Sibling rivalry between seeds within a fruit: Some population genetic models

Competition between seeds within a fruit for parental resources is described using one-locus-two-allele models. While a �normal� allele leads to an equitable distribution of resources between seeds (a situation which also corresponds to the parental optimum), the �selfish� allele is assumed to cause the seed carrying it to usurp a higher proportion of the resources. The outcome of competition between �selfish� alleles is also assumed to lead to an asymmetric distribution of resources, the �winner� being chosen randomly. Conditions for the spread of an initially rare selfish allele and the optimal resource allocation corresponding to the evolutionarily stable strategy, derived for species with n-seeded fruits, are in accordance with expectations based on Hamilton�s inclusive fitness criteria. Competition between seeds is seen to be most intense when there are only two seeds, and decreases with increasing number of seeds, suggesting that two-seeded fruits would be rarer than one-seeded or many-seeded ones. Available data from a large number of plant species are consistent with this prediction of the model.

A high precision instrument to measure angular and binocular deviation introduced by aircraft windscreens by using a shadow casting technique

Objects viewed through transparent sheets with residual non-parallelism and irregularity appear shifted and distorted. This distortion is measured in terms of angular and binocular deviation of an object viewed through the transparent sheet. The angular and binocular deviations introduced are particularly important in the context of aircraft windscreens and canopies as they can interfere with decision making of pilots especially while landing, leading to accidents. In this work, we have developed an instrument to measure both the angular and binocular deviations introduced by transparent sheets. This instrument is especially useful in the qualification of aircraft windscreens and canopies. It measures the deviation in the geometrical shadow cast by a periodic dot pattern trans-illuminated by the distorted light beam from the transparent test specimen compared to the reference pattern. Accurate quantification of the shift in the pattern is obtained by cross-correlating the reference shadow pattern with the specimen shadow pattern and measuring the location of the correlation peak. The developed instrument is handy to use and computes both angular and binocular deviation with an accuracy of less than +/- 0.1 mrad (approximate to 0.036 mrad) and has an excellent repeatability with an error of less than 2%. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769756]

Evolution of polyembryony: Consequences to the fitness of mother and offspring

Polyembryony, referring here to situations where a nucellar embryo is formed along with the zygotic embryo, has different consequences for the fitness of the maternal parent and offspring. We have developed genetic and inclusive fitness models to derive the conditions that permit the evolution of polyembryony under maternal and offspring control. We have also derived expressions for the optimal allocation (evolutionarily stable strategy, ESS) of resources between zygotic and nucellar embryos. It is seen that (i) Polyembryony can evolve more easily under maternal control than under that of either the offspring or the ‘selfish’ endosperm. Under maternal regulation, evolution of polyembryony can occur for any clutch size. Under offspring control polyembryony is more likely to evolve for high clutch sizes, and is unlikely for low clutch sizes (<3). This conflict between mother and offspring decreases with increase in clutch size and favours the evolution of polyembryony at high clutch sizes, (ii) Polyembryony can evolve for values of “x” (the power of the function relating fitness to seed resource) greater than 0.5758; the possibility of its occurrence increases with “x”, indicating that a more efficient conversion of resource into fitness favours polyembryony. (iii) Under both maternal parent and offspring control, the evolution of polyembryony becomes increasingly unlikely as the level of inbreeding increases, (iv) The proportion of resources allocated to the nucellar embryo at ESS is always higher than that which maximizes the rate of spread of the allele against a non-polyembryonic allele.Finally we argue that polyembryony is a maternal counter strategy to compensate for the loss in her fitness due to brood reduction caused by sibling rivalry. We support this assertion by two empirical evidences: (a) the extent of polyembryony is positively correlated with brood reduction inCitrus, and (b) species exhibiting polyembryony are more often those that frequently exhibit brood reduction.