ESM data from Cytoplasmic inheritance of parent-offspring cell structure in the clonal diatom <i>Cyclotella meneghiniana</i>

The data supporting our pape

Supplementary Information (SI) from Cyclic dominance emerges from the evolution of two inter-linked cooperative behaviours in the social amoeba

This document includes the SI Text (for calculation and experimental conditions) and SI figures

Genotype and body size data

Genotyping data for paternity analysis: genotype of seven microsatellite loci for adults and offspring from two ponds. And body size data of adult toads: snout-to-vent length (SVL) of amplectant pairs and non-amplectant males in the two ponds for three years

Lévy Walks Suboptimal under Predation Risk

<div><p>A key challenge in movement ecology is to understand how animals move in nature. Previous studies have predicted that animals should perform a special class of random walks, called Lévy walk, to obtain more targets. However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear. We focused on ecological factors, such as predation risk, and analyzed whether Lévy walk may not be favored. It was remarkable that the ecological factors often altered an optimal search strategy from Lévy walk to Brownian walk, depending on the speed of the predator’s movement, density of predators, etc. This occurred because higher target encounter rates simultaneously led searchers to higher predation risks. Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.</p></div

The relationship between relative encounter rates of targets and predators.

<p>Data in (A–C) and (D–F) correspond to life-cycle types I and II, respectively. (A and D) The lower encounter rate condition, <i>k</i>_BW = 0.1 (e.g., lower predator density or slower predators). (B and E) The middle encounter rate condition, <i>k</i>_BW = 1. (C and F) The higher encounter rate condition, <i>k</i>_BW = 10 (e.g., higher predator density or faster predators). The colors represent the fitness of LW (or any search strategies) compared to BW. The result shows that the life-cycle type and the three parameters, encounter rate to targets, that to predators and strength of predation pressure critically determine the fitness. When the strength of predation pressure is high (C and F), the LW obtains lower fitness even if the encounter rate with targets is high.</p

The relative fitness of a Lévy searcher with life-cycle type II.

<p>The strategy of predators is (A) sit-and-wait (<i>v</i>_p = 0); (B) slow Lévy walker (<i>v</i>_p/<i>v</i>_s = 0.2); (C) middle Lévy walker (<i>v</i>_p/<i>v</i>_s = 1); and (D) fast Lévy walker (<i>v</i>_p/<i>v</i>_s = 5). The horizontal axis represents the number of predators introduced, and the vertical axis represents the Lévy index <i>μ</i> of the searcher. The total search time is 10⁷ for sit-and-wait, slow, and middle predator conditions and 5×10⁷ for fast predator conditions.</p

The relative mean search time changes depending on the density and velocity of predators.

<p>The strategy of predators is (A) sit-and-wait; (<i>v</i>_p = 0); (B) slow Lévy walker (<i>v</i>_p/<i>v</i>_s = 0.2); (C) middle Lévy walker (<i>v</i>_p/<i>v</i>_s = 1); and (D) fast Lévy walker (<i>v</i>_p/<i>v</i>_s = 5). The horizontal axis represents the number of predators introduced, and the vertical axis represents the Lévy index <i>μ</i> of the searcher. The total search time is 10⁷ for sit-and-wait, slow, and middle predator conditions and 5×10⁷ for fast predator conditions.</p

The relative fitness of a Lévy searcher with life-cycle type I.

<p>The strategy of predators is (A) sit-and-wait (<i>v</i>_p = 0); (B) slow Lévy walker (<i>v</i>_p/<i>v</i>_s = 0.2); (C) middle Lévy walker (<i>v</i>_p/<i>v</i>_s = 1); and (D) fast Lévy walker (<i>v</i>_p/<i>v</i>_s = 5). The horizontal axis represents the number of predators introduced, and the vertical axis represents the Lévy index <i>μ</i> of the searcher. The total search time is 10⁷ for sit-and-wait, slow, and middle predator conditions and 5×10⁷ for fast predator conditions.</p

Encounter rates with targets and predators in our simulation setting.

<p>(A) The relative encounter rate with targets increases at an intermediate <i>μ</i>. (B) The mean encounter number of a BW searcher (<i>k</i>_BW) for <i>T</i>_max. As the number or velocity of predators increases, the encounter number increases. (C) The relative encounter rate with predators increases when the movement of a searcher approaches a straight line (i.e., smaller <i>μ</i>). However, the faster the movement of predators, the lower the rate of increase. Similar results for <i>N</i>_p = 30 (left) and <i>N</i>_p = 120 (right) indicate that the relative encounter rate does not change depending on predator densities.</p

Genotype_Morphology_ B. japonicus

Genotype_Morphology_ B. japonicu