Exploiting the adaptation dynamics to predict the distribution of beneficial fitness effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depend on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remain nearly a constant for exponentially decaying distributions and increase when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.Comment: Communicated to PLOS ON

More nonexistence results for symmetric pair coverings

A $(v,k,\lambda)$-covering is a pair $(V, \mathcal{B})$, where $V$ is a $v$-set of points and $\mathcal{B}$ is a collection of $k$-subsets of $V$ (called blocks), such that every unordered pair of points in $V$ is contained in at least $\lambda$ blocks in $\mathcal{B}$. The excess of such a covering is the multigraph on vertex set $V$ in which the edge between vertices $x$ and $y$ has multiplicity $r_{xy}-\lambda$, where $r_{xy}$ is the number of blocks which contain the pair $\{x,y\}$. A covering is symmetric if it has the same number of blocks as points. Bryant et al.(2011) adapted the determinant related arguments used in the proof of the Bruck-Ryser-Chowla theorem to establish the nonexistence of certain symmetric coverings with $2$-regular excesses. Here, we adapt the arguments related to rational congruence of matrices and show that they imply the nonexistence of some cyclic symmetric coverings and of various symmetric coverings with specified excesses.Comment: Submitted on May 22, 2015 to the Journal of Linear Algebra and its Application

On moving averages

We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and which was observed to converge only numerically. Our analysis establishes a rigorous proof of convergence of their algorithm in a special case; moreover, limit is explicitly identified. Moving averages in Banach spaces and Kolmogorov means are also studied. Furthermore, we consider moving proximal averages and epi-averages of convex functions

Parity of Sets of Mutually Orthogonal Latin Squares

Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits. We extend the definition of parity from Latin squares to sets of mutually orthogonal Latin squares (MOLS) and the corresponding orthogonal arrays (OA). Suppose the parity of an $\mathrm{OA}(k,n)$ has an information content of $\dim(k,n)$ bits. We show that $\dim(k,n) \leq {k \choose 2}-1$. For the case corresponding to projective planes we prove a tighter bound, namely $\dim(n+1,n) \leq {n \choose 2}$ when $n$ is odd and $\dim(n+1,n) \leq {n \choose 2}-1$ when $n$ is even. Using the existence of MOLS with subMOLS, we prove that if $\dim(k,n)={k \choose 2}-1$ then $\dim(k,N) = {k \choose 2}-1$ for all sufficiently large $N$. Let the ensemble of an $\mathrm{OA}$ be the set of Latin squares derived by interpreting any three columns of the OA as a Latin square. We demonstrate many restrictions on the number of Latin squares of each parity that the ensemble of an $\mathrm{OA}(k,n)$ can contain. These restrictions depend on $n\mod4$ and give some insight as to why it is harder to build projective planes of order $n \not= 2\mod4$ than for $n \not= 2\mod4$. For example, we prove that when $n \not= 2\mod 4$ it is impossible to build an $\mathrm{OA}(n+1,n)$ for which all Latin squares in the ensemble are isotopic (equivalent to each other up to permutation of the rows, columns and symbols)

Diversification of Fish Culture and Exports among Major Shrimp-producing Countries of Asia: A Spatial and Temporal Analysis

Asian countries contribute nearly 90 per cent to global production of culture fisheries. Diversification of species is not happening in fish culture because of the high value shrimp commands in the export market. Shrimp farming is on the increase in all the major shrimp-producing Asian countries. Higher the growth in shrimp production, higher is the instability in production due to production risks associated with ecosystem complexities and disease incidences. Most of the shrimp-producing countries have been moving towards specialization of shrimp production for export because of the high price that the shrimp asserts in the international market. A comparison between the Asian countries for the period 1976-2002 has revealed that Malaysia has maintained low growth and low instability and higher diversification, and Bangladesh and Vietnam have diversified in fish exports. In a country-level comparison, India, Indonesia, Thailand and Philippines have shown moderate growth in production and export of shrimp. The instability associated with their shrimp production has also been moderate. Diversification in fish production as well as exports has been suggested for assured income to farmers and the country. It has been pointed that replacing, supplementing or rotating the shrimp farming with culture of other high-value fish species like Asian sea bass (Lates calcarifer), grouper (Epinephelus spp), mullets (Mugil spp) and milk fish (Chanos spp) culture may ease the risks in mono-cropping of shrimp.Agricultural and Food Policy,

Characterization of Radiation Modified Sago-Polyvinyl Alcohol Blends Films

Blends from sago starch, poly (vinyl alcohol)(PVA) and distilled water have been prepared and subjected to electron beam irradiation with doses ranging from 10 to 40 kGy to form hydrogels. The hydrogels were then cooled in refrigerator overnight to remove trapped bubbles formed during irradiation reaction. Films were subsequently produced by drying hydrogels in an oven. The characteristic of the irradiated blends and films were then determined. Poly (vinyl alcohol) solution was found to be viscous obviously after irradiation indicated the formation of irradiation induced crosslinking. Radiation degradation of sago starch solution was confirmed by observing the viscosity of the solution which was lowered after irradiation. The gel content of irradiated films was increased compared to unirradiated. Crosslinking/grafting had occurred in the blends at optimum dose of 20 kGy. The gel content of poly (vinyl alcohol) film was maximum at 30 kGy. Above 30 kGy, over crosslinking occurred as the film was shrunk to the smaller size. Melting temperature of PVA film as determined by Differential Scanning Calorimetry decreased with increasing irradiation dose. This indicate that cross linking had lowered the melting point of PVA film. The existence of only one peak of melting temperature by Thermo Gravimetric Analysis revealed the compatibility of the blends. Scanning Electron Miscroscopy studies on the surface morphology and freeze fracture revealed more evidence of the radiation induced crosslinking and grafting of the blends. Studies also done on effect of sago and PVA contents of the blend, addition and types of plastisizers added and irradiation dose on the quality of the film produced. Results show that irradiation has improved the tensile strength but elongation at break was slightly reduced for blends S25/P75, S50/P50 and S75/P25. The biodegradability of sago, PVA and blends films was studied by monitoring its weight loss for 6 months. Sago starch film was totally degraded in the first month of burial period but PVA film remain un intact for the last six months. Incorporating sago starch to the blend sago-PVA improved the weight loss up to 60% in six months