stimulation: t304¼1.65, P ¼ 0.10). Similarly, we tested for influence
of client size on these three behavioural variables and found
no significant relationships (Pearson correlations: inspection
duration: r306¼0.02, P ¼ 0.71; frequency of jolts: r306 ¼ 0.007,
P ¼ 0.91; proportion of interactions with tactile stimulation:
r306 ¼ 0.008, P ¼ 0.89). Time of day and client size were therefore
not considered further.
We then compared the species-specific means (seven species in
Caribbean versus five species in Red Sea) between cleanerfish systems
with independent-samples t tests. In the case of the proportion
of interactions with tactile stimulation,we used a t test with unequal
variances. To examine the effect of service quality on client return
probabilities, we selected only observations in which the focal parrotfish
experienced both a positive interaction (i.e. it left the cleaner
without jolting) and a negative interaction (i.e. it left immediately
after jolting). We calculated for each species the proportion of parrotfish
returns after positive events (number of returns after positive
events divided by the sum of all interactions with positive outcome)
and the proportion of parrotfish returns after negative events
(number of returns after negative events divided by the sum of all
interactions with negative outcome). We then used paired t tests to
compare species’ return probabilities for each cleanerfish system.