Paleontology and paleoecology should not be confused with either archaeology or anthropology.
Paleontology: A branch of science that deals with extinct and fossil animals and plants.
Paleoecology: A branch of science that deals with the ecology of extinct and prehistoric organisms.
Archaeology: The study of ancient cultures.
Anthropology: The study of past and present cultures.
Paleontology and paleoecology are both "natural sciences" and do not deal with human traces, where as the other two studies deal only with traces left by humans.
Any parallels between these four studies are found in the circumstances that all of them are seeking to reconstruct a complete picture from what are usually only bits and pieces.
Paleontology helps archaeologists with the dating of depositions of sedimentary rocks using microfossils.
Paleoecology helps archaeologists and anthropologists understand the environment in which past civilizations were living by using microfossils.