Lek Size Research Articles

Male rank and optimal lek size

Widemo and Owens presented a model that calculates the expected copulation rates of males on leks of a range of sizes. They claim that a negative relationship between lek size and male mating skew will result in low-ranking males having greater optimal lek sizes than higher ranking rivals. Widemo and Owens offered no proof of their claim, and their model assumes that the rank of a male does not change as lek size increases, whereas in reality, rank may change as more males arrive. We present a general model that allows rank to change as lek size increases. We show that the crucial determinant of whether optimal lek size increases with male rank is whether relative competitive differences increase with lek size. Contrary to the claim of Widemo and Owens, the relationship between skew and lek size has no direct bearing on the optimal levels of aggregation of males of different rank. We show that a negative relationship between skew and lek size can exist even when high-ranking males have the greatest optimal lek sizes.

Individual mating success, lek stability, and the neglected limitations of statistical power

The evolution of leks (aggregations of males displaying to females) cannot be explained solely by an increasing average gain in matings for each male as group size increases. This is because the mating skew, that is, the inequality among males in mating success, is often high and may vary with lek size. Here, we show that the common observation that matings become more evenly divided as lek size increases is also insufficient to explain by itself the benefits of aggregating. The benefits to individual males are highly sensitive to the exact relationship between mating skew and lek size, and very similar relationships can lead to opposite predictions concerning individual benefits. With data on published mating success for 18 species (71 leks), we show that different species have very similar skew versus lek size relationships. With current sample sizes, however, there is insufficient statistical power to distinguish between completely different alternatives concerning individual optima of males.

Female encounter rates and fighting costs of males are associated with lek size in Drosophila mycetophaga

Male costs and benefits associated with male display size in field populations of an Australian lekking Drosophila species were examined. Results suggested that male mating success increased with display size, since matings appeared to be more common in large displays, and since the probability of males encountering a female increased as displays contained more males. Female encounter probabilities did not increase once about 20 males or more were present on a display. Male size and fighting costs tended to increase with display size. The distribution of males among displays did not follow the ideal free distribution in the sense that each male did not have equal mating opportunity per unit time. Deviation from an ideal free distribution may have been due to female preference for mating in aggregations rather than with solitary males, since in a field experiment females were more willing for mating in an aggregation of five males than with solitary males.

Location and size of capercaillie Tetrao urogallus leks in relation to territories of hens

In the French Pyrenees, lek habitats of capercaillie Tetrao urogallus are spatially separated from brood‐rearing habitats, which are defended by hens before laying. Spring territories of hens thus determine the placement of leks, which are as near to the geometric centre of the locations of one or more territorial hens as lek habitat allows. The number of cocks on leks on a small and large study area was proportional to the number of territorial hens. Locations of leks were systematically influenced by proximity of brood habitats, and the number of cocks on leks was positively correlated with the total area of brood habitats. Establishment of a lek may depend on the prior presence of one or more territorial hens. Because hens influence establishment and size of leks, territoriality in hens may limit numbers of both cocks and hens. These findings support recent models emphasising the effects of hens on lek formation, and contrast with those from Norway, where behaviour and habitat requirements of cocks determine size and location of leks. This may result from brood habitats in the Pyrenees being in localised patches, whereas those in Norway are available throughout the forest. However, the regular distribution pattern of leks in both the Pyrenees and Norway, supports the aspect of the Norwegian model which attributes lek location to the spacing behaviour of cocks.

Responses of Male and Female Black Grouse to Male Vocal Display

AbstractThe evolution of leks may be explained by several hypotheses. The ‘female preference’ hypothesis, which states that females favour males that have aggregated, has recently gained some empirical support. Low‐quality, unattractive males may, however, settle near attractive males, as predicted by the ‘hotshot’ hypothesis. We tested whether black grouse Tetrao tetrix females use auditory cues to find the preferred leks, and whether males respond to vocal display emitted on leks. We conducted a playback experiment with male vocal display (rookooing) on leks, where the visiting females and displaying males were counted. The number of males tended to increase more on playback leks. Specifically, the number of 1‐year‐old males was greater on playback sites than on control sites. Also, the number of females, in relation to the lek size before the start of the experiment tended to increase. In addition, we used aviary playback trials to test whether females distinguish between single‐male and multi‐male displays. In a choice test, females showed greater preference for the ‘multi‐male’ tape. The tendency for increased male numbers on playback leks resulted from increased visits of young, mobile males which were attracted to leks that they perceived to be large. This suggests a ‘hotshot’‐type mechanism in the settlement of young males. Because females also responded to the supplemented auditory advertisement, or directly to the increased number of males, the ‘female preference’ hypothesis is also supported. Females may, at least in part, base their decision of which lek to visit on auditory cues, but visual contact to males may be also needed.

Neighbours, strangers and male-male aggression as a determinant of lek size

Interactions between males on leks may play an influential role in lek formation and the regulation of lek size. In this paper I present the results of a playback experiment that simulated de novo settlement at sites adjacent to currently existing display territories of the ochre-bellied flycatcher, Mionectes oleagineus. In the study population, males displayed both solitarily and at small leks. A large proportion of males held no display territory at all. A stranger's song was played to both solitary and lekking males from 10 m outside their territorial boundaries. In separate playbacks, lekking males were also played neighbour's song. Both lekking and solitary territorial males reacted to the playback by decreasing their song rate, approaching the playback speaker and, on occasion, attacking the model. Solitarily displaying males responded more aggressively to playback of stranger's song than did lek males. Lek males were able to distinguish between their neighbour's and a stranger's song and did so irrespective of whether it was played from the neighbour's territory or from outside the lek. In addition to distinguishing between neighbours and strangers, lek males modified their responses to these different playbacks depending on where the playback originated. These results suggest that male-male interactions can be influential in structuring leks. In M. oleagineus, interactions between males are aggressive and act to limit rather than augment lek size.

Measuring the Mating Skew

Charles Darwin (1871) defined sexual selection as a difference inreproductive success due to competition over mates, a definition that is still valid today. Being able to quantify such differences is thus essential for explaining the consequences of sexual selection, say, the ornamentation rdisplay behavior of males. In the specific ase of lekking (aggregated, non-resource-based display of males), attempts to do so have proven difficult. Any measure that does not take into account the possibility of random mating to produce the observed pattern of mating success is unsatisfactory as a measure of the intensity of sexual selection (Sutherland 1987; Mackenzie et al. 1995b). That variation in male mating success on leks is systematically higher than expected from pure random mating has been verified by Bradbury et al. (1985) and Mackenzie et al. (1995a). However, these studies do not yet provide means to estimate the expected mating success of individuals displaying together. Since a lek is not itself a trait but an assemblage of several males, each trying to optimize their own fitness (Hoglund and Alatalo 1995), fitness considerations of single individuals are required in explaining the evolution of lekking. The skew index, defined as the ratio of observed to maximum skew (Keller and Vargo 1993; Reeve and Ratnieks 1993), has been gaining popularity as a measure of skewed reproductive success (e.g., Bourke and Heinze 1994; Keller and Reeve 1994; Reeve and Keller 1995), and it has also been used to estimate the expected fitness of lekking individuals (Widemo and Owens 1995). However, this measure has been shown to have undesirable discontinuities (Pamilo and Crozier 1996). Moreover, it interprets random variation as real differences in mating success. This is most clearly seen in models of pure random mating, which nevertheless lead to positive values of the skew measure (Mackenzie et al. 1995b). Recently, Keller and Krieger (1996) proposed a method for correcting the skew index for random variation. We shall show, however, that the corrected measure still is not satisfactory, and we suggest a novel, statistically rigorous method. We give two criteria for a proper measure of skewed mating success. First, it should allow determining the most probable underlying distribution of mating

Lek size variation and its consequences in the ochre-bellied flycatcher, Mionectes oleagineus

Several hypotheses suggest that the costs and benefits of display in aggregations of different sizes play a major role in both the evolution of leks and in the distribution of males across lekj of different sizes. We examined the consequences of variation in lek size for both males and females in a study of the ochre-bellied flycatcher, MiontcUs oltagmrus. We observed 41 solitary display sites and leks, ranging in size from 1 to 5 mates, over S breeding seasons. Although mean visitation rate by females was positively correlated with lek size, female visitation rate per male remained constant across lek sizes. The rate at which females visited the male who had the highest female visitation rate at each lek was positively correlated with lek size as predicted by the hotshot hypothesis. Neither mean nor per capita intrusion rates were correlated with lek size. For the top-ranked male, however, there was a significant correlation between intrusion rates and the size of the lek at which he displayed. Intrusion at leks may be costly, as 28% of female visits were interrupted by intruders. Solitary mates suffered no such interference. Females show no preferences for larger leks, visiting and mating at solitary sites as well as at leks. However, females preferentially visit males with high singing rates, and this male trait may determine visitation patterns. Our data argue that preferences for larger leks are not important in the evolution of lekking in this specie*, nor do they affect lek size. Instead, the data are in accordance with the predictions of both the hotshot and hot-spot models. These processes may be operating simultaneously in this spedes.

Black hole models of ungulate lek size and distribution

Models of lek breeding based on female preferences for mating with high quality males have predicted that leks should be evenly distributed at distances approximating the diameter of female home ranges, and empirical studies have cited lek distribution in support of these models. In the ‘black hole’ model of lek evolution, leks arise because clusters of male territories retain mobile females; female mating preferences are not assumed. Here this model is extended to include sufficient space and animals for multiple leks to form, and it is used to generate predictions about the size and spacing of leks in different populations. Like models based on female choice, black hole models predict that leks will be evenly spaced at distances of approximately one female home range diameter, that lek size will increase with increasing male density, and that females will be concentrated near the centre of leks where male territories will be smallest. The addition of female copying to the model decreases the tendency for leks to form, but this influence is mitigated by an upper limit on harem size. Since similar lek distributions are predicted by contrasting models, the even distribution of leks may imply some mechanism causing females to aggregate at the largest accessible cluster of territories, but does not clarify the nature of this mechanism.

Lekking in marine iguanas: female grouping and male reproductive strategies

The breeding and non-breeding distributions of male and female marine iguanas,Amblyrhynchus cristatus, and their mating behaviour were analysed. The population size was low because of a long lasting El Niño. The distribution of female-sized iguanas was more clumped during the mating season than before and afterwards. Model iguanas placed outside territories attracted more females during the breeding season than during the non-breeding season. The majority (75%) of large males established clustered territories while the remainder established single territories. The locations of the clusters were not related to physical characteristics of the habitat and were only partially related to non-breeding female densities. Non-territorial ‘sneaker’ males, similar in size to females, attempted copulations inside territories when territorial males were absent. Moderate sized, non-territorial males remained in the vicinity of territories and attempted to copulate forcefully with female-sized iguanas. This form of harassment was much higher outside territories, but levels did not differ between lek and single territories. Therefore, while harassment may lead to an increase in grouping among female-sized iguanas, it probably does not influence the type of territory visited. Females preferentially mated with the largest territorial males and reproductive success for these males was independent of lek size. The reproductive success of smaller territorial males, however, increased with lek size. Lekking in marine iguanas, therefore, may represent a ‘hotshot’ phenomenon where small territorial males associate with large males to increase reproductive success. The likely mechanism behind clustering appeared to be a greater propensity for females to mate in leks where stimulation rates were higher.

Pasture soils as carbon sink

Pasture soils as carbon sink

Lek size, male mating skew and the evolution of lekking

DESPITE extensive theoretical effort1–8, the evolution of lekking as a mating system remains a controversial issue9,10. Leks are non-resource-based mating aggregations2, but may also be regarded as patches differing in female encounter rate2, 3, 5, 7. We report here a new distribution model that incorporates variation in male mating skew with lek size. The model predicts that, under specified conditions, high-ranking males have smaller optimal lek sizes than low-ranking males. All males benefit from initial clustering, but only low-ranking males gain from large aggregations. This generates progressive clustering around high-ranking males at hotspots determined by female spatial distributions. The predictions of our model were validated in two ways using empirical data on lekking ruffs, Philomachus pugnax. Our model integrates the basic elements of the previously competing hotspot2, 3 and hotshot4 models of lek evolution by a simple mechanism, and could explain the evolution of lekking.

Leks of leks: a role for hotspots in lek evolution?

A lek is a cluster of males on display territories. Despite the attention that lek mating systems have received, the factors involved in lek evolution are still poorly understood. The ‘hotspot’ hypothesis suggests that population level patterns of female movement and/or dispersion determine male settlement patterns. Males, it is argued, should settle where females are most likely to be encountered or where female densities are greatest. Leks occur as a result of marked heterogeneities in female distributions. I tested three novel interspecific predictions of the hotspot hypothesis: (i) the leks of ecologically similar, sympatric species should be clustered; (ii) the degree of this clustering should be related to the degree of similarity in diet between the species; and (iii) species with similar diets should show correlated changes in the sizes of neighbouring leks. I documented the size and locations of leks of four neotropical bird species over 4 years. All three of the predictions were confirmed. The interspecific aggregation of leks strongly suggests a role of hotspot mechanisms in the evolution of lekking in these species.

Uganda kob mating success does not increase on larger leks

One explanation for the movement of sexually receptive females to clusters of male territories in lek-breeding species is that larger clusters provide females with higher-quality mating partners, as would be the case if males were distributed between leks in an ideal free distribution for unequal competitors. This ideal free model of lek evolution predicts that male competitive ability and mating success will be greater on larger leks than smaller ones. I tested these predictions by comparing the mean number of males on 19 different Uganda kob leks with the sex ratio, the availability of oestrous females, mating rates, male fighting rates and male turnover rates. Contrary to the predictions of the model, numbers of females, receptive females and fights increased proportionally with lek size, but were no greater per male on larger leks. Multivariate analyses of male and female numbers on leks showed that male numbers were associated with female numbers, female numbers in the past, and a variety of habitat variables which may have related to the costs of holding a lek territory, but female numbers varied only with male numbers and female density in the area. These data do not provide evidence that females gain access to superior males by mating on larger leks, though they do support the possibility that lekking may be promoted by a tendency for larger leks to retain females longer.

Costs and consequences of variation in the size of ruff leks

We studied 13 ruff leks in a small region on the island of Gotland (Sweden) to investigate the effect of lek size on the costs and benefits of lekking for individual males. Male ruffs occur in two behaviourally and morphologically distinct forms, “independents” (“residents” plus “marginals”) and “satellites”, whose costs and benefits we have assessed separately. These ruff leks had from 1–10 resident (territory-holding) males and were visited daily by satellites, marginals and females from 5–25 May, when most copulations occurred. We used the average number of independent males, counted during censuses taken every 5 min during 2-h observation periods at each lek, as an index of mean lek size. Per independent male, the numbers of both satellites and females increased significantly with mean lek size. Female arrival rate and attendance (total female-minutes) also increased significantly with mean lek size as did the average per capita rate of mating success for resident males (that of satellites was not quite significant). Thus, the dispersion of both of these male categories did not appear to fit an ideal free distribution with respect to mating success. In addition, the number of independent-independent fights per independent and the rate of satellite-resident dyad formation per resident increased significantly with mean lek size. These results suggest that ruffs on larger leks enjoy higher mating success than those on smaller leks but also that costs increase with lek size. We suggest that independent males distribute themselves so as to maximize their own net benefits and that this factor can account for both the occurrence of ruff leks and the variation in their size.

Inclusive fitness in a homogeneous environment

A general formulation of inclusive fitness is proposed which specifically accounts for competitive effects between relatives. As an example, for an asexual population in a homogeneous inelastic environment, such as is found in a stepping-stone model of dispersal, the inclusive fitness of a breeding female, under weak selection, is independent of her direct effect on the fitness of other individuals in the population. More precisely, suppose a female acts in a way that changes not only her own fitness but the fitness of several other females in the population who may be relatives (i.e. she changes the number of their offspring). I call these changes the direct effects of the action. There will also be indirect effects on the fitness of these and other females which come from the competitive impact of the extra offspring in the next generation. The principal result is that these indirect effects exactly cancel all the direct effects except the direct effect of the actor on herself.

Females prefer larger leks: field experiments with ruffs (Philomachus pugnax)

Preference by females for choosing mates at male aggregations has been hypothesized as the primary selective pressure favoring the formation of leks, but alternative hypotheses account for lek formation without invoking female preference. Observational studies to determine whether male mating success increases with lek size, as predicted under the female preference hypothesis, have produced inconsistent results, possibly due to covariation of lek size with other variables or to male-male or intersexual conflict over lek size. We tested whether females prefer larger leks in a field experiment with ruffs (Philomachus pugnax), a lekking sandpiper, in which male group size, composition, and location were controlled. Wild females chose the larger of two adjacent groups often enough such that males in larger groups had significantly higher per capita rates of female visitation (Table 3). Such behavior would probably lead to higher per male mating rates at larger leks, which is generally considered a necessary condition for female choice to select for lek display (Fig. 2). Lek size in nature will reflect both female preference for larger leks and competition among males, which may favor smaller lek size. All else being equal, however, female ruffs preferred to visit larger groups strongly enough to maintain lekking by males.

Correlates of male mating success and female choice in a lek-breeding antelope

We investigated factors underlying variation in male mating success in Uganda kob (Kobus kob thomasi), a lek-breeding antelope. We found that only heavy (and, possibly, relatively old) males held lek territories and that female choice was an important determinant of nonrandom mating patterns at leks. Our measure of male mating success was closely related to the historical popularity of the territory that a male defended, and individual females showed consistent preferences for particular lek territories, despite changes in territory ownership. Male success increased with body weight and declined independently of territory effects during each bout of lek territory tenure. We also found some evidence that female kob copied one another's choice of mates because females arriving at a lek tended to join territories that already had relatively large harems on them. When compared across leks, average male mating success increased with lek size. Our results suggest that female kob may use a suite of male- and territory-based cues in mate choice at leks and, as a result, mate with particularly large males. However, we were unable to determine whether female kob gain any direct or indirect benefits through mate choice at leks.

The evolution of leks through female choice

It is generally acknowledged that female preferences for mating in large groups of displaying males could cause the evolution of leks. Recent hypotheses differ on what selective advantage would accrue to females with such preferences, but they agree on the need for some such advantage if these preferences are to select for larger lek sizes. A model developed here, adapted from models of female preferences for individual male traits, shows that female preferences for larger leks can evolve and be maintained without any direct selective advantage. Like the individual choice models, it also demonstrates a number of arbitrary or non-adaptive features inherent in such systems. Most notably, instead of a single optimal outcome, there may exist a curve of possible equilibria. These equilibria can be stable or unstable depending on the nature of the female preferences.

Distribution and size of capercaillie leks in relation to old forest fragmentation.

Distribution and size of 38 capercaillie Tetrao urogallus leks were related to amount and configuration of old forest patches in two south-east Norwegian coniferous forests. The smallest occupied patch was 48 ha containing a solitary displaying cock. All patches larger than 1 km2 contained leks. Number of cocks per lek increased with increasing patch size. Number of leks per patch increased in a step-wise manner with one lek added for each 2.5-3 km2 increase in patch size. In large patches there was one lek per 3-5 km2 old forest, and density of lekking cocks was 2-2.5 per km2. In small patches density of cocks varied considerably. Density of cocks was not related to patch isolation or patch shape. However, among leks surrounded by 50-60% old forest within a 1 km radius, number of cocks increased with increasing old forest fine-graininess. We argue that when old forests cover more than 50%, a fine-grained mosaic may support higher densities of lekking cocks than a coarse-grained mosaic. Conversely, when old forests cover less than 50%, a fine-grained mosaic is unfavourable, because each old forest patch becomes too small and isolated. Finally, we present a predictive model of how old forest fragmentation influences density of leks, number of cocks per lek, and total density of cocks.