Maynard Smith and Szathm\'ary's book, The Major Transitions in Evolution, describes eight major events in the evolution of life on Earth and identifies a common theme that unites these events. In each event, smaller entities came together to form larger entities, which can be described as symbiosis or cooperation. Here we present a computational simulation of evolving entities that includes symbiosis with shifting levels of selection.  In the simulation, the fitness of an entity is measured by a series of one-on-one competitions in the Immigration Game, a two-player variation of Conway's Game of Life. Mutation, reproduction, and symbiosis are implemented as operations that are external to the Immigration Game. Because these operations are external to the game, we are able to freely manipulate the operations and observe the effects of the manipulations. The simulation is composed of four layers, each layer building on the previous layer. The first layer implements a simple form of asexual reproduction, the second layer introduces a more sophisticated form of asexual reproduction, the third layer adds sexual reproduction, and the fourth layer adds symbiosis. The experiments show that a small amount of symbiosis, added to the other layers, significantly increases the fitness of the population. We suggest that , in addition to providing new insights into  biological and cultural evolution , this model of symbiosis may have practical applications in evolutionary computation, such as in the task of learning deep neural network models .
We present a computational simulation of evolving entities that includes symbiosis with shifting levels of selection. Evolution by natural selection shifts from the level of the original entities to the level of the new symbiotic entity. In the simulation, the fitness of an entity is measured by a series of one-on-one competitions in the Immigration Game, a two-player variation of Conway's Game of Life. Mutation, reproduction, and symbiosis are implemented as operations that are external to the Immigration Game. Because these operations are external to the game, we are able to freely manipulate the operations and observe the effects of the manipulations. The simulation is composed of four layers, each layer building on the previous layer. The first layer implements a simple form of asexual reproduction, the second layer introduces a more sophisticated form of asexual reproduction, the third layer adds sexual reproduction, and the fourth layer adds symbiosis. The experiments show that a small amount of symbiosis, added to the other layers, significantly increases the fitness of the population. We suggest that the model may provide new insights into symbiosis in biological and cultural evolution .
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Maynard Smith and Szathm\'ary's book, The Major Transitions in Evolution, describes eight major events in the evolution of life on Earth and identifies a common theme that unites these events. In each event, smaller entities came together to form larger entities, which can be described as symbiosis or cooperation. Here we
We
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Evolution by natural selection shifts from the level of the original entities to the level of the new symbiotic entity.
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, in addition to providing
the model may provide
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symbiosis in
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, this model of symbiosis may have practical applications in evolutionary computation, such as in the task of learning deep neural network models