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# The commercial fishery for ocean leatherjackets (Nelusetta ayraudi, Monacanthidae) in New South Wales, Australia

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## Abstract

The ocean leatherjacket (Nelusetta ayraudi) has a long history of commercial exploitation in New South Wales, Australia. Records of reported landings indicate that substantial peaks of between 600 and 900 tonnes per annum occurred during the 1920s and again during the 1950s. These peaks were followed by large declines, which suggest that this species is vulnerable to over-exploitation. In recent years from 2000/01 to 2006/07, annual commercial landings of ocean leatherjackets using oceanic demersal fish traps and demersal otter trawl have increased from 134 to 430 tonnes. Between 2003 and 2005 ocean leatherjackets in commercial landings ranged approximately between 22 and 65 cm in total length. Ocean leatherjackets were fully recruited to the fishery at two years of age, with the majority of the catch (83%) aged either two or three years. The instantaneous total mortality rate was estimated from an age-based catch curve as 1.1. Natural mortality was estimated as approximately 0.5, based on a maximum age of 6 years. Yield per recruit indicated that under current levels of exploitation the yield per recruit would be maximized at a length at first harvest of 35 cm in total length.

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... opposite to the predictions of the TSR model), indicating that in this case the TSR model could be outweighed by variation associated with habitat and nutrition and not just temperature, as previously documented for many other species (Yamahira and Conover 2002;Floeter et al. 2005;Robertson et al. 2005;Lafferty 2007, 2012;Trip et al. 2014). More generally, our findings on age composition are consistent with those reported for other monacanthids in Miller and Stewart (2009) with the exception of the oldest fish recorded here. The maximum age recorded for M. scaber in this study was 19 years, which is much longer than the previous lifespan estimates of 5 years (Poynter 1980), and represents the greatest age reported for the family Monacanthidae to date. ...
... Although this finding highlights an important key demographic feature of this species, our results partially also support the hypothesis that M. scaber might undergo short vertical movements that could be associated with either spawning dynamics or feeding habits. Similar trends have been observed in many gonochoristic lutjanids (Guerra Campos and Bashirullah 1975;Reshetnikov and Claro 1976;Grimes and Huntsman 1980;Grimes 1987;Everson et al. 1989) and in the ocean leatherjacket Nelusetta ayraudi (Lindholm 1984;Miller and Stewart 2009), although actual movement patterns have not been observed. Alternatively, this pattern reflects a possibility that males are more susceptible to trawling. ...
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Demography and life-history characteristics of reef fishes may vary as a consequence of ecological and environmental factors that lead to changes among populations. We evaluated variation in life-history traits in the leatherjacket Meuschenia scaber (Monacanthidae) through age-based analysis of 2112 fish collected from three locations in New Zealand distributed along an 8° latitudinal and 5 °C SST gradients. Meuschenia scaber showed distinct differences in age structure, growth patterns, maximum size and age, sex ratio and mortality across this latitudinal gradient. At warmer lower latitudes (Hauraki Gulf) the population displayed significantly greater mean adult body size (Lmax) and asymptotic length (L∞) in comparison with the other two locations. Fish from Tasman Bay (mid-range latitude) had a longer life span (Tmax) and a maximum age of 19 years, which represents the longest-lived monacanthid documented to date. Fish from Pegasus Bay (cooler higher latitude) showed a slower initial growth than lower latitude counterparts. The difference in maximum age between the sexes declined clinally from 7 years in the Hauraki Gulf to 3 years in Tasman Bay and 1 year in Pegasus Bay. Meuschenia scaber females tended to display heavier and larger body size than males at all three locations. Sex ratios varied among populations and with depth, suggesting females in the Hauraki Gulf and Tasman Bay may move into deeper water with age. Given the increasing global exploitation of monacanthids in multispecies fisheries and their long-living nature, our results provide valuable age-based demographic information essential for future conservation, monitoring and management programs.
... Historical catch data indicate substantial variations in ocean jacket abundance off south-eastern Australia in the 1920s and 1950s (Miller & Stewart 2009). Ocean jacket is a relatively short-lived species (six years), reaching maturity within two to three years and exhibiting large cyclical changes in abundance (Miller & Stewart 2009). ...
... Historical catch data indicate substantial variations in ocean jacket abundance off south-eastern Australia in the 1920s and 1950s (Miller & Stewart 2009). Ocean jacket is a relatively short-lived species (six years), reaching maturity within two to three years and exhibiting large cyclical changes in abundance (Miller & Stewart 2009). As a byproduct species, ocean jacket has not been the subject of formal stock assessments. ...
... In addition, another kyphosid, luderick, Girella tricuspidata, is an important component of the commercial inshore/estuarine gillnet fishery and the recreational line fishery in south-eastern Australia with a combined annual catch of 700-1000 t(Henry & Lyle, 2003;Rowling et al., 2010). Likewise, Kyphosus species are retained in the commercial fisheries in the south-eastern Gulf of California, where catches have increased since the collection of fishery records started in the 1990s(Erisman et al., 2010;Rojo-Vázquez et al., 2001) and Chinaman leatherjacket, Nelusetta ayraud, was typically discarded but is now targeted by commercial trap fishers in south-eastern Australia and is also retained by the Great Australian Bight Trawl Fishery(Miller & Stewart, 2009;Moore et al. 2020).Due to its vast coastline (c. 12,800 km) and the large number of teleosts captured by numerous fisheries, WA is divided into four coastal bioregions, within which teleosts are grouped into five ecological suites(Department of Fisheries, 2011;Newman et al., 2018). ...
Article
... Our positive results could potentially lead to further investigations into monitoring fishery landings of species that are processed at sea, and consequently have been viewed as requiring relatively expensive onboard monitoring (via trained scientific observers). Candidate species include Monacanthids and elasmobranchs that are beheaded at sea (Miller and Stewart, 2009;Braccini et al., 2006;Huveneers et al., 2007). ...
Article
The COVID-19 global pandemic-related restrictions during 2020 severely impacted the Australian seafood industry, including essential scientific monitoring to support stock assessment and to demonstrate sustainability. Here we detail a novel, collaborative monitoring program between scientists and the seafood industry to generate length and age compositions that were representative of one of the largest, most valuable, and controversial fisheries along eastern Australia, the pre-spawning ocean run fishery for Sea Mullet Mugil cephalus that is predominantly a roe fishery. The standard approach to monitoring this fishery has been to base trained scientific staff at the major processing facility for M. cephalus, where they access whole fish from entire catches to generate representative length and age compositions during the peak season, April to May. Covid-19 restrictions prevented this approach for 2020 in eastern Australia. In recognition that in addition to the high-value roe, all components of the female fish are utilized (heads and guts for bait, bodies for human consumption), a multi-stage, spatially stratified sampling design was investigated. Female heads were retained from randomly selected catches from each of the three major fishing zones and transported to the New South Wales Department of Primary Industries fish laboratory based in Sydney. Head lengths (HLs) were measured and converted to Fork Lengths (FLs) using a HL to FL relationship. The resulting fish length compositions from each catch were subsequently combined based on: (i) relative catch size of females within an ocean zone, and; (ii) the relative reported landings of females in each ocean fishing zone. Otoliths were randomly collected from heads sampled from each ocean zone and used to estimate age. The resulting ocean zone to age matrix was combined with the relative reported landings of female fish in each ocean fishing zone to generate a total female age composition for the fishery. The estimated age composition of females were typical in being mainly between ages 3 and 6, with a strong presence of 4-year olds. This stronger cohort was present as 3-year olds in 2018/19 and 5-year olds in 2020/21, thus providing confidence that our sampling was representative of the fishery. The study reinforces the positive outcomes that can be generated through co-management between scientists and the seafood industry.
... Fish trap has been reported to be the principal fishing device throughout the Bahamian and Caribbean islands as it was found to be an efficient device for capturing fishes in areas where coral formation prevents the use of trawls and other nets (Munro, 1974). In New South Wales of Australia, the majority of ocean leather jackets were fished using demersal fish traps (Miller and Stewart, 2009). Development of collapsible trap fishing technique is of recent origin. ...
Article
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The efficiency of four different funnel designs viz., rectangular, oval, heart-in and circular shaped funnels were tested in a serial collapsible fish trap through fishing trials conducted in a coastal fishing ground off Mandapam in Tamil Nadu, south-west coast of India. A total of 24 fishing operations were carried out. Significant difference in overall catch rate of experimental trap with respect to funnel designs could be observed (p<0.05). Among four types of funnels tested with the constant rear end funnel perimeter of 560 mm, traps with oval funnel caught more number of fishes (121 nos. in 24 soaking days) than those fitted with rectangular, heart-in shaped and circular type of funnels with 37; 82 and 70 nos. in 24 soaking days respectively. The study revealed that oval shaped funnel was superior to the other funnel designs with 560 mm circumference.
... a Equivalent to 668 g m −2 seafloor, or 606 g m −2 reef surface area b Equivalent to 384 g m −2 seafloor year −1 , or 302 g m −3 reef year −1 c M reduced to match Z = 0.6(Stewart et al. 2001) d M reduced to match Z = 1.1(Miller and Stewart 2009) e M reduced to match Z = 0.32(Stewart and Hughes 2009) ...
Article
It was recently demonstrated that oil platforms are among the most productive marine fish habitats (Claisse et al. in Proc Natl Acad Sci USA 111:15462–15467, 2014). Designed artificial reef systems are similar, albeit smaller, modified habitats designed to accommodate fish assemblages. We compared fish production at a large designed reef to reported production at oil platforms. Given the focus in artificial reef research on distinguishing between new and aggregated fish production, we used a different approach to that of Claisse et al. (Proc Natl Acad Sci USA 111:15462–15467, 2014) to calculate production, based on a steady-state assumption. This assumption simplifies the analysis and distinguishes ‘local production’, ‘new production’, and ‘biomass flux’. Comparing biomass flux with standing stock biomass enables a new approach to address the production versus attraction debate, by revealing how much biomass is exposed to fishing compared to how much has local production. The local fish production at this artificial reef was 384 g m−2 year−1, which is within the 105–887 g m−2 year−1 range reported by Claisse et al., although our study included visitor species not included by Claisse et al. We estimate that the fish production new to the ecosystem may only be 4–5 % of the local production, due to the large abundance of visitor species on this reef. The annual flux of biomass across this reef was very large, ~380 times greater than the standing stock biomass, meaning that this reef is vulnerable to overexploitation from fishing. Our results show that like oil platforms, designed artificial reefs can be very productive marine habitats, but may not greatly increase the net fish production in a system. The method detailed here will allow similar studies to be done relatively simply at other marine habitats, including fish aggregation devices.
... In group spawners, where large amounts of sperm are advantageous to the chances of males successfully fertilizing eggs, males have gonads of equivalent sizes to females. In contrast, characteristics of being promiscuous and polygynous include their relatively high fecundity, similar growth rates and longevity between sexes (Miller et al. 2010), similar sizes and ages at sexual maturity between sexes and the proposed formation of large spawning aggregations in offshore waters (Miller 2007). It should be noted that the formation of large spawning aggregations has not been directly observed due to the depths at which they are thought to occur, rather inferred from depth soundings of schools of fish and the capture of running ripe fish from those schools. ...
Article
The ocean leatherjacket (Nelusetta ayraudi) is one of the largest members of the family Monacanthidae. Distributed throughout inshore waters around the southern half of Australia, this schooling species supports substantial commercial and recreational fisheries. N. ayraudi do not conform to either of the general reproductive modes reported within the family, but exhibit characteristics of both strong social reproductive behaviour and of being promiscuous and polygynous. Sexual dimorphism, with males and females exhibiting differing colouration and body shapes, and ripe ovaries being an order of magnitude larger than ripe testes, are characteristic of social reproductive behaviour and pair spawning. In contrast, high batch fecundity (mean of 320 oocytes per gram of body weight), similar sizes and ages at sexual maturity (350 mm and 2.5 years respectively) and the formation of large spawning aggregations in offshore waters are characteristic of being promiscuous and polygynous. Similar to many other coastal marine species off the east and west coasts of Australia, N. ayraudi are partial spawners during the austral winter months with spawning restricted to the part of their distribution that is towards the upper area of the prevailing currents. It is hypothesized that N. ayraudi off eastern Australia have evolved a life-history strategy whereby fish move northwards through time, spawning occurs in these more northern waters and the southerly flowing Eastern Australian Current facilitates dispersal of eggs and larvae southwards. The reproductive characteristics described provide various options to fishery managers who wish to enhance the sustainability of the fishery through increased egg production. These include spatial and temporal fishing closures to protect breeding fish during the spawning period, the protection of juveniles through either inshore area closures, improving the selectivity of fishing gears and/or regulated minimum legal lengths.
... Thought to be endemic to Australian waters, N. ayraudi are distributed from North West Cape in Western Australia around the south of the continent to Cape Morton in Queensland (Kailola et al. 1993). In New South Wales (NSW) waters, annual commercial landings of N. ayraudi have increased rapidly from 134 to 430 tonnes between 2000-2001-2007(Miller and Stewart 2009). Despite the rapidly expanding commercial fishery, there exists almost no information on the biology of N. ayraudi on which to base the management of this species. ...
Article
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Nelusetta ayraudi (the ocean leatherjacket) is an endemic Australian monacanthid species distributed from North West Cape (Western Australia) south to southern Queensland. The commercial and recreational fisheries targeting Nelusetta ayraudi have expanded substantially along the coast of New South Wales (NSW) in recent years but there exists little biological information on which to base effective management of this growing fishery. World-wide, only a few studies have aged monacanthids. Of these, researchers have interpreted periodic increments in bony structures such as vertebrae and anterior dorsal spines in preference to those found in otoliths. In this study we estimated age of N. ayraudi by counting growth increments in sectioned otoliths. The periodicity of increment formation was validated using a vital stain, (oxy-tetracycline), injected into young-of-the-year fish. Growth was rapid especially as juveniles with N. ayraudi attaining approximately 220 mm after 1 year and 340 mm after 2 years. No differences in growth rates were detected between sexes or between fish captured at different latitudes (zones). The largest male (605 mm, Total Length—TL) and female (656 mm, TL) were both recorded from northern NSW, with both sexes attaining the maximum age of 6+ years from northern and southern NSW. The von Bertalanffy parameters describing growth for N. ayraudi were $${L_\infty }$$ = 591 mm (TL), k = 0.377 year−1 and t o = −0.247 years.
Article
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The effectiveness of four different funnels such as Rectangular, Oval, heartin and Circular shaped funnels were tested in a serial collapsible fish trap through fishing trials conducted in a coastal fishing ground of Mandapam of Tamil Nadu, India. A total of 24 fishing operations were carried out. The significant difference in the overall catch rate of the experimental trap with respect to funnels could be observed (P<0.05). Among four types of funnels tested with the constant rear end funnel perimeter of 700 mm, traps with Oval funnel caught high number of fishes (89 No’s/24 soaking days) than those fitted with Rectangular, Heart-in shaped and Circular type of funnels with 34 No’s/24 soaking days, 37 No’s/24 soaking days and 15 No’s/24 soaking days respectively. The study revealed that Oval shaped funnel was superior to the other shapes of funnels with 700 mm circumference.
Article
The age and growth of filefish, Thamnaconus modestus (Günther 1877) in the southern waters of Korea were investigated. Samples were collected with commercial trawl catches during the period from May 2009 to December 2011. Of the 2,626 specimens collected, the sex ratio was not significantly different from 1:1 (P > 0.05). The total length ranged from 11.3 to 42.1 cm. The gonadosomatic index for both sexes was the highest in May to June, indicating that May to June is the main spawning period. The length of females at sexual maturity was 25.92 cm. The length-weight relationship of the filefish was TW = 0.0121TL3.0536 (n = 1,692, r2 = 0.9034, P < 0.001). The age of the sampled individuals was estimated by counting growth rings recorded on the 5th vertebrae; ages ranged from 0 to 9 years. The filefish of the same age displayed a high individual variation in total length. Length-at-age data were fitted by using the Von Bertalanffy growth model. The estimated Von Bertalanffy growth parameters were L∞ = 42.04 cm, k = 0.21 year−1 and t0 = −1.56 for females, L∞ = 41.20 cm, k = 0.18 year−1 and t0 = −2.36 for males, and L∞ = 43.16 cm, k = 0.17 year−1 and t0 = −2.18 for the combination of both male and female. These data can be used as useful biological information for the future fishery management of filefish resources in Korean waters.
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Haul-by-haul steam trawler catch and effort data for 1918–23, 1937–43 and 1952–57, which cover a large portion of the history of steam trawling in the Australian South East Fishery, were examined in detail for the first time. There were 64371 haul records in total. The catch-rate for all retained catch combined shows a strong decline overall, with a brief recovery during World War II, probably due to increased retention of previously discarded species. The fishing fleet moved to more distant fishing grounds and deeper waters as the catch-rate declined. The catch-rates of the main commercial species followed a similar pattern in a number of regions within the fishery. The catch-rate of the primary target species – tiger flathead ( Neoplatycephalus richardsoni) – dropped considerably from the early, very high, catch-rates. Chinaman leatherjacket (Nelusetta ayraudi) and latchet (Pterygotrigla polyommata) – species that were apparently abundant in the early years of the fishery, virtually disappeared from catches in later years. The appearance of greater catches of jackass morwong (Nemadactylus macropterus), redfish (Centroberyx affinis) and shark/skate during the war and afterwards was probably due to increased retention of catches of these species. The disappearance of certain species from the catch may be due to high fishing pressure alone, or to a combination of fishing pressure, changes in the shelf habitat possibly caused by the trawl gear, and environmental fluctuations.
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This field guide covers the major resource groups likely to be encountered in the fisheries of Kuwait, Eastern Saudi Arabia, Bahrain, Qatar, and the United Arab Emirates. It includes marine plants, shrimps, lobsters, crabs, bivalves, gastropods, cephalopods, sharks, batoid fishes, bony fishes, sea snakes, sea turtles, sea birds, and marine mammals. In order to serve as a tool for ecological and biodiversity studies, all species know from the Gulf of certain groups are included. These include the sharks, batoid fishes, bony fishes, sea turtles, and marine mammals. Each resource group is introduced by a general section on technical terms and measurements pertinent to that group and an illustrated guide to higher taxonomic groups when relevant. Species are then treated in a subsequent guide that includes scientific nomenclature, common English and Arabic names where available, size information, information on habitat, biology, and fisheries, diagnostic features, and one or more illustrations, some of which are included in colour. The guide is fully indexed and a list of references is appended.
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The growth of the planedhead filefish Stephanolepis hispidus was studied on individuals sampled from a small-scale fishery off Gran Canaria (Canary Islands, central-east Atlantic) between March 1998 and August 1999. The age of the sampled individuals, which ranged from 0 to 3 years, was estimated using both the length frequency distribution and the count of growth rings recorded on the anterior dorsal spine. The mean total length of the 0 age class was 10.9 cm, while the ages classes 1, 2 and 3 showed a mean length of 15.8, 19.4 and 21.4 cm, respectively. Differences in the growth rhythms were observed between the sexes. The asymptotic lengths (L ∞) were 25.7 and 27.4 cm for females and males, respectively. The curvature parameter (K) of the von Bertalanffy growth equation was 0.40 per year. The amplitude of the seasonal growth oscillation of the von Bertalanffy growth equation (C = 0.15) and the Winter Point (WP = 0.19) indicate a seasonality in the growth pattern, being slowest at the end of the winter.
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Ocean leatherjackets (Nelusetta ayraudi) are distributed along the entire coast of New South Wales (NSW) contributing significantly to the total catch of fish taken from the NSW Ocean Trap and Line Fishery (~340 tonnes in 2005/2006), in addition to other NSW fisheries, such as the Ocean Fish, Ocean Prawn and Haul-net Fisheries. In spite of their significance in commercial fisheries world-wide, only few studies have aged monacanthids. Of those, researchers have mainly used bony structures, such as vertebrae and anterior dorsal spines. In this study, commercially captured ocean leatherjackets were aged by counting growth increments in thin-sectioned otoliths. The periodicity of increment formation was validated using a vital stain oxy-tetracycline (OTC) injected into young of the year fish (0+). The von Bertalanffy growth function parameters provided good estimates of growth, k = 0.163 yr-1, t0 = -0.565 yrs and L∞ = 886 mm. The fishery was found to be dominated by two and three year old fish making up 83% of the ocean leatherjackets captured. The oldest fish (5+) and largest fish from both sexes (male - 605 mm, female - 656 mm) were found in northern NSW. All fish displayed a rapid rate of growth especially as juveniles, with no significant differences in growth between sexes and locations (southern and northern NSW). Ocean leatherjackets showed a geographical and temporal 'preference' for spawning. Gonado-somatic indices (GSI) revealed a peak in spawning during August in northern NSW. During this period adult fish were observed, via depth soundings, in large aggregations in depths ranging from 45 to 80 fathoms. Ocean leatherjackets are pelagic egg broadcasters with no parental egg care. Oocytes from ovulated ocean leatherjackets had a mean diameter of 0.66 mm (± S.E. 0.002). The estimated size and age at maturity (L50) for each sex was 352 mm and 2.5+ years old. Mature fish of each sex displayed clear differences in dimorphic and dichromatic features. This research has provided the biological information necessary for future stock assessments of ocean leatherjackets in NSW. In addition, it has contributed to management strategies designed to enhance the sustainability of the ocean leatherjackets fishery.
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The biology and fishery of black pomfret Parastromateus niger (Bloch) have been studied for the first time from the northern part of Bay of Bengal along the West Bengal-Orissa Coast. The fish is a carnivore feeding mainly on Acetes, copepods and jellyfishes. The spawning ground is located in the vast shallow continental shelf lying to the north of River Mahanadi along Orissa -West Bengal Coast. The size at first maturity is 28.0 cm SL in males and 30.0 cm SL for females. The sex ratio is close to one. The species contributes to nearly 4.0% f total drift gill-net catch at Chandipur.
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The rose bitterling (Rhodeus ocellatus ocellatus, Cyprinidae), a spring and summer breeder, was exposed to various temperature and photoperiod regimes during the different phases of the annual reproductive cycle. In early spring, warm temperature stimulated the recrudescence of the gonads regardless of photoperiod. But during late summer and autumn, a long photoperiod was required to maintain or initiate the gonadal maturation especially at high temperatures (22-28°C). These results indicate that the initiating factor of the breeding season in this species is a rising temperature, whereas the terminating one is the decreasing daylength at high temperatures. Therefore, in the rose bitterling, the responsiveness of the gonads to photoperiod varies clearly with season. The critical photoperiod for maturation falls between 13 and 14hours of light per day. This critical photoperiod could be changed by a pretreatment of artificial photoperiod during the breeding season.
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The reproductive activities of the silver pomfret, Pampus argenteus (Euphrasen), in Kuwait waters were investigated from March 1996 to February 1998. Observations on the seasonal distribution of maturity stages and variations in seasonal fluctuations in the gonadosomatic index (GSI) confirmed recent findings that the spawning period begins in May. The species has a prolonged spawning period in the females extending from May to August, whereas the males mature in April and ripe specimens were encountered in monthly samples until September. The recruitment pattern confirmed the one breeding season. There are two spawning peaks, the first in May and the second in August. Variations in GSI relative to fish length indicated that females and males are most fecund at about 24.5–26.4 cm and 20.5–22.4 cm length classes, respectively. The males mature earlier than females, at a minimum size of 12.5–14.4 cm, while the females mature at 20.5–22.4 cm. The oocyte diameter-frequency distribution suggests a serial rhythm of spawning. Fecundity ranged from 28 965 to 455 661 and correlated positively with: (a) standard length (P Document Type: Research Article Publication date: December 1, 2000 $(document).ready(function() { var shortdescription =$(".originaldescription").text().replace(/\\&/g, '&').replace(/\\, '<').replace(/\\>/g, '>').replace(/\\t/g, ' ').replace(/\\n/g, ''); if (shortdescription.length > 350){ shortdescription = "" + shortdescription.substring(0,250) + "... more"; } $(".descriptionitem").prepend(shortdescription);$(".shortdescription a").click(function() { $(".shortdescription").hide();$(".originaldescription").slideDown(); return false; }); }); Related content In this: publication By this: publisher In this Subject: Zoology By this author: Dadzie, S. ; Abou-Seedo, F. ; Al-Shallal, T. GA_googleFillSlot("Horizontal_banner_bottom");
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Biological information on N. ayraudi was collected during a survey of demersal fish of the Great Australian Bight between 1978 and 1980. Fish size increased with water depth, the adults were sexually dichromatic, and the sex ratio of female to male was approximately 2 : 1. Though it is a carnivore, N. ayraudi has a digestive tract that is usually associated with herbivores.
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Modern ichthyology in Kuwait began nearly 30 years ago with the publication in 1972 of Kuronuma & Abe's Fishes of Kuwait. In it, they listed 130 species spread among 64 families. Two additional books have been published on Kuwait's ichthyofauna, but none has included a complete list of the fishes reported to occur in the country. This paper reviews briefly the history of ichthyology in Kuwait, selected oversights and misidentifications, and provides a current list of fish species using the latest terminology. At present, Kuwait's fish list includes 345 species representing 95 families. The establishment of a national reference collection is suggested in order to maintain voucher specimens and document changes among Kuwait's marine biota due to current irreversible environmental alterations.
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Observers onboard commercial trap vessels quantified the sizes of fish in the discarded and retained catch for the major species in the New South Wales (NSW) demersal trap fishery. Selectivity ogives were calculated for the two mesh types used in the fishery, 50mm hexagonal wire mesh and 50mm×75mm welded mesh, by comparing the sizes of fish retained in traps with these meshes with the sizes of fish retained in control traps of 37mm hexagonal wire mesh. The selectivity of 50mm hexagonal wire was inappropriate for all important species with minimum legal size limits in the fishery, with large proportions of catches being undersized fish which were subsequently discarded with unknown mortality. Traps with back panels of 50mm×75mm welded mesh significantly reduced the catch of undersized fish, but also reduced the catches of important species without minimum legal size limits. Mesh selectivity was a direct function of fish body depth and the maximum aperture of the trap mesh on the back panel of fish traps.
Article
The potential annual fecundity of Dover sole becomes fixed before the spawning season when the average diameter of the advanced stock of yolked oocytes exceeds 0.86 mm. About nine batches were spawned over a six-month spawning season (December-May), and spawning ceased when the standing stock of advanced oocytes was exhausted. A 1-kg female released c10 000 eggs per spawning, except for the first and last batches which were smaller than the rest. Near the end of the season, females may spawn more frequently than earlier in the year, increasing the daily production of eggs by the population even though fewer females are reproductively active. Annual reproductive effort of Dover sole was equivalent to c14% of body wet weight per year. Fifty percent of the females had become sexually mature when they reached 332 mm total length. -from Authors
Article
Lake chub obtained from their natural habitat, at three different periods of their annual reproductive cycle, were subjected to four combinations of photoperiod and temperature. Temperature is the major environmental factor controlling spermatogenesis. Higher temperatures (16–21 °C) promote prespermatocytal changes (proliferation of spermatogonia) and hasten or terminate spermiation in prespawning fish; low temperatures (5–12 °C) are essential for normal gonadal proliferation and formation of the primary spermatocytes. Temperature effects are not overridden by either of the two contrasting photoperiods, but at lower temperatures a definite, although slight, photoperiodic effect is evident in the terminal part of all three experiments, Photoperiod does not appear to dominate spermatogenetic processes at any stage. Evidence is presented that an endogenous rhythm of activity is also present and may be partly responsible for the timing of the various testicular changes.
Article
Provinces. PRC landings were 1,228,638 t (44.2% of total ECS land ings), 1,042,233 t (37.5%), 379,403 t (13.6%), and 131,476 t (4.7%), respec ti vel y, for these four provinces, and to talled 2,781,750 t in 1992. The ECS land ings also represented 27.8% oftotal PRC marine landings (9,336,927 t in 1992; China Ministry of Agriculture, 1993). Foreign landings in the ECS are not monitored. Recent estimates suggest that approximately 900,000 t/yr were landed in Taiwan, 400,000 t/yr in the Republic of Korea, and 200,000 t/yr in Japan by overseas fishing vessels oper ating in the ECS for a total foreign catch of 1,500,000 t/yr in the early 1990's.' Total ECS landings in 1992 were there fore about 4,200,000 t of which about 65% were landed by boats based in China. Although adequate data on for eign landings and effort are not avail able, it is important to carry out an as sessment of the ECS landings and fisheries to identify a sustainable manage ment policy for the area and its fisheries.
Article
Using ovaries sampled seasonally from Lake Michigan bloaters in 1968-1969, we determined that one complement or modal group of eggs is produced each year and spawned mainly during January, February, and March. Fecundities estimated for 65 fish taken in October ranged from 3,230 eggs in one medium-size bloater (241 mm long) to 18,768 in the longest (305 mm). We regressed these estimates on lengths and weights of the parental fish to provide a quantitative basis for later evaluating long-term changes in reproductive potential. The resulting rectilinear regression on weight accounted for 75% of the total variation in fecundity.
Article
Monthly changes in mean ova diameter and gonadal weights indicated that spawning of rough shiner, Notropis baileyi, a cyprinid recently introduced in Halawakee Creek (Apalachicola River Drainage), Alabama, occurred during early or middle May through late September or early October. Peak spawning occurred in early or middle June. Several complements of ova matured. Fecundity was linearly related to length and weight of the fish. No significant correlation existed between the diameter of ova and fork length of fish. Versatile food habits, a long successful spawning season and favorable habitat are believed to be the key to the success of this shiner in Halawakee Creek.
Article
Abstract The spawning periodicity of silver pomfret, Pampus argenteus (Euphrasen), was investigated against a background of conflicting evidence on the onset of spawning in this species. Contrary to the existing view that silver pomfret in Kuwait waters begin to spawn in March–April, evidence is presented that indicates a delay in spawning until May. Only an insignificant level of spawning takes place in April which, from the management point of view, may be ignored. The species has a prolonged spawning period extending from May to August in females, although the males mature in April and ripe specimens are encountered in monthly samples until September. There are two spawning peaks, the first one in May and the second in August.
Article
The population dynamics of the black pomfret, Parastromateus niger, sampled from commercial gill-net catches from Kuwaiti waters of the Arabian Gulf, were investigated from October 2003 to September 2005. Length-based stock assessment using the FiSAT software package showed an asymptotic length of 65 cm TL and growth curvature of 0.34 year−1. Raw data as well as that corrected for probability of capture indicated a recruitment from February to September. The total mortality coefficient was estimated to be 1.20, a natural mortality of 0.68 and fishing mortality of 0.52. The selectivity model based on the running average showed that 25% of 14.0 cm TL fish, 50% of specimens reaching 16.3 cm TL, and 75% of all specimens of 20.2 cm TL encountering the gear were retained. Relative yield-per-recruit analyses revealed a current exploitation rate of 0.43; this is below the maximum sustainable yield index, indicating for sustainable fishery of P. niger that the exploitation rate could be increased to 0.6, provided size of the fish at first capture, i.e. the legal size, is also increased to 32.5 cm TL. These results suggest that P. niger stocks in Kuwaiti waters, contrary to existing views, are moderately exploited. This conclusion, however, is critically dependent on the estimate of natural mortality, which requires further confirmation.
Article
Macroscopic and histological studies were carried out to describe the reproductive styles and sex reversal and to follow gonadal changes in captive yellowfin seabream during the second year of life. Four reproductive styles are found in Acanthopagrus latus (Houttuyn, 1782): (i) males and females (gonochorism), (ii) functional males, (iii) transitionals and (iv) functional females. The species is a protandric hermaphrodite and begins life as a functional male with testicular zone undergoing active spermatogenesis, while the ovarian zone is arrested at the primary growth (perinucleolar) phase. Males and females were encountered in virtually all size-classes. Functional males outnumbered the functional females in all size-classes in which they were encountered. Sex reversal begins in the transitionals from July to August, after spawning in the functional males, at 14.9–20.2 cm standard length (SL) and, by November, maturation of the ovarian tissue begins. A. latus in cages in Kuwait waters spawns from January to April with a peak in February for males, and a peak in March for females and transitionals. Spawning begins in the 18.3–20.2 cm size-range fish, peaking in the 20.3–22.2 cm size-range in both males and females and also in the transitionals, although a few of the latter spawn from 14.9 cm SL. In relation to age, spawning begins at 20 months in males and peaks at 21 months. Females begin to spawn at 21 months with a peak at 22 months, while transitionals generally begin to spawn at 20 months, although a few 14–15-month-old sex-changing individuals were encountered. Temperature, either alone or in combination with other unknown factors, triggers spawning in A. latus.
Article
The present study investigated the growth, mortality, recruitment and food habits ofMonacanthus tomentosus. A total of 1038 specimens were collected by beach seine from the seagrass beds of Kotania Bay (Moluccas, Indonesia) from March 1988 to January 1989. Their length-weight relationship wasW=0.011L 3.242. Based on the von Bertalanffy formula, the asymptotic length,L , and growth coefficient,K, were determined as 11.79 cm and 0.86, respectively. Total mortality,Z, was low (2.033). Mean length of minimum capturable size (L c ) was 6.21 cm, and recruitment occurred throughout the year. Food consisted principally of gastropods (21.41%), seagrasses (14.11%), sponges (12.11%), algae (10.82%), amphipods (9.76%) and sedentary polychaetes (9.29%). Pelecypods, opisthobranchs, isopods, copepods, ostracods, foraminiferans, bryozoans, ascidians, nematodes, mollusc eggs and fish eggs were found only in small percentages.
Stock Assessment and Catch prediction of the Filefish, Thamnaconus septentrionalis, with help of Microcomputer
• C Wei-Zhong
• Y Zheng
Wei-Zhong, C., Y. Zheng and Chang-Song, L.I. 1998. Stock Assessment and Catch prediction of the Filefish, Thamnaconus septentrionalis, with help of Microcomputer. Journal of Shanghai Fisheries University. 7 (1): 13-18.
A preliminary study on the age and growth of filefish (Navodon septentrionalis)
• C Shiqin
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Shiqin, C. and H. Yachu. 1980. A preliminary study on the age and growth of filefish (Navodon septentrionalis). Journal of Fisheries of China 4 (2): 197-206.
On the catch of Navodon modestus (Gunther) in the Seto Inland Sea
• S Kakuda
Kakuda, S. 1976. On the catch of Navodon modestus (Gunther) in the Seto Inland Sea. Journal of the Faculty of Fish and Animal Husbandry Hiroshima University 15: 219-231.
On the spawning clusters of the filefish Navodon modestus in the Seto Inland Sea
• S Kakuda
Kakuda, S. 1978. On the spawning clusters of the filefish Navodon modestus in the Seto Inland Sea. Journal of the Faculty of Fish and Animal Husbandry Hiroshima University 17: 165-173.
On the growth of the File-fish, Navodon modestus, in the Seto Inland Sea
• S Kakuda
Kakuda, S. 1979. On the growth of the File-fish, Navodon modestus, in the Seto Inland Sea. Journal of the Faculty of Applied Biological Sciences Hiroshima University 18: 197-205.
Fecundity of the bloater, Coregonus hogi Environmental and endocrine control of teleost reproduction Control of sex in fishes. Department of Fisheries and Wildlife Sciences
• E H Emery
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• Jr
Emery, L and E.H. Brown Jr. 1978. Fecundity of the bloater, Coregonus hogi, in Lake Michigan. Transactions of the American Fisheries Society 107: 785-789, Bethesda. de Vlaming, V.L. 1974. Environmental and endocrine control of teleost reproduction. In: Schreck, C.B.(ed). Control of sex in fishes. Department of Fisheries and Wildlife Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, pp13-83.
Variation of fecundity of pike, Esox lucius (L.). in Windmere
• C Kipling
• W E F Frost
Kipling, C and W.E.F. Frost. 1969. Variation of fecundity of pike, Esox lucius (L.). in Windmere. Journal of Fish Biology 1: 221-237.
On an unusually heavy catch of black pomfret, Formio niger by purse seine along Dakshina Kannada coast. Indian Council of Agricultural Research
• G M Kulkarni
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Kulkarni, G.M., S. Kemparaju, M. Mohan, U. Bhat and C. Puranhhara. 1991. On an unusually heavy catch of black pomfret, Formio niger by purse seine along Dakshina Kannada coast. Indian Council of Agricultural Research. Marine Fisheries Information Service. Technical and Extension Series 114: 34-48.
Observations on the biology of Parastromateus niger (Bloch) and Pampus chinensis (Euphrasen) from the Godavary Estuary
• S Rao
Rao, S. 1973. Observations on the biology of Parastromateus niger (Bloch) and Pampus chinensis (Euphrasen) from the Godavary Estuary. Journal of the Inland Fisheries Society of India 4:207-209.
Report on a collection of carangoid and formionid fishes from the Huuga Nada area, southern Japan
• I Yukio
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Yukio, I., S. Yuichi, O. Koji H. Minori and H. Katsumi. 1992. Report on a collection of carangoid and formionid fishes from the Huuga Nada area, southern Japan. Bulletin of the Faculty of Agriculture, Miyazaki University 39: 109-116.
Rhythm of development in the oocyte of the goldfish, Carassius auratus. Bulletin of the Faculty of Fisheries of Hokkaido University
• F Yamamoto
• Yamazaki
Yamamoto, K and F. Yamazaki. 1961. Rhythm of development in the oocyte of the goldfish, Carassius auratus. Bulletin of the Faculty of Fisheries of Hokkaido University 12: 93-110.22 (2009): 277-284
Marine Fisheries in Indian Economy
• K K Balachandran
• T S G Iyer
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• P A Perigreen
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• Varghese
Sathiadhaas, R.1998. Marine Fisheries in Indian Economy, In Advances and Priorities in Fisheries Technology. (Balachandran.K.K.,Iyer,T.S.G.,Madhavan,P., Joseph, J., Perigreen,P.A., Raghunath,M.R., & Varghese, M.D., Eds),. Society of Fisheries Technologists (India), Cochin:pp. 463-472.
Trends in development in the prawn fishing techniques in India-A review
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Kuriyan,G.K.1965. Trends in development in the prawn fishing techniques in India-A review. Fishery Technology 2: 64 -68.
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Kailola, P.J., M.J. Williams, P.C. Stewart, R.E. Russell, A. McNee and C. Grieve. 1993. Australian Fisheries Resources. Bureau of Resource Sciences, Department of Primary Industries and Energy, and the Fisheries Research and Development Corporation. Australia. 422 pp.
Spawning of a filefish, Navodon modestus (Gunther)
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Murakami, Y. and T. Onbe. 1967. Spawning of a filefish, Navodon modestus (Gunther). Journal of the Faculty of Fish and Animal Husbandry 7: 63-75.
Studies on the fishery biology of the Filefish Navodon modestus (Gunther) in Korean Waters
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Park, B.H. 1985. Studies on the fishery biology of the Filefish Navodon modestus (Gunther) in Korean Waters. Bulletin of the Fisheries Development Agency 34: 1-64.
FAO yearbook. Fishery statistics. Capture production/ FAO annuaire. Statistiques des peches. Captures/ FAO anuario
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FAO. 2006. FAO yearbook. Fishery statistics. Capture production/ FAO annuaire. Statistiques des peches. Captures/ FAO anuario. Estadisticas de pesca. Capturas. Vol. 98/1. Rome/Roma, FAO. 560 pp.


text:
# Induction Proof: $\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2$

Prove by Mathematical Induction . . .

$$\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2$$ for all $n \geq 0$

I tried solving it, but I got stuck near the end . . .

a. Basis Step:

$1\cdot 2^1 = 0\cdot 2^{0+2}+2$

$2 = 2$

b. Inductive Hypothesis

$$\sum_{i=1}^{k+1} i \cdot 2^i = k \cdot 2^{k+2} +2$$ for $k \geq 0$

Prove k+1 is true.

$$\sum_{i=1}^{k+2} i \cdot 2^i = (k+1)\cdot 2^{k+3}+2$$

$\big[RHS\big]$

$k\cdot 2^{k+3}+2^{k+3}+2$

$\big[LHS\big]$

$$\sum_{i=1}^{k+2} {i \cdot 2^{i}}$$

$= \underbrace{\sum_{i=1}^{k+1} i \cdot 2^i} + (k+2)\cdot 2^{k+2}$ (Explicit last step)

$= \underbrace{k\cdot 2^{k+2}+2}+(k+2)\cdot 2^{k+2}$ (Inductive Hypothesis Substitution)

$= k\cdot 2^{k+2}+2+k\cdot 2^{k+2}+2^{k+3}$

$= 2k\cdot 2^{k+2} + 2^{k+3} + 2$

My [LHS] has one too many $2k\cdot 2^{k+2}$ or did it just do it completely wrong?

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# Math Help - Physics problem; Find expression for velocity with varying acceleration

1. ## Physics problem; Find expression for velocity with varying acceleration

Hi. It's been 25 years since my last calculus class and I'm beyond rusty. I hope somebody her might be able to lend me a hand.

I'm working on a machine that discharges spherical solids horizontally in still air at a known speed. I'd like to study the sphere's speed over set time and/or distance intervals. The sphere will be slowed by aerodynamic drag. The standard drag formula D=.5 p (V^2) Cd A [where D is drag force, p is air density, V is velocity, Cd is coefficient of drag, and A is cross sectional area of sphere] can be used to determine the force that decelerates the sphere. As the force tending to decelerate the sphere is a function of velocity, it constantly decays after the sphere is discharged from the machine.

So I'm looking for an expression for V in terms of distance and an expression for V in terms of time.

I hope I've explained what I'm trying to do well enough. Let me know if I can clear up anything. Thanks.

Dave

2. ## Re: Physics problem; Find expression for velocity with varying acceleration

Originally Posted by Wayintense
Hi. It's been 25 years since my last calculus class and I'm beyond rusty. I hope somebody her might be able to lend me a hand.

I'm working on a machine that discharges spherical solids horizontally in still air at a known speed. I'd like to study the sphere's speed over set time and/or distance intervals. The sphere will be slowed by aerodynamic drag. The standard drag formula D=.5 p (V^2) Cd A [where D is drag force, p is air density, V is velocity, Cd is coefficient of drag, and A is cross sectional area of sphere] can be used to determine the force that decelerates the sphere. As the force tending to decelerate the sphere is a function of velocity, it constantly decays after the sphere is discharged from the machine.

So I'm looking for an expression for V in terms of distance and an expression for V in terms of time.

I hope I've explained what I'm trying to do well enough. Let me know if I can clear up anything. Thanks.

Dave
(Borrowed liberally from Fowler's "Analytical Mechanics", 4 ed.)

This is going to be a bit strange if you haven't seen it before. I'll give you some guidance through the solution and have you fill in the steps as you go.

Initially, t = 0, v(0) = const. (That's the best we can do for an initial speed without more information.)

I am going to neglect the weight of the object (so no mg in the problem) and I'm going to assume that the force on the sphere is going to be strictly in the horizontal direction as I am also going to assume that the drag force is horizontal. You can work without these assumptions, but the problem gets really nasty really quickly.

So. We know that
$F(v) = m \frac{dv}{dt}$

$m \frac{dv}{dt} = - \frac{1}{2} \rho C_d A v^2$

This is a bit bulky so I'm going to define
$\alpha = \frac{\rho}{2}C_d A$

and our equation becomes
$m \frac{dv}{dt} = - \alpha v^2$

This is a separable differential equation. I'll leave the details here to you.

So doing the integration and a little cleaning up we have
$v = \frac{v_0}{\frac{\alpha v_0}{m} \cdot t + 1}$

(Recall the definition of $\alpha$ before you quote your answer.)

For the last part let us make a new definition:
$v = \frac{v_0}{kt + 1}$

Where
$k = \frac{\alpha v_0}{m}$

Then the rest falls into place:
x = dv/dt, integrate, solve this for t, then plug this into the equation above for t and there you have it.

Let's see how far you can go with this. Come back if you need more.

-Dan

3. ## Re: Physics problem; Find expression for velocity with varying acceleration

Hi Dan. Wow! Great help; thanks!

I'm stuck at the diferential equation, though. A friend of mine came up with a different expresion for v. I've been playing around with Wolfram Alpha and I can't replicate his expression or yours. If you wouldn't mind walking me through some of the intermediate dif eq seperation and integration steps, I'd greatly appreciate it. Thanks!

Dave

4. ## Re: Physics problem; Find expression for velocity with varying acceleration

Hi Dan.

Got it! Found my mistake.

Thnak you!

Dave


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## Definition

The Affine cipher is a type of simple substitution cipher and as such uses a fixed ciphertext alphabet over the entire message. The ciphertext alphabet gets derived from the plaintext alphabet using an affine mathematical function (also called linear function) as the key.

## Affine function

Simply put, an affine function is the process of multiplying a value $x$ by a constant $a$, then adding a constant $b$ to it.

As we want to make sure we don’t leave the scope of our alphabet with length $m$, we apply the $\text{mod }m$ operation at the end (we subtract $m$ from the result until we get a value smaller than $m$).

Hence, an affine function $f$ can be represented as $f(x)=ax+b\text{ mod }m$.

## How does Affine cipher work?

For this example, we use the Latin alphabet A-Z with length $m=26$ as our plaintext alphabet and the affine function $f(x)=5x+8$ with $a=5,b=8$.

First, we map each letter in the alphabet to its numeric equivalent by taking its position in the alphabet (starting with 0), like so:

Now we apply the affine function $f$ to each of the values above (modulo $m$):

Finally, we convert back the numbers to their letter equivalents:

This gives us the map to encrypt and decrypt any message using the Affine cipher key $f(x)=5x+8$ and the Latin alphabet A-Z.


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New answers tagged rs485

0

RS-232 is single-ended, meaning that the signal is referenced to the ground, while RS-485 is differential - signal is referenced between A and B. That's before we even talk about TE/RE(DE) signalling of half-duplex. What you need is a signal converter between single-ended (UART/RS232) to differential to even start communicating. Whether you implement it ...

1

RS485 networks should just have the 120 ohm terminations on each extreme end of the two wire bus. The RS485 bus driver is designed to handle the DC current flow for this pair of termination resistors. If you build a small network of 3, 4, or maybe even 5 devices the driver will typically have enough drive strength to handle terminations at every node. You ...

0

Step 1) Get a serial terminal program (like realterm) Step 2) Set the device to your RS485 controller Step 3) Set the baud rate (the default for the temp controller is 19200 baud) Step 4) Set the stop bits and parity bits 8, N, 1 (8 bit, no parity, 1 stop) Step 5) EN26Parameter has the same meaning of cycle time for heating action .Parameter ...

1

Here is what I have gathered here from the answers, comments, and some additional research: 1) The cable that shipped with the device should work for my purposes. However, I will need to be able to install the correct driver(s). Upon further research, I was able to figure out that the device manufacturer downloads include a Windows installer for this ...

1

Is it necessary to do the ethernet cable splicing as indicated in the above link, or should I simply be able to use the provided USB cable? If you can find drivers for the R Pi then you can use the converter. I'd start by finding out what chip is in the propriety RS485 to USB, they might have a linux driver. Is it likely that the shipped cable is ...

0

Managing with Profibus over decades as field engineer, I had never found some exotic solution. It's always used with DB9 connectors with termination switches or pass through for daisy chaining. By the way, Profibus max. speed is 12 MBaud, RS485 physical layer. The only weird part are PCB inductors, probably needed to limit $\dfrac{di}{dt}$ in case of ...

0

Impedance is always defined by geometry of conductors and dielectric with respect to (wrt) each other (DM) and wrt power ground and/or earth ground. (CM). Saturn PCB design.exe. May tell you for a typ. Fibre/epoxy dielectric that 50 Ohms is somewhere between 0.5 to 1:1 diameter/gap and 120 Ohms is higher ratio. A track pair or short wire pair may be 1nH/...

2

Yes, you do want to keep the trace impedance on the board as close to 120Ω as you can, mainly because this affects how the signal propagates on the cables attached to it. Presumably these devices are being daisy-chained together, and the reflections caused by impedance discontinuities will accumulate to reduce your overall signal integrity. There are ...

0

With such a small distance and baud rate, the matching will probably not matter because the speed is low, reflections and parasitic effects will be minimal. Parasitic effects start to take hold when you get into the 10's of MHz. Because RS485 is differential, it does not need a ground plane, you could provide shielding if you like to minimize noise. You ...

1

No problem going to 2f is = 50 Mbps. The probability of error depends solely on the Voltage becoming the wrong polarity when the discriminator has computed the polarity for that bit.. What affects the SNR? , that determines the BER. The slew rate indicates a variable amplitude and thus a variable SNR declining signal level, this also means a declining ...

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# Probability and Integrals

Suppose $f(x,y) = c$ for $0\lt y\lt x\lt 1$ and $0$ outside. What is $P(X+Y \leq 1)$? What is $P(X^2+Y^2 \leq 1)$?

So

\begin{equation*} P(X+Y \leq 1) = \int_{0}^{1} \int_{0}^{1-x} 2 \ dy \ dx? \end{equation*}

Likewise,

\begin{equation*} $P(X^2+Y^2 \leq 1) = \int_{0}^{1} \int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} 2 \ dy \ dx$? \end{equation*}

This is assuming that $c=2$.

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For some reason the LaTeX is not parsing. – PEV Nov 1 '10 at 14:40
Fixed. Both < and > give problems, because they are initially interpreted as HTML. Try either \lt and \gt, or use the backslash as an escape character, \< and \>. – Arturo Magidin Nov 1 '10 at 14:41
@GeorgeS Please avoid minor edits on questions more than 4 years old (especially to edit incorrectly). – Did May 21 '15 at 10:16
Okay sure. Will do – George Simpson May 21 '15 at 10:17

Since the joint density is constant on the support region, you can get your answers by considering areas. The answer in each case is the area that corresponds to the event in question divided by the total area of the support region.

Thus, to calculate $P(X + Y \leq 1)$, you want the area of the lower triangular region below (i.e., the region for which $x + y \leq 1$), divided by the total area of the triangle.

This is $$\frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}.$$

Similarly, to calculate $P(X^2 + Y^2 \leq 1)$, you want the area of the circle sector divided by the total area of the triangle.

This is $$\frac{\frac{\pi}{8}}{\frac{1}{2}} = \frac{\pi}{4}.$$

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So $P(X+Y \leq 1)$ also equals $\int_{0}^{1/2} \int_{y}^{1-y} 2 \ dx \ dy$? Likewise, $P(X^2+Y^2 \leq 1) = \int_{0}^{0.5} \int_{y}^{\sqrt{1-y^2}} 2 \ dx \ dy$? – PEV Nov 1 '10 at 15:42
Right on the first one. For the second one, though, the $y$-coordinate of the intersection is $\frac{\sqrt{2}}{2}$. (Do the algebra to see why.) – Mike Spivey Nov 1 '10 at 15:44
Are there any ways of getting the bounds without a picture? How did you go about graphing $x+y \leq 1$? First graph $y \leq 1-x$ and $x \leq 1-y$? – PEV Nov 1 '10 at 17:46
@Trevor: Plop's answer shows one way to do the first without a picture. However, I recommend doing the picture. When I'm evaluating a double integral I nearly always find it helpful to draw a picture of the region of integration. – Mike Spivey Nov 1 '10 at 19:59
@Trevor: As far as graphing $x+y \leq 1$, I graphed $y \leq 1 - x$. You don't need the other, too (as it gives the same graph). – Mike Spivey Nov 1 '10 at 19:59

No, $P(X+Y \leq 1 ) = \int_0^1 \int_0^{\min (x,1-x)} 2 dy dx = \int_0^{1/2} \int_0^x 2 dy dx + \int_{1/2}^1 \int_0^{1-x} 2 dy dx = 1/4+1/4=1/2$

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