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The whiskers of seals are known to function as vibration receptors. Earlier experiments with blindfolded harbour seals in captivity have for example revealed that the animals can detect small water movements, and follow the hydrodynamic trails created by passing objects. But it is unclear if seals in the wild actively use this ability to find prey.
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The Sargasso Sea was identified as the spawning area of the European eel (Anguilla anguilla) 100 years ago, and numerous subsequent surveys have verified that eel larvae just a week old are regularly recorded there. However, no adult eels or eel eggs have ever been found, leaving room for alternative hypotheses on the reproduction biology of this enigmatic species. Chang et al.1 theorize about an area along the Mid-Atlantic Ridge as a potential spawning ground. The main argument for this hypothesis was that the chemical signature found in eel otoliths would indicate that early stage larvae had been exposed to a volcanic environment, such as the one present along the Mid-Atlantic Ridge. Since this correlation was solely based on a mis-interpretation of cited literature data, no new, conclusive information to pinpoint the Mid-Atlantic Ridge as an additional or even alternative spawning area was presented by Chang et al.For more than 100 years, the life history of Atlantic eels remains a matter of scientific debate. In a recent paper by Chang and colleagues, published in Scientific Reports (Sci Rep 10, 15981 (2020)), it is hypothesized that the spawning areas of the European eel (Anguilla anguilla) and the American eel (A. rostrata) are located along the Mid-Atlantic Ridge at longitudes between 50° W and 40° W1. This area lies outside the Sargasso Sea, which has so far been widely assumed to be the spawning region of both species since the beginning of the twentieth century2. The Danish researcher Johannes Schmidt collected eel leptocephali 30 mm long or less, some as short as 9 mm, all south of 30° N and west of 50° W3,4. Since then, Schmidt’s assumption was supported by a number of investigations that found recently hatched European eel larvae ( More

Brazil’s government risks fuelling the climate and biodiversity crisis by offsetting the fertilizer shortage resulting from Russia’s invasion of Ukraine this year (J. Liu et al. Nature 604, 425 (2022); S. Osendarp et al. Nature 604, 620–624; 2022). To produce an alternative fertilizer, it plans to mine up to 12 million tonnes annually of rhodoliths taken from an area in the South Atlantic that is roughly the size of the United Kingdom (see go.nature.com/3yhiyio).A full list of co-signatories to this letter appears in Supplementary Information.
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The Sargasso Sea has long been considered as the spawning area for Atlantic eels, despite the absence of direct observations after more than a hundred years of the survey. We proposed a new insight on the location of Atlantic eels spawning areas eastward of the Sargasso Sea at the intersection between the Mid-Atlantic Ridge and the oceanic fronts1. Our hypothesis is based on a body of corroborating cues from literature. We suggested that European silver eels converge towards the Azores whatever their departure point from Europe and Northern Africa, then they follow the Mid-Atlantic Ridge south westerly until they reach oceanographic fronts where temperature and depths are favourable for reproduction. These orientation behaviours are potentially based on magnetic fields and odours that might be generated by the Mid-Atlantic Ridge volcanic activity and detected by eels during their diel vertical movements. The first favourable meeting point is then located at the crossing between the Mid-Atlantic Ridge and the oceanic thermic isotherms located around 45° W and 26° N. Our hypothesis is supported by (i) microchemical differences between the core of otoliths extracted from leptocephali collected in the Sargasso Sea and from glass eels collected across Europe suggesting that glass eels hatch in different chemical environments than leptocephali (ii) an asymmetric genetic introgression between American and European eels2 suggesting that the overlapping spawning areas favour transport of hybrids towards northern Europe rather than to America and to southern Europe. This supports the possible existence of several distinct spawning areas, where currents favour transport either westward (American eel), north eastward (hybrids and European eels) or eastward (European eels). To test this hypothesis, we developed a transport model and compared the dispersion dynamics of virtual leptocephali released from the Sargasso Sea and from above the Mid-Atlantic Ridge. The transport models showed that virtual eels released from the Mid-Atlantic Ridge reached Europe and America following similar patterns than those released from the Sargasso Sea thus supporting the Mid-Atlantic Ridge spawning hypothesis.Hanel et al.3 have raised several concerns, one of which being that “microchemical evidence was the only was the major argument supporting the Mid-Atlantic Ridge hypothesis”. This was their start point of a critical rebuttal of our findings to question our hypothesis. Instead, we consider that our regrettable error does not fundamentally contradict the possibility that eels do indeed successfully spawn outside the so-called Sargasso Sea.(Comment 1) The importance of seamounts as orientation and navigation cues towards a spawning area was hypothesized, no clear mechanism is proposed for how the migrating eels can detect the ridge.(Response 1) Our Hypothesis does not state that eels find a kind of shallow seamount where they spawn. Instead, we propose that orientation of silver eels during their spawning migration could be based on a combination of behavioural mechanisms including geomagnetism, odours, temperature and salinity gradients4,5,6,7,8. These environmental cues and related gradients are strongly controlled or influenced by the topography of the oceanic floor. The Mid-Atlantic Ridge and the Mariana areas have similarities with ridges and seamount chains oriented perpendicularly to temperature and salinity fronts surrounded by deep abyssal plains. Our Mid-Atlantic Ridge hypothesis proposed that Atlantic eels could use similar signposts as Japanese eel, which hatch near the Mariana Ridge9. Indeed, as for the Japanese eels, the orientation mechanism that lead Atlantic eels from the growth areas to the ridge are not understood, but the empirical observations from Righton et al.10 suggest that eels converge towards the Azores whatever their release point across Europe and that their diel vertical migration takes them down to 500–1000 m every day. The reasons for this behaviour are not elucidated, but since they cost energy, they are likely compensated by advantages such as orientation together with predator avoidance and sexual maturation11,12,13. Following our hypothesis, eels search for orientation cues during DVM. The geomagnetic fields are suggested to provide detectable information for silver eels on their oceanic spawning migration14. However, whether magnetic characteristics of the Mid-Atlantic ridge may provide detectable orientation cues still needs to be documented. Similarly, the existence of detectable odours that might be generated by the tectonic activity and hydrodynamics of the Mid-Atlantic ridge and serve as orientation cues for eels is still unknown. Hydrodynamic mesoscale turbulence and vertical flows have been shown to be generated along the Mid-Atlantic Ridge15, which we propose eels might be able to detect. There are no well supported spawning areas of freshwater eels other than A. japonica and one north Pacific population of A. marmorata. The spawning areas of the other species remain unknown. In the south west Indian Ocean, spawning areas of 3 species (A. mossambica, A. marmorata and A. bicolor) were proposed on the east of the Mascarene Ridge with a similar topography (although shallower) than along the Mid-Atlantic Ridge and the Mid-Pacific ridge and seamounts16,17. Inaccurate spawning areas were also proposed for the South Pacific A. diffenbachii between Fiji, New Caledonia and New Zealand; in the vicinity of a number of oceanic ridges and trenches18 that may also serve as landmarks. Because all eel species studied on their spawning migration show similar diel vertical migration behaviours, it is likely that common orientation mechanisms could lead to detection of oceanographic variability related to the topography of the sea floor and related geomagnetism, local hydrodynamic turbulence and odour caused by vertical currents. This kind of oceanic landscape (chains of seamounts) occurs on narrow areas which strongly increase the meeting probability of spawners searching for partners and favourable spawning places.(Comment 2) Drift simulation with departures from the Mid-Atlantic Ridge and from the Sargasso Sea showed similar results. This is not surprising since the modelling of larval drift seems essentially just to reflect the slow westward drift prevailing both in the Sargasso Sea and Mid-Atlantic Ridge areas. The assumption of using the intersection of the Mid-Atlantic Ridge by the two thermal fronts as presumed spawning places seems to have little basis. There is no indication neither of one nor two temperature fronts at depths where leptocephali are found along a 45  W latitudinal section in the middle of the Mid-Atlantic Ridge area.(Response 2) We agree with the comments that the similar distributions between the departure from the Sargasso Sea and the Mid-Atlantic Ridge are expected, as they mainly reflect the ocean circulation. This is also what we wanted to address, if different departures could lead to similar distributions, either Sargasso Sea or Mid-Atlantic Ridge could be candidates for the spawning area. We also agree that many eel larvae were collected at the two fronts in the Sargasso Sea, but not near the Mid-Atlantic Ridge. However, if the departure from the Sargasso Sea and the Mid-Atlantic Ridge led to similar distributions after 720 days, they were not the result of westward current, but the cause of a relatively quiet ocean in the Sargasso Sea and its surrounding area (i.e. Fig. 1). Without prevailing current, small larvae were mainly transported by ocean dispersion, and would later be transported by the major currents that lie in the north (Azores Current), south (North Equatorial Current), and west (Gulf Stream) of the Sargasso Sea. So, we compared departures at 100 km from west and east of the Mid-Atlantic Ridge. Subtle differences occurred (figure below). V-larvae departing from the east of the ridge dispersed relatively less northward compared to larvae released 100 km at the west of the ridge (this figure and original paper). Secondly v-larvae released at the south east of the study area (red dots on the figure, right panel) disperse relatively less towards the Caribbean Sea than when released at the west (red dots of the figure, left panel). This suggests that the dispersion of European eel larvae is optimum in an area comprised between the Mid-Atlantic Ridge and the Sargasso Sea (our previous simulation in the original paper), and declines eastward of the Mid-Atlantic Ridge (present simulation below).Figure 1Distribution of v-larvae released departure at the west (left) and east (right) of Mid-Atlantic Ridge. The tracking method is the same as described in the paper, v-larvae were release within 100 km west and east of the ridge.Full size imageHanel et al. also indicate that the convergence front weakens from West, in the Sargasso Sea, to East above the ridge. We consider that this constitutes an additional argument that the Mid-Atlantic Ridge is indeed at the edge of the convergence zone at the first area of the Atlantic Ocean where currents and temperatures are favourable for reproduction of eels.(Comment 3) Elevated manganese (Mn) concentrations in the otolith cores of glass eels as a hint for successful spawning only in areas with volcanic activity based on observations of Martin et al.18. However, the results from Martin et al.19 were entirely misread, resulting in a mis-interpretation of the data.(Response 3) Based on Martin et al.19, we stated that higher concentrations of Mn were found in glass eels’ otoliths collected across European estuaries than in otoliths of leptocephali larvae sampled in the Sargasso Sea. We suggested that this was the indication that glass eels were born in areas where volcanic activity produces high loads of Mn and other metals. This formed one of the arguments supporting our hypothesis that Atlantic eels could spawn in the proximity to the Mid-Atlantic Ridge. Thanks to Reinhold Hanel and colleagues, we realized that Martin et al.19 in fact showed that concentrations of Mn were higher in the center of otoliths of leptocephali larvae than in those of glass eels collected along the European coasts. Consequently, this argument is no longer valid. Nonetheless, otolith microchemical fingerprints significantly differ between young leptocephali sampled in the Sargasso Sea in 2008 and glass eels collected in Europe, hence suggesting that they have distinct spawning areas19. These authors indicated that the incorporation of elements from the environment to the otoliths needed to be better understood, namely as stated by Hanel et al., because of physiological and environmental control such as temperature and salinity. In addition, they outline that the dynamics of elements from the sea floor to the subsurface is not well understood and could be slow. We totally share these conclusions that are well known facts, and that simply confirm that environmental characteristics (trace element concentrations, salinity and temperature) are responsible for the elemental signature of the central part of otoliths. Hanel et al. also state that the composition of otoliths are also controlled by elemental maternal transfer from the egg to the otoliths. We are aware of this fact that has been shown is other fish species. However, the laser ablations were performed after the first feed check where maternal influence is reduced and is overruled by environment18. This supports the idea that glass eels collected in Europe do not originate from the same environments as leptocephali captured in the Sargasso Sea.(Comment 4) Insufficient sampling efforts and a limited area coverage of recent surveys as a possible reason for “false negative” observations along the Mid-Atlantic Ridge. This statement does not recognize the investigations by Johannes Schmidt as well as earlier and later surveys in the Mid-Atlantic Ridge area. The ICES “Eggs and Larvae database” records a total of 48 A anguilla leptocephali caught within the area 15–29 N and 43–48 W, at 10 stations between 1913 and 1970.Thanks for pointing out that larvae have been caught near the Mid-Atlantic Ridge, in which larvae were not newly hatched because of their relatively large size (23–45 mm). Ocean currents were weak and could flow either eastward or westward in this region, indicating that the spawning could occur from west to east of the ridge, without considering swimming. Note that ocean currents could change directions, so that it was also possible to spawn near the ridge after been transported eastward and westward.The observed distribution of small larvae  More

Study population and song recordingsAll animal procedures were carefully reviewed by the Williams College IACUC (WH-D), the Bowdoin College Research and Oversight Committee (2009–18), and the University of Guelph Animal Care Committee (08R601), and were carried out as specified by the Canadian Wildlife Service (banding permit 10789D).We studied Savannah sparrows (Passerculus sandwichensis) at the Bowdoin Scientific Station on Kent Island, New Brunswick, Canada (44.5818°N, 66.7547°W). Since 1988, individuals nesting within a 10 ha study area in the middle of the island (30–70 pairs each year; part of a larger population of 350–500 males breeding on Kent Island and two adjacent islands) have been colour-banded to facilitate visual identification, and complete demographic information is available for birds on the study site (though not for the entire population) for the years 1989–2004 and 2009–2013. Because of strong natal and breeding philopatry51, birds hatched on the study site itself represent 40–80% of adult breeders in that area, and because of the systematic banding program, ages are known. Each year adds a new generation to the population, with yearlings making up approximately half of the adult breeding males. The birds banded and recorded on the study site are estimated to make up 10–20% of the Savannah sparrow population on Kent Island and two nearby islands.Details of the recording methods used in this study (covering the years 1980, 1982, 1988-9, 1993-8, and 2003–13) can be found elsewhere36,49. Using digitally generated sound spectrograms (using SoundEdit Pro and Audacity), birds were scored as having either a) high note cluster=a final introductory segment interval including at least two different note types, or b) a click train=one or more introductory segment intervals including at least two clicks and no other note types, or c) both features36 (see Supplementary Fig. 1 for a full description of note types). Although a small proportion of birds (mean = 8.3%) did not include either feature in their songs (such birds either had no feature in the introductory segment intervals or one non-click note type in the final interval), we did not include this option in the model and omitted these birds from summaries of the data. We did not include data after the breeding year 2013 because of we began an experimental field tutoring study in the summer of 201364.ModellingWe used a dynamic, discrete time model which allowed us to focus our analysis to specific time points within the year that are related to song learning (the beginning and end of the breeding season). These were: (1) the return of older birds between breeding seasons, (2) the recruitment of young birds singing newly crystallized songs in the spring, and (3) reproduction, resulting in the addition of juveniles during the summer breeding season.Because survival data were not available for every year during the time span we studied, we captured the variation in survival rates observed in the field57 by using a binomial distribution centered on the average historical survival rate for each age class (addressing the possibility that cultural drift resulting from random differences in survival rates was responsible for the shift in song features). The model incorporates stochasticity to capture the variation in population dynamics and return rates by assigning parameter values for survival and return rates from empirically generated probability distributions.We did not include spatial distribution of song variants in the model; although spatial patterns can be important for the dynamics of language loss58, territories with birds singing click trains and high note clusters were intermixed and no spatial structure was apparent (Fig. 3).The model assumes that males choose which features to incorporate into the introductory sections of their songs during song development. Individuals fall into one of six mutually exclusive classes of male Savannah sparrows. The classes are defined by (1) the bird’s developmental stage in the song learning process: juvenile (J, the first year, when the song is plastic) or adult (A, after the first spring, when the song is crystallized), and (2) the variant or variants sung as part of the bird’s introduction (high note clusters, click trains, or both). Denoting note high note clusters with X and click trains with C, the adult classes are therefore AX, AC, and AXC, and the juvenile classes are JX, JC, and JXC. The sum of the individuals in these classes is the total male population.We used two times during each year – late spring and late summer – to correspond to stages in song development (Fig. 5). At a given time t, when breeding is underway in the late spring, the male population consists entirely of adults singing crystallized song, and therefore each juvenile class is empty. At the end of the summer, the population of males has been augmented by juveniles, which are initially assigned to the same variant class as their fathers. To capture these dynamics, we define an intermediate time step, denoted ti. Time t + 1 then corresponds to the following breeding season (late spring), when juvenile males hatched the previous year have completed song development, crystallized their songs, and joined the adult class.Fig. 5: Model of song development.We used two age classes (J = juvenile and A = adult) and three classes of introductions (C = click trains, X = high note clusters, and  XC = both). In the late spring of a given year (time = t), only adult males are present. In late summer, those adults have bred and both they and juvenile males are present; at this intermediate time (ti) each male is initially allocated the same introduction type as his father (solid lines). Then, as song development progresses and juvenile males can be influenced by other tutors, they may retain their initial introduction type or switch to either of the other two types (dashed lines) before they crystallize their songs late in the following spring (time = t+1), and join the breeding cohort, which also includes adult males from the previous year who returned to breed again.Full size imageIn the late summer the male population increases with the addition of juveniles hatched that year, some of which will return to join the singing population the following year; survivors will return to breed within a few hundred meters of where they hatched51. To fit the observed historical decline in the Kent Island population57, the total number of returning juveniles, r (including both those hatched on site and those immigrating from nearby populations at time), follows a Poisson distribution where m = 33.6 – .182x and x is the number of years since 1980 (this function results in a decline of 5 males per decade; the initial number on the study site used in the model, 70, was extrapolated from historical data). The size of each returning juvenile class at time ti then takes the form:$${{{{{{rm{JY}}}}}}}_{{{{{{{rm{t}}}}}}}^{{{{{{rm{i}}}}}}}} sim {{{{{rm{Poisson}}}}}}left(mright)frac{{{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}}{{{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{rm{t}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}}+{{{{{rm{AX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}}}$$
(1)
for each Y ∈ {X, C, XC}.After the following winter, the proportion of surviving adults at time t + 1 follows a binomial distribution where the mean survival rate s = 0.48 is derived from historical data. Therefore, each adult class takes the form:$${{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{rm{t}}}}}}+1} sim {{{{{rm{Binomial}}}}}}left({{{{{rm{AY}}}}}},{{{{{rm{s}}}}}}right)* {{{{{rm{A}}}}}}{{{{{{rm{Y}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
(2)
At the beginning of the next breeding season, juveniles complete song learning64, choosing which variant to crystallize as part of the song, and enter an adult song class; thus all of the juvenile classes disappear at t + 1. Which adult class juveniles join depends on separate learning functions for each of the two variants, ϕX for the high note cluster and ϕC for the click train. The ϕ function takes values between 0 and 1 and gives the probability of crystallizing a song form during the transition from natal year to breeding, depending upon the frequency-dependent bias and selection parameters (see below). These functions define the proportion of features that appear in the next generation as compared to that of the previous generation. Therefore we have:$${{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{rm{t}}}}}}+1}={left({{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
(3)
$${{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{rm{t}}}}}}+1}={left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{left({{{upphi }}}_{{{{{{rm{C}}}}}}}right)}^{2}{{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right){{{upphi }}}_{{{{{{rm{C}}}}}}}{{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+{{{{{rm{A}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
(4)
$${{{{{rm{A}}}}}}{{{{{{rm{XC}}}}}}}_{{{{{{rm{t}}}}}}+1}=2{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right){{{{{rm{J}}}}}}{{{{{{rm{X}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+2{{{upphi }}}_{{{{{{rm{C}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{J}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}+({{{upphi }}}_{{{{{{rm{X}}}}}}}{{{upphi }}}_{{{{{{rm{C}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)left(1-{{{upphi }}}_{{{{{{rm{C}}}}}}}right){{{{{rm{JX}}}}}}{{{{{{rm{C}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}})+{{{{{rm{A}}}}}}{{{{{{rm{XC}}}}}}}_{{{{{{{rm{t}}}}}}}_{{{{{{rm{i}}}}}}}}$$
(5)
The sum of probabilities defining all of song crystallization outcomes for the songs of fathers with song type X is:$${left({{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}+{left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)}^{2}+2{{{upphi }}}_{{{{{{rm{X}}}}}}}left(1-{{{upphi }}}_{{{{{{rm{X}}}}}}}right)=1$$
(6)
Learning curvesTo define how young males’ song learning is influenced by the songs they hear, we used learning curves based on type III Holling response curves59 which provide a means to numerically capture functional responses. In our model, the type III curve models the response of juvenile to the song form of adults in the population based on two variables: (1) frequency-dependent bias that favors one form based on its prevalence within the adult population, and (2) selection that favors a particular form of the song.The learning curves, ϕx for the high note cluster and ϕc for the click train, are modified forms of the type III Holling response curve):$${{{upphi }}}_{{{{{{rm{x}}}}}}}=frac{{x}^{{{{{{rm{beta }}}}}}}/{{{{{rm{sigma }}}}}}}{{(1-x)}^{{{{{{rm{beta }}}}}}}+({x}^{{{{{{rm{beta }}}}}}}/{{{{{rm{sigma }}}}}})}$$
(7)
and$${{{upphi }}}_{{{{{{rm{c}}}}}}}=frac{{{{{{rm{sigma }}}}}},{c}^{{{{{{rm{beta }}}}}}}}{{(1-c)}^{{{{{{rm{beta }}}}}}}+{{{{{rm{sigma }}}}}}{{c}}^{{{{{{rm{beta }}}}}}}}$$
(8)
where x is the proportion of the high note cluster within the population, c is the proportion of the click train within the population, β is frequency-dependent bias (favoring learning the novel or retaining the common variant), and σ is selection on the novel variant (a preference for learning the variant that is not dependent on frequency of the variant and includes factors such as prestige bias, success bias, status, and content bias). Note that the two learning curves do not have identical equations, because selection is not frequency-dependent. In these equations, β  > 1 corresponds to conformist selection, and when β  1 correspond to selection for a novel variant and values of σ  More