Start with what it is not. It is not minimalism. Minimalism is characterized by simplistic drawings that look like they have been drafted by a geometry set. The lines and colors are very simple and straight. If an object you are familiar with is drawn the use of color variation is at a minimum.
It's not cubism. Cubism is characterized by it's flat 2 dimensional surface and as far as I can see lack of contrasting color. It ignores many of the techniques it took centuries to develop.
It is not Fauvism which is characterized by its powerful use of contrasting color and shape. It favors more the feeling something gives you rather than the way it actually is.
So there is only one answer left. It is a very realistic drawing using pale light to emphasize the couple and baby(and not the young child) and a few people behind them. The yellow in the painting is very unusual. I've never seen 2 yellows used quite like that. It draws you to it, but the people themselves don't look that interesting.
Although most of this artists had certain special interests in different areas only Peale was infatuated by the fossils and animal specimens. Therefore, he is also a founder of a famous Pennsylvania Museum, where the first skeleton of mastodon was displayed. That is why this museum is also known as Peale Museum.