The presence of territorial damselfish predicts choosy client species richness at cleaning stations

Abstract Mutualisms are driven by partners deciding to interact with one another to gain specific services or rewards. As predicted by biological market theory, partners should be selected based on the likelihood, quality, reward level, and or services each partner can offer. Third-party species that are not directly involved in the interaction, however, may indirectly affect the occurrence and or quality of the services provided, thereby affecting which partners are selected or avoided. We investigated how different clients of the sharknose goby (Elacatinus evelynae) cleaner fish were distributed across cleaning stations, and asked what characteristics, relating to biological market theory, affected this distribution. Through quantifying the visitation and cleaning patterns of client fish that can choose which cleaning station(s) to visit, we found that the relative species richness of visiting clients at stations was negatively associated with the presence of disruptive territorial damselfish at the station. Our study highlights, therefore, the need to consider the indirect effects of third-party species and their interactions (e.g., agonistic interactions) when attempting to understand mutualistic interactions between species. Moreover, we highlight how cooperative interactions may be indirectly governed by external partners.

of time of day. Station ID was included as a random term, with observation time of day (minutes since 12 am) included as a predictor. Both response variables were transformed to meet normality assumptions (richness: log + 1, visit frequency: arcsinh). Assumptions were checked with the performance package (Lüdecke et al., 2020). We found no evidence that the number of choosy client species visiting stations or the frequency of choosy client visits to stations differed across the day (choosy client richness: Х 2 1 = 1.49, p = 0.226, choosy client visit frequency: Х 2 1 = 2.42, p = 0.120).
Richness values, adjusted for choosy client visit frequency, were included in the main analyses. Points show raw values whilst line and shaded 95% CI are based on predicted values from mixed models.
Confidence intervals are calculated based on fixed effect uncertainty only. These median values (one per station) were used for analyses. Due to the variable sampling effort across stations it was necessary to randomly select two observations per station (repeated 1,000 times) for analysis to ensure observed numbers were not simply observed as a result of greater sampling effort.
Using a Spearman's rank correlation, we found no evidence that the number of observations for each station correlated with the median richness value for each station (rho = -0.12, p = 0.449). This confirms Number of observations that our approach of taking two random observations per station (replicated 1,000 times) is appropriate for investigating patterns in species richness at cleaning stations: lower richness values are not more likely to be found at lower observation counts, whilst higher richness values are not more likely to be found at higher observation counts. Calculated richness values are therefore independent of observation count.
Further details on each trait used to predict the number of choosy client species visiting each cleaning station.
Unless otherwise stated, we calculated multiple trait values for each station using subsets of the original data (two observations per station) replicated 1,000 times. Median values across runs were then used as a single trait value for each individual cleaning station.

a)
Likelihood of receiving cleaning service We identified five traits relating to the likelihood of receiving a cleaning service that could influence a client's decision to visit a particular cleaning station.
When observing a cleaning station, cleaners would regularly be out of view in holes/crevices in the coral. When cleaners are out of view, visiting clients may therefore be less likely to receive a cleaning service. For each station we calculated the probability of at least one cleaner being observed on the cleaning station and used this as a measure of "Likelihood of cleaner present at station". To calculate this, we used cleaner presence-absence data collected in 2016 (as also used in Dunkley et al. 2020).
Multiple presence-absence surveys were conducted at cleaning stations randomly throughout the day, and using these data, we calculated the proportion of times at least one E. evelynae cleaning goby was observed at each station.
Stations may attract more choosy clients if there are more cleaners present on the station. For example, an increased abundance of cleaners may increase the chances that a client is cleaned. For each station, using presence-absence data, we therefore calculated the median number of cleaners occupying each station over the six-week sampling period. This provided a measure of the "Number of cleaners on station".
Clients can visit cleaning stations and fail to get cleaned, because cleaners choose whether to clean a client or not Dunkley et al. 2018). For each station, therefore, we calculated the probability that a visit event would lead to a cleaning event, irrespective of client identity. To calculate this measure ("Likelihood of cleaner cleaning visiting client"), we divided the total number of cleaning events for each station by the total number of visits.
Choosy clients can select cleaner fish that give them priority access/service over resident species (Bshary and Grutter 2002). This may encourage choosy clients to visit particular stations where they are more likely to be cleaned over resident species. For each station, therefore, we calculated the likelihood that choosy clients are cleaned over resident clients ("Preference for cleaning choosy client"). For each station, we divided the total number of cleans towards a choosy client by the total number of cleans (for both resident and choosy clients).
Finally, clients can compete with each other for access to cleaners -clients can arrive at a cleaning station where another client may already be being cleaned, or multiple clients can arrive at a station simultaneously (Bshary and Noë 2003). This may lower the chances of the visiting client being cleaned, and therefore may choose to visit a station that is visited less frequently by clients. We therefore calculated the "Choosy client visit frequency" of each station using the total frequency of choosy client visits each station received.

b) Quality of cleaning service
Cleaners could "outbid" each other by providing a higher quality service compared to other cleaners.
This outbidding could attract more clients (Bshary and Noë 2003) and increase the number of species that visit the station. We therefore identified two traits representing the relative quality of the cleaning service received at each station, to ask whether they linked with visitation patterns of choosy clients to stations.
First, an extended cleaning duration is hypothesised to increase the payoffs in a cleaning interaction, hence increasing the quality of the service (Gingins and Bshary 2015). For each station, therefore, we calculated the median cleaning duration received by choosy clients ("Cleaning duration"), with higher durations expected to be observed cleaning stations with higher richness. Here we used only one observation per station in subset data (replicated 1,000 times) and calculated median durations within each run. We used one observation because cleaning Areas surrounding cleaning stations are often co-inhabited by resident territorial damselfish species which aggressively defend their territory from intruding species Whiteman et al. 2002). Whilst these territorial damselfish can visit the cleaning station(s) within their territory (be within ~ 20 cm of focal cleaner) and attempt to elicit a cleaning event, they can also disrupt other client species' cleaning interactions by chasing the client from the station . This disruption will likely reduce the pay-offs of the interaction to both cleaner and choosy client. An increased presence of a territorial damselfish at a cleaning station may thus deter choosy clients from visiting the station, reducing the number of choosy clients visiting. For each station we therefore calculated a "Frequency of visits by territorial damselfish" value, which represented the frequency of client visits to the station by territorial damselfish (see Supplementary Table 1 for fish species assigned as territorial damselfish).      territorial damselfish, b) redband parrotfish (Sparisoma aurofrenatum) and c) ocean surgeonfish (Acanthurus bahianus). Out of the 116 cleaning events observed towards choosy client species, the redband parrotfish was cleaned the most frequently (n = 37 events across 69 visits) while the ocean surgeonfish was the most common visitor to the stations which was also cleaned the most frequently (n = 117 visits, n = 13 cleans (third most commonly cleaned client overall)). The Queen parrotfish (Scarus vetula) was the second most commonly cleaned client but visited very few stations (n = 14 cleans at only 5 of the 45 stations) so was not included here. As there was no evidence for a relationship between richness values and redband parrot (F1 = 0.14, p = 0.708), and ocean surgeonfish (F1 = 0.01, p = 0.932), visit frequencies, this suggests that the presence of other choosy clients at cleaning stations is not altered by the presence of these two commonly cleaned species. Together this suggests that having a species that may monopolises access to cleaning services at a cleaning station does not deter other species from visiting the station. Instead, this suggests that damselfish may be deterring client species to protect their algal resources, but this requires further experimental manipulations. Median species richness residual values were calculated using the residuals from a GLM asking how median species richness varied as