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Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus)

Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus) When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber’s Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species. . . . Keywords Approximate number system Foraging Numerosity Rufous hummingbird Introduction large numbers (Carey, 2009; Pepperberg, 2017). Each of these systems is best suited to different tasks, dependent on which When it comes to survival, the name of the game is efficiency. system’s associated shortcomings carry the smallest impact in Organisms live and die by how much energy they expend and terms of fitness. The object-tracking system is useful when acquire during their daily lives (Hurly, 2003). The more ener- assessing small quantities (e.g. the difference between one or gy that is saved, the more energy can be dedicated towards two peanuts), the counting system is useful if the time spent is reproduction. A simple way to gain energy is to exploit only outweighed by the cost of being wrong (e.g. a bird not detecting the most valuable resource available, and one way to deter- an extra egg laid by a brood parasite in its nest), while the ap- mine the value of a resource is by its numerosity. proximate number system is useful when the cost of picking the There are three main systems employed to evaluate lesser resource is outweighed by the time needed to count and numerosity: the object-tracking system with highly accurate discriminate between resources (e.g. a solitary zebra hesitating and rapid evaluation of small numbers; counting, with highly between joining a herd of 100 or 110 zebra and losing the pro- accurate but slow evaluation of large numbers; and the approx- tection of either). imate number system with rapid but low accuracy evaluation of Animals appear to use the approximate number system to rapidly determine the numerosity of groups that are too large for the object tracking system (N > 3–4) (Feigenson & Carey, Supplementary Information The online version contains supplementary material available at https://doi.org/10.3758/s13420-020- 2005; Hyde, 2011). This system allows the production of rough 00448-z. counts of resources, such as mates, predators or food, and is found in a wide variety of species: beetles (Tenebrio molitor), * Susan D. Healy various fish species (Gambusia holbrooki, Gambusia affinis), [email protected] red-backed salamanders (Plethodon cinereus), some birds (Petroica longipes, Corvus corone, Psittacus erithacus)and mul- School of Biology, University of St Andrews, St Andrews KY16 tiple primates (Agrillo, Dadda, Serena, & Bisazza, 2008; Beran, 9TH, UK 2007; Carazo, Font, Forteza-Behrendt, & Desfilis, 2009;Dadda, Department of Biological Sciences, University of Lethbridge, Piffer, Agrillo, & Bisazza, 2009;Ditz& Nieder, 2016; Garland, Lethbridge, Alberta, Canada 68 Learn Behav (2021) 49:67–75 Low, & Burns, 2012; Hanus & Call, 2007; Pepperberg, 1994; Alberta in the Canadian Rocky Mountains. Male rufous hum- Uller, Jaeger, Guidry, & Martin, 2003). While this system pro- mingbirds established individual territories around individual vides an approximation and not an exact value, it is far more commercial hummingbird feeders containing a 16% w/w su- rapid and requires less effort and attention than the exact alterna- crose solution at sites along the valley in early May. Once a tive of counting. The details of this approximation can be male had been identified as territorial (consistently feeding summarised using Weber’s Law: the just-noticeable difference from and defending the feeder from intruders), he was cap- between two stimuli is proportional to the size of the stimuli, tured and marked on the feathers on his upper chest and back rather than remaining a constant amount. In the context of the using a non-toxic water-based ink (Jiffy Eco-marker Ink) to approximate number system, this means that the just-noticeable allow individual identification (Fig. 1a). difference between two numerosities changes as a constant ratio One day after a bird was marked, we trained him to feed as the numerosities change (Cantlon & Brannon, 2006;Hauser, from an experimental flower containing a 25% w/w sucrose Tsao, Garcia, & Spelke, 2003), or that the approximate number solution. The artificial flowers (hereafter referred to as system becomes more imprecise as the ratio between the values “flowers”) were made of a yellow foam sheet cut into a circle approaches 1. with a 6 cm diameter (Fig. 1b). A hole in the middle of the Rufous hummingbirds (Selasphorus rufus)are very small flower held a 120 μL syringe tip with the needle removed, vertebrates (weighing around 3–4 g; Chai & Millard, 1997) which held the sucrose. The flowers (made from the yellow and are fiercely territorial (Carpenter, Hixon, Temeles, Russell, plastic-foam circles and a syringe tip) were supported by sy- &Paton, 1993). Feeding as they do almost exclusively on flower ringe caps taped to 60-cm long sticks stuck in the ground. The nectar (López-Calleja, Fernàndez, & Bozinovic, 2003), their high syringe caps acted as holders for the flowers, keeping the metabolic rate and expensive flight leads to them living on tight flowers stable (Fig. 1b). Male rufous hummingbirds are read- energy budgets. The foraging ecology of these birds appears to ily trained (within 1 or 2 h) to feed from different types of have favoured a variety of cognitive abilities: they can learn and artificial flowers not least because these birds preferentially track the reward refill rates of the flowers that they visit use spatial over visual information when learning to feed from (Henderson, Hurly, Bateson, & Healy, 2006;Tello-Ramos, a new resource (Tello-Ramos et al., 2014). Depending on the Hurly, Higgott, & Healy, 2015b) and produce traplines, where type of experiment, however, these birds will use the most they repeatedly use only a small selection of possible routes salient cue when learning which flowers are rewarded and between flowers (which are often also the most efficient routes; which are not (Healy & Hurly, 2013). For the current study, Tello-Ramos, Hurly, & Healy, 2015a, 2019). all flowers were visually identical and during flower training Rufous hummingbirds might thus be expected to have other we reduced the possibility that the birds used spatial cues to methods of saving energy, such as using systems that allow them learn which flower contained reward by moving the training to distinguish between resources of different quality by the cues flower at least 1 m away from the previous location between presented, as already seen with spatial location and colour (Hurly feeding bouts. Once a bird was flower trained the experiments &Healy, 2002). And, given that these birds can correctly locate a began. single rewarded flower in a sequential array of ten flowers, using a numerical ability called ordinality (Vámos, Tello-Ramos, Hurly, & Healy, 2020), then it seems plausible they might use Ethical note an approximate number system to allow them to choose foraging opportunities based on the number of flowers available. If these The University of St Andrews Ethics Committee and the birds have an approximate number system then, when multiple University of Lethbridge Animal Welfare Committee ap- options (e.g. plants) are available, we would expect them to proved all work, which was also conducted under permit from choose to visit first plants or patches that offer more rewarded the Alberta Sustainable Resource Development and resources or to defend locations that have more flowers available. Environment Canada. We tested this possibility by offering wild, free-living rufous hummingbirds a series of pairs of patches of artificial flowers, in which each of the pairs contained a different number of Experimental design flowers. We expected the birds to visit first the patch that contained more flowers. Experiment 1: Do hummingbirds prefer an array with more flowers? Methods The subjects were 13 wild male rufous hummingbirds. The experiment consisted of a series of training trials and tests. A The subjects were wild male rufous hummingbirds in visit was defined as a bird having fed from at least one flower Westcastle Valley (N49.349153, W114.410864), Southern in the array and leaving the array for at least 30 s. Learn Behav (2021) 49:67–75 69 Fig. 1 Photographs of the subjects and the tests. a A male rufous which contains four rewarded flowers. The training array in the first hummingbird hovers above a test array made up of artificial flowers. experiment was arranged in a square shape. c Example of a test layout. The circle surrounds the marking used to identify individual birds. b A Here the test depicted is a choice between seven flowers and one flower. male rufous hummingbird feeding from a flower in a training array, During training we removed the bird’s feeder and present- tests was at the midpoint between the two test arrays. All ed him with a square array of four flowers, with each flower flowers in the test arrays were empty. The order of train- 20 cm from its two nearest neighbours (Fig. 1b). Each flower ing and testing was repeated so that the bird was present- contained 25 μL of 25% sucrose solution, leading to a total of ed with a test after every set of five training visits (e.g., 100 μL available for consumption on each visit. We presented five training trials, test 1, five training trials, test 2, etc.). the training array for five visits, moving the array 50–100 cm This was done to reduce the probability that the birds between each visit so that birds would associate the reward learned that flowers were not rewarded when they were with the flowers rather than with the flowers’ spatial locations. presented with the pairs of arrays. In total there were 11 Between visits, we replaced all flowers with other, identical tests with five training visits between each test. The first flowers and refilled with the same sucrose volume as before. test consisted of one array of seven flowers and one array The replacement flowers were haphazardly selected from a of one flower (Fig. 1c). The second test consisted of one bag and used to reduce the possibility of associating the pres- array of six flowers and one array of one flower. This ence or absence of sucrose with visual cues of a particular pattern continued until the sixth test, which was one array flower (Hornsby et al., 2014). of two flowers and one array of one flower (e.g. one vs. Once the bird had visited the training array five times, seven, one vs. six, one vs. five, and so on). The seventh we presented the first probe test array. Each test was test consisted of one array of seven flowers and one array composed of two flower arrays that were 2 m apart, set of two flowers. The eighth test presented one array of so that the location of the last training array before the seven flowers and one array of three flowers (e.g., two 70 Learn Behav (2021) 49:67–75 vs. seven, three vs. seven, four vs. seven, and so on). This second experiment between 10 and 22 days of completing the pattern continued until the 11th test, which was one array first. As all birds were experienced with feeding from the of six flowers and one array of seven flowers (Fig. 2). artificial flowers, we did not need to train them again. Eight When the hummingbird visited the test array, we recorded birds completed both sets of the tests, whereas one bird com- which of the two arrays the bird visited first. We alternated the pleted only one set of tests (one vs. two through one vs. seven position of the more numerous array with each test from left to but not two vs. seven through six vs. seven). right, where ‘left’ and ‘right’ were defined as relative to the The experiment consisted of two training trials and two sets experimenter’s location when looking towards the feeder lo- of test trials, the same 11 tests as in Experiment 1 but this time cation. The angle of the test layout was then fixed for all tests the flowers in each array were rewarded and the reward was at this site from this point and did not rotate relative to the different, depending on the number of flowers in each array. feeder. During training we first presented an array of seven flowers, The next training array was then set up 50–100 cm from the each containing 25 μL of 25% sucrose solution. Once the bird location of the last training array, and the training trials and had visited this array once, we presented a single flower array tests continued from there. in which the flower contained 25 μL of 5% sucrose solution, a sucrose concentration that is much less preferred by the hum- Experiment 2: Can hummingbirds learn to use mingbirds (Morgan, Hurly, & Healy, 2014). The test trials numerosity to choose the array containing a reward? then began. The test trials were made up of two arrays set 2 m apart. The subjects were nine wild male rufous hummingbirds. All One array was made up of flowers that held 25 μLof25% nine birds had already completed Experiment 1 and started the sucrose solution, while the other array was made up of flowers Fig. 2 Illustrations of the 11 test layouts presented to the experimental subjects. Dots represent the placement of the experimental flowers. Lines represent the spacing between the flowers, set at 20 cm. The centre point of each of the two arrays was 2 meters from the other. Learn Behav (2021) 49:67–75 71 that held 25 μL of 5% sucrose solution. The array in which the Where appropriate we report effect size as r for t-tests and flowers contained 25% sucrose always had more flowers than Cohen’s d in the case of the binomial tests. did the 5% array, and we pseudorandomly changed the posi- tion of the array with flowers containing 25% sucrose. As in Experiment 1, in each test we recorded which array Results the bird visited first. The first set of tests went as follows. The first test consisted of one array of one flower and one array of Experiment 1: Do hummingbirds prefer an array with seven flowers (i.e. Test 1 = one vs. seven). We used one of two more flowers? criteria to end a test. The first criterion was reached if the bird visited the array with more flowers first three times in a row. Thirteen birds completed this experiment. On average across The second criterion was completing ten visits to the pair of all tests, birds visited the more numerous array significantly arrays. Once one of the criteria was fulfilled, the test ended more than expected by 50% chance (mean ± SE: 63.63 ± 3.71; and the next test began. For the next test in this set we pre- t = 3.67, p < 0.01, r = 0.72). Examination of choices relative sented one array of one flower and one array of six flowers. to each test condition (Fig. 3) similarly reveals an overall This pattern continued until the sixth test, which was one array greater number of choices to the larger array, but for only of two flowers and one array of one flower (i.e., Test 2 = one two of the test conditions were the results significant (one vs. six, Test 3 = one vs. five, and so on; Fig. 2). vs. two (ratio 0.5): 11/13, Z = 2.50, p = 0.023, Cohen’sd= The second set of tests went as follows. In the first test we 0.74; one vs. four (ratio 0.25): 12/13, Z = 3.05, p = 0.003, presented the bird with one array of two flowers and one array Cohen’s d = 0.99 ; see Table 1 in Online Supplementary of seven flowers, in the second test we presented one array of Material for other outcomes). No test conditions resulted in three flowers and one array of seven flowers (i.e., two vs. the smaller array being chosen significantly more often than seven, three vs. seven, four vs. seven, and so on). This pattern chance. continued until the fifth test, which was one array of six We performed correlation analysis to determine whether flowers and one array of seven flowers (Fig. 2). some aspects of test conditions influenced choices. The num- Of the eight birds that completed all the tests, four received ber of birds choosing the larger array was negatively correlat- the first set of tests first and four received the second set of ed with the total number of flowers in the two arrays (r tests first. Once all tests were completed, the feeder was 0.72, p = 0.01, n = 13; Fig. 4). The ratio of the array sizes returned to its original location. (small/large) had no significant effect on choices (r =0.22, p= 0.5, n = 13; Fig. 4). An additional way to examine the effect of the number of Data analysis flowers on the birds’ choices is to divide the tests into two separate series: those in which one of the arrays always con- We used one-sample t-tests to determine whether the birds tains only one flower versus those in which one of the arrays visited the larger array significantly more often than would always contains seven flowers (Figs. 2 and 3). We excluded be expected by chance (50%) at the 0.05 significance level. the test condition one versus seven because it was not unique For Experiment 1, where each subject was tested with each to one of these series. Birds visited the array with more test condition only once, we use binomial tests to determine if flowers significantly more frequently when the constant array more birds visited the larger (more numerous) array more was the array with one flower (75.38 ± 4.02) than when the often than expected by chance. We used Spearman correlation constant array had seven flowers (52.31 ± 3.60; t 6.04, p < 12 = tests to determine whether choices to the larger array (the 0.001,r =0. 86). percentage of birds in Experiment 1; percentage of choices in Experiment 2) was correlated with either the total number of flowers present during a test or with the ratio of the number Experiment 2: Can hummingbirds learn to use of flowers between the two arrays. We used a t-test to compare numerosity to choose the array containing a reward? the number of times birds visited the more numerous array when the constant array had one flower than when it had seven Hummingbirds visited the array with more flowers signifi- flowers. We used one-sample t-tests to determine if the birds cantly more than expected by 50% chance (mean ± SE: visited the array with more flowers for each test in Experiment 77.54 ± 1.62; t = 16.97, p < 0.001, r = 0.98). In all of the 2. We used Spearman correlation tests to determine if the tests except one (six vs. seven, ratio = 0.85: t =0.007, p = performance of birds during Experiment 1 correlated with 0.99, r = 0.003), birds visited the array that had more flowers the performance of birds in Experiment 2. We used a two- significantly more than expected by 50% chance (Fig. 5;all sample t-test to compare the percentage of correct choices t ≥ 2.9, all p ≤ 0.01, all r ≥ 0.72 ; see Online Supplementary 7/8 by each bird between Experiment 1 and Experiment 2. Material, Table 2). 72 Learn Behav (2021) 49:67–75 Fig. 3 The number of birds in each test that visited the array containing to chance (50%). Asterisks indicate performance that was statistically more flowers in Experiment 1 for each of the pairs of arrays. The dashed significant from chance: ** p < 0.01, *p < 0.05. line indicates the expected performance if the birds performed according As in Experiment 1, test condition did influence choices, as the relative size of the arrays (smaller ratio) increased (r = but in this case the ratio of the number of flowers between 0.63, p = 0.04, n = 9; Fig. 4). Choices were not correlated with arrays was more important than the total number of flowers in the total number of flowers in the test (r = 0.43, p = 0.18, n = the test. The percentage of visits to the larger array increased 9; Fig. 4). There was, however, an effect of flower number Fig. 4 Correlations between the number of choices to the more numerous array and test condition, when test condition was characterized either by the total number of flowers (sum of the two arrays) or the ratio of the two arrays (small/large). Learn Behav (2021) 49:67–75 73 when we compared all test conditions in which one of the The data from both experiments are consistent, but the data arrays always contained one flower (81.93 ± 1.87) versus test from Experiment 1 are weaker than those from Experiment 2. conditions in which one of the arrays always contained seven These latter demonstrate that until the two arrays contained flowers (71 ± 2.74; t 3.04, p = 0.01,r =0.75). seven and six flowers each (ratio = 0.85), the birds could 7= Choices to the more numerous array were significantly distinguish between them, and chose to visit the more numer- greater in Experiment 2 (77.54 ± 1.62) than in Experiment 1 ous array. The difference in outcome between the two exper- (63.63 ± 3.71; t = 2.22 p = 0.03, r = 0.44). To examine iments is not especially surprising, as with Experiment 1 we whether the two experiments assessed similar aspects of tapped into spontaneous choices, whereas in Experiment 2 we numerosity, we correlated the mean responses of the nine both explicitly linked numerosity to resource quality and pro- birds common to the two experiments but found no significant vided some minor training. In this context the birds not only relationship (r = 0.26, p = 0.49, n = 9). were able to choose the more appropriate array, they did so readily up until a ratio of the numbers of flowers in the two arrays consistent (or better than) with the ratios that other animals are capable of discriminating. For example, Discussion mosquitofish (Agrillo et al., 2008), guppies (Poecilia reticulata) (Lucon-Xiccato, Petrazzini, Agrillo, & Bisazza, In Experiment 1, in which birds were trained to feed from an 2015), and New Zealand robins can all discriminate up to array of four, equally rewarded, flowers and then tested with ratios of 1:2 (Garland et al., 2012); chicks (Gallus domesticus) pairs of flower arrays containing different numbers of flowers can discriminate one versus two (ratio = 0.5) and two versus (all empty), overall the birds spontaneously chose the array three (ratio = 0.66) stimulus sets but not sets of four versus six, containing more flowers. However, detailed examination of four versus five, and three versus four (ratios = 0.6, 0.8, and each test condition revealed limited significant choices. In 0.75, respectively; Rugani, Regolin, & Vallortigara, 2008; Experiment 2, we specifically trained the birds that the larger Rugani, Vallortigara, & Regolin, 2013b); rhesus macaques training array contained a higher quality reward than the (Macaca mulatta) approached whichever of two boxes had smaller array, and tests indicated that they recognized all but the larger quantity of apple pieces when the differences in one of the differences in array size. Detailed analyses revealed pieces was one versus two, two versus three, three versus four, that choices to the larger array were influenced by the total and three versus five (ratios = 0.5, 0.66, and 0.6, respectively; number of flowers in Experiment 1, and by the relative size of Hauser, Carey, & Hauser, 2000), while apes will discriminate the two arrays (ratio) in Experiment 2. between a pile of nine pellets and another of ten pellets (ratio = Fig. 5 The proportion of visits to the array containing more flower for each of the pairs of arrays. The dashed line indicates the expected performance if the birds performed according to chance (50%). Asterisks indicate performance that was statistically significant: *** p < 0.001, ** p < 0.01, * p < 0.05. 74 Learn Behav (2021) 49:67–75 0.9; Hanus & Call, 2007), albeit with much greater training about time (Marshall, Hurly, Sturgeon, Shuker, & Healy, than our hummingbirds experienced. Honey bees (Apis 2013; Samuels, Hurly, & Healy, 2014), but not always mellifera) can not only discriminate between similar ratios, (Marshall, Hurly, & Healy, 2012). including zero versus one (Howard et al., 2018), but they In summary, wild, free-living rufous hummingbirds are can also spontaneously transfer their choices to match size able to discriminate between arrays of flowers based on the rather than number (Bortot, Stancher, & Vallortigara, 2020). number of flowers in those arrays, which is consistent with That our hummingbirds provided evidence of their numer- these birds having an approximate number system. These ical discrimination much more strongly in Experiment 2 is hummingbirds may not be able to match Alex’s ability to give consistent with data from bees: in both cases, when the ani- voice to his numeracy (e.g. Pepperberg, 1987;Pepperberg & mals were trained that one of the options contained the reward Carey, 2012), but coupled with the evidence that they also can and the other did not (Howard et al., 2019), both bees and our also determine ordinality in a sequence of flowers, they pro- hummingbirds showed that they were capable of numerical vide evidence that ecology may have shaped numerical discrimination that is not seen when the training was much capabilities. less, and importantly, involved only a rewarding option Open practices statement The data will be made available on request by (Howard et al., 2020). Indeed, substantial differences in the reviewers, and will be uploaded to DRYAD. numerical abilities of animals are found depending on whether spontaneous numerical abilities are tested or if animals are Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adap- first trained to associate a reward with a higher or lower tation, distribution and reproduction in any medium or format, as long as numerosity (Agrillo & Bisazza, 2014). Our hummingbirds you give appropriate credit to the original author(s) and the source, pro- appeared to show a spontaneous preference for the more nu- vide a link to the Creative Commons licence, and indicate if changes were merous array only when the choice was between one versus made. The images or other third party material in this article are included two and one versus four, but as the training array was made up in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's of four flowers, it is possible that the preference for the more Creative Commons licence and your intended use is not permitted by numerous array in the latter choice was due to the similarity to statutory regulation or exceeds the permitted use, you will need to obtain the training array rather than to spontaneous discrimination. permission directly from the copyright holder. To view a copy of this Given that the hummingbirds do appear to possess an ap- licence, visit http://creativecommons.org/licenses/by/4.0/. proximate number system (see also Vámos et al., 2020), their lack of spontaneous discrimination suggests that they do not use the system to preferentially visit a more numerous re- source over another less numerous resource when they are References naïve to the quality of both resources. Although this behaviour Agrillo, C., & Bisazza, A (2014). Spontaneous versus trained numerical might at first sight seem inefficient, it is consistent when con- abilities. A comparison between the two main tools to study numer- sidered in the context of the rufous hummingbird’secology. ical competence in non-human animals. Journal of Neuroscience The nectar in the flowers that the birds visit across the day can Methods, 234,82-91. vary in both quality and quantity depending on whether the Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2008). Do fish count? 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D. (2020). Numerical ordinality in a wild nectarivore. Proceedings of the Royal Hyde, D. C. (2011). Two systems of non-symbolic numerical cognition. Society B, 287, 20201269. Frontiers in Human Neuroscience, 5,150. Jakobsen, H. B., & Kritjánsson, K. (1994). Influence of temperature and floret age on nectar secretion in Trifolium repens L. Annals of Publisher’snote Springer Nature remains neutral with regard to jurisdic- Botany, 74, 327-334. tional claims in published maps and institutional affiliations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Learning & Behavior Springer Journals

Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus)

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1543-4494
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10.3758/s13420-020-00448-z
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Abstract

When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber’s Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species. . . . Keywords Approximate number system Foraging Numerosity Rufous hummingbird Introduction large numbers (Carey, 2009; Pepperberg, 2017). Each of these systems is best suited to different tasks, dependent on which When it comes to survival, the name of the game is efficiency. system’s associated shortcomings carry the smallest impact in Organisms live and die by how much energy they expend and terms of fitness. The object-tracking system is useful when acquire during their daily lives (Hurly, 2003). The more ener- assessing small quantities (e.g. the difference between one or gy that is saved, the more energy can be dedicated towards two peanuts), the counting system is useful if the time spent is reproduction. A simple way to gain energy is to exploit only outweighed by the cost of being wrong (e.g. a bird not detecting the most valuable resource available, and one way to deter- an extra egg laid by a brood parasite in its nest), while the ap- mine the value of a resource is by its numerosity. proximate number system is useful when the cost of picking the There are three main systems employed to evaluate lesser resource is outweighed by the time needed to count and numerosity: the object-tracking system with highly accurate discriminate between resources (e.g. a solitary zebra hesitating and rapid evaluation of small numbers; counting, with highly between joining a herd of 100 or 110 zebra and losing the pro- accurate but slow evaluation of large numbers; and the approx- tection of either). imate number system with rapid but low accuracy evaluation of Animals appear to use the approximate number system to rapidly determine the numerosity of groups that are too large for the object tracking system (N > 3–4) (Feigenson & Carey, Supplementary Information The online version contains supplementary material available at https://doi.org/10.3758/s13420-020- 2005; Hyde, 2011). This system allows the production of rough 00448-z. counts of resources, such as mates, predators or food, and is found in a wide variety of species: beetles (Tenebrio molitor), * Susan D. Healy various fish species (Gambusia holbrooki, Gambusia affinis), [email protected] red-backed salamanders (Plethodon cinereus), some birds (Petroica longipes, Corvus corone, Psittacus erithacus)and mul- School of Biology, University of St Andrews, St Andrews KY16 tiple primates (Agrillo, Dadda, Serena, & Bisazza, 2008; Beran, 9TH, UK 2007; Carazo, Font, Forteza-Behrendt, & Desfilis, 2009;Dadda, Department of Biological Sciences, University of Lethbridge, Piffer, Agrillo, & Bisazza, 2009;Ditz& Nieder, 2016; Garland, Lethbridge, Alberta, Canada 68 Learn Behav (2021) 49:67–75 Low, & Burns, 2012; Hanus & Call, 2007; Pepperberg, 1994; Alberta in the Canadian Rocky Mountains. Male rufous hum- Uller, Jaeger, Guidry, & Martin, 2003). While this system pro- mingbirds established individual territories around individual vides an approximation and not an exact value, it is far more commercial hummingbird feeders containing a 16% w/w su- rapid and requires less effort and attention than the exact alterna- crose solution at sites along the valley in early May. Once a tive of counting. The details of this approximation can be male had been identified as territorial (consistently feeding summarised using Weber’s Law: the just-noticeable difference from and defending the feeder from intruders), he was cap- between two stimuli is proportional to the size of the stimuli, tured and marked on the feathers on his upper chest and back rather than remaining a constant amount. In the context of the using a non-toxic water-based ink (Jiffy Eco-marker Ink) to approximate number system, this means that the just-noticeable allow individual identification (Fig. 1a). difference between two numerosities changes as a constant ratio One day after a bird was marked, we trained him to feed as the numerosities change (Cantlon & Brannon, 2006;Hauser, from an experimental flower containing a 25% w/w sucrose Tsao, Garcia, & Spelke, 2003), or that the approximate number solution. The artificial flowers (hereafter referred to as system becomes more imprecise as the ratio between the values “flowers”) were made of a yellow foam sheet cut into a circle approaches 1. with a 6 cm diameter (Fig. 1b). A hole in the middle of the Rufous hummingbirds (Selasphorus rufus)are very small flower held a 120 μL syringe tip with the needle removed, vertebrates (weighing around 3–4 g; Chai & Millard, 1997) which held the sucrose. The flowers (made from the yellow and are fiercely territorial (Carpenter, Hixon, Temeles, Russell, plastic-foam circles and a syringe tip) were supported by sy- &Paton, 1993). Feeding as they do almost exclusively on flower ringe caps taped to 60-cm long sticks stuck in the ground. The nectar (López-Calleja, Fernàndez, & Bozinovic, 2003), their high syringe caps acted as holders for the flowers, keeping the metabolic rate and expensive flight leads to them living on tight flowers stable (Fig. 1b). Male rufous hummingbirds are read- energy budgets. The foraging ecology of these birds appears to ily trained (within 1 or 2 h) to feed from different types of have favoured a variety of cognitive abilities: they can learn and artificial flowers not least because these birds preferentially track the reward refill rates of the flowers that they visit use spatial over visual information when learning to feed from (Henderson, Hurly, Bateson, & Healy, 2006;Tello-Ramos, a new resource (Tello-Ramos et al., 2014). Depending on the Hurly, Higgott, & Healy, 2015b) and produce traplines, where type of experiment, however, these birds will use the most they repeatedly use only a small selection of possible routes salient cue when learning which flowers are rewarded and between flowers (which are often also the most efficient routes; which are not (Healy & Hurly, 2013). For the current study, Tello-Ramos, Hurly, & Healy, 2015a, 2019). all flowers were visually identical and during flower training Rufous hummingbirds might thus be expected to have other we reduced the possibility that the birds used spatial cues to methods of saving energy, such as using systems that allow them learn which flower contained reward by moving the training to distinguish between resources of different quality by the cues flower at least 1 m away from the previous location between presented, as already seen with spatial location and colour (Hurly feeding bouts. Once a bird was flower trained the experiments &Healy, 2002). And, given that these birds can correctly locate a began. single rewarded flower in a sequential array of ten flowers, using a numerical ability called ordinality (Vámos, Tello-Ramos, Hurly, & Healy, 2020), then it seems plausible they might use Ethical note an approximate number system to allow them to choose foraging opportunities based on the number of flowers available. If these The University of St Andrews Ethics Committee and the birds have an approximate number system then, when multiple University of Lethbridge Animal Welfare Committee ap- options (e.g. plants) are available, we would expect them to proved all work, which was also conducted under permit from choose to visit first plants or patches that offer more rewarded the Alberta Sustainable Resource Development and resources or to defend locations that have more flowers available. Environment Canada. We tested this possibility by offering wild, free-living rufous hummingbirds a series of pairs of patches of artificial flowers, in which each of the pairs contained a different number of Experimental design flowers. We expected the birds to visit first the patch that contained more flowers. Experiment 1: Do hummingbirds prefer an array with more flowers? Methods The subjects were 13 wild male rufous hummingbirds. The experiment consisted of a series of training trials and tests. A The subjects were wild male rufous hummingbirds in visit was defined as a bird having fed from at least one flower Westcastle Valley (N49.349153, W114.410864), Southern in the array and leaving the array for at least 30 s. Learn Behav (2021) 49:67–75 69 Fig. 1 Photographs of the subjects and the tests. a A male rufous which contains four rewarded flowers. The training array in the first hummingbird hovers above a test array made up of artificial flowers. experiment was arranged in a square shape. c Example of a test layout. The circle surrounds the marking used to identify individual birds. b A Here the test depicted is a choice between seven flowers and one flower. male rufous hummingbird feeding from a flower in a training array, During training we removed the bird’s feeder and present- tests was at the midpoint between the two test arrays. All ed him with a square array of four flowers, with each flower flowers in the test arrays were empty. The order of train- 20 cm from its two nearest neighbours (Fig. 1b). Each flower ing and testing was repeated so that the bird was present- contained 25 μL of 25% sucrose solution, leading to a total of ed with a test after every set of five training visits (e.g., 100 μL available for consumption on each visit. We presented five training trials, test 1, five training trials, test 2, etc.). the training array for five visits, moving the array 50–100 cm This was done to reduce the probability that the birds between each visit so that birds would associate the reward learned that flowers were not rewarded when they were with the flowers rather than with the flowers’ spatial locations. presented with the pairs of arrays. In total there were 11 Between visits, we replaced all flowers with other, identical tests with five training visits between each test. The first flowers and refilled with the same sucrose volume as before. test consisted of one array of seven flowers and one array The replacement flowers were haphazardly selected from a of one flower (Fig. 1c). The second test consisted of one bag and used to reduce the possibility of associating the pres- array of six flowers and one array of one flower. This ence or absence of sucrose with visual cues of a particular pattern continued until the sixth test, which was one array flower (Hornsby et al., 2014). of two flowers and one array of one flower (e.g. one vs. Once the bird had visited the training array five times, seven, one vs. six, one vs. five, and so on). The seventh we presented the first probe test array. Each test was test consisted of one array of seven flowers and one array composed of two flower arrays that were 2 m apart, set of two flowers. The eighth test presented one array of so that the location of the last training array before the seven flowers and one array of three flowers (e.g., two 70 Learn Behav (2021) 49:67–75 vs. seven, three vs. seven, four vs. seven, and so on). This second experiment between 10 and 22 days of completing the pattern continued until the 11th test, which was one array first. As all birds were experienced with feeding from the of six flowers and one array of seven flowers (Fig. 2). artificial flowers, we did not need to train them again. Eight When the hummingbird visited the test array, we recorded birds completed both sets of the tests, whereas one bird com- which of the two arrays the bird visited first. We alternated the pleted only one set of tests (one vs. two through one vs. seven position of the more numerous array with each test from left to but not two vs. seven through six vs. seven). right, where ‘left’ and ‘right’ were defined as relative to the The experiment consisted of two training trials and two sets experimenter’s location when looking towards the feeder lo- of test trials, the same 11 tests as in Experiment 1 but this time cation. The angle of the test layout was then fixed for all tests the flowers in each array were rewarded and the reward was at this site from this point and did not rotate relative to the different, depending on the number of flowers in each array. feeder. During training we first presented an array of seven flowers, The next training array was then set up 50–100 cm from the each containing 25 μL of 25% sucrose solution. Once the bird location of the last training array, and the training trials and had visited this array once, we presented a single flower array tests continued from there. in which the flower contained 25 μL of 5% sucrose solution, a sucrose concentration that is much less preferred by the hum- Experiment 2: Can hummingbirds learn to use mingbirds (Morgan, Hurly, & Healy, 2014). The test trials numerosity to choose the array containing a reward? then began. The test trials were made up of two arrays set 2 m apart. The subjects were nine wild male rufous hummingbirds. All One array was made up of flowers that held 25 μLof25% nine birds had already completed Experiment 1 and started the sucrose solution, while the other array was made up of flowers Fig. 2 Illustrations of the 11 test layouts presented to the experimental subjects. Dots represent the placement of the experimental flowers. Lines represent the spacing between the flowers, set at 20 cm. The centre point of each of the two arrays was 2 meters from the other. Learn Behav (2021) 49:67–75 71 that held 25 μL of 5% sucrose solution. The array in which the Where appropriate we report effect size as r for t-tests and flowers contained 25% sucrose always had more flowers than Cohen’s d in the case of the binomial tests. did the 5% array, and we pseudorandomly changed the posi- tion of the array with flowers containing 25% sucrose. As in Experiment 1, in each test we recorded which array Results the bird visited first. The first set of tests went as follows. The first test consisted of one array of one flower and one array of Experiment 1: Do hummingbirds prefer an array with seven flowers (i.e. Test 1 = one vs. seven). We used one of two more flowers? criteria to end a test. The first criterion was reached if the bird visited the array with more flowers first three times in a row. Thirteen birds completed this experiment. On average across The second criterion was completing ten visits to the pair of all tests, birds visited the more numerous array significantly arrays. Once one of the criteria was fulfilled, the test ended more than expected by 50% chance (mean ± SE: 63.63 ± 3.71; and the next test began. For the next test in this set we pre- t = 3.67, p < 0.01, r = 0.72). Examination of choices relative sented one array of one flower and one array of six flowers. to each test condition (Fig. 3) similarly reveals an overall This pattern continued until the sixth test, which was one array greater number of choices to the larger array, but for only of two flowers and one array of one flower (i.e., Test 2 = one two of the test conditions were the results significant (one vs. six, Test 3 = one vs. five, and so on; Fig. 2). vs. two (ratio 0.5): 11/13, Z = 2.50, p = 0.023, Cohen’sd= The second set of tests went as follows. In the first test we 0.74; one vs. four (ratio 0.25): 12/13, Z = 3.05, p = 0.003, presented the bird with one array of two flowers and one array Cohen’s d = 0.99 ; see Table 1 in Online Supplementary of seven flowers, in the second test we presented one array of Material for other outcomes). No test conditions resulted in three flowers and one array of seven flowers (i.e., two vs. the smaller array being chosen significantly more often than seven, three vs. seven, four vs. seven, and so on). This pattern chance. continued until the fifth test, which was one array of six We performed correlation analysis to determine whether flowers and one array of seven flowers (Fig. 2). some aspects of test conditions influenced choices. The num- Of the eight birds that completed all the tests, four received ber of birds choosing the larger array was negatively correlat- the first set of tests first and four received the second set of ed with the total number of flowers in the two arrays (r tests first. Once all tests were completed, the feeder was 0.72, p = 0.01, n = 13; Fig. 4). The ratio of the array sizes returned to its original location. (small/large) had no significant effect on choices (r =0.22, p= 0.5, n = 13; Fig. 4). An additional way to examine the effect of the number of Data analysis flowers on the birds’ choices is to divide the tests into two separate series: those in which one of the arrays always con- We used one-sample t-tests to determine whether the birds tains only one flower versus those in which one of the arrays visited the larger array significantly more often than would always contains seven flowers (Figs. 2 and 3). We excluded be expected by chance (50%) at the 0.05 significance level. the test condition one versus seven because it was not unique For Experiment 1, where each subject was tested with each to one of these series. Birds visited the array with more test condition only once, we use binomial tests to determine if flowers significantly more frequently when the constant array more birds visited the larger (more numerous) array more was the array with one flower (75.38 ± 4.02) than when the often than expected by chance. We used Spearman correlation constant array had seven flowers (52.31 ± 3.60; t 6.04, p < 12 = tests to determine whether choices to the larger array (the 0.001,r =0. 86). percentage of birds in Experiment 1; percentage of choices in Experiment 2) was correlated with either the total number of flowers present during a test or with the ratio of the number Experiment 2: Can hummingbirds learn to use of flowers between the two arrays. We used a t-test to compare numerosity to choose the array containing a reward? the number of times birds visited the more numerous array when the constant array had one flower than when it had seven Hummingbirds visited the array with more flowers signifi- flowers. We used one-sample t-tests to determine if the birds cantly more than expected by 50% chance (mean ± SE: visited the array with more flowers for each test in Experiment 77.54 ± 1.62; t = 16.97, p < 0.001, r = 0.98). In all of the 2. We used Spearman correlation tests to determine if the tests except one (six vs. seven, ratio = 0.85: t =0.007, p = performance of birds during Experiment 1 correlated with 0.99, r = 0.003), birds visited the array that had more flowers the performance of birds in Experiment 2. We used a two- significantly more than expected by 50% chance (Fig. 5;all sample t-test to compare the percentage of correct choices t ≥ 2.9, all p ≤ 0.01, all r ≥ 0.72 ; see Online Supplementary 7/8 by each bird between Experiment 1 and Experiment 2. Material, Table 2). 72 Learn Behav (2021) 49:67–75 Fig. 3 The number of birds in each test that visited the array containing to chance (50%). Asterisks indicate performance that was statistically more flowers in Experiment 1 for each of the pairs of arrays. The dashed significant from chance: ** p < 0.01, *p < 0.05. line indicates the expected performance if the birds performed according As in Experiment 1, test condition did influence choices, as the relative size of the arrays (smaller ratio) increased (r = but in this case the ratio of the number of flowers between 0.63, p = 0.04, n = 9; Fig. 4). Choices were not correlated with arrays was more important than the total number of flowers in the total number of flowers in the test (r = 0.43, p = 0.18, n = the test. The percentage of visits to the larger array increased 9; Fig. 4). There was, however, an effect of flower number Fig. 4 Correlations between the number of choices to the more numerous array and test condition, when test condition was characterized either by the total number of flowers (sum of the two arrays) or the ratio of the two arrays (small/large). Learn Behav (2021) 49:67–75 73 when we compared all test conditions in which one of the The data from both experiments are consistent, but the data arrays always contained one flower (81.93 ± 1.87) versus test from Experiment 1 are weaker than those from Experiment 2. conditions in which one of the arrays always contained seven These latter demonstrate that until the two arrays contained flowers (71 ± 2.74; t 3.04, p = 0.01,r =0.75). seven and six flowers each (ratio = 0.85), the birds could 7= Choices to the more numerous array were significantly distinguish between them, and chose to visit the more numer- greater in Experiment 2 (77.54 ± 1.62) than in Experiment 1 ous array. The difference in outcome between the two exper- (63.63 ± 3.71; t = 2.22 p = 0.03, r = 0.44). To examine iments is not especially surprising, as with Experiment 1 we whether the two experiments assessed similar aspects of tapped into spontaneous choices, whereas in Experiment 2 we numerosity, we correlated the mean responses of the nine both explicitly linked numerosity to resource quality and pro- birds common to the two experiments but found no significant vided some minor training. In this context the birds not only relationship (r = 0.26, p = 0.49, n = 9). were able to choose the more appropriate array, they did so readily up until a ratio of the numbers of flowers in the two arrays consistent (or better than) with the ratios that other animals are capable of discriminating. For example, Discussion mosquitofish (Agrillo et al., 2008), guppies (Poecilia reticulata) (Lucon-Xiccato, Petrazzini, Agrillo, & Bisazza, In Experiment 1, in which birds were trained to feed from an 2015), and New Zealand robins can all discriminate up to array of four, equally rewarded, flowers and then tested with ratios of 1:2 (Garland et al., 2012); chicks (Gallus domesticus) pairs of flower arrays containing different numbers of flowers can discriminate one versus two (ratio = 0.5) and two versus (all empty), overall the birds spontaneously chose the array three (ratio = 0.66) stimulus sets but not sets of four versus six, containing more flowers. However, detailed examination of four versus five, and three versus four (ratios = 0.6, 0.8, and each test condition revealed limited significant choices. In 0.75, respectively; Rugani, Regolin, & Vallortigara, 2008; Experiment 2, we specifically trained the birds that the larger Rugani, Vallortigara, & Regolin, 2013b); rhesus macaques training array contained a higher quality reward than the (Macaca mulatta) approached whichever of two boxes had smaller array, and tests indicated that they recognized all but the larger quantity of apple pieces when the differences in one of the differences in array size. Detailed analyses revealed pieces was one versus two, two versus three, three versus four, that choices to the larger array were influenced by the total and three versus five (ratios = 0.5, 0.66, and 0.6, respectively; number of flowers in Experiment 1, and by the relative size of Hauser, Carey, & Hauser, 2000), while apes will discriminate the two arrays (ratio) in Experiment 2. between a pile of nine pellets and another of ten pellets (ratio = Fig. 5 The proportion of visits to the array containing more flower for each of the pairs of arrays. The dashed line indicates the expected performance if the birds performed according to chance (50%). Asterisks indicate performance that was statistically significant: *** p < 0.001, ** p < 0.01, * p < 0.05. 74 Learn Behav (2021) 49:67–75 0.9; Hanus & Call, 2007), albeit with much greater training about time (Marshall, Hurly, Sturgeon, Shuker, & Healy, than our hummingbirds experienced. Honey bees (Apis 2013; Samuels, Hurly, & Healy, 2014), but not always mellifera) can not only discriminate between similar ratios, (Marshall, Hurly, & Healy, 2012). including zero versus one (Howard et al., 2018), but they In summary, wild, free-living rufous hummingbirds are can also spontaneously transfer their choices to match size able to discriminate between arrays of flowers based on the rather than number (Bortot, Stancher, & Vallortigara, 2020). number of flowers in those arrays, which is consistent with That our hummingbirds provided evidence of their numer- these birds having an approximate number system. These ical discrimination much more strongly in Experiment 2 is hummingbirds may not be able to match Alex’s ability to give consistent with data from bees: in both cases, when the ani- voice to his numeracy (e.g. Pepperberg, 1987;Pepperberg & mals were trained that one of the options contained the reward Carey, 2012), but coupled with the evidence that they also can and the other did not (Howard et al., 2019), both bees and our also determine ordinality in a sequence of flowers, they pro- hummingbirds showed that they were capable of numerical vide evidence that ecology may have shaped numerical discrimination that is not seen when the training was much capabilities. less, and importantly, involved only a rewarding option Open practices statement The data will be made available on request by (Howard et al., 2020). Indeed, substantial differences in the reviewers, and will be uploaded to DRYAD. numerical abilities of animals are found depending on whether spontaneous numerical abilities are tested or if animals are Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adap- first trained to associate a reward with a higher or lower tation, distribution and reproduction in any medium or format, as long as numerosity (Agrillo & Bisazza, 2014). Our hummingbirds you give appropriate credit to the original author(s) and the source, pro- appeared to show a spontaneous preference for the more nu- vide a link to the Creative Commons licence, and indicate if changes were merous array only when the choice was between one versus made. The images or other third party material in this article are included two and one versus four, but as the training array was made up in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's of four flowers, it is possible that the preference for the more Creative Commons licence and your intended use is not permitted by numerous array in the latter choice was due to the similarity to statutory regulation or exceeds the permitted use, you will need to obtain the training array rather than to spontaneous discrimination. permission directly from the copyright holder. 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