A Guide for the Multiplexed: The Development of Visual Feature Maps in the Brain

—Neural maps are found ubiquitously in the brain, where they encode a wide range of behaviourally relevant features into neural space. Developmental studies have shown that animals devote a great deal of resources to establish consistently patterned organization in neural circuits throughout the nervous system, but what purposes maps serve beneath their often intricate appearance and composition is a topic of active debate and exploration. In this article, we review the general mechanisms of map formation, with a focus on the visual system, and then survey notable organizational properties of neural maps: the multiplexing of feature representations through a nested architecture, the interspersing of ﬁne-scale heterogeneity within a globally smooth organization, and the complex integration at the microcircuit level that enables a high dimensionality of information encoding. Finally, we discuss the roles of maps in cortical functions, including input segregation, feature extraction and routing of circuit outputs for higher order processing, as well as the evolutionary basis for the properties we observe in neural maps.

The orderly organization of functionally related neurons in the brain, commonly known as neural maps, has captivated the intrigue of neuroscientists since their first observations in the late 19th century (Fritsch and Hitzig, 1870;Jackson, 1875;Gru¨nbaum and Sherrington, 1902;Holmes, 1918;Penfield and Boldrey, 1937). Subsequent research solidified the idea that neural maps hold a biological significance. A striking ubiquity of maps in nervous systems has been observed -neural maps are found throughout the nervous system in a vast range of species, representing properties ranging from sensory modalities to cognitive abstractions to motor commands. Moreover, researchers have uncovered an elaborate set of mechanisms underlying the development of neural maps, including intricate attractive and repulsive interactions of axons with molecular guidance cues in work that was pioneered by Friedrich Bonhoeffer and colleagues (Bonhoeffer and Huf, 1980Walter et al., 1987a,b). The preva-lence of maps as well as the metabolic resources devoted to their formation in developing circuits suggests that neural maps are necessary for brain function. While a connection between map organization and brain function is widely accepted, a detailed understanding of this connection continues to undergo thorough investigation and speculation. An important scientific question is how do neural maps facilitate information processing in the brain.
At first glance, maps appear to be a straightforward solution for the brain to encode and process complex, multidimensional information during an organism's interaction with its environment. Neural maps conform to the mathematical definition of functions: they uniquely assign elements from the input set X to elements of the output set Y, where X is feature space in the environment and Y is neuroanatomical space in the brain. The form of a neural map reflects the feature space it represents ( Fig. 1(A)). Some maps are continuous, such as retinotopic maps representing visual space and tonotopic maps for auditory frequencies. In these maps, neurons that are closer to each other tend to represent stimulus features that are closer to each other in the input space. Other neural maps are discrete, such as glomerular maps for odorants. Here, receptors distributed throughout the olfactory epithelium project to corresponding glomeruli in the olfactory bulb, with each type of olfactory receptor associating with a discrete set of olfactory glomeruli. Somatosensory, motor, and higher-order maps tend to be a combination of continuous and discrete maps.
A fundamental property of neural maps is the possibility for multiple features to be coextensively represented within the same anatomical area. A prominent example of this is found in the mammalian visual cortex (Fig. 1(B)). The primary visual cortex (V1) receives topographically organized input from the lateral geniculate nucleus, and serves as a first stop in the visual cortex where various properties of visual stimuli are extracted and distributed for further processing in higher order visual areas. Within the framework of retinotopy, in many mammalian species the population of V1 neurons further displays modular organization of properties like ocular dominance, orientation, and direction selectivity. The overlay of these feature maps in V1 not only presents an elegant solution to the encoding, parallel processing, and distribution of a vast amount of information, but also allows neural computations to be performed locally within circuits of V1 itself.
In this review we will analyze the significance of neural maps as an effective scheme for information encoding. We will approach this subject from two aspects, drawing from examples in the visual system. We first discuss the mechanisms underlying map development, highlighting how they drive the formation of maps with complex structure. We then describe how these map structures enable the brain to perform its complex functions.

DEVELOPMENT OF MAPS
Do maps serve a necessary biological function, or are they simply an epiphenomenon arising from the mechanisms that permit a circuit to perform functions that do not inherently require patterned circuit organization? While the answer to this question is elusive, one thing we can reliably observe in vivo is that biological systems appear to invest considerable resources in establishing and maintaining maps, and the developmental fine-tuning of these maps contributes to the ability of the system to properly respond to the environment.
Maps are thought to emerge from an interplay between (1) molecular guidance cues, (2) activity-dependent plasticity in which the circuit applies specific rules to adjust synapses and connections based on spontaneous or evoked neuronal activity, and (3) competition among neurons for available space and resources (Huberman et al., 2008;Feldheim and O'Leary, 2010). While these three mechanisms can act independently of each other and vary in their observed influence on map organization at different developmental timepoints, it is important to note that in natural systems all three mechanisms work in tandem throughout development, and their individual contributions to network organization often cannot be completely isolated from each other.

Molecular guidance cues
The fact that molecular guidance cues play a role in the establishment of maps was demonstrated by Roger Sperry in studies on the retinotectal projection from the eye to the optic tectum of fish and amphibians (Sperry, 1963). Sperry rotated the eyes of frogs by 180 degrees, and observed that the regenerated retinal axons formed an inverted visual field map in the tectum where axons innervated sites corresponding to their original targets within the tectum. Based on this observation, he proposed the ''chemoaffinity hypothesis", which states that each retinal axon and tectal neuron relies on unique chemical cues to specify their connectivity, allowing axons to find their original tectal targets even after eye rotation. Membrane stripe assays developed by Bonhoeffer and colleagues provided further evidence for this hypothesis at a cellular level (Walter et al., 1987a,b). When chick temporal retinal ganglion cell (RGC) axons were plated on interleaved stripes of anterior and posterior tectal membranes, temporal axons actively avoided posterior membranes, preferring instead to grow on anterior tectal membranes that correspond with their topographically appropriate target.
Since then, molecular guidance cues of the Ephrin/ Eph family have been identified as key factors in the establishment of topographic maps in the optic tectum, as well as across multiple other brain areas and sensory systems (reviewed in McLaughlin and O'Leary (2005), Flanagan (2006)). Ephrins and Eph receptors are distributed along anatomical axes in expression gradients, exerting either attractant or repellent activity on axons, depending on concentration, to guide axons to their appropriate target locations (Hansen et al., 2004).
Apart from the well-characterized roles of Ephrins, graded expression of morphogens such as Wnt, Sonic hedgehog (Shh), and BMP, as well as cell adhesion molecules such as Sidekicks, Dscam, and cadherins, have also been found to play important roles in topographic map formation (reviewed in Charron and Tessier-Lavigne (2007), Yam and Charron (2013), Missaire and Hindges (2015)).
The origin of Ephrin/Eph signaling can be traced back as far as premetazoan choanoflagellates (Arcas et al., 2020), indicating that the elements for creating organized projections have been available since nervous systems first appeared evolutionarily (Anctil, 2015;Burkhardt and Sprecher, 2017). It is reasonable to surmise that the efficiency provided by molecular guidance offers an evolutionary advantage by fast-tracking the assembly of developing sensory circuits based on a genetically encoded template. Rapid circuit formation would be especially important to animals that depend on their sensory systems for survival before the underlying neural circuit is fully developed, as is the case, for example, with vision in externally fertilized frogs and fish (Sakaguchi and Murphey, 1985;Burrill and Easter, 1994;Kita et al., 2015;Li et al., 2022).

Activity-dependent mechanisms for map refinement
The role of activity in the refinement of topographic maps has been studied by observing map refinement following deprivation of neuronal activity. In fish, intraocular or systemic application of tetrodotoxin (TTX) leads to abnormal local structure of retinotectal maps at relatively late stages in development, as opposed to large-scale topographic mistargeting (Stuermer et al., 1990;Gnuegge et al., 2001), though it appears to cause more extensive disruption to regenerating retinotectal projections (Schmidt and Buzzard, 1990;Olson and Meyer, 1991).
The participation of neural activity in map formation roughly falls into two categories: a permissive role, where neuronal activity is required to enable the signaling of molecular guidance cues; and an instructive role, where activity provides information that is used to direct the refinement of neural projections and the maintenance or elimination of connections.
There are a number of well-established examples of activity exerting a permissive role in circuit formation. In the chick, disrupting rhythmic activity leads to pathfinding errors in the dorsal-ventral motor neuron projections through the regulation of the expression of EphA4 and polysialic acid on NCAM (Hanson and Landmesser, 2004). Axonal responses to chemoattractant guidance molecules such as Netrin-1 can also be regulated by electrical activity through changes in intracellular cAMP levels (Ming et al., 2001). Nicol et al. (2007) established a retinocollicular co-culture preparation that reproduces the topographic ordering of axonal projections. They showed that TTX administration prevented this topographic targeting by altering the underlying retinal growth cone response to ephrin-A5 through calcium-dependent regulation of cAMP oscillations.
In the case of instructive mechanisms, patterned activity, such as visual experience, provides a valuable source of information about the relationship of inputs. Developing neuronal circuits have been found to use this information to instruct the fine-scale organization of maps by applying plasticity rules that exploit patterned sensory activity to regulate the growth and connectivity of neuronal arbors (Kutsarova et al., 2017). Furthermore, simulations with computational models also bolster the idea that biologically realistic molecular cues alone may not be sufficient to produce the precise retinotopic mapping that has been observed in vivo (Yates et al., 2004;McLaughlin and O'Leary, 2005). In the visual system, patterned activity can either arise from evoked activity in response to visual experience or from spontaneous waves of activity (Pratt et al., 2016). Spontaneous activity has been recorded in the developing retina (Maffei and Galli-Resta, 1990;Meister et al., 1991;Feller et al., 1996;Warland et al., 2006), lateral geniculate nucleus (Weliky and Katz, 1999;Martini et al., 2021), and the cortex (Adelsberger et al., 2005). Spontaneous activity is thought to mimic evoked activity, standing in for its role in instructing circuit plasticity before the developing animal gains access to visual experience Xu et al., 2015;Smith et al., 2018).
There are three stages of retinal waves that have been observed in development: the first stage, Stage I, is mediated by gap junctions and takes place prenatally; Stage II occurs primarily during the first postnatal week in mice and depends on cholinergic transmission; and Stage III consists of glutamatergic retinal waves (Arroyo and Feller, 2016). Stage II and III waves coincide with the period of map establishment in the superior colliculus, consistent with their involvement in the process of activitydependent visual map refinement (reviewed in Assali et al. (2014)).
Cholinergic transmission has been implicated in stage II wave generation. Mice lacking the b2 subunit of the nicotinic acetylcholine receptor exhibit disrupted retinal waves, which results in the degradation of retinocollicular and retinogeniculate topographic projections (McLaughlin et al., 2003;Dhande et al., 2011). In addition, the segregation of RGC axons into eye-specific layers in the lateral geniculate nucleus (LGN) is also believed to result from patterned neural activity and is disrupted in b2 À/À mutant mice (Sretavan et al., 1988;Bansal et al., 2000;Muir-Robinson et al., 2002;Sun et al., 2008). Following the period of cholinergic waves, between P11 and P15-16, retinal activity blockade by chronic TTX delivery into the vitreous humor prevents the developmental reduction in the number of retinal afferent inputs terminating on individual LGN relay neurons, suggesting a failure of synaptic pruning in the absence of patterned activity during the period dominated by Stage III spontaneous waves (Hooks and Chen, 2006). N-methyl-D-aspartate (NMDA) type glutamate receptors have been suggested as a possible molecular detector of correlated activity in the network, due to their requirement of concurrent membrane depolarization and glutamate binding for activation. Preventing glutamatergic transmission through NMDA receptor blockade leads to disorganized afferent projections, supporting the idea that correlated firing are necessary for the development and maintenance of the topographic map (Cline et al., 1987;Simon et al., 1992;Li et al., 2022).
The next level in the hierarchy of visual processing is the primary visual cortex, which also shows input selection by eye preference (ocular dominance). Here we find further evidence for sensory experience shaping developing neural circuits. Wiesel and Hubel (1963) found that, during a developmental critical period, deprivation of normal binocular vision by closing one eye leads to an initial decrease of responsiveness to that eye and strengthening of input from the non-deprived eye. Conversely, artificially inducing strabismus by misaligning the two eyes decorrelates activity between the two eyes, which causes V1 neurons to lose their binocular responses and become driven almost exclusively by monocular inputs (Hubel and Wiesel, 1965).

Rules for activity dependent plasticity
Several plasticity rules apply and act conjointly in the activity-dependent shaping of the neural circuit. Donald O. Hebb postulated that synapses strengthen when neurons ''repeatedly or persistently" participate in exciting their postsynaptic partners (Hebb, 1949). Hebbian plasticity is thus often summarized as ''neurons that fire together wire together" (Katz and Shatz, 1996). A form of Hebbian plasticity is the spike-timing-dependent long-term potentiation that occurs at retinotectal synapses when there is synchronous firing of inputs from neighboring sites in the eye (Zhang et al., 1998). Structurally, this leads to stabilization of synapses and suppression of exploratory axonal branching (Munz et al., 2014). Hebbian plasticity is therefore useful for promoting the maintenance and reinforcement of topographically appropriate convergent inputs which have a high probability of being coactive (Vislay-Meltzer et al., 2006;Kutsarova et al., 2017;Fassier and Nicol, 2021).
Serving as a corollary to Hebbian mechanisms is Stentian plasticity, wherein ''neurons that fire out of sync lose their link" (Stent, 1973). In this form of plasticity, pre-and postsynaptic neurons that repeatedly fail to fire synchronously experience synaptic long-term depression, which weakens the synapse and increases the rates of axon branch remodeling (Lisman, 1989;Rahman et al., 2020). This destabilizes topographically inappropriate stray inputs and allows them to explore and form new connections. For example, Zhang et al. (2012) optogenetically manipulated retinal activity in mice before eye opening to either increase or decrease the amount of interocular correlation. They found that increasing synchronous activity between the eyes reduced eye-specific segregation in the superior colliculus, whereas asynchronous activation sharpened eye-specific segregation.
In addition, other associative forms of synaptic plasticity that deviate from classic spike-timingdependent plasticity (STDP) rules or use neuronal signals that extend beyond the timeframe for STDP have also been described (see Suvrathan (2019) for review).
Simulations using computational models have shown that applying plasticity rules alone may be sufficient to allow a model network to self-organize into a biologically plausible map gradient (Fraser and Perkel, 1990;Simpson et al., 2009). For example, in the primary visual cortex, stimulus orientation preference is mapped onto columns nested within the larger macroscale map of visual space (Hubel and Wiesel, 1977), organized as a ''pinwheel" arrangement of orientation preferences (Blasdel and Salama, 1986;Bonhoeffer and Grinvald, 1991) (Fig. 1B(i)). This iconic pinwheel pattern has been reproduced by models implementing Hebbian-based rules (Von der Malsburg, 1973;Willshaw and Von Der Malsburg, 1976;Sirosh and Miikkulainen, 1994;Stevens et al., 2013), as well as reaction-diffusion models (Wolf, 2005;Kaschube et al., 2008;Wilson and Bednar, 2015). Some models show that a patterned map gradient can be produced even from white noise input subjected to bandpass filtering, raising the question of whether certain map patterns are simply a byproduct of the computational filtering performed by the specific microcircuit (Rojer and Schwartz, 1990).
These computational demonstrations suggest that activity-dependent plasticity by itself could be sufficient to direct the wiring of a circuit into the observed patterns. However, given that both nascent and regenerating neural circuits in vivo have been found to extensively rely on molecular guidance for circuit wiring (Fraser and Perkel, 1990;Becker and Becker, 2007;Simpson et al., 2009), it can be surmised that map pat-terning through plasticity in biological systems is likely too time-and resource-consuming and capricious to serve as the sole mechanism for establishing the wiring of a largescale neural circuit.

Axon competition and space-filling mechanisms
Along with molecular guidance cues and activitydependent plasticity, another key mechanism that shapes the organization of neuronal circuits is competition among developing axons for target space and resources (Prestige and Willshaw, 1975;Xiong et al., 1994). Experiments in which molecular gradients are altered or removed provide insight into the nature of interaxonal competition in the absence of molecular guidance cues. In animals in which Ephrin-A or EphA gradients have been ablated, the precise targeting of retinal axons along the anteroposterior gradient in the tectum becomes severely disrupted and discontinuous (Feldheim et al., 2000;Feldheim et al., 2004;Cang et al., 2005b;Tsigankov and Koulakov, 2006;Cang et al., 2008). Nonetheless, in these animals, bulk labeling of the retinocollicular projection reveals no gaps in the neuropil, suggesting that axons continue to grow to occupy available space. In Islet2-EphA3 knock-in (EphA3 ki/ki ) mice, there are two overlapping retinal EphA gradients, one with high and another with low levels of expression, resulting in the formation of two tandem retinotopic maps (Reber et al., 2004). The compression of two maps into the colliculus suggests that it is not absolute levels of Ephrin/Eph signaling which determines how the map forms, but rather the signaling relative to other inputs in a given target space. In other words, it is a competitive space-filling mechanism.
Axons seem to be further restricted in space by an upper limit to the size of an individual arbor. In zebrafish lakritz mutants that are incapable of generating RGCs, transplanting a blastomere from a wildtype fish allows some of the mutants to develop a single RGC (Gosse et al., 2008). The axonal arbor of the transplanted RGC does not fill the whole tectum, but is targeted to its retinotopically appropriate position where it grows to be larger and more complex than under normal conditions. This experiment demonstrates that competition constrains the amount of target space occupied by each axon but the potential for arbor expansion is not unlimited.
The existence of such competitive mechanisms may confer an adaptive advantage for matching input to available target space. In animals with a partially ablated retina or tectum/superior colliculus, the resultant projection gradually expands or contracts to more uniformly fill the available target space to form a smooth map of visual space (Finlay et al., 1979;Fraser and Hunt, 1980;Simon et al., 1994). Competition between axons does not only serve to fill the available target space but also maintains the relative rather than absolute spatial relationship between neurons constituting the map.

ROLES OF MAPS BEYOND TOPOGRAPHY
The mechanisms and phenomenology described above paint a picture of a program in which coarse but consistent map organization emerges under the direction of molecular guidance cues, and subsequent fine-tuning of the map requires activity-dependent mechanisms. These mechanisms additionally appear to be regulated by competition among inputs that ensures proper scaling of the final map to the inputs from which it is composed. Nonetheless, it would be an errant oversimplification to consider the ultimate goal of neural map formation to be the reconstruction in the brain of a precise duplicate of the sensory receptor surface.
Central maps perform at least three additional roles with respect to their inputs, internal organization, and outputs. These roles respectively are the segregation of inputs based on functional properties, higher order feature extraction, and routing of selected outputs forward to higher order processing areas, as well as providing feedback to earlier stations. The visual system serves as an insightful example: both spatial location and feature selectivity are simultaneously encoded by mesoscale structures (e.g., laminae, stripes, and columns) nested within the larger macroscale maps in the thalamus and primary visual cortex (Sedigh-Sarvestani and Fitzpatrick, 2022) ( Fig. 1(B)).

Input segregation in the thalamus
Input segregation has been one of the most intensively studied aspects of functional brain mapping, primarily because it is strikingly evident at the anatomical and morphological levels. Segregation of retinal inputs from the two eyes into discrete layers of the LGN in mammals is a classic illustration of this phenomenon, but other types of functional segregation are also observed in the thalamus (Huberman et al., 2008). One example is the prominent segregation of ON and OFF RGC axons into leaflets in the LGN of mustelids like minks and ferrets (Stryker and Zahs, 1983;McConnell and LeVay, 1984). Another is the parallel, segregated routing of magnocellular, parvocellular, and koniocellular pathways from retina to cortex. In primates, this segregation results in the anatomical division of the LGN into 6 stacked layers separated by interlaminar cells (Kaplan and Shapley, 1982), while in carnivores, it assorts within the A and C laminae (Linden et al., 1981;Sherman and Spear, 1982;Spear et al., 1989).
Eye segregation is particularly intriguing from a neurodevelopmental perspective, because the optic nerves from the two eyes enter independently and initially intermingle in the early developing thalamus, only to be resegregated into thalamic layers through activity-dependent mechanisms over subsequent days of development (Sretavan and Shatz, 1984;Sretavan et al., 1988;Huberman et al., 2008). Thus, in this case, the developing visual system has committed precious metabolic resources toward re-establishing labeled lines for eye segregation, only to see it all undone in the binocular neurons of the primary visual cortex. This begs the intriguing evolutionary biological question of whether effective processing of visual information in the cortex requires that not just some, but all thalamic inputs be monocular, effectively rendering the thalamus a relay from eye to cortex. Monocular segregation is apparently important for extraction of depth information from binocular disparity, and is consistent with the strong thalamic segregation of monocular inputs in arboreal and predatory mammals like primates and carnivores. Eye segregation in the LGN of less binocular rodents is more subtle, requiring anatomical labeling of retinal inputs for visualization (Muir-Robinson et al., 2002).

Input segregation in the visual cortex
The early segregation of eye preference extends from the thalamus into the input layer 4C of the primary visual cortex in primates and carnivores, where thalamocortical axons sort into eye-specific ocular dominance bands that can be revealed anatomically using transneuronal tracing. The injection of tritiated amino acids or wheat germ agglutinin-conjugated horseradish peroxidase (WGA-HRP) into one eye results in an impressive pattern of alternating right and left eye stripes in layer 4 of Rhesus macaque and many other primates, while periodic eye-specific bead-like patches are observed in area 17 in the cat and ferret (Wiesel et al., 1974;LeVay et al., 1985;Anderson et al., 1988;Law et al., 1988;Horton and Hocking, 1996b). In contrast, the primary visual cortex of rodents does not appear to have anatomical segregation of inputs representing the left and right eyes, instead exhibiting a ''salt-and-pepper" distribution of cortical neurons with a range of ocular preferences (Dra¨ger, 1974;Thurlow and Cooper, 1988;Fagiolini et al., 1994;Cang et al., 2005a;Laing et al., 2015). In addition to ocular dominance, ON and OFF RGC inputs from the thalamus are also segregated in primary visual cortex of the cat, mink, and ferret (McConnell and LeVay, 1984;Zahs and Stryker, 1988;Jin et al., 2008).
In primate cortex, there is a physical segregation of inputs from magnocellular, parvocellular, and koniocellular thalamic sources, with koniocellular inputs specifically targeting cytochrome oxidase (CO) rich ''blobs" in extragranular cortical layers (Livingstone and Hubel, 1982;Fitzpatrick et al., 1983;Lachica and Casagrande, 1992;Hendry and Yoshioka, 1994;Solomon, 2002). This segregation is maintained in the form of thick, pale and thin CO stripes in V2, and even into higher cortical areas as the dorsal (''where") and ventral (''what") processing streams (Sincich and Horton, 2005;Sedigh-Sarvestani and Fitzpatrick, 2022). Interestingly, while early cortical areas like V1 have pronounced segregation of features like ocular dominance, this is progressively lost in these higher processing areas as visual information processing becomes increasingly specialized. This suggests that multiplexing of segregated input feature representations may facilitate subsequent sorting and routing by information relevance for specialized processing in higher order areas.
An important, largely unresolved question is whether ocular dominance band segregation in the cortex follows a developmental program similar to topographic map refinement, in which some as yet unidentified molecular guidance cue sets the coarse pattern of alternating ocular dominance band formation, with subsequent activity-dependent processes sharpening their boundaries. In seminal experiments in the cat by Stryker and Harris (Stryker and Harris, 1986), RGCs were silenced by intraocular injection of tetrodotoxin from the time of eye opening until several weeks later when wellsegregated ocular dominance bands are normally anatomically detectable by transneuronal tracing. The experiment showed a failure of eye-specific segregation in the absence of patterned retinal activity. However, subsequent evidence suggested that initial segregation actually predates eye-opening (Horton and Hocking, 1996a;Crair et al., 2001). The retinal silencing may therefore have had the unintended effect of desegregating already patchy ocular dominance bands. Moreover, in the ferret, targeted injections of biotinylated dextran amine into a monocular lamina of the LGN results in patchy tufts of labeled axons in layer 4 of visual cortex as early as P16, just a few days after initial thalamocortical innervation and two weeks before eye opening, considerably earlier than initially reported using transneuronal labeling techniques (Ruthazer et al., 1999;Crowley and Katz, 2000). This is unsurprising as it has long been appreciated that the segregation of retinogeniculate inputs into eyespecific layers, although believed to be activitydependent, occurs much earlier in development than eye opening. The discovery that prior to the period of photoreceptor-mediated vision, waves of spontaneous activity sweep across RGCs, as well as the thalamus, in ferrets, rats, and mice during the period of retinogeniculate segregation provides a plausible explanation for how axons are sorted based on their eye of origin, relying on the different patterns of spontaneous neuronal firing in the two eyes (Maffei and Galli-Resta, 1990;Meister et al., 1991;Feller et al., 1996;Warland et al., 2006;Martini et al., 2021). Indeed, retinogeniculate segregation of afferents is severely disrupted when early spontaneous neural activity is blocked either by infusion of TTX into the thalamus in kittens or by intraocular injection of epibatidine in ferrets to prevent the generation of retinal waves (Sretavan et al., 1988;Penn et al., 1998).
The requirement of spontaneous activity for eyespecific segregation is challenged by the observation by Crowley and Katz (1999) that patchy thalamocortical projections are present in animals enucleated shortly after birth, presumably lacking retinal-derived activity cues. However, it should be noted that patchy projections in eyeless animals may not represent a substrate for ocular dominance. Enucleation has been shown to lead to restructuring of thalamic anatomy in the Rhesus macaque, resulting in thalamic lamination into gross magnocellular, parvocellular, and koniocellular layers that target different layers of the cortex and in some cases also segregate into patchy projections (Dehay et al., 1996).

Feature extraction in the visual cortex
Another challenge concerning the function and formation of ocular dominance columns is their heterogeneity across and within species. The characteristic stripe-like ocular dominance bands observed in primate cortex differ from the patchy, bead-like organization of ocular dominance in the cortex of cats and ferrets (Wiesel et al., 1974;LeVay et al., 1985;Anderson et al., 1988;Law et al., 1988;Horton and Hocking, 1996b). A clever model by Jones and coworkers (Jones et al., 1991) proposed that this difference in patterns could emerge as a simple consequence of boundary effects related to the relative shapes of the LGN and V1 in these species. More difficult to account for, however, are the stereotypical heterogeneities in ocular dominance band widths seen in some species. In the ferret, unlike the cat, ocular dominance bands consistently converge into large islands near the area 17/18 border, despite having a more regular patchy appearance in peripheral zones (Law et al., 1988;Redies et al., 1990;Ruthazer et al., 1999). Ocular dominance bands in the squirrel monkey, by comparison, can be quite unpredictable, with the degree of segregation differing across V1, apparently dissipating near the foveal representation in some animals, and with others mysteriously lacking any segregation at all (Adams and Horton, 2003). Another surprising observation is that the periodic distances between ocular dominance stripes in the Rhesus macaque can vary nearly twofold from one animal to another (Horton and Hocking, 1996b). Perhaps the most extreme case is that of the tree shrew (Tupaia glis) in which eye-specific thalamocortical projections from the well-segregated, laminated LGN do not terminate as alternating columnar bands. Instead, they terminate as uniform sublayers within layer 4 of primary visual cortex, with inputs representing the contralateral eye spanning the entire layer, while ipsilateral eye inputs target only the upper-and lower-most strata of layer 4 (Casagrande and Harting, 1975). Such diversity of organization highlights the convergent evolutionary forces that favor input segregation in the binocular primary visual cortices of many mammalian species.
Orientation and direction selectivity are prominent emergent features extracted by the primary visual cortex. While direction selective neurons are found in the retina (Demb, 2007;Wei and Feller, 2011) and LGN (Shou and Leventhal, 1989), orientation selectivity is a hallmark of the primary cortical visual response. In contrast to the retina and thalamus, spots and full field flashes are very poor stimuli for evoking activity in cortical neurons. As discovered serendipitously by Hubel and Wiesel (1962), cortical neurons respond robustly to oriented edges and lines. Orientation selectivity in the cortex is computed by the interactions of local circuitry and the selection of aligned thalamic inputs (Chapman et al., 1991;Ferster et al., 1996;Ferster and Miller, 2000;Vidyasagar and Eysel, 2015). In carnivore and primate cortex, there is a hypercolumnar organization in which retinotopy, ocular dominance, orientation selectivity, and other visual features are organized in an orthogonal, periodically repeating layout. Hubel and Wiesel initially schematized the hypercolumn using an ''ice cube model": for a particular visual location, orientations were systematically represented along one axis and eye-preference along the orthogonal axis (Hubel and Wiesel, 1977). However, subsequent experiments using voltage sensitive dyes and intrinsic signal optical imaging revealed that orientations were instead organized as a periodic series of ''pinwheels" with all orientations radiating from a central axis (Blasdel and Salama, 1986;Bonhoeffer and Grinvald, 1991). Individual neurons located at pinwheel centers were not found to lack orientation selectivity, but are typically more broadly tuned than cells further from the centers (Nauhaus et al., 2008;Koch et al., 2016). Pinwheel centers tended to be located near ocular dominance band centers, thus manifesting an orthogonal relationship of these two feature maps (Crair et al., 1997). An intriguing consequence of this configuration is that more binocular cells should be found at cortical sites where orientation is most narrowly tuned and thus potentially well-suited to compute depth information from binocular disparity at edges. Thus, the cortical hypercolumn appears to be not just a scheme for multiplexing various feature maps within the same neural substrate, but also creates opportunities for heterogeneity of information processing to extract parallel information streams within a single cortical area.
The question of how the periodic organization of orientation columns arises is fundamental to understanding the multiplexing of feature maps in the brain. On the one hand, there is good precedent for repeating motifs under the control of molecular signaling and mutual transcriptional suppression signals from the development of the eye, perhaps best understood in Drosophila eye development (Zipursky, 1989;Chen and Desplan, 2020). It is conceivable that a similar form of local signaling might lead to the periodic waxing and waning of transcriptional regulation across the cortical surface, leading to hypercolumnar organization. On the other hand, in supra-and infragranular layers of primary visual cortex of mammals with hypercolumnar organization, long-range horizontal connections link neighboring hypercolumns and have been shown to connect columns with that prefer similar orientations (Gilbert and Wiesel, 1989;Lo¨wel and Singer, 1992;Bosking et al., 1997). In cats and ferrets, a patchy periodic network of longrange horizontal connections forms prior to eye opening and the maturation of orientation selectivity, and subsequently undergoes further refinement with visual experience (Callaway and Katz, 1990;Durack and Katz, 1996). Interestingly, even in early binocularly enucleated ferrets, this initial clustering of long-range horizontal connections occurs, although infusion of TTX into the developing cortex prevents it entirely, implicating spontaneous patterned activity within the cortex or thalmocortical loop in the establishment of this early earmark of columnar periodicity (Ruthazer and Stryker, 1996). An impressive calcium imaging study performed in the visual cortex of immature ferrets by Smith et al. (2018) confirmed the existence of spontaneous cortical oscillations that exhibited temporal synchrony over very long distances and which predicted the future layout of orientation columns, long before the initial formation of horizontal connections. The long-range spatial periodicity of these oscillations is hypothesized to arise from the local connectivity of excitation and inhibition in the immature cortex. This study provides a compelling proof-of-principle for activity-dependent mechanisms being sufficient to orchestrate the global organization of hypercolumnar architecture, relying solely on local canonical cortical microcircuitry.

Routing of selected outputs in the visual system
Of course, the most fundamental form of labeled line input segregation is the topographic map itself. Unlike the binary nature of eye-specific laminae, retinotopic maps take the form of smooth, continuous gradients. While it is easy to understand how preserving topographic organization of inputs to visual centers permits the brain to extract critical positional information about where stimuli are located, there is also evidence for ethologically specialized visual processing in different parts of the visual field (Sedigh-Sarvestani and Fitzpatrick, 2022). The most obvious form of topographically specialized visual processing is the photoreceptor composition in the fovea of the primate retina, which consists of such a densely packed array of cones, in the absence of rods, that even the corresponding RGC cell bodies are displaced peripherally (Hendrickson, 1994). Parafoveal RGCs consist disproportionately of color-sensing, small dendritic field midget type cells, in comparison to peripheral retina where large dendritic field, contrast-sensitive parasol cells are found in near equal proportion (Dacey and Petersen, 1992). This heterogeneous retinal organization propagates throughout the visual system of primates leading to a large magnification factor in visual cortex where foveal and parafoveal visual fields are disproportionately represented (Sheth and Young, 2016), as befitting an animal with frontally positioned eyes capable of visual smooth pursuit and having extensive binocular coverage of the visual field. Moreover, differences in the information encoding by midget and parasol type RGCs are converted into complex map features as a result of functional segregation in higher order areas. Thus, midget RGCs constitute the primary source of visual information at CO-rich ''blobs" in V1, with the interblob territory receiving innervation downstream of parasol RGCs. These non-homogeneities in the visual maps are further preserved as V1 outputs are targeted to distinct zones in V2 and ultimately culminate in the dorsal and ventral cortical processing streams (Sheth and Young, 2016;Sedigh-Sarvestani and Fitzpatrick, 2022). This segregation of specialized processing pathways leads to dorsal (''where") extrastriate areas like the middle temporal (MT) area of cortex that exhibit a relatively greater peripheral field representation where parasol-like features appropriate for motion detection are maintained, and a ventral (''what") stream with areas like V4, dominated by color-sensitive responses in more central visual fields (Mishkin et al., 1983).
The existence of highly specialized processing by morphologically and transcriptionally distinct cell types in the retina, with the possibility of being propagated and spatially remapped at downstream stations in the visual system, implies a molecular logic akin to Sperry's chemoaffinity model. Such a mechanism could account not only for topographic organization, but also for the assembly of higher order processing modules, hard-wired to selectively probe for specific features (Kawasaki et al., 2004).
A number of findings suggest the possibility of molecularly defined processing streams. Transgenic mouse lines have been used to identify RGCs with specific functional properties and precise dendritic laminar targeting that extend axonal projections with highly specific subregional and laminar terminations in the dLGN and superior colliculus (Kim et al., 2010). For example, a class of direction-selective ganglion cells (DSGCs), selective for upward motion, have been defined by their expression of junctional adhesion molecule B (JAM-B). These DSGCs selectively target their axonal projections to the superficial layers of the superior colliculus and outer shell of the dLGN, where they have been suggested to account for the presence of directionselective neurons in these locations (Dra¨ger and Hubel, 1975;Kim et al., 2008). However, it is not known if these classes of cells might mediate information streams that produce direction selectivity in cortical neurons (Dhande and Huberman, 2014).
This also raises the question of whether ocular dominance column segregation in primary visual cortex may be similarly predetermined by the existence of putative molecular cues for sorting out inputs representing the two eyes (Katz and Crowley, 2002). However, in the absence of direct evidence for such molecular cues that definitively explain this kind of functional segregation, activity-dependent developmental plasticity offers a compelling alternative explanation for the emergence of ocular dominance maps.

MAPS AT THE LOCAL SCALE: LOCAL HETEROGENEITY AND INFORMATION CODING
In a map with ideal ''smooth" topographic organization, neurons would be positioned close to, and be strongly connected to, other similarly tuned neurons, forming a relatively homogeneous population. However, while maps at the macroscale have a stereotyped and smooth organization, local scale circuits are less homogeneous, interspersed with neurons that have disparate responses ( Fig. 1(C)) (Nauhaus et al., 2008). These incongruous neurons are generally linked by weak connections which are pared during activity-dependent refinement but not completely eliminated (Cossell et al., 2015). Another manifestation of local heterogeneity is the fluctuation in neural responses, in which responses from an individual neuron tend to fluctuate from trial to trial even when presented with the same stimulus.
It is easy to dismiss local heterogeneity as glitches, a result of incomplete circuit refinement. However, increasing evidence points to the possibility that there is information available within this ''noise" which the system can potentially utilize in local computation. One such example is the finding that trial-to-trial response fluctuation in pairs of neurons can be correlated, a phenomenon referred to as noise correlation (NC). Zohary et al. (1994) found a positive mean NC in pairs of neurons in area MT of monkeys, on the order of 0.15, a result that was corroborated by subsequent studies in a number of different mammalian species and brain regions (e.g. Ahissar et al. (1992), Bathellier et al. (2012)). In a homogeneous neuronal population, positive NC would amplify errors and impair stimulus decoding. However, when the neuronal population is more heterogeneous, the detrimental effects of NC are mitigated, and in some cases NC can even enhance decoding performance, as shown by theoretical models (e.g. Abbott and Dayan (1999), Averbeck et al. (2006)) as well as experimental evidence (Romo et al., 2003;Graf et al., 2011;Bejjanki et al., 2017). This suggests information available within NC can potentially be exploited by the local circuit to facilitate information processing (see Rothschild and Mizrahi (2015) for review).
A recent study in mouse V1 (Stringer et al., 2021) illustrated how much information discrimination can be encoded with a heterogeneous neural population. Orientation responses in V1 are distributed in a salt-andpepper fashion (Ohki et al., 2005), in stark contrast to the orderly organization of orientation selectivity in the primary visual cortex of the cat, ferret, and primates. Stringer and colleagues captured calcium imaging data simultaneously from up to 50,000 mouse V1 neurons, and calculated an impressive stimulus discrimination threshold of 0.35°in an orientation decoding task using a computational model. Comparing this result to decoding performance measured in macaque V1, which generally yielded decoding thresholds of > 2° (Vogels and Orban, 1990;Graf et al., 2011), it would seem that the mouse V1 has an encoding capacity comparable to (if not greater!) than that of primate V1, despite being far smaller in size. However, the mouse visual system does not seem to be able to fully utilize this encoded information, as the actual behavioural orientation discrimination threshold in mice is in the range of 20°$30° ( Abdolrahmani et al., 2019) compared to $ 3°in macaque (Goris et al., 2017).
This begs the question of whether the better behavioural decoding performance in primates is conferred by having an organized orientation map. Koch et al. (2016) provided a possible answer to how properties in the orientation map pattern can be utilized in higher order feature detection: reproducing experimental observations (Nauhaus et al., 2008) with a computational model, they showed that a neuron can gain different properties (e.g., broader orientation tuning, less contrast saturation, and reduced cross-orientation suppression) simply from being located near a pinwheel center.
Recent studies have reported weak spatial clustering of similarly-tuned orientation-selective neurons in mice (Kondo et al., 2016;Ringach et al., 2016), which can potentially represent the beginnings of orientation columns. Ho et al. (2021) showed that the V1 orientation columns in the mouse lemur, one of the smallest living primates, are similar in size and statistics to the macaque, indicating the primate-type orientation map organization may be constrained by a size limitation beyond which substructures such as orientation columns cannot be further miniaturized. The mouse lemur possesses one of the largest V1-tocortex ratios in primates, presumably to accommodate the orientation map structure within such a small cortex. In comparison, the mouse cortex may be too small to accommodate a similar organization structure without overly compromising visual field coverage, resulting in the salt-and-pepper organization.

Dimensionality of information
The complexity of the local organization of the primary visual cortex is likely a reflection of the complexity of information processing that the brain must perform. Different maps do not operate in isolation but in combination with each other, enabling coverage and continuity of the input space, but also supporting the emergence of novel response properties, such as orientation tuning and multimodal integration (Rothschild and Mizrahi, 2015). How individual and multiple maps simultaneously encode for both spatial location and feature selectivity has to do with how a neural circuit processes behaviourally relevant information through a population code.
Neurons in the primary visual cortex simultaneously encode for multiple features, forming feature maps that overlap and operate in combination with each other. Given that there is an ultimate constraint to the available neuroanatomical resources, the brain must choose between encoding strategies to ensure both the efficiency and robustness of the neural code.
There are two possible directions for population coding in the brain. The first approach is to represent ''unique" or non-redundant information by eliminating correlations in the input, as per the efficient coding hypothesis, resulting in high-dimensional and sparse neural code (Barlow, 1961;Atick and Redlich, 1990;Olshausen and Field, 1996;Simoncelli and Olshausen, 2001). This form of encoding is most efficient, requiring only relatively simple downstream networks to read out complex features. On the other hand, neural code can also span a low-dimensional space, where encoding correlated and redundant information allows for more robust computation even in the presence of noise (Shadlen and Newsome, 1998;Reich et al., 2001).
To probe the structure of information encoding in a biological system, Stringer et al. (2019) recorded simultaneous activity from about 10,000 neurons in the mouse visual cortex in response to natural stimuli. Using crossvalidated principal component analysis, they characterized the geometry of the population responses in terms of the variance in dimensions encoding increasingly fine features. They found that the geometry of the neural code allows the representation to be as high-dimensional as possible, while still allowing for smooth rather than fractal encoding. By balancing the need for smoothness and high-dimensionality, the neural code appears to achieve both robustness and efficiency. It is interesting to consider whether the dimensionality of information encoding would be different in animals like primates with more complex feature maps with local map structure, and how this might impact visual perception.

Local computation units
How neural maps achieve sparse and robust coding to produce flexible behaviour is an exciting topic of ongoing investigation. The ''canonical cortical microcircuit" (Douglas et al., 1989;Harris and Shepherd, 2015) and the ''grid cell-like code" (Constantinescu et al., 2016;Hawkins et al., 2019) have been proposed as models for the local computational units that process information across multiple domains in a map-like representation. The canonical cortical microcircuit models a stereotyped assembly of cells and their connections that constitute the cortical columnar architecture, acting as a neural substrate for predictive processing. The specific connectivity within cortical microcolumns serves as an experience-expectant filter for the extraction of relevant features in the inputs (Kolb and Gibb, 2014). Based on this information, the brain continually updates a generative model of the world that it uses to predict sensory input (Bastos et al., 2012;Keller and Mrsic-Flogel, 2018).
Grid cells are neurons found in the entorhinal cortex that respond to periodically distributed locations in space. Extending this concept into the neocortex, gridlike encoding has been proposed as a substrate for forming models of objects based on their features (Constantinescu et al., 2016). It has been suggested that there exists a repeating pattern of microcircuitry across neocortical areas, with variations for the different types of information each region must process, allowing for the emergence of complex representations like object compositionality and abstractions (Harris and Shepherd, 2015;Hawkins et al., 2019).
Together, multiplexing of information through the superimposition of macroscale and mesoscale maps permits the integration of heterogeneous inputs within the microcircuitry, allowing for the extraction of behaviourally relevant features from the input space and their integration into rich, multi-dimensional representations.

EVOLUTIONARY PERSPECTIVE
We have discussed the mechanisms underlying map development, the phenomenology of multiplexed representations, and the existence of fine-scale microcircuitry that underlies information processing in the brain. It has been proposed that the emergence of feature maps could be a mere artifact of the rules of self-organization (Kaschube et al., 2010). Notably, carnivores (cats, ferret) and ungulates (sheep) share similar orientation map organization with primates (Scholl et al., 2017), but such organization is absent from mice and rabbits (Van Hooser et al., 2005). Additionally, tree shrews, a close relative to primates, have primate-like orientation columns but ocular dominance organized in layers instead of columns (Fitzpatrick, 1996). This presence of mesoscale feature maps is a common trait among many species with large brains, however, it is unlikely to merely be a result of larger brain size. For example, large rodents like the red-rumped agouti lack periodic cortical orientation columns, whereas one of the smallest primates, the mouse lemur, has archetypal hypercolumns (Schmidt and Wolf, 2021). Thus, the detailed properties of maps appear most likely to be a consequence of evolutionary selection based on adaptive requirements. The ubiquity and diversity of feature maps suggest that they embody principles of organization for more ethologically efficient representations of noisy, multidimensional information from complex environments.