trees dashed lines

Question

I would like reproduce the following tree in a mathematical text. But for copyright reasons, I cannot use includegraphics{} and I must draw this figure in latex. What do you advise me ? What is the (relatively simple) suitable package to produce the dashed lines ?

Answer 1

To give you a start. When trying to find an answer, I stole from (and of course upvoted) many many brilliant answers by @cfr. Hope (s)he will provide you with a less clumsy solution.

\documentclass[tikz,border=10pt]{standalone}
% stolen from nice cfr answers such as https://tex.stackexchange.com/a/278184/121799
\usepackage{forest}
\begin{document}
\begin{forest}
  anchors/.style={anchor=#1,child anchor=#1,parent anchor=#1},
  /tikz/every node/.append style={font=\footnotesize},
  for tree={
    s sep=5mm,l=15mm,
    if n=0{anchors=east}{
    if n=1{anchors=east}{anchors=west}},
     content format={$\forestoption{content}$},
  },
  anchors=south, outer sep=2pt,
  nodot/.style={content format={},draw=none},
  dot/.style={tikz+={\draw[#1](.anchor)circle[radius=2pt];}},
  if content={}{}{dot={fill}}
  [\phi,dot=fill
    [y_{1,1},dot=fill
      [y_{1,1}y_{2,1},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      [y_{1,1}y_{2,2},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      [,edge=dashed]
      [y_{1,1}y_{2,{m_2}},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      ]
    [y_{1,1},dot=fill
        [,edge=dashed]
        [,edge=dashed]
      ]
    [y_{1,{m_1}},dot=fill
      [y_{{m_1},1}y_{2,1},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      [y_{{m_1},1}y_{2,2},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      [,edge=dashed]
      [y_{{m_1},1}y_{2,{m_2}},dot=fill
       [,edge=dashed]
       [,edge=dashed]]
      ]
    ]
  ]
\end{forest}
\end{document}