A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

A compact proof of Fisher�s Fundamental Theorem for multiple loci

A systematic method is formulated to carry out theoretical analysis in a multilocus multiallele genetic system. As a special application, the Fundamental Theorem of Natural Selection is proved (in the continuous time model) for a multilocus multiallele system if all pairwise linkage disequilibria are zero.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Socio-economic survey of fisher families, 1958-59

Fisher families had been investigated by the Department of Commerce and Industries in earlier economic surveys conducted in 1935, 1938 and 1939 (Das Gupta, 1937 a & b; 1944 a & b). These surveys were directed at the general economic conditions of the urban and rural sectors of the population and therefore did not provide much information in particular on the life of the fisherman or his environment. The Department of Fisheries in 1954 conducted a rapid enquiry into the living conditions of fishermen to obtain some data on their income, indebtedness and general social conditions, at the request of the Canadian Co-operative Consultant for incorporation in his report on the "Status and Possibilities of Co-operative Development of the Fisheries of Ceylon” (MacDonald, 1954). The present survey was undertaken to provide more definite socio-economic information on the fishermen of Ceylon, covering such aspects as income, expenditure, indebtedness and living conditions. The survey was started in June, 1958, but was interrupted by the unsettled conditions of the Island at the time, taking therefore a little over a year for completion. Some of the data collected was used as a basis for a report on the living conditions of fishermen, incorporated in the “Guide to the Fisheries of Ceylon", a hand book published by the Department of Fisheries (Anon. 1958).

Monitoring of the socio-economics status of fisher communties on Lake Victoria, Uganda

The objectives of the study was to provide information on the changes in the socio- economis status of the fisher communities.The study aimed at contributing to the following selected OVIs of the IFMP log frame:"10% increased in incomes from fish catches by fishing crews by EOP",20% women in BMUs reporting increased household incomefrom fishing by EOP","50% women and fishing crews in BMUs reporting greater say in fisheries decision making.

Assessment of impact of ten days fishing ban in the major spawning grounds of hilsa (Tenualosa ilisha, Fisher and Bianchi, 1984)

A study was undertaken to find out the impact of ten days fishing ban in the major spawning grounds of hilsa during October to December. The study revealed a positive impact of fishing ban during spawning season on reproduction success of hilsa. Proportionate distribution of male and female hilsa also showed a significant level of distribution in and around the spawning grounds where the ratio was 35:65. Percent of oozing hilsa during fishing ban period in the spawning grounds was observed 1.61%. About 5% spent hilsa was observed in the fish landing centers and was compared with the data of Global Environment Facility (GEF) and Bangladesh Fisheries Research Institute (BFRI) studies and was found about 2.80-3.57 times higher than that of the findings of 2002 and 2003. Estimated egg production value showed about 46,800 Kg of eggs could have been produced that indicating a positive impact of 10 days fishing ban in spawning season. Abundance of higher percentages of gravid hilsa was found which were not available in the same quantity and condition in the non-fishing ban period. During the present investigation, fairly higher amount of spent hilsa and juveniles were also observed in the spawning grounds. Along with the jatka fry, spawn and fries of other fishes were also found in higher quantity than the previous years and thus it is assumed that fishing ban also might have positive impact on the successful breeding of other fishes. Overall, the fishing ban was found effective for successful breeding of hilsa.

Co-management approach on fisher group: a case study on Ramsar site, Tanguar haor in Bangladesh

In Bangladesh, wetlands are managed through leasing system traditionally from time immemorial. Recently the Government accepted co-management approach for wetland fisheries management and this approach is being practiced in few wetlands for maximize revenue income. A study was carried out to evaluate trend and impact of co-management in Tanguar haor (a Ramsar site wetland) on fisheries resources and livelihood of resident people in the immediate vicinity of the wetland. In Tanguar haor, conflict between leaseholders and the local community was a common phenomenon in the past. Since 2003 the district administration of Sunamganj has been managing the vast wetland resources, however, local people participation was ignored in haor management system. Average monthly fish catch of fishermen increased by 17% after introduction of co-management system and 7 fish species reappeared after introduction of co-management. Average monthly volume of fish catch has increased from 70 kg to 87 kg. A well-defined management structure has been developed for integration of all people of Tanguar haor which would enable them to raise voice jointly and influence policy in their favour.

Youth power: interview [with an] artisanal fisher

Michael Rojas, a 24-year-old artisanal fisher from Caballo Island in Costa Rica, believes that youth can pursue fishing in an artisanally responsible and sustainable way.

Issues of HIV/AIDS/ health among the fisher communities of Lake Albert and Kyoga

The fisheries resources of Lakes Albert and Kyoga present a high potential for economic growth, food, employment and foreign earnings. However, livelihoods appear to be compromised with the emergence and rapid spread of HIV/AIDS in the fisher communities of L. Albert and Kyoga. HIV/AIDS is considered a silent epidemic that is unique, posing a great challenge to the fisheries managers, health service providers, development planners and the resource users themselves. Fishers have high HIV prevalence, as well as AIDS-related illnesses and mortality rates. The high HIV prevalence rates among the fishing communities in Uganda is between 10-40% compared to the national rates which lie between 6% and 7%. This indicates that the national programmes have not adequately addressed the plight of the fishing communities of Lakes Albert, and Kyoga and the consequences have been devastating. Men and women living in fishing villages across the world have been found to be between five and ten times more vulnerable to the disease than other communities (Tarzan et al 2005, FAO, 2007). The present prevalence rates among the fishing communities stands at 10 to 40 % (LVFO, 2008). Meanwhile the same fishing communities are the essential labour for the Lakes’ fishery industry which is thriving nationally and internationally. That resource potentially can alleviate poverty and the HIV/AIDS threat. Fishing communities are the hidden victims of the disease, mixing patterns with the general population could act as a reservoir of infection that could spill over into the general population to drive the epidemic. On L. Albert, a quarter of the fisher folk were HIV-positive by 1992 compared to 4% in a nearby Agricultural village. Since then, there have been no targeted studies to address or monitor the prevalence rates eight years later, yet the multiplicity factor is high. HIV/AIDS can be linked to unsustainable fisheries, as the labour force available would not go to deep waters to fish, instead would fish in the shallow waters as a coping mechanism. A further effect is the loss to National and local economies and reduced nutritional security for the wider population. HIV/AIDS remains a significant challenge that has created a mosaic of complexity in the fishery sector. This needs to be addressed. It is, therefore, paramount that a comprehensive study was under taken to address this pandemic and the phenomenon of HIV/AIDS based on the study objectives. 1. To determine the trend in HIV/AIDS infection among fishing communities and the factors affecting it 2. To assess the impacts of HIV/AIDS on fish production and the implications for fisheries management.