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This Concept Map, created with IHMC CmapTools, has information related to: n7. Evolution and Fitness Landscapes, In short, in the mid-term of the process, the adaptive branching populations should begin to climb local hills. ???? Again, this is just what happened in the Cambrian explosion. After species with a number of different major body plans sprang into existence, this radical creativity slowed, and then dwindles d to slight tinkering. Evolution concentrated its sights closer to home, tinkering and adding filigree to its inventions., Non-equilibrium systems can be robust also, in the near-equilibrium states, where small changes in construction yield small changes in behavior. But when non-equilibrium systems are far-from equilibrium, small changes in initial conditions yield large changes in behavior, and these systems are very sensitive to initial conditions. These structures are unstable. ???? There is a clear link between the stability of the dynamic system and the ruggedness of the landscape over which it adapts., NK landscapes have a well defined correlation length. Basically, the length shows how far apart points on the landscape can be, so that knowing the fitness at one point still allows us to project something about the fitness of the second point. On NKlandscapes, this correlation falls off exponentially with distance. ???? A long-jump adaptation on NKlandscapes with K = 2, is plotted for different values of N. Each curve shows the fitness attained on the y-axis, plotted against the number of tries. Each curve, showing fitness with increasing Nnodes in each jump, increases rapidly at first, and then ever more slowly, suggesting exponential slowing with lengthening correlation length., If an adapting population were to “jump” randomly into such a landscape many times, and climb uphill each time to a peak, we would find that there is a relationship between how high the (highest?) peak is and how often the population climbed to it. ???? If we turned our landscape upside down and sought instead the lowest valleys, we would find the deepest valleys drain the widest basins., Therefore, Kmeasures the epistatic coupling among genes in one organism, and how interdependent they are. The “fitness contribution” a given gene makes to the entire genome can be modeled by assigning a random number between 0.0 and 1.0for each of the combination of states of that gene and its Kepistatic inputs. The fitness of the whole genotype is the average for the fitness contributions of each gene. The result is the fitness landscape. ???? The same NKmodel can be used to show how traits of one organism interact with the traits of other organisms in an ecosystem., All organisms, and all complex systems, evolve on correlated landscapes tuned somewhere between “Fujiyama” K = 0 landscapes, and K = N – 1 "moonscapes", landscapes that are rugged, but not random. ???? When K is low, peaks cluster near one another. With few conflicting constraints, the landscape is non-isotropic: there is a special region where the high peaks cluster. Therefore, it is useful for an adaptive process to locate this special region in the space of possibilities., We attempt to capture the right statistical features of real landscapes with our model of correlated landscapes. Thus we are able to understand the kind of epitsasis that occurs in organisms and its effect on landscapes and evolution without needing to establish all the myriad possible details. ???? Assign to each of Ngenes Kother genes chosen at random. The contribution of each gene to the whole genotype depends on its own allele, 1or 0,plus the 1or 0allele of each of the Kother genes that are its inputs. Hence the fitness contributions depend on the alleles present in K + 1genes. Since each gene can be in one of its alleles, 1or 0, the total number of possible allele combinations is 2(K+1)., Recombination allows an adapting populations to make use of large-scale features of the landscape to find high peaks. These same large peaks would be relatively or fully invisible to haploid populations climbing uphill guided only by local clues. ???? If the highest peaks “drain” the largest basins, then recombination can also make use of this large-scale feature. If two coupled organisms are high up on the sides of high peaks, recombination allows the offspring to have a very good chance of landing at spots that are already of high fitness, and more importantly, a spot from where they can climb to still higher peaks., Unlike the jagged landscapes with jagged cliffs plummeting and soaring from each perch, these landscapes (correlated, where nearby peaks tend to have similar heights) are smooth and flat, or smooth and rounded, or even rugged. Evolution can proceed on such (correlated) landscapes. Rugged landscapes may be staggering, but they are easy to scale compared to random moonscapes. ???? Natural selection alone does not shape the biosphere. Evolution requires landscapes that are not random. The deepest source of such landscapes may be self-organization. This is one part of the marriage of self-organization and selection., The rate of collision of interacting molecules colliding with one another depends on the velocities of the molecules. Temperature is a measure of the average motion of the molecules, the average kinetic energy. High temperature means that the molecules are in violent random motion. Zero temperature means that the molecules are not moving at all. ???? Energy landscapes drain downhill and are just the inverse of fitness landscapes, which move uphill. The statistical landscape features are the same in either direction., Self-organization is a prerequisite for evolvability, and it generates the kinds of structures that can benefit from natural selection. It generates structures that can evolve gradually, that are robust, for there is an inevitable relationship among spontaneous order, robustness, redundancy, gradualism, and correlated landscapes. ???? Systems with redundancy have the property that many mutations cause no or only slight modifications in behavior. Redundancy yields gradualism., The first essential step of an adaptive walk is that the genotype climbs uphill until a local peak is reached. Such local peaks are higher than any other point in the immediate vicinity, but may be far lower than the highest peak, which is the global optimum. ???? Adaptive walks stop at such local peaks. There is no higher point in the immediate vicinity, so they are trapped, with no way to get to the distant summits., Over evolutionary time, the very process of evolution itself undoubtedly evolves, perhaps driving toward the Red Queen regime, perhaps toward the ESS regime. ???? Perhaps there is a phase transition between the chaotic and ordered regimes in the evolution of co-evolution. Perhaps the evolution of co- evolution tends to favor strategies that lie in this regime, near the edge of chaos., Kauffman - We are seeking a new conceptual framework to state and study the interleaving of self-organization, selection, chance, and design. ???? The first theme is self-organization. Whether we confront lipids spontaneously forming bi-lipid membranes vesicles, a virus self-assembling to a low energy state, the Fibonacci series of a pinecone phyllotaxis, the emergent order of parallel-processing networks of genes in the ordered regime, the origin of life as a phase transition in chemical reactions, the supra-critical behavior of the biosphere, or the patterns of evolution at higher levels, we have found the signature of law., It is the same with technological evolutions. Early inventions tend to be multiple and different, while later ones tend to be just simple improvements n the existing ones. ???? Mutations occurring early on in development of the fetus are adapting on a more rugged landscape than mutants occurring later on in development. Therefore, mutations occurring early tend to be more lethal than those occurring earlier., But when all minor variations cause catastrophic variations in the behavior of the system, or organism, the fitness landscape is essentially random; therefore no local clues exist to detect directions that are uphill toward distant peaks. ???? Search in such circumstances also becomes random. It is clear that if the landscape is random, providing no clues about good directions to search, then the only way to find the highest pinnacle is to search the entire space of possibilities., The NKmodel generates a family of increasingly rugged landscapes as K,the number of “epistatic" inputs per gene, increases. Increasing Kincreases the conflicting constraints. These increasing constraints make the landscape more rugged and multi-peaked. When Kreaches its maximum value (K = N-1), in which every gene is dependent on every other), the landscape becomes fully random. ???? Begin with a simple idealized kind of adaptive walk, a long jump adaptation, on a rugged landscape. Adaptive walks proceed by generating and selecting single mutations which lead to fitter variants. An adaptive walk proceeds step-by-step in the space of possibilities, marching steadfastly uphill to a local peak., But suppose we turn the K knob up the other way, to its maximum value, N – 1, so that every gene is affected by every other gene. ???? When K increases to its maximum value, N – 1, the fitness landscape is completely random., Mutations occurring early on in development of the fetus are adapting on a more rugged landscape than mutants occurring later on in development. Therefore, mutations occurring early tend to be more lethal than those occurring earlier. ???? The rate of slowing depends, in the NKmodel, on K. The slowing is faster when the conflicting constraints are higher and the landscape is more rugged. Adaptive walks on rugged landscapes eventually reach a local optimum and then cease further improvement., The “temperature” of the system specifies the probability of accepting a move that increases cost by any given amount. In the simulation, the algorithm wanders all over the space of possible tours. Lowering the temperature amounts to decreasing the probability of accepting moves that go the wrong way. Gradually the algorhythm settles into the drainage basins of deep, excellent minima. ???? Simulated annealing uses the same principle. In the case of the traveling salesman problem, one moves from a tour to a neighboring tour if the second tour is shorter. But, with some probability, one also accepts a move in the wrong direction; to a neighboring tour that is longer and “costs” more.