In the children's game of rock-scissors-paper, players each choose one of three strategies. A rock beats a pair of scissors, scissors beat a sheet of paper and paper beats a rock, so the strategies form a competitive cycle. Although cycles in competitive ability appear to be reasonably rare among terrestrial plants, they are common among marine sessile organisms and have been reported in other contexts. Here we consider a system with three species in a competitive loop and show that this simple ecology exhibits two counter-intuitive phenomena. First, the species that is least competitive is expected to have the largest population and, where there are oscillations in a finite population, to be the least likely to die out. As a consequence an apparent weakening of a species leads to an increase in its population. Second, evolution favours the most competitive individuals within a species, which leads to a decline in its population. This is analogous to the tragedy of the commons, but here, rather than leading to a collapse, the 'tragedy' acts to maintain diversity.
A general method for building and training multilayer perceptrons composed of linear threshold units is proposed. A simple recursive rule is used to build the structure of the network by adding units as they are needed, while a modified perceptron algorithm is used to learn the connection strengths. Convergence to zero errors is guaranteed for any boolean classification on patterns of binary variables. Simulations suggest that this method is efficient in terms of the numbers of units constructed, and the networks it builds can generalize over patterns not in the training set.
Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by 'star graphs', that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.
Though conventional OO design suggests programs should be built from many small objects, like Lego bricks, they are instead built from objects that are scale-free, like fractals, and unlike Lego bricks.
Large amounts of Java software have been written since the language's escape into unsuspecting software ecology more than ten years ago. Surprisingly little is known about the structure of Java programs in the wild: about the way methods are grouped into classes and then into packages, the way packages relate to each other, or the way inheritance and composition are used to put these programs together. We present the results of the first in-depth study of the structure of Java programs. We have collected a number of Java programs and measured their key structural attributes. We have found evidence that some relationships follow power-laws, while others do not. We have also observed variations that seem related to some characteristic of the application itself. This study provides important information for researchers who can investigate how and why the structural relationships we find may have originated, what they portend, and how they can be managed.
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