more fights decrease same day mating success, but increase matings the next day

per day. Although higher-ranked males secured most matings during the rut, their ﬁ ght rates decreased towards the end. We propose that engaging in more ﬁ ghts negatively affects daily individual mating success but may bene ﬁ t mating success on the following day and potentially increase long-term ﬁ tness bene ﬁ ts. Additionally, engaging in more ﬁ ghts as the rut progresses probably allows lower-ranked males to secure some matings before the availability of oestrous females ends for almost a year

In species with polygynous mating systems, dominance status depends on male competitive ability, and impacts female mate choice and reproductive success (Fanjul & Zenuto, 2017;Farrell et al., 2011;Willisch et al., 2012;Wyman et al., 2021).High degrees of polygyny are characterized by strong reproductive skew, where a few males get most copulations during a mating season (Emlen & Oring, 1977).Dominance position within a social hierarchy determines individual mating success, where dominance can be achieved through a variety of aggressive (e.g.fights) and nonaggressive (e.g.avoidance, grooming) behaviours (Ellis, 1995;Lewis, 2022).
Direct intrasexual competition (e.g.fighting) between males is an important factor for establishing certainty on dominance relationships and for gaining access to females (Clutton-Brock & Huchard, 2013;Silk et al., 2019).However, fights carry high risks of injury and high energetic costs (Emery-Thompson & Georgiev, 2014;Lukas & Clutton-Brock, 2014).To reduce such costs, social dominance hierarchies are commonly established and function to limit unnecessary conflict, namely when lower-quality individuals avoid fighting with more dominant males (Lewis, 2022;Magaña et al., 2011;Willisch & Neuhaus, 2010).Increased knowledge of their social environment may allow individuals to optimize the directionality of aggressive behaviours (i.e. with whom to fight according to social rank; Hobson et al., 2021).Moreover, males may use information on social environment to decide whether to fight or not with a given individual and the intensity of these fights.
Fighting closely ranked males involves potential costs and associated risks of injury for males, but winning is more probable in these cases than when fighting males that are high above their social status.Additionally, the benefits of winning (e.g.increased social status and resource-holding potential) against closely ranked males are probably higher than the benefits associated with winning against males much lower in rank (Dehnen, Papageorgiou, et al., 2022).
In polygynous ungulates, males use different mating tactics depending on their quality, rank and specific environmental circumstances to increase access to females and mating success (Bowyer et al., 2020).Greater body size and mass indicate higher male quality, as well as a greater fighting ability (i.e.large and heavy males are more likely to win fights), and thus increasing probability of achieving high dominance positions (McElligott et al., 2001;Willisch et al., 2012).Nevertheless, these relationships may vary between species with different degrees of polygyny (Bowyer et al., 2020).Mating tactics can differ in 'ways' to approach a female or 'times' when to approach a female, and males may switch between tactics according to the prevailing conditions (Isvaran, 2005;Moore, Kelly, et al., 1995).Dominant males often use high-cost high-benefit mating tactics, such as tending, lekking or harem holding, while subordinates use alternative tactics that have much lower chances of mating, while avoiding risky contact with higher-ranked males (Foley et al., 2018;McElligott et al., 2001;McElligott & Hayden, 2000;Wyman et al., 2021).Dominant individuals are likely to invest more in rutting activities during the startepeak of the mating season, when more oestrous females are available (Farrell et al., 2011;McElligott et al., 1998).Instead, subordinates may increase investment in mating when prime-aged males are absent or exhausted towards the end of the rut, when they have higher probability of mating with younger females or unmated females going through their second oestrus (Briefer et al., 2013;Farrell et al., 2011).In lekking populations, subordinates arrive later to lekking areas and leave earlier than more competitive males.Subordinates may be attending leks to increase experience but may be leaving the lek and following females that retreat from the area as a potential alternative mating strategy (Ciuti & Apollonio, 2016).
As the mating season advances, body condition of males decreases and information on these changes in body condition is communicated to the rest of the population through, for example, changes in the structure of their vocalizations (McElligott et al., 2003;Mysterud et al., 2008;Vannoni & McElligott, 2009).Body size strongly influences the structure of vocalizations in fallow deer, Dama dama, red deer, Cervus elaphus, reindeer, Rangifer tarandus, North American plains bison, Bison bison (Blank, 2021;Frey et al., 2007;Vannoni & McElligott, 2009).Furthermore, at the end of the mating season, dominant males are likely to decrease investment in mating-related activities and switch to self-maintenance behaviours (e.g.feeding, resting).As a result, subordinates have increased likelihood of securing a mating at that time (Farrell et al., 2011).
The fallow deer is a polygynous species with strong reproductive skew, in which males actively compete for access to females (Clutton-Brock et al., 1988;McElligott & Hayden, 2000).Male fallow deer can be described as socially immature ( 3 years old) or mature (!4 years old), according to the behaviours they exhibit during the mating season, also called 'rut ' (McElligott et al., 1999).Socially immature males rarely participate in contests during the rut, avoiding fighting costs and potential injuries, unlike socially mature males, which actively participate (McElligott et al., 1998).Socially mature males shape their dominantesubordinate relationships before the mating season or 'prerut', mainly through low-cost, noncontact, agonistic interactions.Dominance relationships among fallow deer males may shift slightly throughout the mating season, as is the case for other species with hierarchical structures (Chase et al., 2022;Shizuka & McDonald, 2012).However, the main resulting ranks from prerut interactions tend to persist during the breeding period (Ciuti & Apollonio, 2016;McElligott et al., 1998).
Investment in fights increases as a function of the number of available oestrous females and individual male condition in both fallow deer and red deer (McElligott et al., 1998(McElligott et al., , 2003;;Mysterud et al., 2008).Costs of fights are likely to be higher in strongly skewed species, where higher-ranked males gain most matings (Leimar & Bshary, 2022).Average contact fight duration in fallow deer is approximately 90 s (Jennings et al., 2004;Mattiangeli et al., 1998).However, fight duration can be longer on average (about 3 min) when alternating low-risk behaviours (e.g.parallel walk, vocalizing) with more risky ones (e.g.antler clashing; Bartos et al., 2007;Mattiangeli et al., 1998).Dominant fallow deer males, usually in prime age (6e7 years old), are of greater body mass and size and grow larger antlers, features that indicate higher quality.Dominant individuals also tend to have the highest mating success (Ciuti & Apollonio, 2011;McElligott et al., 2001).However, whether the dominance rank established before the mating season affects the number of fights during the rut in male fallow deer remains unknown.Moreover, changes in body condition throughout the rut can affect individual investment in fights and matings, leading to possible changes in the relationship between male rank, fight rate and mating success.Disentangling these changes can help improve our knowledge of fallow deer and other ungulate mating systems.
Ungulate females are expected to choose the most suitable partner based on costs and benefits associated with mating, given their high investment in reproduction.Fallow deer females may choose their mates based on features such as vocalization quality (Charlton et al., 2007), which is linked to body condition (Vannoni & McElligott, 2008), antler size (Ciuti & Apollonio, 2011;Morina et al., 2018) or territory location (Apollonio et al., 1990).The availability of oestrous females changes during the rut following a normal-type distribution, peaking during mid-rut (Farrell et al., 2011).Oestrus in fallow deer lasts around 24 h and, during that time, females may visit numerous potential mates before finally mating (Briefer et al., 2013;Naulty et al., 2013).Indirect mate choice may also occur due to temporal shifts in oestrus.For example, fallow deer females may delay oestrus when only undesirable males are present (Komers et al., 1999), and younger females typically mate later in the rut, which may allow for indirect avoidance of mating with bigger and more dominant males.Younger females may benefit from not mating with larger, highquality males, given the potential energetic demands of their offspring during gestation, which could be detrimental to the fitness of younger, lower-quality females (Farrell et al., 2011).
We investigated the relationship between the prerut social rank of socially mature and active male fallow deer (i.e. that fight at least once during the rut) and their fight rate, fighting success and mating success and the relationship between the number of fights in a day and mating success.We further investigated whether there is a rank-dependent change in the fight rate and mating success of males throughout the rut, to understand the costs and benefits of fighting.We predicted that higher-ranked males would have lower fight rates and higher mating success at the peak of the rut, given that these individuals are of higher quality and are potentially avoided by lower-ranked males (Willisch & Neuhaus, 2010).We also anticipated that males with the highest numbers of fights per day would have lower mating success, linked to a potential tradeoff in energy and time investment between fighting versus mating.However, we predicted that males that more often win fights would gain more matings, given that winning is an attractive trait to females (Gerber et al., 2010;House et al., 2019).Lastly, we expected males to change their investment in fights and matings as the rut progressed, given the change in oestrous female availability, the energetically costly rut-related activities and the existence of various mating tactics expressed in this species (Ciuti & Apollonio, 2016;Farrell et al., 2011).

Study Site and Population
Data used for this study were collected over 2 years (1994e1995), as part of a long-term study of a European fallow deer population in Phoenix Park (53 22 0 N, 6 21 0 W), Dublin, Ireland.The park is approximately 709 ha, of which 80% is pasture and 20% is woodland, providing enough foraging resources for the herd to survive without additional food supply.Deer identities in this study were known as a result of the tagging efforts by the park authorities (McElligott & Hayden, 2000).In 1991, the whole population had been captured and all untagged males were tagged.Thus, all males used in this study were individually recognizable (McElligott & Hayden, 1999;Moore, Cahill, et al., 1995).Population size in 1994 was 620 (315 adult females and 200 adult males) and 689 in 1995 (353 adult females and 200 adult males; McElligott & Hayden, 2000).Males and females in this population live separately during most of the year and outside the breeding season (McElligott et al., 1999;Moore, Kelly, et al., 1995).Males cast their antlers from early April onwards.During new growth, antlers are covered in a highly vascularized skin, called velvet; tissue that is shed when antlers are fully grown and hardened, around late August (Kierdorf et al., 2021).From late September until the first days of November, all males generally move from their usual range and start interacting with females as well as with males.Females are nearby when males fight with each other and are able to roam freely among males (McElligott & Hayden, 2000;Naulty et al., 2013).Only socially mature males seen interacting with each other were included for analyses in this study (Table 1).

Data Collection
Data collection was done by a group of 6e11 observers during the mating season of each year.The season is divided into two periods: prerut and rut.The prerut starts when the last male has cleaned the velvet from its antlers, after which antlers are fully grown and hardened, and finishes the day before the first mating of the season occurs.The rut starts with the first mating of the season and ends with the last mating.The prerut started at the end of August, with a total of 32 days sampled in 1994 and 39 days in 1995.The rut lasted 15 days in 1994 and 19 days in 1995, starting mid-October and ending on 1 November, both years.
The group of observers were able to monitor the whole herd during the observation days.From early October, observations were carried out every day from dawn to dusk (ca.11 h) until the rut ended.However, when observing such a large number of individuals during the whole rut, it is not possible to record absence of behaviour in a meaningful way from all individuals in the population.Therefore, males were specifically recorded when fighting or mating, which are a good assessment of fight rates and mating success (Table 1; McElligott & Hayden, 2000).

David's Score Method
The outcomes of agonistic interactions between male dyads are categorized as win/loss, where one male wins (i.e.chases off opponent) and the other loses (i.e.retreats from fight location) that interaction, or as undetermined, where no male clearly wins or loses.A win or a loss has consequences for subsequent male agonistic behaviour, known as the winnereloser effect, increasing dominant or subordinate behaviours (Hsu & Wolf, 2001;Oldham et al., 2020).Clear outcomes of agonistic interactions between males during the prerut were used to calculate the dominance rank based on the David's score (DS) method.The DS is a suitable ranking method when large numbers of interactions have been observed, as it considers repeated interactions between the parties of a dyad in which win/loss asymmetries may be clarified.To clarify win/loss asymmetries, the DS uses the proportion of wins and losses of a male over the total number of interactions with a given opponent, taking wins and losses of the opponent into account, and weighs individual victories within the group.This method avoids an artificially increased or lowered position of the dominance rank of certain individuals due to potential minor deviations from the general dominance direction or simple observer mistakes.Nevertheless, the ranking position of an individual may be erroneously increased or lowered when this individual interacts with a small proportion of the population only, or when it obtains only wins or only losses in all its interactions.In this case, it would be appropriate to exclude it from the dominance rank calculation (Gammell et al., 2003).
To calculate the dominance hierarchy, mature male dyads were selected from the prerut period.Only agonistic interactions with a clear winner (i.e.interactions with resolved outcomes) were selected, considering that the method uses dyadic interactions where one of the parties 'scores' while the other 'loses' (David, 1987;Gammell et al., 2003).First, the percentage of interactions that each male had with other mature males during the prerut was calculated.Those males interacting with fewer than 10% of the total mature male population (31 males) were removed, which included males that had only wins or only losses (Briefer et al., 2010;Gammell et al., 2003).Scores were transformed into a hierarchical sequence (1Àn), where number 1 determined the highest score, hence the top dominant male that year, followed by males with lower scores until the last male in the hierarchy that year ('n') with the lowest score, 61 in 1994 and 73 in 1995 (Table 1).

Statistical Analyses
All data analyses and graphical representations were performed in R software version 3.6.1 with RStudio (an integrated development environment for R; R Core Team, 2022).Generalized linear mixed-effects models (GLMMs; lme4 library; Bates et al., 2015) were used to investigate the following effects: (1) the effect of rank (1e73 ranks) on the number of fights per male per day (1e21 fights/ male per day), on the ratio of won to lost fights (0e1; using the 'cbind' function, calculated per male per day), and on the number of matings per male per day (0e22 matings/male per day) (in three separate models); (2) the effect of fights on the number of matings/ male per day, and on the number of matings/male the next day (in two separate models); and (3) the effect of the interaction between prerut rank and the ratio of won to lost fights on the number of matings/male per day, and on the number of matings/male the next day (in two separate models).
To test the assumptions of normality and homoscedasticity, residuals of the models were visualized in QeQ plots and scatterplots using the function 'simulateResiduals' (DHARMa library; Hartig, 2020).When the assumptions were not met, a quadratic, log or binary transformation of the response variable was performed.All response variables (fights/male per day, matings/male per day and matings/male the next day) had a better fit when binarytransformed and were thus input in a GLMM using the glmer function (lme4 library; Bates et al., 2015), fitted with binomial family distribution and logit link function, instead of a linear mixed-effects model (Model example 1; Bongi et al., 2011).To this aim, data were transformed as follows: the number of fights/male per day as !2 fights ¼ 1 and 0e1 fight ¼ 0, the number of matings/ male per day and the number of matings/male the next day as !1 matings ¼ 1 and 0 matings ¼ 0. Thus, fight rate should be interpreted in our results as the proportion of days during which a male fought at least twice (i.e.!2 fights/male per day) or less (i.e.0e1 fight), and mating rate as the proportion of days during which a male mated (i.e.!1 matings/male per day) or not at all (i.e.0 matings).The outcome of fights was calculated as the ratio of won to lost fights (calculated per male per day) using the 'cbind' function in R. As such, it ranged between 0 and 1 and was entered in a GLMM fitted with binomial family distribution and logit link function as well.
For each model, we decided whether fixed factors of interest (prerut rank, fights/male per day, ratio of won to lost fights) should be input as linear, quadratic or logarithmic terms based on the model's Akaike information criterion adjusted for small sample sizes (AICc; Burnham et al., 2011).The model with the smallest AICc values was chosen, and the fixed effects were fitted as linear only, linear and quadratic or logarithmic terms accordingly.If in one case, the AICc values of two or three models differed by less than 2 (delta AICc: DAICc < 2), both models were considered to have support and thus were considered as potential fits to explain the data.Nevertheless, if these similarly supported models (DAICc < 2) differed in the number of parameters used (K), the one with the lower K was chosen as the most parsimonious answer (Burnham et al., 2011).Only the selected models are described in the Results section (for further information on model selection, see Tables A1eA5).
All models included male identity as a random effect and itself crossed with male identity nested within year, to control for repeated measures of the same individual between and within years, variation between years and phenotypic differences between individuals (Briefer et al., 2010).The day of the rut was added as an additional linear and quadratic fixed term to control for the daily change in fights and matings over the rut (Model example 1).To calculate the P values for each GLMM fixed effect, we used the parametric bootstrap test, based on 1000 replicates, through the comparison of a model with and a model without the fixed factor of interest (PBmodcomp function, pbkrtest library; Halekoh & Højsgaard, 2014).The parametric bootstrap test was used whenever possible because it takes the random-effects structure into account more correctly than a likelihood ratio test (LRT; Halekoh & Højsgaard, 2014).However, when the bootstrap method failed, we used an LRT instead.
Model example 1: glmer The analyses included all ranked males that engaged in at least one fight during the rut (N ¼ 128).Nonranked males (N ¼ 34) were not included in the analyses.To test the effect of fights on the number of matings/male per day and on the next day, entries in which males had 0 fights and !1 mating/s the same day (N ¼ 15) were excluded from the model for the following reason: as males that had 0 fights and 0 matings in 1 day were not recorded (i.e. during field data sampling, males that do not fight or mate are not registered, given the difficulty of collecting data on absence of behaviour), such calculations give a wrong output suggesting that 100% of males that did not fight obtained a mating otherwise.
We further tested the effect of the interaction between prerut rank and the period of the rut (start, peak, end) on the proportion of days males fight at least twice (i.e.!2 fights) and the proportion of days males mate at least once (i.e.!1 matings).The ruts of both years were divided into three independent periods, based on the mating activity.To determine the peak, the day with the highest percentage of matings was selected for each year (15.45% of matings on days 7 and 10 of the rut of 1994 and 13.5% on day 12 in 1995).Those days with a percentage of matings of at least half of the maximum were included in the 'peak' of the rut (days 6e11 with !7.7% of matings in 1994; days 9e15 with !6.8% in 1995; Fig. A1).The days before the peak of the rut were attributed to the 'start' of the rut and the days after the peak to the 'end' of the rut.In 1995, although day 17 had more than 6.8% of the matings, it was not included in the peak due to the discontinuity in the number of matings, as day 16 did not reach the minimum percentage (Fig. A1).
We then built a GLMM using the glmer function (lme4 library; Bates et al., 2015), fitted with binomial family distribution and logit link function.The model included the following terms: fights/male per day and matings/male per day (binary transformed as described above) were included as response variables in two separate models, the interaction between prerut rank and the period of the rut (start, peak, end) was included as a fixed term and male identity crossed with male identity nested within year were included as random factors.We then used an LRT to calculate P values (Halekoh & Højsgaard, 2014).Given the marginally significant interaction between rut period and rank (P ¼ 0.058) on the proportion of days males fight at least twice (i.e.!2 fights), we then analysed the effect of rank on fights in the three periods (start, peak, end) separately, following the same procedure as described above to test the assumptions of normality and homoscedasticity.These new models included the same fixed and random effects as described above and shown in Model example 1.To calculate the P values, we used the parametric bootstrap test for the start and peak of the rut (PBmodcomp function, pbkrtest library; Halekoh & Højsgaard, 2014) and an LRT for the end, when the bootstrap failed.

Ethical Note
The research was part of a long-term study on the behaviour and ecology of a city park fallow deer herd (Briefer et al., 2010(Briefer et al., , 2013;;Farrell et al., 2011;McElligott et al., 2002).Given that the animals were observed in a public park, and no experiments were carried out, no ethical approval was required to conduct the research at the time (1994 and 1995).Phoenix Park is located close to the centre of Dublin, surrounded by the city, and is accessible to the public.Thus, the deer are habituated to human presence and are not usually disturbed by people standing nearby.Behavioural data collection was usually carried out at a minimum distance of about 30 m from the animals, using spotting scopes mounted on tripods, and did not cause disturbance to their normal activities.

Group Size and Data Distribution
Of the 134 ranked males, 128 participated in the rut and had a total of 470 matings and 2992 fights over the ruts of the 2 years.
From the total of sampled observations, 95% of instances were males that had 0e6 fights per day, while only 5% of observations were males engaging in !7 fights in a day.The highest number of fights per day a male was involved in was 21 and the highest number of matings secured by a male during a day was 22.The top 10 males secured 81% of the matings and were involved in 25% of the total fights.Additionally, 95 males (71%) that engaged in fights during the rut secured no matings at all (Table 2).

Effect of Dominance, Fight Rate and Fighting Success
Higher-ranked males fought at least twice (i.e.!2 fights) per day on a higher proportion of days (calculated per male per day; GLMM: quadratic relationship: R 2 m ¼ 0.078, R 2 c ¼ 0.166, P ¼ 0.03; Fig. 1a) and won more fights (GLMM: logarithmic relationship: R 2 m ¼ 0.063, R 2 c ¼ 0.217, P ¼ 0.001; Fig. 1b) compared to lower-ranked males.Higher-ranked males mated at least once (i.e.!1 matings) per day on a higher proportion of days during the rut compared to the lower-ranked ones (GLMM: logarithmic relationship: R 2 m ¼ 0.349, R 2 c ¼ 0.538, P ¼ 0.001; Fig. 1c).The proportion of males that secured at least one mating was positively related to the number of fights they engaged in on that same day, up to a threshold (approximately 10 fights/male per day), after which mating success decreased.Males with more than 15 fights a given day secured 0 matings that day (GLMM: quadratic relationship: R 2 m ¼ 0.135, R 2 c ¼ 0.606, P ¼ 0.001; Fig. 2a).Instead, a higher proportion of males involved in the highest numbers of fights a given day mated at least once on the next day, compared to those males engaging in fewer fights (GLMM: logarithmic relationship: R 2 m ¼ 0.084, R 2 c ¼ 0.580, P ¼ 0.001; Fig. 2b).
Males that won more fights during a given day did not have higher mating success that same day (GLMM: logarithmic relationship: R 2 m ¼ 0.398, R 2 c ¼ 0.551, P ¼ 0.52; Fig. 3a).Higher-ranked males with higher fighting success had higher chances of mating the next day compared to higher-ranked males that won fewer fights.However, this was not the case for lower-ranked males (GLMM: linear relationship: R 2 m ¼ 0.399, R 2 c ¼ 0.595, P ¼ 0.02; Fig. 3b; for further information on model selection, seeTables A1eA5)

Differences Between the Three Rut Periods
The effect rank had on the proportion of days males fought at least twice (i.e.!2 fights) depended on the period of the rut (GLMM: linear relationship: P ¼ 0.058).Higher-ranked males fought at least twice (i.e.!2 fights) per day on a higher proportion of days than lower-ranked males, during the start (GLMM: linear relationship: R 2 m ¼ 0.027, R 2 c ¼ 0.073, P ¼ 0.035; Fig. 4a) and peak (GLMM: linear relationship: R 2 m ¼ 0.091, R 2 c ¼ 0.214, P ¼ 0.001; Fig. 4b) of the rut, but not at the end of the rut (GLMM: linear relationship: R 2 m ¼ 0.098, R 2 c ¼ 0.399, P ¼ 0.11; Fig. 4c).Higherranked males fought at least twice per day less often at the end of the rut compared to the start and peak of the rut, while lowerranked males seemed to maintain their rates (Fig. 4aec).In contrast, the effect rank had on the proportion of days males mated at least once (i.e.!1 matings) did not depend on the period of the rut (GLMM: logarithmic relationship: P ¼ 0.36; for further information on model selection, see Table A6).

DISCUSSION
We studied the relationship between dominance rank and the proportion of days during the rut on which socially mature fallow deer males were involved in at least two fights (i.e.!2 fights), and the effect of these two factors on their mating success (i.e.proportion of days that males mated at least once, i.e. !1 matings).We found that higher-ranked males fought at least twice a day on a higher proportion of days during the beginning and peak of the rut and had higher mating success compared to lower-ranked males.Higher-ranked males won a higher proportion of the fights they engaged in compared to lower-ranked males.Males engaging in more than 10 fights per day were less likely to secure a mating that same day, and those males exceeding 15 fights per day secured no matings at all.Nevertheless, males with the highest numbers of fights (i.e.15e21 fights per day) on a given day had higher mating success the next day, suggesting that males gain delayed longer-term benefits from fighting.Contrary to what was initially expected, we found no relationship between fighting success and mating success the same day, no matter the rank of the male.However, fighting success did affect mating success the next day, depending on the rank.Moreover, higher-ranked males fought at least twice per day (i.e.!2 fights) on a lower proportion of days towards the end of the rut, compared to the start and peak of the rut.While changes in the proportion of days that males engage in at least two fights may not affect mating success of higher-ranked males, it may allow some lower-ranked males to secure a mating.Overall, our results suggest that males likely increase current costs by fighting more, to increase future shortterm mating success (Dehnen, Arbon, et al., 2022;Lewis, 2022;Tibbetts et al., 2022).
Higher-ranked males were engaged in at least two fights per day (i.e.!2 fights) on a higher proportion of days throughout the rut compared to lower-ranked males.According to previous studies, higher-ranked fallow deer males, which are of higher quality, can afford to fight more while strongly reducing food intake and have an earlier onset of vocalizations (Apollonio & Di Vittorio, 2004;Vannoni & McElligott, 2009).Indeed, high-energy expenditure by successful males does not significantly affect their overwinter survival or lifetime success, besides the inherent risk of injury when fighting (Ciuti & Apollonio, 2016;McElligott et al., 2002McElligott et al., , 2003)).Moreover, in domestic pigs, Sus scrofa domesticus, and fallow deer, more experienced males assess their competitors for longer, with noncontact behaviours (e.g.parallel walk), before engaging in a fight, hence reducing costs of unnecessary fights (Camerlink et al., 2017; McElligott et al., 1998;Oldham et al., 2020).Thus, higherranked males may engage in more fights, but their greater quality and experience may help reduce the costs of fighting.
Higher-ranked males won a higher proportion of fights compared to lower-ranked males.Nevertheless, the large variation in the resulting proportion of won fights by lower-ranked males suggests that males low in the hierarchy may be more likely to engage in fights with closely ranked males than against males high above them in the social hierarchy.Indeed, fallow deer males are likely to fight others that are near in rank distance (Barto s et al., 2007), given that they have a greater chance of winning (Tibbetts et al., 2022).Lower-ranked males, many of which are probably still young (4e5 years old), potentially avoid fights against higherranked males to reduce the probability of injury.However, fights among lower-ranked males might help them to gain experience in contests, to reduce costs of future fights (Camerlink et al., 2017;McElligott et al., 1998).
Our results indicate that a high number of fights per day negatively affects male mating success.The proportion of males that mated at least once had more fights, but only up to approximately 10 fights per day, after which fewer males secured at least one mating on that same day.Males engaging in the highest numbers of fights secured no matings that same day.How high aggression rates and proportion of males that mated at least once (i.e.!1 matings) that same day (calculated per male per day, binary transformed).(b) Relationship (logarithmic) between the number of fights (per male per day) and the proportion of males that mated at least once (i.e.!1 matings) the next day (calculated per male per day, binary transformed).The black line represents the regression line and the grey areas indicate the 95% confidence interval.
among males may affect their individual mating success may be related to females leaving areas of high conflict, as previously observed in fallow deer, or to time or energy budget constraints as observed in other species, for example California sea lions, Zalophus californianus (Apollonio et al., 1989a;Gerber et al., 2010;Naulty et al., 2013).Fallow deer fights can vary from 1.5 to 3 min, depending on the inclusion of low-risk (e.g.parallel walks) and high-risk (e.g.clashing of antlers) behaviours (Bartos et al., 2007;Jennings et al., 2004;Mattiangeli et al., 1998;McElligott et al., 1998).
Experienced males are likely to use low-risk behaviours before engaging in contact fights.Moreover, encounters among symmetric dyads may be of longer duration, with increased time and energy invested in disputing dominance, and higher risk of injury (Bartos et al., 2007;Mattiangeli et al., 1998;McElligott et al., 1998).However, 95% of males in our study did not exceed six fights per day, while only a few males fought more than 10 fights in a day.Therefore, we suggest that higher-ranked males are likely to engage in few fights per day, while fighting during most rut days, hence maintaining their ranking position throughout the rut as a result.
Males that fought more on a given day had greater chances of securing at least one mating the following day compared to those males engaging in fewer fights.Our results further suggest that male fighting success may predict mating success the next day, however, dependent on rank.Higher-ranked males that win fights may benefit from mating the following day, while lower-ranked winners do not necessarily gain any matings at all.The effect of engaging in a high number of fights on high individual mating success the following day may potentially be associated with female mate choice.Indeed, female fallow deer in Phoenix Park roam and choose which male to mate with (Farrell et al., 2011).Moreover, male fighting success in fallow deer and red deer is related to male mating success (Clutton-Brock et al., 1979, 1988;Moore, Kelly, et al., 1995).Therefore, our results could be explained by females somehow keeping track of male rank as well as winners in fights and mating with them the following day(s) after fights have settled.
We found that higher-ranked males secured most matings throughout the rut, with no mentionable difference between the three rut periods (start, peak, end).Instead, higher-ranked males fought at least twice (i.e.!2 fights) per day on a higher proportion of days at the start and peak of the rut compared to lower-ranked males, but not at the end.The daily investment in fights may affect body condition of higher-ranked males, some of which may start switching to self-maintenance behaviours, reducing overall investment in intrasexual competition towards the end of the rut (Pitcher et al., 2014;Vannoni & McElligott, 2009;Wyman et al., 2021).By Relationship between the ratio of won to lost fights (calculated per male per day) and proportion of males mated at least once (i.e.!1 matings) that same day (calculated per male per day, binary transformed).(b) Relationship between the ratio of won to lost fights (calculated per male per day) and proportion of males that mated at least once (i.e.!1 matings) the next day (calculated per male per day, binary transformed).Circles represent data for higher-ranked males (ranks 35) and the black solid line represents the regression line.Triangles represent data for lowerranked males (ranks > 35) and the dot-dashed line represents the regression line.
Grey areas indicate the 95% confidence interval.contrast, lower-ranked males were involved in at least two fights per day less often during the rut, and some of them may increase their effort later in the mating season (Mason et al., 2012;Nieminen et al., 2016).This provides a suitable scenario where lower-ranked males can successfully use alternative mating tactics, when fewer higherranked males are preoccupied in further disputing dominance relationships.
Our study population experienced an almost three-fold increase in fight rates from 1994 to 1995, despite similar sampling efforts and population sizes between the years.There were only seven more socially mature males, and 38 more females, in 1995 compared to 1994.In addition, just before the rut in 1995 (in early September), the most dominant male with the highest mating success from the previous 2 years died from an accident (A.G.McElligott, personal observation).Although speculative, this may have contributed to higher fight rates between formerly lessdominant males as the rut progressed.Similarly, in a lekking population, Apollonioet al. (1989b) found that when dominant males were removed, fight rates increased the next year.

Conclusion
To conclude, our results indicate that higher-ranked fallow deer males fight more, while maintaining higher mating success than other socially mature males.Our results suggest that high numbers of fights in a day negatively affect mating success the same day but can result in delayed benefits by increasing mating success the next day.Males with higher fighting success also gain more matings the following day(s).Males fighting more and winning more fights successfully displace other competitors and get access to female groups, where they are more likely to be chosen by females for mating.Furthermore, changes in the proportion of days that males fight may allow lower-ranked males to secure a mating towards the end of the rut.Overall, our results suggest that fighting does not always provide immediate fitness benefits but can provide delayed and potentially longer-term fitness benefits (Dehnen, Arbon, et al., 2022;Tibbetts et al., 2022).The current study may allow us to adjust what we know about male intrasexual competition and female choice, and how these factors impact male mating success.Moreover, these results complement current knowledge on how population fitness is shaped and can thus be used for conservation management and population monitoring programmes (Cally et al., 2019).

Table A3
Summary of the model output for the effect of fights/male per day on the proportion of days males mate at least once (i.e.!1 matings) the same day and the next day    1994and 1995. Solid (1994) and dashed (1995) ) horizontal lines show the days that were attributed to the peak of the rut, depending on the percentage of matings for a day in relation to the peak (7.7% in 1994 and 6.8% in 1995).

Figure 1 .Figure 2 .
Figure1.(a) Relationship (quadratic) between rank (prerut dominance hierarchy) and proportion of days that males fought at least twice (i.e.!2 fights; calculated per male per day, binary transformed).(b) Relationship (logarithmic) between rank (prerut dominance hierarchy) and ratio of won to lost fights (calculated per male per day).(c) Relationship (logarithmic) between rank (prerut dominance hierarchy) and proportion of days that males mated at least once (i.e.!1 matings; calculated per male per day, binary transformed).The black line represents the regression line and the grey areas indicate the 95% confidence interval.

Figure 3 .
Figure 3. (a)  Relationship between the ratio of won to lost fights (calculated per male per day) and proportion of males mated at least once (i.e.!1 matings) that same day (calculated per male per day, binary transformed).(b) Relationship between the ratio of won to lost fights (calculated per male per day) and proportion of males that mated at least once (i.e.!1 matings) the next day (calculated per male per day, binary transformed).Circles represent data for higher-ranked males (ranks 35) and the black solid line represents the regression line.Triangles represent data for lowerranked males (ranks > 35) and the dot-dashed line represents the regression line.Grey areas indicate the 95% confidence interval.

Figure 4 .
Figure 4. Relationship between rank (prerut dominance hierarchy) and proportion of days that males fought at least twice (i.e.!2 fights; calculated per male per day, binary transformed) at (a) the start, (b) the peak and (c) the end of the rut (linear relationship).The black line represents the regression line and the grey areas indicate the 95% confidence interval.

Figure A1 .
Figure A1.Percentage of matings per day during the rut in1994  and 1995 .Solid (1994) )  and dashed (1995) horizontal lines show the days that were attributed to the peak of the rut, depending on the percentage of matings for a day in relation to the peak (7.7% in 1994 and 6.8% in 1995).

Table 1
Prerut male fallow deer, participating ranked males and nonranked males during the rut and total number of fights and matings for 1994 and 1995 A.Bateman-Neubert et al. / Animal Behaviour 200 (2023) 37e48 Summary of the model output for the effect of rank (prerut hierarchical dominance) on proportion of days males mate at least once (i.e.!1 matings) Summary of the model output for the effect of the ratio of won to lost fights (using 'cbind' function), dependent on rank (prerut hierarchical dominance), on the proportion of days males mate at least once (i.e.!1 matings) the same day RV): matings same day: proportion of males that mate at least once (i.e.!1 matings) the same day.Estimates of parameters (fixed factors): dayofrut: day of rut; Srank: rank scaled to fit the data; cbind(Wins, Losses): ratio wins to losses (per buck per day); I(parameter^2) for quadratic term; log(parameterþ1) for logarithmic term.Random factors were the identity of the buck (buckID) and the identity of the buck nested within year.Res.df:residualdegrees of freedom; loglik: logarithmic likelihood; AICc: Akaike information criterion for small sample sizes; DAICc: delta AICc; ui: weight (probability of being the best model).Best model or competing models (DAICc < 2) are highlighted in bold.(e)indicatesparameter is not included in the model.Summary of the model output for the effect of the ratio of won to lost fights (using 'cbind' function), dependent on rank (prerut hierarchical dominance), on the proportion of days males mate at least once (i.e.!1 matings) the next day Response variable (RV): matings next day: proportion of males that mate at least once (i.e.!1 matings) the next day.Estimates of parameters (fixed factors): dayofrut: day of rut; Srank: rank scaled to fit the data; cbind(Wins, Losses): ratio wins to losses (per buck per day); I(parameter^2) for quadratic term; log(parameterþ1) for logarithmic term.Random factors were the identity of the buck (buckID) and the identity of the buck nested within year.Res.df:residualdegrees of freedom; loglik: logarithmic likelihood; AICc: Akaike information criterion for small sample sizes; DAICc: delta AICc; ui: weight (probability of being the best model).Best model or competing models (DAICc < 2) are highlighted in bold.(e)indicatesparameter is not included in the model.A.Bateman-Neubert et al. / Animal Behaviour 200 (2023)37e48Table A6Summary of the model output for the effect of rank (prerut hierarchical dominance), dependent on the period of the rut (RutPer: start, peak, end), on the proportion of days males fight at least twice (i.e.!2 fights)RV: fights fightsdayBIN ~RutPer*(Srank) þ RutPer*(Srank þ I(Srank^2)) þ RutPer*(log(rankþ1)) þ (1jyear/buckID) þ (1jbuckID)Response variable (RV): fights: proportion of days males fight at least twice (i.e.!2 fights).Estimates of parameters (fixed factors): RutPer: rut period; Srank: rank scaled to fit the data; I(parameter^2) for quadratic term; log(parameterþ1) for logarithmic term.Random factors were the identity of the buck (buckID) and the identity of the buck nested within year.Res.df: residual degrees of freedom; loglik: logarithmic likelihood; AICc: Akaike information criterion for small sample sizes; DAICc: delta AICc; ui: weight (probability of being the best model).Best model or competing models (DAICc < 2) are highlighted in bold.(e) indicates parameter is not included in the model.