Characterization of the critical values of branching random walks on weighted graphs through infinite-type branching processes

We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We characterize the weak critical value and relate it to another geometrical parameter. We prove that, at the strong critical value, the process dies out locally almost surely; while, at the weak critical value, global survival and global extinction are both possible.Comment: 14 pages, corrected some typos and minor mistake

Survival, extinction and approximation of discrete-time branching random walks

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte

First insights into the vertical habitat use of the whitespotted eagle ray Aetobatus narinari revealed by pop‐up satellite archival tags

The whitespotted eagle ray Aetobatus narinari is a tropical to warm‐temperate benthopelagic batoid that ranges widely throughout the western Atlantic Ocean. Despite conservation concerns for the species, its vertical habitat use and diving behaviour remain unknown. Patterns and drivers in the depth distribution of A. narinari were investigated at two separate locations, the western North Atlantic (Islands of Bermuda) and the eastern Gulf of Mexico (Sarasota, Florida, U.S.A.). Between 2010 and 2014, seven pop‐up satellite archival tags were attached to A. narinari using three methods: a through‐tail suture, an external tail‐band and through‐wing attachment. Retention time ranged from 0 to 180 days, with tags attached via the through‐tail method retained longest. Tagged rays spent the majority of time (82.85 ± 12.17% S.D.) within the upper 10 m of the water column and, with one exception, no rays travelled deeper than ~26 m. One Bermuda ray recorded a maximum depth of 50.5 m, suggesting that these animals make excursions off the fore‐reef slope of the Bermuda Platform. Individuals occupied deeper depths (7.42 ± 3.99 m S.D.) during the day versus night (4.90 ± 2.89 m S.D.), which may be explained by foraging and/or predator avoidance. Each individual experienced a significant difference in depth and temperature distributions over the diel cycle. There was evidence that mean hourly depth was best described by location and individual variation using a generalized additive mixed model approach. This is the first study to compare depth distributions of A. narinari from different locations and describe the thermal habitat for this species. Our study highlights the importance of region in describing A. narinari depth use, which may be relevant when developing management plans, whilst demonstrating that diel patterns appear to hold across individuals

Reproductive Strategy of the Giant Electric Ray in the Southern Gulf of California

The objective of the present study was to describe and characterize macroscopic and microscopic aspects of the reproductive biology of the Giant Electric Ray Narcine entemedor, a viviparous elasmobranch targeted by commercial fishers in Mexico. A total of 305 individual rays were captured (260 females, 45 males); all males were sexually mature. The median size at maturity for females was estimated to be 58.5 cm TL, the median size at pregnancy was 63.7 cm TL, and the median size at maternity was 66.2 cm TL. The range of ovarian follicles recorded per female was 1–69; the maximum ovarian fecundity of fully grown vitellogenic oocytes was 17, and uterine fecundity ranged from 1 to 24 embryos per female. The lengths of the oblong ovarian follicles varied significantly among months, and the largest ovarian follicles were found in July, August, and September. Median embryo size was largest in August, and the size at birth was between 12.4 and 14.5 cm TL. Histological evidence of secretions from the glandular tissue of the uterine villi indicate that this species probably has limited histotrophy as a reproductive mode. Vitellogenesis in the ovary occurred synchronously with gestation in the uterus. The Giant Electric Ray has a continuous annual reproductive cycle; a period of ovulation occurs between May and September and two peaks of parturition, one in January and one in August, occur, suggesting that embryonic diapause occurs in some individuals. These results provide useful information for the management of this important commercial species in Bahía de La Paz, Mexico, and will allow possible modification of the current Mexican regulations to enable better protection of this species

Histomorphological study of the spinal growth plates from the convex side and the concave side in adolescent idiopathic scoliosis

Asymmetrical growth of the vertebrae has been implicated as one possible etiologic factor in the pathogenesis of adolescent idiopathic scoliosis. The longitudinal vertebral growth derives from the endochondral ossification of the vertebral growth plate. In the present study, the growth plates from the convex and concave side of the vertebrae were characterized by the method of histology and immunohistochemistry to evaluate the growth activity, cell proliferation, and apoptosis. Normal zoned architectures were observed in the convex side of the growth plate and disorganized architectures in the concave side. The histological grades were significantly different between the convex and the concave side of the growth plate in the apex vertebrae (P < 0.05). The histological difference was also found significant statistically between end vertebrae and apex vertebrae in the concave side of vertebral growth plates (P < 0.05). The proliferative potential indexes and apoptosis indexes of chondrocytes in the proliferative and hypertrophic zone in the convex side were significantly higher than that in the concave side in the apex vertebral growth plate (P < 0.05). There was a significant difference of the proliferative potential index (proliferating cell nuclear antigen, PCNA index) between convex side and concave side at the upper end vertebra (P < 0.05). The difference of the proliferative potential index and apoptosis index were found significant statistically in the concave side of the vertebral growth plate between end vertebrae and apex vertebrae (P < 0.05). The same result was also found for the apoptosis index (terminal deoxynucleotidyl transferase mediated deoxyuridine triphosphate biotin nick end labeling assay, TUNEL index) in the convex side of vertebral growth plate between end vertebrae and apex vertebrae (P < 0.05). Some correlation were found between radiographic measurements and proliferation and apoptosis indexes. The difference in histological grades and cellular activity between the convex and concave side indicated that the bilateral growth plate of the vertebrae in AIS patients have different growth kinetics which may affect the curve progression

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements