The Geometric World of Fishes | Encyclopedia MDPI

The Geometric World of Fishes: Comparison

Please note this is a comparison between Version 1 by Greta Baratti and Version 4 by Vivi Li.

SpAnimals inhatial orientation may be led by the distinctive geometry of an environment: fish can use metric and left-right direction to reach convenient locbit species-specific ecological environments and acquire knowledge about the surrounding space to adaptively behave and move within it. Spatial cognition is important for achieving basic survival actions such as detecting the position of a food site or a mate, going back home or hiding from a predator. As such, animals possess multiple mechanisms for spatial mapping, including the use of individual reference points or positional relations,hips among them. One such as a foraging site. This remarkable capacity requires to handle the macrostructural characteristics of space, which are based on the Euclidean concepts of point, surface, and boundarymechanism allows disoriented animals to navigate according to the distinctive geometry of the environment: within a rectangular enclosure, they can simply reorient by using “metrics” (e.g., longer/shorter, closer/farther) and “sense” (e.g., left, right) attributes. Navigation based on the environmental geometry has been widely investigated across the animal kingdom, including fishes. In particular, research on teleost fish has contributed to the general understanding of geometric representations through both visual and extra-visual modalities, even vertebrates phylogenetically remote from mammals.

navigation
spatial geometry
reorientation
teleosts
fishes

1. History

Ecological habitats share spatial characteristics that allow animals to find useful supplies such as food, shelter, and companions, for survival. The ability to make use of these characteristics falls within “spatial cognition”, which embraces a set of orientation strategies used by animals to better adapt in life spaces. One of these strategies relies on geometric spatial information, such as metric (length, distance, angular magnitudes) and positional sense (left-right direction), so representing stable cues animals can rely on to efficiently navigate through an environment.

The classic example of geometric reorientation is the following. You are standing in the center of a perfectly rectangular room where in one corner there is a prize. You are blindfolded and turned in place, during which time the prize is removed. Afterwards, you are asked to take the blindfold off and identify the corner where you saw the prize before. Rather than choosing one of the four corners at random or always choosing the correct corner (i.e., the position where there was the prize), you will also choose the symmetric corner on the diagonal at 180°, since it was characterized by the same geometric cues (e.g., a short wall on the left) as the correct corner position.

Freshwater and seawater species of fish make use of several orientation strategies for adaptative behavior^[1]. Some of these strategies request to detect, process, and memorize specific sets of spatial cues, according to self-based coordinates, while others involve spatial relationships in world-based coordinates^[2]. Spatial orientation based on the environmental geometry has been widely investigated across species, starting from Cheng’s original observations with rats^{[3][4][5][6][7]}. His findings led him to advance the hypothesis that a “geometric module” might exist in the brain of animals to encode metric and sense properties of surfaces.

Traditionally, experiments to investigate the use of metric and sense spatial cues have been carried out in arenas with a geometric shape that is defined well (most of all, rectangular, but also diamond-, parallelogram-, or trapezoid-shaped arenas^[8][9][10]). Animals are required to identify the position of a reward that is usually hidden at the level of one of the four corners. In the case of perfectly rectangular environments, two corners have the shorter wall on the left (and the longer wall on the right), while two corners have the shorter wall on the right (and the longer wall on the left). Thus, it is possible to draw two diagonals, which are characterized by opposite geometric cues. If one corner only is rewarded, animals will make “rotational errors” towards the other corner on the diagonal, proper due to these spatial contingencies. However, the use of nongeometric cues, such as conspicuous or local landmarks, allows animals to discriminate the equivalent corners, significantly reducing rotational errors. For example, if one of the four wall is painted with a different color, it is possible to conjoin geometry and such a landmark to resolve the two-way symmetry and choose the correct corner position. Another relevant geometric cue is that provided by relative or absolute distances, from the arena's center to the corners, or considering the goal-position as a reference.

2. Research in fish

Fish possess excellent capacities in spatial mapping and navigation: they can plan and execute adaptive movements to remembered goals^[11], by means of learning and memory processes comparable to those displayed by land tetrapods. Beyond that, fish can resolve spatial reorientation tasks in which:

environmental geometries are interlaced with featural information, such as conspicuous (blue wall, blue 3D cylinder) or local landmarks (corner panels);

different behavioral methodologies and memory systems are engaged, those based on spontaneous ("social-cued memory task") or acquired ("rewarded exit task") behavior;

nonvisual transparent environments or blindness conditions request to use other sensory systems or motion patterns in alternative to sight.

An example of acquired reorientation behavior of fish under nonvisual conditions is that performed within a rectangular transparent arena. To resolve the geometric task, the fish had to choose one of the two target corners on the geometrically correct diagonal allowing it to leave the arena. These two corners share the same geometry, having a short wall on the right and a long wall on the left. The transparency of the rectangular space requests the fish to use other sensory channels than vision to properly reorient. The behavioral pattern became increasingly consistent with repeated experience, as the fish is typically rewarded with food in the case of correct choices. Original unpublished data are revealing that different species of fish reoriented similarly through transparent surfaces, which defined a distinctive global shape, supporting spatial reorientation under undefined situations (e.g., seek out food within a visually lacking environment) as a shared skill among teleosts, despite ecological specificities. Moreover, this spatial capacity would be highly dependent on task’s demands: actually, fish show no reorientation in the case of spontaneous behavior, where attentional factors (rather than motivational states driven by food) seem to determine short-term (“working”) memories.

During geometric spatial reorientation, the involvement of other sensory channels than sight, as well as the use of alternative orientation strategies based on motion patterns, would have a twofold implication. First, it would increase the ecological relevance of metric and sense relationships, which could also be detected through sensory systems that are assigned to other functions (e.g., the lateral line to detect hydrodynamic gradients^[12][13]), or developing intelligent solutions based on adaptive behaviors (e.g., “wall-following” strategies^[14][15]). Second, it would lead to consider the recruitment of modalities driven by touch for determining spatial geometric characteristics during reorientation. As such, a promising link between other vertebrates and humans takes place, in consideration of the orientation mechanisms used to face situations of visual deprivation or impairments^[16].

3. Conclusions

Behavioral observations with blind fishes^[17], and eyed fishes in visual transparency contexts^[18], have suggested that the shape of an environment can be experienced through multiple sensory systems (e.g., the lateral line, the sense of touch), thus supporting the ecological importance of geometric information. More than other animal groups, teleosts are increasingly emerging as a powerful model to explore spatial memory and its neural correlates, starting from their precision at navigating through underwater environments. The geometric world of fish has been sculpted by ecological pressures to use macrostructural spatial cues for survival purposes.

Table 1. Summary of major findings on geometric navigation by fishes, within visual and nonvisual spatial layouts. Working and reference memory tasks are specified to distinguish across behavioral protocols, visual and nonvisual to distinguish across experimental modalities.

Studies	Major results
Sovrano et al., 2002 ^[1]	In a reference memory task in visual modalities, X. eiseni learn to use both the rectangular geometry and the blue wall to reorient.
Sovrano et al., 2003 ^[2]	In a reference memory task in visual modalities, X. eiseni show a preference for geometry after the all-panels removal; for the trained local landmark after diagonal transposition; for geometry and the local landmark after the affine transformation, even in conflict. Some sex-specific differences found after the correct-panels removal (only females use geometry).
Vargas et al., 2004 ^[3]	In a reference memory task in visual modalities, C. auratus learn to use both the rectangular geometry and a corner landmark to reorient but show a preference for the landmark after affine transformation.
Sovrano et al., 2005 ^[4]	In a reference memory task in visual modalities, X. eiseni mainly reorient by geometry if trained in a small arena and tested in a big one and use the blue wall if trained in a big arena and tested in a small one.
Sovrano et al., 2005 ^[5]	In a reference memory task in visual modalities, lateralized X. eiseni is better at combining geometry and the blue wall, and at using local landmarks in the absence of metric attributes.
Vargas et al., 2006 ^[6]	In a reference memory task in visual modalities, C. auratus with lateral pallium lesions do not use geometry to reorient and just rely on the landmark.
Sovrano et al., 2007 ^[7]	In a reference memory task in visual modalities, X. eiseni mainly reorient with geometry in a small arena and with the blue wall in a big arena, after affine transformation of big landmarks (blue walls).
Brown et al., 2007 ^[8]	In a reference memory task in visual condition, controlled rearing conditions with or without featural cues affect the influence of landmarks, but not the ability to use geometry alone, in convict fish (A. nigrofasciatus).
Vargas et al., 2011 ^[9]	In a reference memory task in visual modalities, C. auratus with lateral pallium lesions are not totally impaired at using geometry to reorient when the target can be unambiguously located.
Lee et al., 2012 ^[10]	In a working memory task in visual modalities, X. eiseni and D. rerio use the rectangular geometry in the absence of training. Some species- and sex-specific differences have been found at simultaneously using geometry and the blue wall (females find harder the disengagement from geometry).
Lee et al., 2013 ^[11]	In a working memory task in visual modalities, D. rerio reorient according to boundary distance and sense but not by corners or boundary length.
Lee et al., 2015 ^[12]	In a working memory task in nonvisual modalities, D. rerio fail to merge several kinds of features with the geometry of a transparent rectangular arena. Some effects of proximity found in relation to the target position.
Sovrano & Chiandetti, 2017 ^[13]	In a reference memory task in visual modalities, X. eiseni reared within circular tanks reorient just as well as fish reared within rectangular tanks. The encoding of environmental geometries is “inborn” and independent from early experience.
Sovrano et al., 2018 ^[14]	In a reference memory task in nonvisual modalities, hypogean A. mexicanus and P. andruzzii learn to use both the rectangular geometry and a tactile landmark with embossed stripes to reorient.
Sovrano et al., 2020 ^[15]	In working and reference memory tasks in nonvisual modalities, X. eiseni, D. rerio, and C. auratus learn to use nonvisual geometry only over time under rewarded training (but not in the absence of training), probably relying on extra-visual sensory modalities. The different outcome of the geometric reorientation is strongly based on the type of experimental procedure.
Sovrano et al., 2020 ^[16]	In working and reference memory tasks in visual modalities, X. eiseni use features only to determine if the target is close regardless of metric attributes but overcome this limit over time under rewarded training.
Baratti et al., 2020 ^[17]	In a reference memory task in visual modalities, D. rerio learn to use the rectangular geometry to reorient, also showing improvements over time.
Baratti et al., 2021 ^[18]	In a reference memory task in visual modalities, D. rerio learn to use both corners and boundary length, in addition to distance combined with sense, to reorient.