Mathematical foundations of social anthropology by Paul A. Ballonoff

By Paul A. Ballonoff

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H+1-. 0-h+l P (4,4) r ,6. h + 2 ( I P (4,4) (t-2) Essentially, everything depends on the value of h, and on the initial β for the initial population(s). "regular" behavior. ) as δ > 3, depending on initial R, and dependent on the initial inbreeding of the initial pair, and on the "age structure" p^, ρ^ of breeding pairs after that. Notice, we do not have recursion in the proportions p.. or dependence of ρ 13 (t) other than for the same time period t, because we assume no on any values of relationship (independence) if fertility and matrix type by "age class", providing the class exists at all in a particular time period t.

For i ψ j, or Therefore, at time t, = δ ^ + 1 for all i, j. = i for i = j, χ „ = + 1 We get, for each pair-type i, j δ. Γ 2 ( ί "ij-Slj + 1) G tJ<1 + f a>(t) Concentrating on the exponent, we notice 26.. V δ. " . for convenience. i] Δ f^'" 2; for G. '^'~δ.. + 2; for G t ~ x, t ι] ι] t 2 or δ. "small", 13 13 2. Also, recall that in general, δ. is 13 — a small integer such as 0, 1, 2, 3, 4. Looking at the inbreeding of each pair's parents, we can notice that the inbreeding f recurrence: of the ancestors of a particular pair will, in fact, be defined by a the parents of {(i, j) | i = j} are precisely the pair (i - 1, j - 1), or at least the inbreeding is the same, so that f^ here becomes 1 <Δ1-2, j-2 + W 1 Θ.

2; for G t ~ x, t ι] ι] t 2 or δ. "small", 13 13 2. Also, recall that in general, δ. is 13 — a small integer such as 0, 1, 2, 3, 4. Looking at the inbreeding of each pair's parents, we can notice that the inbreeding f recurrence: of the ancestors of a particular pair will, in fact, be defined by a the parents of {(i, j) | i = j} are precisely the pair (i - 1, j - 1), or at least the inbreeding is the same, so that f^ here becomes 1 <Δ1-2, j-2 + W 1 Θ. i-1, j - 1 - 2*1-2, 3-2 = I<2> 15 / ( „ a i-2, X j J 17 F o r d i a g o n a l e n t r i e s i n R, we h a v e e n t r y (i, Now, 11 = 11 t l A(t> .

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