Solving for two unknowns: An extension of vector-based models of landmark-based navigation.

Abstract

Vectors are mathematical representations of distance and direction information that take the form of line segments where length represents distance and orientation in space represents direction. Vector-based models have proven beneficial in understanding the spatial behavior of a variety of species in tasks that require landmark-based navigation via vector addition and vector averaging to determine a location. Extant research regarding vector-based representational and computational accounts of landmark-based navigation has involved tasks that required solving for one unknown (i.e., a location). Using a novel landmark-based navigation task, we provide evidence consistent with a form of vector algebra that involves solving two simultaneous equations with two unknowns in order to determine a location in space. Results extend vector-based accounts of landmark-based navigation and provide a novel methodological approach to the testing of mobile organisms.

Evidence consistent with the multiple-bearings hypothesis from human virtual landmark-based navigation

“…Regardless of level of complexity, the study of landmark use for navigation has received considerable attention. Defined as learning about spatial relationships among objects in the environment, landmark learning may involve landmark-to-goal or landmark-to-landmark spatial relationships ( Cheng, 1988 , 1989 , 1990 , 1994 ; Sturz and Katz, 2009 ; Sturz et al, 2011 ; for a review, see Cheng and Spetch, 1998 ). Such learning has been studied in a variety of animals including bees, birds, rats, monkeys, and humans (for a review, see Brown, 2006 ; Kelly and Gibson, 2007 ), and extant research suggests that many animals are able to utilize landmarks for navigation between locations in the environment.…”

“…Most relevant to present purposes, both human children and adults are able to use individual landmarks or a landmark array to locate a goal location ( Spetch, 1995 ; Spetch et al, 1996 , 1997 ; Waller et al, 2000 ; Hartley et al, 2003 ; MacDonald et al, 2004 ; Foo et al, 2005 ; Sturz and Bodily, 2010 ; Sturz et al, 2011 ; Bodily et al, 2012 ). Following initial learning in the presence of landmarks or a landmark array, landmark manipulations reveal that humans appear to encode distance and direction information from multiple landmarks in much the same ways as described above for various birds.…”

On Discriminating between Geometric Strategies of Surface-Based Orientation

“…On the one hand are principal-axis-based strategies which propose that organisms extract the major and minor principal axes of space. The major and minor principal axes pass through the centroid and approximate length and width of the entire space, respectively (for a detailed mathematical and mechanical definition, see Cheng, 2005; see also Cheng and Gallistel, 2005; Bodily et al, 2011; Sturz et al, 2011; left panel, Figure 1). On the other hand are medial-axis-based strategies which propose that organisms extract a trunk-and-branch system similar to the skeleton of a shape (see Blum, 1967; Cheng, 2005; Kelly and Durocher, 2011; Kelly et al, 2011a,b; see right panel, Figure 1).…”