2.1 Study system and organism

We studied a naturally regulated population of Przewalski horses within the 2450-ha Pentezug Reserve, a grassland steppe system within Hortobágy National Park (HNP) in eastern Hungary (47°51′75 N, 21°09′28 E). The Pentezug Reserve is characterised by relatively flat terrain (about 87 m ASL) supporting native, alkali steppe vegetation communities, including grasslands, meadows, marshes and forests (Deák, Valkó, Alexander, et al., 2014; Deák, Valkó, Török, & Tóthmérész, 2014; Deák, Valkó, Tóthmérész, & Török, 2014; Zimmermann et al., 1998). The climate is continental, with four distinct seasons and average temperatures ranging from −2.5°C (min. −28°C) in January to 21°C (max. 38°C) in July, average rainfall of 50, and 2–10 cm of winter snow (average of 40–45 days per year). Two small, perennial rivers provide year-round drinking water for horses, with autumn and spring rains providing temporary ponds (Zimmermann et al., 1998). Climatic conditions are becoming increasingly non-stationary (e.g. decreasing level of summer rains, increasing temperature), with evidence over the past decade of effects on phenology of wildlife migration (Végvári & Kovács, 2010).

The reserve is bounded by a 3-wire, New Zealand style electric fence (24.8 km long, 1.4 m high; Gallagher, Budapest, Hungary), which restricts large mammal immigration and emigration while allowing smaller wildlife (e.g. roe deer (Capreolus capreolus), wild boar (Sus scrofa), red fox (Vulpes vulpes) and badger (Meles meles)) to move unimpeded. In addition to Przewalski horses, Heck cattle (Bos primigenius taurus) are free ranging within the reserve (Zimmermann et al., 1998, 2009). The horses and cattle graze year-round throughout the reserve without supplemental forage or veterinary care (since 2001) (Kerekes et al., 2021).

Originally introduced in 1997 as part of an international breeding program (Kerekes et al., 2019), Pentezug's Przewalski horse population is without harvest, round ups, or removal by humans and free of natural predation. There are no large carnivores (felids or canids) in the reserve. The founder population of horses introduced to Pentezug Reserve consisted of 21 horses (13 mares and 8 stallions), which were introduced from different European zoos over a 5-year period, beginning in 1997 (Kerekes et al., 2019). To increase genetic diversity, one additional mare was translocated to the reserve in 2007 and one stallion in 2010.

Changes in climate can influence resource availability, body condition, and mortality of large, harem-forming herbivores in this system (Kerekes et al., 2019), with implications on the acquisition, composition, and size of Przewalski horse harems, as also seen in feral horses (Manning et al., 2015; Manning & McLoughlin, 2017). In addition to these external forces, intrinsic population processes likely also determine harem size within and among years, similarly to those expected in other polygynous species translocated to conservation reserves (Beck, 2016; Dingle, 2014). Intrinsic processes that underlie the 12-month-cycle of harem phenology in Przewalski horses in the reserve include the dispersal of 18–24-month-old female offspring from their natal harem to another harem, the expulsion of subadult males from their natal harem, adult mortality, and displacement of a dominant stallion by another from outside the harem (Bouman, 1986). Female offspring may also leave their natal harem to join a bachelor stallion or other harem for an extended period and later return to their natal harem, and this can happen multiple times before the female settles (Bouman, 1986). These likely have additive and interactive effects with extrinsic processes that shape the 12-month phenological cycle of Przewalski horse harem sizes that evolutionarily evolved through ecological relationships between the distribution of resources, habitat, and feeding style (Szemán et al., 2021).

Initially after reintroduction, the horses formed spatially distinct harems of one to eleven mares led by individual stallions (Kerekes et al., 2019). Stallions without harems live solitarily or form loose, ephemeral bachelor bands (Bouman, 1986). Since 2001, the population experienced positive population growth due to reproduction; immunocontraception of mares began in 2013 (Kerekes et al., 2021). Subsequently, the population exhibited behavioural synchrony, such that animals were coordinating with conspecifics within and among harems (Kerekes et al., 2021; Maeda et al., 2021). The relatively distinct harem and bachelor groups that were present during our study period provided a unique opportunity to investigate the singular and additive effects of intrinsic and extrinsic factors that influence the phenology of harem size during a period of positive population growth after initial introduction and prior to behavioural synchrony.

2.2 Field data collection

We used an individual-based, longitudinal dataset of monthly field observations of the entire population of Pentezug's Przewalski horses from May 1998 to December 2012, obtained from the HNP Directorate. Park personnel have used standardised, non-invasive sampling protocols and a photographic database to monitor horses since their introduction in 1997. Over the study period, age, sex, breeding status, and harem affiliation were recorded from 267 individuals (39 harems comprised of 174 adults and 93 subadults). Harems and individual horses were observed with binoculars from a vehicle or on foot from 5 to 30 m at least once a month (for details please see Kerekes et al., 2021). Horses were individually identified according to phenotypic traits (i.e. sex, colour, stripes, whorls, mane position (left or right), belly colouration and specific marks such as scarfs, white marks or special colour patterns; Kerekes et al., 2019, 2021; Zimmermann et al., 2009). Mares were assigned to harems based on their social interactions (i.e. driving, following, and mutual grooming; Glatthaar, 2012) with other mares in a harem or with a dominant stallion. During each observation, individual IDs of all harem members were recorded.

As young stallions and mares disperse from their natal harem before they reproduce, and the age at first reproduction in mares in this population was two years, we defined an adult female as being ≥2 years old and not being affiliated with its natal harem. We considered stallions that were ≥3 years old and had left their natal harem to have entered the adult stallion age class. As our focus was on the composition of breeding individuals within and among harems, we classified sub-adults each year as those that had not left their natal harem before they had reached these age classes and excluded them from analyses.

2.3 Harem phenology

We used mean harem size each month to generate a 12-month phenology of harem sizes each year (Figure 1), from which we calculated annual mean harem size and three phenology-based harem size metrics. Annual mean harem size represented the average, commonly viewed steady state of harem size over a 12-month period, which enabled us to evaluate how intrinsic and extrinsic factors influenced inter-annual patterns in the within-year steady state of harem size. We also calculated the annual maximum harem size, defined as the largest monthly mean harem size within a 12-month cycle. We assumed that years with a relatively high maximum harem size reflected relatively better environmental and meteorological conditions that enabled stallions to retain and increase harem sizes and greater male mating success (Manning & McLoughlin, 2017). Additionally, we calculated the within-year dispersion of harem sizes as the coefficient of variation in mean monthly harem size each year ($$$ {\mathrm{CV}}_{\mathrm{mmhs}}=\left(\mathrm{SD}/\overline{x}\ \mathrm{monthly}\ \mathrm{harem}\ \mathrm{size}\right)\times 100 $$$) (Figure S1). We assumed that years with relatively greater dispersion reflected an increased degree of male mating inequality and opportunity for sexual selection (Emlen & Oring, 1977), which has been shown to emerge in feral horses from factors including local demography and drought conditions (Manning & McLoughlin, 2017, 2019). Lastly, because harem size is expected to vary within and among years, we calculated a monthly harem size metric for each year by first measuring the difference in mean monthly harem size (the ith month of the jth year) from the long-term average monthly harem size over the 15-year period (mean harem_ij – 15 year monthly mean harem). We then summed the number of months in each year that were below the 15-year average, and considered this as a harem size monthly departure index (HSMDI). An HSMDI = 0 indicated a year when all monthly average harem sizes were larger than the long-term normal harem size (Figure 1). We summarise our harem phenology metrics in Table 1. Due to low sample size in 2009 and 2010 (n = 2 observations each year), these two years were excluded from analyses.

2.4 Explanatory variables

To investigate how factors intrinsic to the population may influence the four phenology-based harem size metrics, we calculated empirical estimates of five demographic parameters annually. As harem size and the probability of acquiring harems have been linked to the adult sex ratio (ASR; proportion of adult males in the population) in other large ungulates (Bonenfant et al., 2004; Kaseda & Khalil, 1996; Manning & McLoughlin, 2019), we calculated ASR annually as the 12-month mean of the monthly proportion of adult stallions in the entire population (males ≥3 years old/[males ≥3 years old + females ≥2 years old]) (Ancona et al., 2017; Andersson, 2004; McNamara et al., 2000). We calculated annual adult mortality as the number of adult horse mortalities reported to HNP personnel within a 12-month period/mean annual size of the adult population. The mortality data were recorded during weekly visual monitoring of the horses by HNP personnel within the fenced park, where horses were identified at the individual level within groups throughout the study period. This involved targeted searches for every individual horse not detected during a weekly survey until either the animal was located alive or dead or several months had past, at which time the missing individual would be recorded as dead. The open grassland and gentle topography minimised missing animals and bias in our estimates of mortality. We also used this data to calculate annual juvenile female mortality. For this, we calculated a juvenile female mortality rate per-capita by dividing the number of juvenile female mortalities reported to HNP personnel by annual mean number of juvenile females in the entire population. In the analyses, we used this predictor with a 1-year (t − 1) time lag to consider the reduction in new adult females available for joining harems the following year. Because age can influence a stallion's ability to retain harems and mares within harems (Bouman, 1986), we calculated the mean age of harem holding stallions during each 12-month period. We used this variable as a second-degree polynomial function in our analyses to reflect a gradual threshold in harem acquisition and retention due to stallion senescence, creating a ∩-shaped correlation between age, resource holding abilities, and paternity success (Mainguy & Côtè, 2008; Mysterud et al., 2003; Perlman et al., 2016; Setchell et al., 2006; Silk et al., 2020; Van Noordwijk & Van Schaik, 1985; Watts, 2019; Yoccoz et al., 2002). Lastly, we calculated the annual mean number of harems from monthly counts conducted each year.

Because climatic conditions have been found to underly ASR and polygyny thresholds in feral horses (Manning et al., 2015; Manning & McLoughlin, 2017), we also developed an annual drought severity index (DSI) from measures of average monthly temperature and total precipitation obtained from worldclim.org. Here, DSI served as an index of variable food quality and subsequent body condition over the year, which we posited may influence female mate choice, and hence harem size and retention by stallions. We reasoned that the most severe drought conditions would be those with hottest temperatures and lowest total precipitation. We used the climate rasters with resolutions of 0.5° × 0.5°, retrieved from worldclim.org and selected the single grid covering the whole of the study area. In the following step we extracted the climate values from this raster grid. For each month, we standardised average temperature and total precipitation, as monthly mean temperature or total precipitation—15-year average temperature or precipitation. Then, we calculated the standardised average temperature – standardised total precipitation, such that higher (positive) values corresponded to relatively hotter and drier drought conditions, whereas lower (negative values) characterised relatively cooler and wetter conditions (Figure 2). We then summed the number of months with values >0 within a year to represent the number of months above normal drought conditions each year and used this as a DSI in our models (see Table 2 for details).

2.5 Statistical analysis

We developed four parallel analyses to evaluate the importance of demographic and meteorological factors on variation in harem size. For each phenology-based harem size metric, we constructed an a priori candidate set of 16 linear models based on biologically relevant combinations of intrinsic and extrinsic covariates (Anderson & Burnham, 2002). For HSMDI, we used a negative binomial model; the other three response variables were modelled using ordinary least squares regression. We tested for bivariate correlations among the covariates and found all Spearman's |r| values to be <.7 (Table S1). We considered 0.7 as a threshold for collinearity because collinearity above this value begins to severely distort model estimation and subsequent prediction in ecological studies (Dormann et al., 2013; Tabachnick et al., 2007). While there are many options on how to statically handle this situation (Gregorich et al., 2021), given these results and our small sample sizes, we constrained the model sets to 2-structural parameter additive models. We used Information Theory with the second-order small-sample bias-corrected Akaike's Information Criterion (AICc) and AICc weights ($$$ {w}_{\mathrm{AICc}} $$$) (Anderson & Burnham, 2002) to quantify the support of each model within each parallel analysis using the bbmle package in R (version 4.1.2; Bolker, 2022; R Core Team, 2021). We tested for normality of residuals (marginal residuals vs. fitted values and Q–Q plots) in the most supported model in each parallel analysis and also assessed the r-square, F-statistic, and p-value metrics of these models. Following Akaike (1973) and Anderson and Burnham (2002), we considered the model with the lowest ΔAICc-value and highest $$$ {w}_{\mathrm{AICc}} $$$ within a candidate set as having the greatest empirical support for inference regarding the coinciding phenology-based measure of harem size. We considered models with ΔAICc ≤2 as competing.

3.1 Factors influencing annual average harem size

Annual mean harem size was best predicted by the additive effects of ASR and annual adult mortality (annual mean harem size model w_AICc = 0.98; Table 3); this model fit the data well and exhibited a symmetric pattern of marginal residuals versus fitted values (i.e. normality; Figure S2). For every 10% increase in ASR, mean harem size decreased by 0.479, and every 10% increase in adult mortality led to mean harem size increasing by 0.877 ($$$ \mathrm{mean}\ \mathrm{harem}\ \mathrm{size}=4.28-4.79\left(\mathrm{ASR}\right)+8.77\left(\mathrm{adult}\ \mathrm{mortality}\right) $$$; adjusted R² = .91, F_2,9 = 59.62, p < .001; Figure 4). There was no evidence that other demographic processes or extrinsic factors influenced mean harem size (all ΔAICc ≥2; Table 3).

3.2 Factors influencing annual maximum harem size

Three competing models explained annual maximum harem size (model ASR + annual mean number of harems (w_AICc = 0.37), model ASR (ΔAICc = 0.57, w_AICc = 0.28), and model DSI + ASR (ΔAICc = 1.81, w_AICc = 0.15); Table 3). These three models contained ASR and had a combined w_AICc = 0.80, providing strong evidence that ASR is an important predictor of annual maximum harem size. The presence of annual mean number of harems and DSI in the more complex competing models indicate that these intrinsic and extrinsic forces may also have underlying effects on annual maximum harem size. However, because these models were nested, we considered the simpler model (model ASR) as the most parsimonious for making inference. This model fit the data well (i.e. normality; Figure S3) and predicted that each 10% increase in ASR led to a decrease in maximum harem size of 1.24 females ($$$ \mathrm{maximum}\ \mathrm{harem}=11.43-11.24\left(\mathrm{ASR}\right) $$$; adjusted R² = .61, F_1,10 = 17.92, p = .002; Figure 5). There was little evidence that other demographic factors influenced annual maximum harem size (all other models ΔAICc ≥2; Table 3).

3.3 Factors affecting variation in harem size (CV)

Annual variation in dispersion of harem sizes was explained best by annual mean number of harems (w_AICc = 0.51; Table 3), which fit the data well (Figure S4). We found no evidence that extrinsic or other intrinsic factors affected the dispersion of harem sizes (all ΔAICc ≥2; Table 3). This ‘best’ supported model predicted that for every 1 unit increase in annual mean number of harems, the dispersion of harem sizes decreased by 1.24% during the study period ($$$ \mathrm{variation}\ \mathrm{of}\ \mathrm{harem}\ \mathrm{sizes}=91.50-1.24\left(\mathrm{annual}\ \mathrm{mean}\ \mathrm{number}\ \mathrm{of}\ \mathrm{harem}\mathrm{s}\right) $$$). However, this model explained a low amount of variation in annual dispersion of harem size (adjusted R² = .26, F_1,10 = 4.90, p = .05; Figure 6).

3.4 Factors affecting annual deviations from the long-term, normal harem size (HSMDI)

Our most supported negative binomial model of harem size monthly departure index contained the single effect of ASR (w_AICc = 0.44; Table 3, Figure S5) ($$$ \mathrm{HSMDI}=10.01-29.98\left(\mathrm{ASR}\right) $$$; Figure 7). In addition to ASR, there was some slight evidence of an additive quadratic effect of mean age of harem stallions on HSMDI (ΔAICc = 2.74; w_AICc = 0.11; Table 3). There was little evidence of other demographic processes or extrinsic factors influencing HSMDI (Table 3).