生命周期分为 n 个阶段，从卵到成虫。个体只有达到成虫阶段才能进行生产。p11、p22... 是生存概率，p12、p23... 过渡概率 R 是状态 n 到 1 的生产率。
答案1
此示例可用于进一步调整图形以满足您的需求。我之前没有更改过最终节点成人至n-1和n。
给出马尔可夫链的九个步骤的示例代码：
\documentclass[11pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,automata,decorations.markings,decorations.pathreplacing,decorations.text,backgrounds,shapes.geometric}
\begin{document}
\begin{tikzpicture}
[trans/.style={to path={ .. controls +(60:1.5) and +(120:1.5) .. (\tikztotarget) \tikztonodes}},radius=2cm]
\path (4,0) -- +(180:2cm) node(p0) {0} arc [start angle=-180, delta angle=-40] node(p1) {1};
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p0) arc [start angle=-180, delta angle=-32] (p1);
\draw[fill=blue!30, opacity=0.2] (p0) circle[radius=3mm] (p1) circle[radius=3mm];
\path[->] (p0) edge [trans,red,rotate=90] (p0);
\path[->] (p1) edge [trans,above,red,rotate=50] (p1);
\path (4,0) --+(160:1.6cm) node {$p_{01}$};
\path (4,0) --+(180:3.3cm) node[red,rotate=90] {$p_{00}$};
\path (4,0) --+(140:3.3cm) node[red,rotate=50] {$p_{01}$};
\foreach [count=\i, evaluate=\px as \hk using 140+\px*40, % calculate next arc angle
evaluate=\hk as \hkp using \hk+20, % calculate halfway angle to place nodes on arc
evaluate=\px as \lpr using 90-\px*40, % calculate edge to place loop
evaluate=\px as \lpa using \hk+40] % calculate angle to place nodes on loop
\px in {2,3,...,8}{
\path[font=\small] (p\i) arc [start angle=-\hk, delta angle=-40] node(p\px) {\px};
\draw[fill=blue!30, opacity=0.2] (p\px) circle[radius=3mm];
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p\i) arc [start angle=-\hk, delta angle=-32] (p\px);
\path (4,0) -- +(-\hkp:1.6cm) node {$p_{\i\px}$};
\path[->] (p\px) edge [trans,red,rotate=\lpr] (p\px);
\path (4,0) --+(-\lpa:3.3cm) node[red,rotate=\lpr] {$p_{\px\px}$};
}
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p8) arc [start angle=-140, delta angle=-32] (p0);
\path[font=\bfseries\small] (4,0) --+(-160:1.6cm) node {R};
\node[left of= p8, font=\bfseries\small] {adult};
\node[right of= p0, font=\bfseries\small] {egg};
\end{tikzpicture}
\end{document}
添加
查看上面的代码，节点和n-1/n节点没有被放置在图中。节点中的下标看起来根本不像下标。tikz图片下面的代码解决/补充了所有问题：
\begin{tikzpicture}
[trans/.style={to path={ .. controls +(60:1.5) and +(120:1.5) .. (\tikztotarget) \tikztonodes}},radius=2cm]
\path (4,0) -- +(180:2cm) node(p0) {0} arc [start angle=-180, delta angle=-40] node(p1) {1};
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p0) arc [start angle=-180, delta angle=-32] (p1);
\draw[fill=blue!30, opacity=0.2] (p0) circle[radius=3mm] (p1) circle[radius=3mm];
\path[-{Stealth}, shorten >=2pt] (p0) edge [trans,red,rotate=90] (p0);
\path[-{Stealth}, shorten >=2pt] (p1) edge [trans,above,red,rotate=50] (p1);
\path (4,0) --+(160:1.6cm) node {$p_{{\textstyle\mathstrut}01}$};
\path (4,0) --+(180:3.3cm) node[red,rotate=90] {$p_{{\textstyle\mathstrut}00}$};
\path (4,0) --+(140:3.3cm) node[red,rotate=50] {$p_{{\textstyle\mathstrut}11}$};
\foreach [count=\i, evaluate=\px as \hk using 140+\px*40, % calculate next arc angle
evaluate=\hk as \hkp using \hk+20, % calculate halfway angle to place nodes on arc
evaluate=\px as \lpr using 90-\px*40, % calculate edge to place loop
evaluate=\px as \lpa using \hk+40] % calculate angle to place nodes on loop
\px in {2,3,...,5}{
\path[font=\small] (p\i) arc [start angle=-\hk, delta angle=-40] node(p\px) {\px};
\draw[fill=blue!30, opacity=0.2] (p\px) circle[radius=3mm];
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p\i) arc [start angle=-\hk, delta angle=-32] (p\px);
\path (4,0) -- +(-\hkp:1.6cm) node {$p_{{\textstyle\mathstrut}\i\px}$};
\path[-{Stealth}, shorten >=2pt] (p\px) edge [trans,red,rotate=\lpr] (p\px);
\path (4,0) --+(-\lpa:3.3cm) node[red,rotate=\lpr] {$p_{{\textstyle\mathstrut}\px\px}$};
}
\path (4,0) -- +(260:2cm) node(p7) [font=\footnotesize] {$n\!\shortminus\!1$};
\path (4,0) -- +(220:2cm) node(p8) {$n$};
\draw[fill=blue!30, opacity=0.2] (p7) circle[radius=3mm] (p8) circle[radius=3mm];
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p7) arc [start angle=-100, delta angle=-32] (p8);
\path[-{Stealth}, shorten >=2pt] (p7) edge [trans,red,rotate=170] (p7);
\path[-{Stealth}, shorten >=2pt] (p8) edge [trans,above,red,rotate=130] (p8);
\path (4,0) --+(260:1.6cm) node {$p_{{\textstyle\mathstrut}n(n\!\shortminus\!1)}$};
\path (4,0) --+(220:3.3cm) node[red,rotate=130] {$p_{{\textstyle\mathstrut}nn}$};
\path (4,0) --+(260:3.3cm) node[red,rotate=170] {$p_{{\textstyle\mathstrut}(n\!\shortminus\!1)(n\!\shortminus\!1)}$};
\draw[-{Stealth},shorten <=8pt, font=\footnotesize] (p8) arc [start angle=-140, delta angle=-32] (p0);
\path[font=\bfseries\small] (4,0) --+(-160:1.6cm) node {R};
\node[left of= p8, font=\bfseries\small] {adult};
\node[right of= p0, font=\bfseries\small, xshift=-2mm] {egg};
\draw[-{Stealth},shorten <=8pt, font=\footnotesize,dashed] (p5) arc [start angle=-20, delta angle=-70] (p7); % decorate,decoration={shape=circle, shape size=2mm, shape sep={5mm, between centers}}, doesn't work unfortunately
\end{tikzpicture}
现在的结果看起来几乎和提供的照片一样：
由于正常数学模式使用相当大的minus符号，因此我使用了答案短减号在节点中。要使用此答案，请将以下几行添加到序言中：
\usepackage{amssymb} % provided it isn't loaded by another package
\DeclareMathSymbol{\shortminus}{\mathbin}{AMSa}{"39}
可以找到降低下标的选项这里。