According to Culum Brown from Macquarie University, "Fish are more intelligent than they appear. In many areas, such as memory, their cognitive powers match or exceed those of ‘higher’ vertebrates including non-human primates."
Fish hold the records for the relative brain weights of vertebrates. Most vertebrate species have similar brain-to-body weight ratios. The deep sea bathypelagic bony-eared assfish, has the smallest ratio of all known vertebrates. At the other extreme, the elephantnose fish, an African freshwater fish, has the largest brain-to-body weight ratio of all known vertebrates.
Fish typically have quite small brains relative to body size compared with other vertebrates, typically one-fifteenth the brain mass of a similarly sized bird or mammal. However, some fish have relatively large brains, most notably mormyrids and sharks, which have brains about as massive relative to body weight as birds and marsupials.
The cerebellum of cartilaginous and bony fishes is large and complex. In at least one important respect, it differs in internal structure from the mammalian cerebellum: The fish cerebellum does not contain discrete deep cerebellar nuclei. Instead, the primary targets of Purkinje cells are a distinct type of cell distributed across the cerebellar cortex, a type not seen in mammals. The circuits in the cerebellum are similar across all classes of vertebrates, including fish, reptiles, birds, and mammals. There is also an analogous brain structure in cephalopods with well-developed brains, such as octopuses. This has been taken as evidence that the cerebellum performs functions important to all animal species with a brain.
In mormyrid fish (a family of weakly electrosensitive freshwater fish), the cerebellum is considerably larger than the rest of the brain put together. The largest part of it is a special structure called the valvula, which has an unusually regular architecture and receives much of its input from the electrosensory system.
Individual carp captured by anglers have been shown to become less catchable thereafter. This suggests that fish use their memory of negative experiences to associate capture with stress and therefore become less easy to catch.
This type of learning has been shown not just in carp but also in paradise fish (Macropodus opercularis) which avoid places where they have experienced a single attack by a predator and continue to do so for many months. Also, several fish species are capable of learning complex spatial relationships and forming mental maps  and integrate experiences which enable the fish to generate appropriate avoidance responses. This means that a fish can exhibit strong aversive behavior if exposed to injury or a predator. As a result, any reduction in the stressfulness of capture by an angler should be beneficial to angling in the long-term, since recapture of the fish should be less difficult.
Some fish species can exhibit long-term memory. Channel catfish can remember the human voice call announcing food five years after last hearing that call. Goldfish remember the colour of a tube dispensing food one year after the last tube presentation. Sockeye salmon still react to a light signal that precedes food arrival up to eight months since the last reinforcement. Some common rudd and European chub could remember the person who trained them to feed from the hand, even after a 6-month break. Crimson-spotted rainbowfish can learn how to escape from a trawl by swimming through a small hole in the center and they remember this technique 11 months later. Rainbow trout can be trained to press a bar to get food, and they remember this three months after last seeing the bar. Red Sea clownfish can recognize their mate 30 days after it was experimentally removed from the home anemone.
Fish orient themselves using landmarks and may use mental maps based on multiple landmarks or symbols. Fish behaviour in mazes reveals that they possess spatial memory and visual discrimination.
Tool use is often perceived as a sign of intelligence in animals, but it may be that the behaviours are mostly innate. There are not many examples of tool use in fishes, perhaps because fishes have only their mouth in which to hold objects. Several species of wrasse, and the blackspot tuskfish, have been seen holding clams or urchins in their mouth and smashing them against the surface of a rock (an "anvil") to break them up. Whitetail damselfish clean the rock face where they intend to lay eggs by blowing sand grains from their mouth onto it. Triggerfish can blow water onto urchins to turn them over and expose their more vulnerable ventral side. Archerfish can squirt jets of water at insects that sit on plants above the surface to knock them off their perch and into the water; they can adjust the size of the squirts to the size of the insect to be knocked off, and they can learn to shoot at moving targets. Banded acaras, Bujurquina vittata, lay their eggs on a loose leaf, and they carry the leaf away when a predator approaches.
In a study of Atlantic cod, a basic feeding machine was set up in which the fish used their mouth to pull a string to get the food out. This is operant conditioning rather than tool use. However, the researchers had also tagged the fish by threading a bead in front of their dorsal fin. By accident, some fish caught the string with their bead, resulting in food delivery. These fish eventually learned to swim in a special way to make the bead catch the string again and again to get food. Inasmuch as the fish used an object more or less external to their body in a goal-oriented way, they can be said to have used a tool.
As for tool use, construction behaviour may be mostly innate. Yet it can be sophisticated, and the fact that fish can make judicious repairs to their creation suggests intelligence. Construction methods in fishes can be divided into three categories: excavations, pile-ups, and gluing.
Excavations may be simple depressions dug up in the substrate, such as the nests of bowfin, smallmouth bass, and Pacific salmon, but it can also consist of fairly large burrows used for shelter and for nesting. Burrowing species include the mudskippers, the red band-fish Cepola rubescens (burrows up to 1 m deep, often with a side branch), the yellowhead jawfish Opistognathus aurifrons (chambers up to 22 cm deep, lined with coral fragments to solidify it), the convict blenny Pholidichthys leucotaenia whose burrow is a maze of tunnels and chambers thought to be as much as 6 m long, and the Nicaragua cichlid, Hypsophrys nicaraguensis, who drills a tunnel by spinning inside of it. In the case of the mudskippers, the burrows are shaped like a J and can be as much as 2 m deep. Two species, the giant mudskipper Periophthalmodon schlosseri and the walking goby Scartelaos histophorus, build a special chamber at the bottom of their burrows into which they carry mouthfuls of air. Once released the air accumulates at the top of the chamber and forms a reserve from which the fish can breathe – like all amphibious fishes, mudskippers are good air breathers. If researchers experimentally extract air from the special chambers, the fish diligently replenish it. The significance of this behaviour stems from the facts that at high tide, when water covers the mudflats, the fish stay in their burrow to avoid predators, and water inside the confined burrow is often poorly oxygenated. At such times these air-breathing fishes can tap into the air reserve of their special chambers .
Mounds are easy to build, but can be quite extensive. In North American streams, the male cutlip minnow Exoglossum maxillingua, 90–115 mm long (3.5-4.5 in), assembles mounds that are 75–150 mm high (3–6 in), 30–45 cm in diameter (12–18 in), made up of more than 300 pebbles 13–19 mm in diameter (a quarter to half an inch). The fish carry these pebbles one by one in their mouths, sometimes stealing some from the mounds of other males. The females deposit their eggs on the upstream slope of the mounds, and the males cover these eggs with more pebbles. Males of the hornyhead chub Nocomis biguttatus, 90 mm long (3.5 in), and of the river chub Nocomis micropogon, 100 mm long (4 in), also build mounds during the reproductive season. They start by clearing a slight depression in the substrate, which they overfill with up to 10,000 pebbles until the mounds are 60–90 cm (2–3 ft) long (in the direction of the water current), 30–90 cm wide (1–3 ft), and 5–15 cm high (2–6 in). Females lay their eggs among those pebbles. The stone accumulation is free of sand and it exposes the eggs to a good water current that supplies oxygen. Males of many mouthbrooding cichld species in Lake Malawi and Lake Tanganyika build sand cones that are flattened or crater-shaped at the top. Some of these mounds can be 3 m in diameter and 40 cm high. The mounds serve to impress females or to allow species recognition during courtship.
Male pufferfish, Torquigener sp., also build sand mounds to attract females. The mounds, up to 2 m in diameter, are intricate with radiating ridges and valleys.
Several species build up mounds of coral pieces either to protect the entrance to their burrows, as in tilefishes and gobies of the genus Valenciennea, or to protect the patch of sand in which they will bury themselves for the night, as in the Jordan's tuskfish Choerodon jordani  and the rockmover wrasse Novaculichthys taeniourus.
Male sticklebacks are well known for their habit of building an enclosed nest made of pieces of vegetation glued together with secretions from their kidneys. Foam nests, made up of air bubbles glued together with mucus from the mouth, are also well known in gouramis and armoured catfish.
Fish can remember the attributes of other individuals, such as their competitive ability or past behavior, and modify their own behavior accordingly. For example, they can remember the identity of individuals to whom they have lost in a fight, and avoid these individuals in the future; or they can recognize territorial neighbors and show less aggression towards them as compared to strangers. They can recognize individuals in whose company they obtained less food in the past and preferentially associate with new partners in the future.
Fish can seem mindful of which individuals have watched them in the past. In an experiment with Siamese fighting fish, two males were made to fight each other while being watched by a female, whom the males could also see. The winner and the loser of the fight were then, separately, given a choice between spending time next to the watching female or to a new female. The winner courted both females equally, but the loser spent more time next to the new female, avoiding the watcher female. In this species, females prefer males they have seen win a fight over males they have seen losing, and it therefore makes sense for a male to prefer a female that has never seen him as opposed to a female that has seen him lose.
Knowing that if A>B and B>C, then A>C, is another type of evidence for intelligence, and it can be applied in the context of dominance hierarchies. In a study with the cichlid Astatotilapia burtoni, eight observer fish could watch individual A beat individual B, then B over C, C over D, and D over E. The observer fish were then given a choice of associating with either B or D (both of which they had seen win once and lose once). All eight observer fish spent more time next to D. Fish in this species prefer to associate with more subordinate individuals, so the preference for D showed that the observers had worked out that B was superior to C, and C to D, and therefore D was subordinate to B.
A few examples of deception suggest that fishes can put themselves in the mind of others, though it remains possible that the behaviors are mostly innate. In the threespine stickleback, males sometimes see their nest full of eggs fall prey to groups of marauding females; some of the males, when they see a group of females approaching, move away from their nest and start poking their snout in the ground, as would a female raiding a nest. This commonly fools the females into thinking that a nest has been discovered there and they rush to that site, leaving the male's real nest alone. Bowfin males caring for their free-swimming fry do something similar when a potential fry predator approaches: they move away and thrash about as if injured, drawing the predator's attention onto himself.
In the Malili Lakes of Sulawesi, Indonesia, one species of sailfin silverside, Telmatherina sarasinorum, is an egg predator. It often follows courting pairs of the closely related species T. antoniae. When those pairs lay eggs, T. sarasinorum darts in and picks at the eggs, eating them. On four different occasions in the field (out of 136 observation bouts in total), the following behaviour was witnessed: a male T. sarasinorum who was following a pair of courting T. antoniae eventually chased off the male T. antoniae and took his place, courting the heterospecific female. That female released eggs, at which point the male fell upon the eggs and ate them. This sneaky courtship behaviour on the male’s part may simply be innate, but it is tempting to interpret it as a deliberate attempt at deception in order to get food.
Death feigning as a way to attract prey is another form of deception. In Lake Malawi, the predatory cichlid Nimbochromis livingstonii have been seen first remaining stationary with their abdomen on or near sand and that then dropping onto their sides. In a variant behaviour, some N. livingstonii fell through the water column and landed onto their side. The fish then remained immobile for several minutes. Their colour pattern was blotchy and suggested a rotting carcass. Small inquisitive cichlids of other species often came near and they were suddenly attacked by the predator. About a third of the death-feigning performances led to an attack, and about one-sixth of the attacks were successful. Another African cichlid, Lamprologus lemairii, from Lake Tanganyika, has been reported to do the same thing. A South American cichlid, the yellowjacket cichlid Parachromis friedrichsthalii, also uses death feigning. They turn over onto their sides at the bottom of the sinkholes they inhabit and remain immobile for as long as 15 minutes, during which they attack the small mollies that come too close to them. The comb grouper Mycteroperca acutirostris may also be an actor, though in this case the behaviour should be called dying or illness feigning, rather than death feigning, because while lying on its side the fish occasionally undulates its body. In 1999, off the coast of southeastern Brazil, one juvenile comb grouper was observed using this tactic to catch five small prey in 15 minutes.
Cooperative foraging reflects some mental flexibility and planning, and could therefore be interpreted as intelligence. There are a few examples in fishes.
Yellowtail amberjack can form packs of 7-15 individuals that maneuver in U-shaped formations to cut away the tail end of prey shoals (jack mackerels or Cortez grunts) and herd the downsized shoal next to seawalls where they proceed to capture the prey.
In the coral reefs of the Red Sea, roving coralgrouper that have spotted a small prey fish hiding in a crevice sometimes visit the sleeping hole of a giant moray and shake their head at the moray, and this seems to be an invitation to group hunting as the moray often swims away with the grouper, is led to the crevice where the prey hides, and proceeds to probe that crevice (which is too small to let the grouper in), either catching the prey by itself or flushing it into the open where the grouper grabs it. The closely related coral trout also enrolls the help of moray eels in this way, and they only do so when the prey they seek is hidden in crevices, where only the eel can flush them. They also quickly learn to invite preferentially those individual eels that collaborate most often.
Similarly, zebra lionfish that detect the presence of small prey fishes flare up their fins as an invitation to other zebra lionfish, or even to another species of lionfish (Pterois antennata), to join them in better cornering the prey and taking turns at striking the prey so that every individual hunter ends up with similar capture rates.
Experiments at the University of Padova in Italy have revealed that mosquitofish, Gambusia holbrooki, can distinguish better than chance (but not all the time) between two doors marked with either two or three geometric symbols, only one of which allowed the fish to rejoin its shoalmates. They could do this even when the array of two symbols covered the same total surface area, had the same density, and had the same brightness as the array of three symbols. Additional experiments showed that this discrimination persisted (again above chance level, but only at around 60% accuracy) when the two doors were marked with 4 vs 8, 15 vs 30, 100 vs 200, 7 vs 14, and 8 vs 12 symbols, again controlling for non-numerical factors.
Many studies have shown that when given a choice, shoaling fish prefer to join the largest of two shoals. It has been argued that several aspects of such choice reflect an ability by fish to distinguish between numerical quantities.
Fish can learn how to perform a behavior simply by watching other individuals in action. This is variously called observational learning, cultural transmission, or social learning. For example, fish can learn a particular route after following an experienced leader a few times. One study trained guppies to swim through a hole marked in red while ignoring another one marked in green in order to get food on the other side of a partition; when these experienced fish (“demonstrators”) were joined by a naive one (an “observer”), the observer followed the demonstrators through the red hole, and kept the habit once the demonstrators were removed, even when the green hole now allowed food access. In the wild, juvenile French grunt follow traditional migration routes, up to 1 km long, between their daytime resting sites and their nighttime foraging areas on coral reefs; if groups of 10-20 individuals are marked and then transplanted to new populations, they follow the residents along what is for them – the transplants – a new migration route, and If the residents are then removed two days later, the transplanted grunts continue to use the new route, as well as the resting and foraging sites at both ends.
Through cultural transmission, fishes could also learn where good food spots are. Ninespine stickleback, when given a choice between two food patches they have watched for a while, prefer the patch over which more fish have been seen foraging, or over which fish were seen feeding more intensively. Similarly, in a field experiment where Trinidadian guppies were given a choice between two distinctly marked feeders in their home rivers, the subjects chose the feeder where other guppies were already present, and in subsequent tests when both feeders were deserted, the subjects remembered the previously popular feeder and chose it.
Through social learning, fishes might learn not only where to get food, but also what to get and how to get it. Hatchery-raised salmon can be taught to quickly accept novel, live prey items similar to those they will encounter once they will be released in the wild, simply by watching an experienced salmon take such prey. The same is true of young perch. In the laboratory, juvenile European seabass can learn to push a lever in order to obtain food just by watching experienced individuals use the lever.
Fishes can also learn from others the identity of predatory species. Fathead minnows, for example, can learn the smell of a predatory pike just by being simultaneously exposed to that smell and the sight of experienced minnows reacting with fear, and brook stickleback can learn the visual identity of a predator by watching the fright reaction of experienced fathead minnows. Fish can also learn to recognize the odor of dangerous sites when they are simultaneously exposed to it and to other fish that suddenly show a fright reaction. Hatchery-raised salmon can learn the smell of a predator by being simultaneously exposed to it and to the alarm substance released by injured salmon.
Latent learning is the ability to "put two and two together", that is, to learn two things separately (at two different times and in two different contexts) and then to show an appropriate response in a third time and context from the combination of the two things learned. An example in fish comes from work on the three spot gourami. Dominance hierarchies exist in this species, and individuals quickly learn, from a few aggressive interactions, who is dominant to them. To appease dominants, subordinates adopt a typical posture with the body at an angle of 15-60 º to the horizontal, all fins folded, body colors becoming paler. In the laboratory, Individuals can also learn to associate a signal (a light being turned on) with the imminent arrival of food. They express this learning by approaching the surface where the food is normally dropped as soon as the light comes on, even before the food actually arrives. If a subordinate that has learned about the light and about the hierarchy is placed in a tank with a dominant it knows, and then the light is turned on, the subordinate immediately assumes the submissive posture rather than approach the surface. It has figured out that coming to the surface to get food would place it in competition with the dominant, and right away it tries to appease the dominant.
The bluestreak cleaner wrasse performs a service for “client” fishes (belonging to other species) by removing and eating their ectoparasites. Clients can invite a cleaning session by adopting a typical posture or simply by remaining immobile near a wrasse's cleaning station. They can even form queues while doing so. But cleaning sessions do not always end up well, because wrasses are sometimes tempted to cheat and eat the nutritious body mucus of their clients, rather than just the ectoparasites, something that makes the client jolt and sometimes flee. This system has been the subject of extensive observations which have suggested cognitive abilities on the part of the cleaner wrasses and their clients. For example, clients refrain from soliciting a cleaning session if they have witnessed the cleaning session of the previous client ending badly.   Cleaners give the impression of trying to maintain a good reputation, because they cheat less when they see a big audience (a long queue of clients) watching. Cleaners sometimes work as male-female teams, and when the smaller female cheats and bites the client, the larger male chases her off, as if to punish her for having tarnished their reputation.
Cleaner wrasses seem to advertise their service and try to convince clients to submit to a bout of cleaning by performing a type of caress, in which they brush their pelvic and pectoral fins against the dorsal fins and back of the prospective client. Swimming clients are more likely to stop if a cleaner starts by caressing them rather than going straight into an inspection of their body for parasites. It has also been suggested that the caress is a way to appease a potentially dangerous or wary client, because cleaners in the field are more likely to caress predatory rather than non-predatory clients, are more likely to caress predators that have not eaten for a while, and are more likely to caress a client if the last interaction with this client ended badly (with a jolt by the client, indicating that the cleaner had bitten it).
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