Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of the Feldman-Karlin Conjecture on the Maximum Number of
  Equilibria in an Evolutionary System   Feldman and Karlin conjectured that the number of isolated fixed points for
deterministic models of viability selection and recombination among n possible
haplotypes has an upper bound of 2^n - 1. Here a proof is provided. The upper
bound of 3^{n-1} obtained by Lyubich et al. (2001) using Bezout's Theorem
(1779) is reduced here to 2^n through a change of representation that reduces
the third-order polynomials to second order. A further reduction to 2^n - 1 is
obtained using the homogeneous representation of the system, which yields
always one solution `at infinity'. While the original conjecture was made for
systems of viability selection and recombination, the results here generalize
to viability selection with any arbitrary system of bi-parental transmission,
which includes recombination and mutation as special cases. An example is
constructed of a mutation-selection system that has 2^n - 1 fixed points given
any n, which shows that 2^n - 1 is the sharpest possible upper bound that can
be found for the general space of selection and transmission coefficients.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: eess