Movement Scenario 2

The second movement scenario was initially tested using model 1 (distance- only), model 2 (distance + novelty) and model 3 (distance + memory). In the following figures, 𝑆𝑅_𝐷 song frequency is plotted between 0 and 15 for each of the two populations (15 = maximum number of agents for each population). The three learning biases were compared using the same set of parameters. With BGS & FGS = 5, model 1 (distance- only) produced some abrupt increases in 𝑆𝑅_𝐷 song frequency, from 0 to 15, but in the majority of cases, the immigrant agent of population D conformed quickly to the new 𝑆𝑅𝐸1 song majority of population E1 (the median 𝑆𝑅𝐷 song frequency in population D

decreased in this case from 15 to 14; Figure 3.6). Upon returning to its original breeding areas (population D) the agent reacquired the new majority 𝑆𝑅_𝐷 song, hence the

increase in median frequency from 14 to 15 (thick black line; Figure 3.6). 𝑆𝑅_𝐷 song frequency when model 2 (distance + novelty) was used followed a different pattern. During the first feeding season, the frequency of the revolutionary song in population E1 increased and stabilised at around five agents (𝑆𝑅_𝐷 song frequency = 5, i.e. ≈ 30% of E1 population; Figure 3.6). However, during the second breeding season 𝑆𝑅𝐷 song

frequency decreased within population D resulting in 𝑆𝑅_𝐸1 songs diffusing to ≈ 30% of agents of population D (𝑆𝑅𝐷 song frequency = 10; Figure 3.6), representing a partially

inverse or failed revolution going in the opposite direction than the temporary immigration.

The implementation of model 3 (memory conservatism 𝑐 = 0.9, blue lines; Figure 3.6) led to a higher likelihood of song revolutions compared to the other two learning biases. During the first feeding season, the introduction of the immigrant agent from population D into population E1 feeding area triggered a steep increase in

frequency of 𝑆𝑅𝐷 songs up to more than 60% of population E1 (𝑆𝑅𝐷 song frequency =

10; Figure 3.6). After the agent from population D abandoned population E1 to return to its own population, the frequency of the revolutionary song stabilised at around 12 E1

78 agents during the northward migration and finally reached 100 % of the E1 during the breeding season of the second migration cycle (𝑆𝑅_𝐷 song frequency = 15; Figure 3.6).

Figure 3.6. Song frequencies after temporary immigration. 𝑆𝑅𝐷 song frequency when the size of the breeding and feeding ground was set to 5 compared across three learning biases: distance-only (model 1; black lines), distance + novelty (model 2, yellow lines) and distance + memory (model 3, 𝑐 = 0.9, blue lines). In movement scenario 2, one immigrant agent from population D mixed temporarily with population E1 during the first feeding season. Thick lines represent the median for each learning bias set of 100 experiments (thin lines). The light and dark grey areas represent breeding and feeding seasons respectively.

With a larger BGS & FGS (50) the overall frequency pattern of the

revolutionary song using model 1 did not change compared to the smaller ground size (Figure 3.7). However, the 𝑆𝑅_𝐷 song frequency variability between experiments increased, with some runs resulting in song revolutions in population E1 (𝑆𝑅𝐷 song

frequency = 15) and others in complete inverse revolutions where the 𝑆𝑅_𝐸1 songs diffused into population D (Figure 3.7). Model 2 results were broadly similar to those under a small BGS & FGS. The initial increase in revolutionary song frequency was slower with a larger BGS & FGS, but during the second breeding season 𝑆𝑅_𝐷 songs frequency decreased in population D similarly to results using smaller breeding and feeding grounds. The most notable change with larger BGS & FGS was in the outcomes of model 3 (thick blue line, 𝑐 = 0.9; Figure 3.7). The decrease in agent density, driven by the increase in breeding and feeding ground size, impacted negatively on the

79 diffusion of the revolutionary song in population E1. Across multiple experiments, only about 30% of population E1 ever produced 𝑆𝑅_𝐷 songs (5 ≤ 𝑆𝑅_𝐷 song frequency ≤ 10; Figure 3.7), and the overall median frequency indicated an absence of song revolutions (𝑆𝑅_𝐷 song frequency in E1= 0; Figure 3.7).

Figure 3.7. The effect of large feeding and breeding grounds on song frequency after temporary immigration. 𝑆𝑅𝐷 song frequency when the size of the breeding and feeding ground was set to 50 compared across three learning biases: distance-only (model 1; black lines), distance + novelty (model 2, yellow lines) and distance + memory (model 3, 𝑐 = 0.9, blue lines). Thick lines represent the median for each learning bias set of 100 experiments (thin lines). The light and dark grey areas represent breeding and feeding seasons respectively.

Once the differences between models 1, 2 and 3 were explored, the focus of the analysis shifted towards a more thorough testing of model 3 (distance + memory) and, more specifically, the effect of different values of memory conservatism (𝑐) on the emergence of song revolutions in population E1. Ten different 𝑐 values were tested, from low (0.1) to high (0.999) memory conservatism, for each 𝑐 value, 200 experiments were run (100 with BGS & FGS = 5; 100 with BGS & FGS = 50) totalling in 2000 further model runs. Due to the large amount of resulting data, I present only the median 𝑆𝑅_𝐷 song frequency for each 𝑐 value (Figure 3.8); however, the results of all the

individual model runs for all 𝑐 values can be found in Appendix 3 (Figures A3.1 & A3.2).

80 The value of 𝑐, the memory conservatism parameter, strongly affected

revolutionary song diffusion across population E1. A low 𝑐 (0.1) produced a slight increase of 𝑆𝑅_𝐷 song frequency in the beginning of the first feeding season, triggered by the arrival of the agent from population D into E1 feeding area V. However, this slight increase is then rapidly followed by a steady decrease resulting in the immigrant agent conforming to the 𝑆𝑅_𝐸1 song repertoire (𝑆𝑅_𝐷 song frequency in population D = 14; Figure 3.8). Higher 𝑐 values (0.2, 0.3, 0.4 and 0.5) generated higher revolutionary song frequency peaks that nonetheless ultimately resulted in the disappearance of the

revolutionary song type in population E1 once the agents reached their breeding areas (𝑆𝑅𝐷 song frequencies in population E1 = 0; Figure 3.8). In experiments where 𝑐 = 0.6

the revolutionary song median frequency reached roughly 60% of population E1 (𝑆𝑅_𝐷 song frequency ≈ 10; Figure 3.8) at the end of the first feeding season to subsequently decrease towards ≈ 50% of the E1 population; in this case population E1 produced consistently both 𝑆𝑅_𝐷 and 𝑆𝑅_𝐸1 songs. Runs with 𝑐 values higher than 0.7

predominantly produced song revolutions in population E1 (𝑆𝑅𝐷 song frequency = 15;

Figure 3.8). Revolutionary song frequencies for this set of 𝑐 values showed sharp increases during the first feeding season followed by the completion of the song

revolution events during the second breeding season of population E1. At this stage the immigrant agent from population D already returned to its original population,

indicating that, given enough memory inertia, revolutions could occur even if the

interaction between the immigrant agent and population E1 is limited to a single feeding season.

81

Figure 3.8. Memory conservatism affects song frequencies after temporary immigration. Median 𝑆𝑅_𝐷 song frequencies compared across ten distinct 𝑐 values (from 0.1 to 0.999) each indicated with a line of different colour. The light and dark grey areas represent breeding and feeding seasons respectively. The size of the breeding and feeding grounds was set to 5.

Model 3 experiments run with larger breeding and feeding grounds (BGS & FGS = 50) did not display song revolutions at any 𝑐 value (Figure 3.9). The arrival of the immigrant agent in population E1 feeding area triggered a slight increase of 𝑆𝑅_𝐷 song frequency (0 ≤ 𝑆𝑅𝐷 song frequency in E1 ≤ 2; Figure 3.9); however, once

population E1 started its northward migration 𝑆𝑅𝐷 songs disappeared almost entirely

82

Figure 3.9. Increased memory conservatism does not rescue revolutions when feeding and breeding grounds are large. Median 𝑆𝑅𝐷 song frequencies compared across ten distinct 𝑐 values (from 0.1 to 0.999) each indicated with a line of different colour. The light and dark grey areas represent breeding and feeding seasons respectively. The size of the breeding and feeding grounds was set to 50.