Article title: When being the center of the attention is detrimental: Copiers may favour the use of evasive tactics

Journal name: Behavioural Ecology and Sociobiology

Author names: Frédérique Dubois

Affiliation and e-mail address of the corresponding author: Frédérique Dubois (), Département de Sciences biologiques, Université de Montréal, Canada

Expected payoffs when no rival present

Unselective males do not evaluate the quality of potential partners and, therefore, display normal courtship behaviour towards every encountered female. Their average expected payoff is then:

. / (A1)

The first and second terms of equation (A1) correspond to the expected performance of an unselective male when the female is of high or low-quality, respectively.

Because selective males display normal courtship behaviour when no rival is present, irrespective of whether they are sensitive or insensitive to the presence of others, their average expected payoff is then:

. / (A2)

Finally, copier males who are on a territory occupied by a female but have no social information about her quality behave as unselective males, and therefore, display normal courtship behaviour towards every encountered female. Their average expected payoff is then:

. / (A3)

Expected payoffs when a rival male is present

When two unselective males compete with each other, they both mate with the female in a random order, and, consequently, have on average a fertilization success of ½. Their expected gain is then:

. / (A4)

Similarly, when an unselective male competes with a copier male, they both display a normal courtship display, and hence have a mating probability which is one. However, because a copier male necessarily mates with the female after having observed the courtship behaviour of its rival, the chance that the unselective male fertilizes the eggs of the female is then, while that of its copier rival is . The expected payoffs of an unselective and a copier male, when they compete with each other, are then:

/ (A5)

and

. / (A6)

By contrast, when an unselective male competes with a selective rival, this latter does not necessarily mate with the female, as it may either judge the female as a low-quality partner (with a probability  or (1-) if the female is of high or low quality, respectively) or it may display a reduced courtship and then fail in attracting the female, with a probability (1-k). When both males mate sequentially with the female, the order of mating is random, and each male, therefore, has a fertilisation probability of ½. If one considers that the selective male displays courtship behaviour of intensity i, its expected payoff can be estimated using the following general equation:

/ (A7)

which simplifies to:

, / (A8)

whereas the expected payoff of the unselective male equals:

. / (A9)

When two selective males compete with each other, only one of them reproduces with the female if they have assessed her differently or only one male succeeded in mating, and its fertilization probability is then one. Conversely, if the two males have judged the female as a high-quality partner and both have successfully mated with her, their fertilization success is ½. As above, let us assume that the two competing males display courtship behaviour of intensity i1 and i2, respectively. The expected payoff of male 1 can then be estimated using the following general equation:

, / (A10)

which simplifies to:

. / (A11)

Alternatively, when a selective male competes with a copier male, the chance that the selective male fertilizes the eggs of the female, if both males have successfully mated with her, is. Considering that the selective male displays courtship behaviour of intensity i, its average expected payoff and that of its copier rival can be calculated using the following two equations:

, / (A12)

and

. / (A13)

Finally, when two copier males compete with each other for a female, they do not attempt to breed. Their expected payoff I(C,C) is then zero.

Mean probability that a male mates with a randomly encountered female

The probability that a male mates with a randomly encountered female depends on its strategy and is equal to:

/ (A14)