Movement Scenario 3

In the movement scenario 3 the immigrant agent from population D that spent the feeding season in the feeding area V (E1 feeding area, Figure 3.1) joined the northward migration towards population E1’s breeding ground, and remained with population E1 for the entire second migration cycle. Similarly to the analysis for the second movement scenario, models 1, 2 and 3 were initially compared using the same set of parameters, using both small (5) and large (50) breeding and feeding areas.

The revolutionary song frequency pattern using model 1 (distance-only) did not show great differences compared with movement scenario 2. Similarly to the previous scenario, in a few runs song revolutions in population E1 did emerge as soon as the immigrant agent from population D reached area V during the first feeding season (Figure 3.10). However, in the majority of cases the 𝑆𝑅_𝐷 songs introduced by the immigrant agent did not diffuse in the E1 population. After the first feeding season, the immigrant agent generally permanently acquired the 𝑆𝑅_𝐸1 song repertoire, abandoning its old songs (Figure 3.10). 𝑆𝑅𝐷 song frequency using model 2 (distance + novelty)

83 presented a stable pattern, without the decrease observed in scenario 2 (thick yellow line; Figure 3.10). This was because the immigrant agent did not return to its population of origin (population D). The implementation of the novelty bias did not produce any song revolutions in population E1 across all the 100 experiments run (Figure 3.10). The median 𝑆𝑅_𝐷 song frequency using model 3 (distance + memory) presented a very similar trend to the one in scenario 2: a sharp increase in the frequency during the first feeding season followed by the finalisation of the song revolution during the second breeding season of the two migration cycles (thick blue line, 𝑆𝑅_𝐷 song frequency = 15; Figure 3.10).

Figure 3.10. Song frequencies after long-term immigration. 𝑆𝑅_𝐷 song frequency 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 3, one immigrant agent from population D joined permanently population E1 from the first feeding season till the end of the experiment. 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. The size of the breeding and feeding grounds was set to 5.

When model 1 was tested using larger breeding and feeding areas the frequency of the revolutionary 𝑆𝑅_𝐷 in population E1 did not differ compared to BGS & FGS = 5 (Figure 3.11). Model 2 displayed a slower increase in song frequency due to lower agent spatial density but the pattern of 𝑆𝑅_𝐷 song frequency values was extremely similar to results from smaller breeding and feeding areas (Figure 3.11). The greatest

84 difference between small and large breeding/feeding grounds was again seen in model 3’s results. Similarly to the temporary immigration scenario, the decrease in agents’ density prevented the emergence of song revolutions in population E1 (Figure 3.11). However, if compared to the same BGS & FGS experiments of the movement scenario 2 (Figure 3.9), the prolonged population switch of the immigrant agent had a notable effect on the frequency of the revolutionary song type in population E1. While in scenario 2 the median 𝑆𝑅_𝐷 song frequency fluctuated around 0 (i.e. no agent of

population E1 acquired 𝑆𝑅_𝐷), in scenario 3 𝑆𝑅_𝐷 songs diffused to ≈ 30 % of population E1 (𝑆𝑅𝐷 song frequency ≈ 3; Figure 3.11).

Figure 3.11. The effect of large feeding and breeding grounds on song frequency after long-term immigration. 𝑆𝑅𝐷 song frequency 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. The size of the breeding and feeding grounds was set to 50.

The patterns of median 𝑆𝑅_𝐷 song frequency across the different memory

conservatism (𝑐) values can be grouped in three qualitative categories. First, runs where 𝑐 ≤ 0.3 displayed revolutionary song frequencies that rapidly decreased in population E1 after introduction by the immigrant agent during the first feeding season (Figure 3.12). Second, memory conservatism values that ranged between 0.4 and 0.6 resulted in a greater increase in frequency during the first feeding season, and a stabilisation around

85 30% of population E1 (𝑆𝑅_𝐷 song frequency ≈ 5; Figure 3.12), followed by a decrease of the frequencies once the agents reached E1 breeding ground during the second

migration cycle. Thirdly, similarly to results under movement scenario 2, experiments with 𝑐 ≥ 0.7 generally produced 𝑆𝑅𝐷 song revolutions; the revolutionary song frequency

reached 100 % of population E1’s agents during the breeding season of the second migration cycle (Figure 3.12).

Figure 3.12. Memory conservatism affects song frequencies after long-term immigration. 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 5.

Similar to results from the short term immigration scenario, when agent density decreased due to larger ground sizes (BGS & FGS = 50) the distance + memory

learning bias was not as effective in triggering song revolutions. Median 𝑆𝑅_𝐷 song frequencies never exceeded 30% of the E1 population regardless of 𝑐 level (0 ≥ 𝑆𝑅𝐷

song frequencies ≥ 5; Figure 3.13). The permanent switch of the immigrant agent during the whole second migration cycle had only a minor effect on revolutionary song

86

Figure 3.13. Increased memory conservatism does not rescue revolutions when feeding and breeding grounds are large, even when immigration is permanent. 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.