Statistical and methodological innovations in the study of change are advancing rapidly, and visual tools have become an important component in model building and testing. Graphical representations such as path diagrams are necessary, but may be insufficient in the case of complex theories and models. Topology is a visual tool that connects theory and testable equations believed to capture the theorized patterns of change. Although some prior work has made use of topologies, these representations have often been generated as a result of the tested models. This article argues that utilizing topology a priori, when developing a theory, and applying analogous statistical models is a prudent method to conduct research. This article reviews topology by demonstrating how to build a topological representation of a theory and recover the implied equations, ultimately facilitating the transition from complex theory to testable model. Finally, topologies can guide researchers as they adjust or expand their theories in light of recent model testing.

Understanding what another agent can see relates functionally to the understanding of what they can do. We propose that spatial perspective taking and perceiving other's affordances, while two separate spatial processes, together share the common social function of predicting the behavior of others. Perceiving the action capabilities of others allows for a common understanding of how agents may act together. The ability to take another's perspective focuses an understanding of action goals so that more precise understanding of intentions may result. This review presents an analysis of these complementary abilities, both in terms of the frames of reference and the proposed sensorimotor mechanisms involved. Together, we argue for the importance of reconsidering the role of basic spatial processes to explain more complex behaviors.

When humans and animals navigate through environments, they form spatial memories important for supporting subsequent recall of locations relative to their own position and orientation, as well as to other object locations in the environment. The goal of the current study was to examine whether individual differences in initial exploration of a large-scale novel environment relate to subsequent spatial memories. A majority of studies examining spatial memory formed in large-scale spaces have constrained encoding of the environment by leading participants on pre-determined paths, thereby limiting their free exploration. We allowed participants to freely explore a large-scale, virtual environment to locate a set of objects within. We then tested their ability to navigate back to those objects as well as their ability to point to them from one another. Based on previous work suggesting gender differences in navigation strategies and spatial anxiety, we predicted that males and females would show different patterns of initial exploration and that these exploration patterns would account for gender differences in measures of spatial memory. We found that females revisited previous locations more often and showed lower rates of spreading through an area. These measures of exploration partially accounted for gender differences in efficiency in navigation and pointing accuracy to remembered locations. The results demonstrate the importance of exploration in spatial memory and provide a new perspective on gender differences in spatial cognition.

The current review introduces a new program of research that suggests the perception of spatial layout is influenced by emotions. Though perceptual systems are often described as closed and insulated, this review presents research suggesting that a variety of induced emotions (e.g., fear, disgust, sadness) can produce changes in vision and audition. Thus, the perceptual system may be highly interconnected, allowing emotional information to influence perceptions that, in turn, influence cognition. The body of work presented here also suggests that emotion-based changes in perception help us solve particular adaptive problems because emotion does not change all perceptions of the world. Taking the adaptive significance of emotion into account allows us to make predictions about when and how emotion influences perception.

Venturing into novel terrain poses physical risks to a female and her offspring. Females have a greater tendency to avoid physical harm, while males tend to have larger range sizes and often outperform females in navigation-related tasks. Given this backdrop, we expected that females would explore a novel environment with more caution than males, and that more-cautious exploration would negatively affect navigation performance. Participants explored a novel, large-scale, virtual environment in search of five objects, pointed in the direction of each object from the origin, and then navigated back to the objects. We found that females demonstrated more caution while exploring as reflected in the increased amounts of pausing and revisiting of previously traversed locations. In addition, more pausing and revisiting behaviors led to degradation in navigation performance. Finally, individual levels of trait harm avoidance were positively associated with the amount of revisiting behavior during exploration. These findings support the idea that the fitness costs associated with long-distance travel may encourage females to take a more cautious approach to spatial exploration, and that this caution may partially explain the sex differences in navigation performance.