With no blood relationship, is there a standard way of presenting step, foster and adopted children in descendant charts?
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The National Genealogical Society Quarterly or NGSQ-style (also Quarterly-Style) is one of the better known and documented standards. NGSQ/Quarterly-style recognizes step-children and adopted children and provides a standard by which they are carried forward (ie., provides for continued reporting about them and their families).*
See Joan F. Curran, Madilyn C. Crane, and John H. Wray, edited by Elizabeth Shown Mills, Numbering Your Genealogy: Basic Systems, Complex Families, and International Kin, rev. ed. (Washington: National Genealogical Society, 2008).
Madilyn Coen Crane's chapter, "Complex Families," pp. 17-25, is fully on point. In the introduction to the chapter, she writes
Whether or how specific genealogical software output follows/would follow the NGSQ standard guidelines is probably a separate consideration. The practices of different software varies (evident by the different answers others have posted). Yet a further consideration, the terms "descendant [charts/reports, etc.]" can evoke some controversy.
*At least as I have read and interpreted the work, foster children/guardianship relationships would follow. Your interpretation might vary, depending on the actual foster-relationship.
You may want to consider including the individual in the chart, but no decendants of that person. Instead, create a new tree for them and descendants.
"... is there a standard way of presenting step, foster and adopted children"
No, there is no standard way.
But there are various ways these children can (and should) be differentiated. There could be dotted or dashed or colored lines, or a word above their box ("step", "foster", etc.), or their name could be differentiated (colored or italic).
There could also be another line connecting the child to their other set of parents, but those connections are often not wanted to be shown (and would additionally mess up the appearance of the chart).
Should they be included? I would say yes, because the majority of the time, these relations are considered part of the "family" and affected the lives of the parents and direct children. They will be important in both your family history research and in your genealogy research.
Each time we ask "What are the rules?" there is an unspoken second question "Whose rules?".
If you plan to follow strict genealogy practice, then the focus is on direct ancestors and blood relationships so the types of "children" you ask about are not part of the scheme. Unless of course, the client or other person of importance is the adoptee (but that is another question).
On the other hand, if you take a broader, family history view of the world then the the working assumption is that all children will be included; and the key question is How?
Some tools make it easier than others to do this. You may need to consider how the data is stored and how it is presented as separate issues.
A key characteristic in storage is flexibility in describing the parent-child relationship. As in most areas, Gramps offers a list of common descriptors for the relationship and the ability to create others. When it comes to creating a display chart, Gramps treats all "children" in the same way and does not distinguish how they are presented. A detailed textual report includes details of the nature of the relationship. Other software packages may offer different options.
To summarise: If you want a hard and fast rule, then you have it -- DON'T. If you don't accept that (as many others here do not) then you need to live with the fact that there are different ways of working around the problem. So do what works best for you and document exhaustively what you have done and why. Then if a broadly accepted standard emerges in the future, you (or a successor who takes over your work) will have a sound basis for adapting without starting again.
In a word: no.
Charts are done by individual genealogy software programs or charting programs and depend on blood relationships.
The only way to include step, foster, or adopted relationships is to lie to the software and trick it into thinking such relationships are really blood relationships.
Yes, you can show them. Brother's Keeper http://bkwin.com/ keeps track of all that and allows you to print (step), (foster), or (adopted) before or after a child's name on both reports and charts.
Personally, I always show legally adopted children, never show foster children, and only show step children in unusual cases (e.g. child took step-father's name when entered the army, thus his descendants share MY surname, and I need to keep track of them.)