Cumulative cultural evolution and mechanisms for cultural selection in wild bird songs
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
