types. Comparisons of methods are required to evaluate the benefits of each of them, and survey methods should be validated for the conditions in which they will be used. In this study, we compare the performance of direct methods (kilometric abundance index and distance sampling) in two seasons and at two times of day (dusk and night) for estimating wild rabbit abundances in agricultural landscapes. Estimates based on direct methods were highly correlated and detected similar seasonal population changes. Night counts provided better estimates than did dusk counts and exhibited more precision. Results are discussed within the context of rabbit behaviour and their implications for rabbit population surveys.Funding was provided by FEDENCA. ICB was supported by a PhD fellowship from the Spanish Ministry of Science and Innovation. PA is currently enjoying a Juan de la Cierva research contract awarded by the Spanish Ministry of Science and Innovation and is supported by the project CGL2006-09567/BOS.Peer Reviewe

Analysis of polymorphisms in candidate’s genes for meat quality in Lidia cattle

The aim of this paper was to analyze the segregation of some polymorphisms in three genes ( CAPN1 , CAST and DGAT1 ) re- lated to meat quality in the Lidia cattle breed and some of its main lineages. To that effect, 119 individuals from the Lidia breed were analyzed. Although the association between the polymorphisms and the phenotype has never been demonstrated in this breed, the absence of fixed genotypes for these polymorphisms in the studied population makes the Lidia cattle a good candidate to de- velop selection objectives. The clear differentiation among lineages for most of the genes studied reinforces the high reproductive isolation presented in the Lidia cattle as revealed by previous studies on the structure of the population within the Lidia breed using microsatellite markers. Considering both issues in the design of breeding schemes will be necessary to save the lineages and not to lose this valuable genetic resource. Finally, it would be necessary to carry out an in depth search for new polymorphisms in genes associated with meat quality and to perform needed association analyses between the SNPs segregating in Lidia cattle and traits of economic interes

Past, present and future distributions of an Iberian endemic, Lepus granatensis: ecological and evolutionary clues from species distribution models

The application of species distribution models (SDMs) in ecology and conservation biology is increasing and assuming an important role, mainly because they can be used to hindcast past and predict current and future species distributions. However, the accuracy of SDMs depends on the quality of the data and on appropriate theoretical frameworks. In this study, comprehensive data on the current distribution of the Iberian hare (Lepus granatensis) were used to i) determine the species' ecogeographical constraints, ii) hindcast a climatic model for the last glacial maximum (LGM), relating it to inferences derived from molecular studies, and iii) calibrate a model to assess the species future distribution trends (up to 2080). Our results showed that the climatic factor (in its pure effect and when it is combined with the land-cover factor) is the most important descriptor of the current distribution of the Iberian hare. In addition, the model's output was a reliable index of the local probability of species occurrence, which is a valuable tool to guide species management decisions and conservation planning. Climatic potential obtained for the LGM was combined with molecular data and the results suggest that several glacial refugia may have existed for the species within the major Iberian refugium. Finally, a high probability of occurrence of the Iberian hare in the current species range and a northward expansion were predicted for future. Given its current environmental envelope and evolutionary history, we discuss the macroecology of the Iberian hare and its sensitivity to climate change.P.A. was supported by the Vicerrectorado de Investigación of the University of Malaga and partially by the project CGL2009-11316/BOS of the Spanish Government and FEDER. Currently, P.A. holds a Beatriu de Pinós fellowship funded by “Comissionat per a Universitats i Recerca del Departament d’Innovació, Universitats i Empresa” of the Generalitat de Catalunya, and the COFUND Programme - Marie Curie Actions under 7th Marc Programme of the European Community. J.M.-F. was funded from the SFRH/BPD/43264/2008 post-doctoral grant by by Portuguese Fundação para a Ciência e a Tecnologia (FCT) and the European Social Fund. Financial support was partially obtained from the Research Projects PTDC/BIA-EVF/111931/2009 and PTDC/BIA-EVF/115069/2009, by FCT and FEDER.Peer Reviewe

Evidence for niche similarities in the allopatric sister species Lepus castroviejoi and Lepus corsicanus

[Aim]: Lepus castroviejoi and Lepus corsicanus are sister species with allopatric distributions that share extensive phenotypic and genetic variation. Under the framework of niche conservatism, we assessed whether these species have similar ecological niches, which could provide insights into their mode of divergence, conservation, and taxonomic status. [Location]: The distribution range of L. castroviejoi in the northern Iberian Peninsula, and that of L. corsicanus in mainland Italy and Sicily. [Methods]: We developed spatially explicit ecological models to characterize the niches of the two species by modelling them separately and together. Individual models were transferred to the territory of the sister species to explore their niche relationships. Predictions were assessed for discrimination and calibration in a cross-assessment procedure. [Results]: The model trained with L. castroviejoi was not able to predict the range of L. corsicanus, whereas the model trained with L. corsicanus was able to discriminate the L. castroviejoi distribution better than by chance alone (AUC = 0.814), although the reliability of the predictions was limited. The model trained with L. corsicanus in Italy's mainland (excluding the range in Sicily), however, discriminated L. castroviejoi presences/absences (AUC = 0.788) and accurately predicted its probability of occurrence. Furthermore, a well-calibrated model, which was able to discriminate the species distributions (L. castroviejoi, AUC = 0.828; L. corsicanus, AUC = 0.956), was obtained when the species were considered together. [Main conclusions]: Our results suggest that L. castroviejoi and L. corsicanus share extensive niche properties, which reinforces their possible conspecific status. The ecological niche of their ancestor may have resembled the present occupied niche of L. corsicanus in mainland Italy, given that this model was able to accurately predict the distribution range of both species. Finally, ecological evidence suggests that niche conservatism may explain the fragmentation in the distribution range of their ancestor, which may have been the driver of the initial stages of divergence.P.A. received a José Castillejo fellowship (2010 –2011)in Portugal awarded by the Ministerio de Ciencia e Innovación to conduct this study, and was also partly supported bythe CGL2009-11316/BOS Spanish Government and FEDER project. P.A. and J.M.-F. currently hold postdoctoral grantsfrom the Fundaçao para a Ciência e a Tecnologia (FCT),funded by Programa Operacional Potencial Humano (POPH)– Quadro de Referência Estratégico Nacional (QREN) fromthe European Social Fund and by the Portuguese Ministério da Educaçao e Ciência (SFRH/BPD/90320/2012 and SFRH/BPD/43264/2008, respectively). Financial support was partly obtained from the research project grants PTDC/BIA-EVF/111931/2009 and PTDC/BIA-EVF/115069/2009, funded by FEDER through the COMPETE program and Portuguese national funds through the FCT.Peer Reviewe