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--- 진화생물학:한곳_짝짓기_경쟁 [2021/07/30 15:45] – [검증] jiwon
+++ 진화생물학:한곳_짝짓기_경쟁 [2023/09/05 15:46] (current) – external edit 127.0.0.1
@@ Line 131: / Line 131: @@
 $$
 \begin{cases}
-x'_1 = f_1(x_1,...,x_{21}) \approx \left.\frac{\partial f_{1}}{\partial x_1}\right\vert_{(1,0,...,0)} x_1 + \cdots + \left.\frac{\partial f_{1}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
+x'_1 = f_1(x_1,...,x_{21}) \approx \left.\frac{\partial f_{1}}{\partial x_1}\right\vert_{(1,0,...,0)} (x_1 - 1) + \cdots + \left.\frac{\partial f_{1}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
-x'_2 = f_2(x_1,...,x_{21}) \approx \left.\frac{\partial f_{2}}{\partial x_1}\right\vert_{(1,0,...,0)} x_1 + \cdots + \left.\frac{\partial f_{2}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
+x'_2 = f_2(x_1,...,x_{21}) \approx \left.\frac{\partial f_{2}}{\partial x_1}\right\vert_{(1,0,...,0)} (x_1 - 1) + \cdots + \left.\frac{\partial f_{2}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
 \qquad\qquad\cdot\\
 \qquad\qquad\cdot\\
 \qquad\qquad\cdot\\
-x'_{21} = f_1(x_1,...,x_{21}) \approx \left.\frac{\partial f_{21}}{\partial x_1}\right\vert_{(1,0,...,0)} x_1 + \cdots + \left.\frac{\partial f_{21}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
+x'_{21} = f_{21}(x_1,...,x_{21}) \approx \left.\frac{\partial f_{21}}{\partial x_1}\right\vert_{(1,0,...,0)} (x_1 - 1) + \cdots + \left.\frac{\partial f_{21}}{\partial x_{21}}\right\vert_{(1,0,...,0)} x_{21}\\
 \end{cases}
 $$
+이제 이 20x20 행렬의 가장 큰 고윳값을 $r$과 $s$에 따라 그리고, 고윳값이 1보다 작은 영역을 보면 다음을 얻는다.
+{{ :진화생물학:out.png?600 |}}
+이로써 $N=2$일 때 평형 성비는 $r=0.214$가 됨을 알 수 있다.
+그리고 한 쌍이 $(RRXR)$이라고 가정하고 $x'_2,x'_3,x'_4,x'_5,x'_9$를 가지고 5x5 행렬을 써보면 이 행렬이 윗 절의
+$$
+\begin{pmatrix}
+pu & 0 & \frac{1}{4N} & 0 & 0\\
+(1-p)u & 0 & \frac{2N-1}{4N} & 0 & 0\\
+& pu & \frac{1}{4N} & \frac{1}{4N} & 0\\
+& (1-p)u & \frac{2N-1}{4N} & \frac{2N-1}{4N} & 1\\
+(N-1)p & (N-1)p & \frac{N-1}{2N} & \frac{2N-1}{4N} & 0
+\end{pmatrix}
+$$
+와 같음을 확인할 수 있다.
 ======참고문헌======
   * W. D. Hamilton, //Extraordinary Sex Ratios//, Science **156**, 477--488 (1967).
   * P. D. Taylor and M. G. Bulmer, //Local Mate Competition and the Sex Ratio//, J. Theor. Biol. **86** 409--419 (1980).