Rainfall driven changes in behavioural responses confound measuring trends in lion population size

Population size estimates must be comparable through time to interpret trends in threatened carnivore populations. Because prey distribution and dynamics drive carnivore distribution, and sampling methods often utilise behavioural responses to attractants, habitat variability among sampling occasions may confound such estimates. We explored whether a marked and unexpected reduction in lion Panthera leo population size estimates in Kruger National Park, was real or represented changes in behavioural responses to call-up stations given reduced rainfall between sampling periods. Rainfall drives savannah landscape heterogeneity, surface water and lion prey food availability. Hence landscape factors should more strongly influence lion behaviour during dryer conditions. We compared proportion of stations visited and mean numbers visiting stations, among three sampling years (2005, 2006 and 2008) belonging to the two sampling periods 2005/2006 and 2008. We then modelled the influence of landscape factors and spotted hyena Crocuta crocuta presence on visits and numbers. We distinguished behavioural from real changes by simulating pseudo-absences of cubs (these are observations of females which do have cubs but did not show up with them at calling stations) and comparing observed with predicted population estimates. Adult males responded similarly among sampling years. However, in 2008 the driest year, adult females and those with cubs visited a lower proportion of stations, and landscape influences on these groups was stronger. A switch from rainfall explaining adult females with cubs visiting stations during wetter sampling years, to distance to rivers in 2008 confirmed landscape driven changes in lion responses consistent with prey distribution in dry conditions. However, simulations indicated that while behavioural responses accounted for some population reduction, some was real. Reduced rainfall induced behavioural effects were difficult to unravel from real population size changes. We advocate caution when interpreting trends from lion population estimates reliant on behavioural responses subject to variability in landscape factors. Particularly, for estimators sensitive to behavioural changes in females with cubs — the demographic component most affected by variable conditions.

Population size estimates form vital information for understanding the interactions between a species and its environment (Krebs 2003) and thus lie at the heart of many wildlife and conservation management strategies. Th is is especially the case for threatened carnivore species which often suff er from multiple stressors including human induced pressures (Ogutu and Dublin 2002, Ogutu et al. 2005, Woodroff e and Frank 2005, Loveridge et al. 2007, Kiff ner et al. 2009, Packer et al. 2011) and disease (Mollel 1977, Brown et al. 1994, Roelke-Parker et al. 1996, Keet et al. 1997, Packer et al. 1999, Cleaveland et al. 2005. However, for carnivores, estimating and monitoring changes in population size is challenging . Carnivores are positioned at the top of the food chain, such that their distribution and behavioural responses are infl uenced by the distribution of their prey in relation to key resources, which in turn is modulated by the availability of structural and functional resources of systems to which they belong (Karanth et al. 2004, Valeix et al. 2011. Hence, variation in these resources can markedly infl uence population estimates. Th is may be especially true when utilising sampling designs for one-off surveys that rely on carnivore behavioural responses (Ogutu andDublin 1998, Ferreira andFunston 2010) because fl ow-on eff ects from prey responses to the distribution of food and water may alter lion responses to attractant stimuli. Th is is important, because variation in responses between sampling occasions may lead to incorrect estimates of population size, with serious consequences for conservation management decisions.
We explored if this was the case for African lions Panthera leo in Kruger National Park, South Africa (Kruger). Although Kruger hosts one of the largest lion populations in Africa (Chardonnet 2002, Bauer andvan der Merwe 2004), emerging bovine tuberculosis (bTB) was fl agged as a potential threat to the wellbeing of lions there (Keet et al. 1996). However, although no population level eff ects suggest threats to lion persistence (Ferreira and Funston 2010), two recent population estimates noted a decline of 19 -31% per annum from 1684 lions (95% CI: 1617 -1751) in 2005/2006 (Ferreira and Funston 2010) to 1016 lions (95% CI: 862 -1180) in 2008 (SANParks, unpubl.data). If real, such a decline raises a key concern. Lions are vulnerable (Packer et al. 2013) and now only exist in 67 populations across Africa, of which Kruger is one of ten conservation strongholds for this species (Riggio et al. 2013). In this study, we assessed whether this decline was real, or the product of variation in behavioural responses to variation in structural and functional landscape factors between sampling years. Note that our two sampling periods of 2005/2006 and 2008 and respective population estimates comprised data from three sampling years 2005, 2006 and 2008. Call-up stations are a preferred survey technique for lions in mesic savannah (Ogutu andDublin 1998, Ferreira andFunston 2010) and were used in all our sampling years. Because this method relies on lion responses to prey-distress calls, we were concerned that the two population estimates may have been sensitive to a marked reduction in rainfall and/or an inadvertent increased distance to waterholes noted for the latter sampling period (SANParks, unpubl. data).
Rainfall and the distribution and availability of water sources infl uence lion behaviour. Rainfall drives the spatial arrangement, quality and quantity of limiting food and water in savannah systems at the landscape scale, with fl ow-on eff ects on carnivore distribution and density (Hopcroft et al. 2005, De Boer et al. 2010, Valeix et al. 2010. Indeed, in woodlands, lion kills are typically closer to rivers ) and to artifi cial water points than expected (De Boer et al. 2010) particularly in the dry season when lions may prefer wooded areas for shade and cover for cubs, and when prey species are spatially restricted to areas where surface water is available (Hopcroft et al. 2005, De Boer et al. 2010, Valeix et al. 2010. Moreover vegetation cover associated with rivers may render these areas more favourable for hunting by lions ). We therefore hypothesised that decreased rainfall between surveys and/or the increased distance of call-up stations to waterholes infl uenced the behavioural response of adult female lions with cubs. Th is in turn infl uenced calculated population estimates according to the response estimator derived for lions in Kruger (Ferreira and Funston 2010).
To test our hypothesis, we explored the infl uence of rainfall, distance to closest waterholes, distance to closest river and prey food availability on lion responses to call up stations. We expected the relationships between these structural and functional landscape factors and lion responses would be stronger during periods of low rainfall when lions take advantage of their prey being limited to available water sources (Hopcroft et al. 2005, De Boer et al. 2010, Valeix et al. 2010) and/or more easy to target ). In addition to these landscape level factors, we also explored the local infl uence of the presence of spotted hyena Crocuta crocuta (hereafter hyena) on lion responses. Because hyenas are competitors of lions (Owen-Smith and Mills 2008) and thus may modulate lion behaviour, we asked if the presence of hyenas diff ered among sampling years, and whether their presence modulated the response of lions to our call up stations. Finally, to distinguish between changes in behavioural responses and real changes in the number of females, and/or number of females with cubs, we also explored the eff ect on population estimates if behavioural choices resulted in pseudo-observations of females without cubs. We reasoned that if predicted estimates diff ered from observed estimates during 2008, changes other than, or in addition to, female behavioural changes had occurred.
Our study highlights the need for caution when estimating lion population sizes from one-off surveys that rely on behavioural responses. We argue that variation in structural and functional landscape factors among sampling years can generate fl ow-on eff ects in prey dynamics and lion behavioural responses that need to be accounted for when interpreting trends in population size among surveys.

Study area
Th e Kruger National Park (Kruger) is situated in the lowlying savannah of the eastern parts of the Limpopo and Mpumalanga Provinces, South Africa. Mozambique abuts the Park in the east, while Zimbabwe forms the boundary to the north. Th e Park covers an area of 19 485 km ² and has a mean annual rainfall that varies from 750 mm in the south to 450 mm in the north, with ∼ 80% of rain falling during October to March (Gertenbach 1980). Granite and gneiss soils dominate Kruger ' s western half and nutrient-rich basalt soils dominate the eastern half, with a narrow band of Karoo sediment occurring at the junction of the granite and basalt (Schutte 1986).
Th e vegetation on the southern basalts is largely wooded savannah, with Sclerocarya caff ra and Acacia nigrescens dominating the tree canopy. Mixed Combretum spp. and Acacia spp. dominate the southern granites. In the north Colophospermum mopane dominates both the basalt and granite substrates. However, taller C. mopane as well as Combretum spp. and Acacia spp. occur more often on the granites, while stunted or shrub like C. mopane sparsely interspersed by S. caff ra are found on the basalts (Gertenbach 1983).
Large herbivore densities closely match substrate and vegetation patterns with higher densities on the fertile basalts than the granites, and at markedly lower densities in the dry north than the south irrespective of substrates (Ferreira and Funston 2010). In addition, there are zonal bTB prevalence diff erences within buff alo with 38.0%, 16.0% and 1.5% in the southern, central and northern regions of the Park respectively (Rodwell et al. 2000). Th e Olifants River is the boundary between the northern and central region while the Sabie River is the boundary between the central and southern zones. Ferreira and Funston (2010) originally defi ned six zones: low prey -low disease, medium prey -low disease, high prey -medium disease, very high prey -medium disease, high prey -high disease, and very high prey -high disease zones.

Lion responses
We used three datasets collected across the Park in 2005, 2006 and 2008. Each dataset was collected in the dry season months (May, June, July, August and September). Because the survey in 2005 focused primarily in the south of the park, and in 2006 from the middle to northern reaches of the park (thus together forming a total coverage of Kruger, Ferreira and Funston 2010), we analysed datasets for 2005 and 2006 both individually, and as a combined dataset. We note that this approach makes our reporting of results and discussion complicated. However, it provided us with the ability to interpret results collectively across the park, but also independently among years with relevance to the diff erence between the population estimates of concern. Hence, to assist the fl ow of reading, hereinafter we refer to 2005, 2006 and 2008 as sampling years, and 2005/2006 combined and 2008 as sampling periods. Note that the sampling year and period for 2008 are therefore one and the same and may be referred to twice for ease of reading.
All sampling locations were stratifi ed according to a combination of prey biomass and tuberculosis incidence (Ferreira and Funston 2010). For our 2005 (n ϭ 101 call-up stations) and 2006 (n ϭ 124 call-up stations) sampling years, stations were placed no closer than 10 km apart in a systematic grid design ( ≈ 12 per 1000 km 2 ). For our 2008 sampling year (127 call-up stations) stations were placed no closer than 11.5 km apart ( ≈ 8 per 1000 km 2 as per recommendation by Ferreira and Funston 2010), following the same sampling design as before (i.e. also stratifi ed by prey biomass and tuberculosis incidence). Th is latter sampling intensity was based on optimal requirements that stabilized variance in estimates (Ferreira and Funston 2010). Call-ups comprised a buff alo distress call and were played for one hour at night (Ferreira and Funston 2010). For each call-up station, we recorded whether the station was visited, the total number of lions that visited the station, the total number of males, the total number of females, and whether cubs visited the station within the hour play period. We also recorded the presence of spotted hyenas, but did not record their numbers. Call-up station response rates have been calibrated by Ferreira and Funston (2010) providing for the eff ective area over which lions may respond, the probability that a group within that area will respond, and the probability that an individual within a responding group will respond. Th ey also calibrated the effi ciency of call-up stations by defi ning the survey eff ort required to achieve estimates with known precision in Kruger National Park, South Africa. Together these calculations render call-up station data similar to that of block counts (Ferreira et al. 2011) albeit with a circular sampling area.

Structural and functional landscape explanatory factors
For each call up station, we assigned prey biomass as low, medium, high and very high as per Ferreira and Funston (2010) based on data from the 2006 census (Judith Kruger, Scientifi c Services, SANParks, unpubl. data) from which we calculated the biomass of eight key prey species that make up Ͼ 95% of the lion ' s prey in Kruger Shenk 1992, Radloff anddu Toit 2004).
We used the normalised diff erence vegetation index (NDVI) as an index of prey food availability. NDVI is good proxy for vegetation productivity (Pettorelli et al. 2005) and prey food availability because ungulate abundance associates with productivity (Verlinden and Masogo 1997, van Bommel et al. 2006, Pettorelli et al. 2009). We downloaded NDVI values for July 2005, July 2006 and July 2008 from Ͻ http://free.vgt.vito.be/ Ͼ . Data were at the resolution of 1 km 2 , with NDVI-values calculated from 10-day composites of remotely sensed images from the VEGETATION sensor aboard the SPOT4 and SPOT5 satellites for July of each year. For each of July 2005, 2006 and 2008, three 10-day composites were available so we used the middle composite from 11 -21 July to represent NDVI values of July that year. We then calculated the sum of total NDVI within an assumed eff ective operating area we calculated for each call-up station based on the probability of a lion to respond within that area as calculated by Ferreira and Funston (2010). Lions respond to call-up stations from a mean distance of 4.5 km (Ferreira and Funston 2010). Using this distance as a radius, we assumed an eff ective operating area of 64 km 2 about each call-up station location and, for each, created a round buff er of this size using the spatial analyses toolbox in ARCGIS ver 9.0. For each round buff er we calculated the total concurrent standing prey food availability (sum of NDVI of round buff er at time of call-up).
We also used the spatial analyses toolbox in ARCGIS ver 9.0 to calculate the Euclidian distance (in km) from each call-up station to the nearest waterhole (artifi cial or natural) and to the nearest river.
We calculated the total volume of rainfall in the twelve months prior to each respective July for each sampling station. To do this we used total rainfall recorded from 26 rainfall stations in 2005, 22 in 2006 and 19 in 2008 for the 12 month period prior to sampling. For each year we calculated a thin plate spline using a generalised additive model in the R-package ' fi elds ' ( Ͻ http://pages.cs.wisc.edu/ ∼ xie/ thin_plate_spline_tutorial.html Ͼ ) to predict rainfall across Kruger at a resolution of 1 km 2 . We then extracted predicted rainfall values for each station in its respective sampling year.
Finally, rainfall increases in Kruger National Park in a north to south direction forming a distinct rainfall gradient (Gertenbach 1980). To assist in distinguishing between the infl uence of inter-annual variability and spatial-variation in rainfall on lion responses, we also used the latitude of each call-up station as an explanatory factor in our analyses.

The presence of hyenas
In addition to the explanatory factors above, we recorded the presence of hyena at each call up station. As per our introduction, the presence of hyena was treated as both a response variable (probability of visiting a station) and a localised explanatory factor for lion responses.

Analytical approach
We compared lion responses to call up stations among all three sampling years (2005, 2006 and 2008) and then between the 2005/2006 and 2008 sampling periods. We calculated the proportion of call up stations for each sampling year and sampling period that were visited by any lions, by adult males, by adult females (with and without cubs -hereinafter adult females), by adult females with cubs, and by hyena, and noted diff erences in these between sampling years (note that on only four occasions did cubs visit a station independent of an adult female so we did not calculate proportion of stations visited by cubs separately), useful or plausible (Hastie et al. 2001, Boyce et al. 2002. For our Poisson models, we calculated the deviance explained from the predicted means of the models (D 2 ) where D 2 ϭ (null deviance -residual deviance)/null deviance. We also calculated the correlation between observed and predicted values (COR) as a measure of model accuracy.
For both our logistic regressions and Poisson models we calculated model stability, being the performance of the model to predict correct values from subsets of the data, using fi ve-fold cross validation (Hastie et al. 2001). Where cross validation values were Ͻ 0.6 and or departed considerably from respective ROC or COR values, we considered models unstable in their ability to accurately predict correct values from new data.
For each response variable, we evaluated diff erences in its relationship with explanatory factors among sampling occasions together and independently by comparing model statistics (D 2 and AUC-ROC values), performance under cross validation, included explanatory factors, relative importance of these and associated shape of relationships.
All models were calculated using generalised regression and spatial prediction (GRASP, Lehmann et al. 2002) in the R statistical environment ver. 1.12.3.
To distinguish between behavioural responses and real declines, we simulated the likely eff ect on the lion population estimator developed before (Ferreira and Funston 2010) if females made behavioural choices resulting in pseudoobservations of females without cubs (i.e. these are observations of females which do have cubs but did not show up with them at calling stations). We simulated a fi xed number of females changing progressively from nearly all turning up with cubs to nearly all turning up without cubs. By fi tting a linear relationship between predicted population estimates (estimated by applying Ferreira and Funston ' s 2010 estimator) and percentage of females visiting call-up stations with cubs, we could estimate the likely eff ect of such behavioural changes on a population estimates when all else stays equal.
We then collated survey data for 2005/2006 (Ferreira and Funston 2010) and 2008 (SANParks, unpubl. data) and calculated the observed percentage of females visiting call-up stations with cubs for each of the two surveys. Using the derived linear relationship, we then predicted the population estimate as well as the estimated number of adult females for 2008 if the population did not change, but behavioural responses did as indicated by the change in percentage of females with cubs visiting stations. We reasoned that if this predicted estimate diff ers from observed estimates during 2008 we have reason to believe there were changes other than, or in addition to female behavioural changes.

Among 2005, 2006 and 2008 sampling years
Th e proportions of stations that were visited by any lions, adult females, adult females with cubs, cubs and hyena were lower in 2008 relative to 2005, 2006 (Fig. 1A). However, in and between sampling occasions. We then used one way analyses of variance and Tukey ' s post hoc tests to compare mean group size, mean number of adult males, mean number of adult females and mean number of cubs per station between the three sampling years (2005, 2006 and 2008) and one way t-tests to compare between the two sampling periods (2005/2006 combined and 2008).
Next we compared the spatial distribution of sampling sites in relation to distance to closest waterhole, and distance to closest river, and also compared the sum of NDVI (our index of prey food availability) and total predicted rainfall in the twelve months prior to sampling between the three sampling years, and between the two sampling periods. As above, we used one way analysis of variance (ANOVA) and Tukey's post hoc tests to compare means between the sampling years, and one tailed t-tests to compare means between the sampling periods.
To establish the infl uence of our explanatory factors on lion responses and on the presence of hyenas, we modeled suites of alternative hypotheses being diff erent combinations of explanatory factors for: the probability of a station being visited; 1) by any lions, 2) by adult males, 3) by adult females, 4) by adult females with cubs, and 5) by hyena, and for each station the mean number of; 6) lions in the total group, 7) adult male lions, 8) adult female lions, and 9) lion cubs. For each response variable we calculated generalised additive models for : 1) 2005 2) 2006 3) 2008, 4)  For each candidate model we calculated the Akaike ' s information criterion corrected for small sample size (AICc) (Burnham and Anderson 2002) and stepwise selected the model with the lowest AICc value as the most likely model to represent the data (Burnham and Anderson 2002). We also calculated AICc diff erences (AICc ( Δ i)) to assess support for each model where for the best model AICc ( Δ i) ϭ 0; values from 0 to 2 indicate substantial support; values of 4 -7 less support and values Ͼ 10 no support (Burnham and Anderson 2002). Next we calculated AICc weights (AIC(wi)) to indicate the probability that each model was the most likely model of all candidate models to represent the dataset. Where the diff erence between best fi t models and next fi t model(s) according to AIC(wi) was negligible and mostly involved the removal of one explanatory factor with limited reduction in evidential support for the model fi t to the data i.e. AICc ( Δ i) Ͻ 2, we also report the respective variable.
We used logistic regressions for response variables 1) to 5) (probability models), and the Poisson family of models for response variables 6) to 9) (explanation of variance). For our logistic regressions, we calculated the discriminative ability of models as the area under the curve (AUC) of the receiver operating characteristic (AUC-ROC). Th e ROC curve is calculated as the curve of true positives versus false positives and therefore varies from 0.5 (discriminating power no better than chance) to 1.0 (perfect discriminating power). Accordingly the AUC-ROC represents the percentage of all possible pairs of cases in which the model assigns a higher probability to a correct case than to an incorrect case. Accordingly AUC-ROC values below 0.7 are considered to have poor discriminatory ability (Hosmer and Lemeshow 2000) and we categorised models with AUC-ROC values Ͼ 0.7 as

Between the 2005/2006 and 2008 sampling periods
Th e mean group size and mean number of cubs were lower in 2008 than during the 2005/2006 sampling period, although for the former this diff erence fell just below statistical signifi cance (one tailed t-test: p ϭ 0.07, p Ͻ 0.0001 respectively). Th e mean number of adult males and adult females did not diff er between the two sampling periods combined (one tailed t-test: p ϭ 0.42, p ϭ 0.29 respectively).

Among 2005, 2006 and 2008 sampling years
Th e distance to closest river, sum of NDVI and rainfall in the

Between the 2005/2006 and 2008 sampling periods
In 2008, call-up stations were distributed further from the closest waterhole than in the 2005/2006 sampling period (one way t-test: p Ͻ 0.0001). Sum of NDVI was smaller in 2008 than 2005/2006 (one way t-test: p Ͻ 0.0001), and rainfall in the 12 months preceding sampling was lower for 2008 than for 2005/2006 (one way t-test: p Ͻ 0.0001). Th e distribution of sampling sites in relation to the closest river did not diff er between sampling occasions (one way t-test , p ϭ 0.46).

Probability of visits to call-up stations
Our best fi t models diff ered among sampling years and sampling periods in their ability to plausibly explain the probability of a station being visited by our lion groups (any lions, adult males, adult females, adult females with cubs) and hyenas. Note that the suite of explanatory factors included in selected models were relatively consistent among years for explaining adult male lion visits, but in contrast changed sampling year. However, for the probability of a station being visited by any lions or by hyenas, our best fi t models were only plausible for the 2005 and 2008 sampling years (Table 1). For the likelihood of adult females visiting a station, our best fi t model was only plausible for the 2008 sampling year. For all of our models, except those for the likelihood of a station being visited in 2008, and male lions visiting a station in 2008, the diff erence between ROC and cvCOR values suggested some degree of instability, particularly for hyenas visiting stations in 2005 and 2008 where cvCOR values are less than 0.6. Th e diff erence between best fi t models and next fi t model(s) for which there was support according to AICc ( Δ i) and AIC(wi) for most response variables was often negligible and mostly involved the removal of one explanatory factor with limited reduction in evidential support for the model fi t to the data as per AICc ( Δ i) and AIC(wi) ( considerably for adult females and adult females with cubs among sampling years (Table 1). In the wetter years of 2005 and 2006, the likelihood of visits by adult females with cubs was explained predominantly by rainfall and the presence of hyenas. By contrast in the dry year of 2008, distance to rivers was the most important explanatory variable followed by sumNDVI and distance to closest water (Table 1). Other notable distinctions include a strong and consistent ability for latitude to explain adult male visits to stations, but this was not the case for explaining the visits of adult females and females with cubs to call-up stations (Table 1). Finally, the visits of adult female lions to call up stations could only plausibly be explained during the driest sampling year (2008).

Discriminatory ability among sampling years
Our best fi t models plausibly explained the probability of adult males and females with cubs visiting a station in each Table 1. Summaries of best fi t generalised additive models selected according to AIC for four visitation response variables where AUC-ROC is the discriminatory ability of the model (Methods) and cvROC represent the models performance under fi vefold cross validation (Methods). Explanatory factors are those included in the selected model and relative importance is their respective percentage of the model's total discriminatory ability. Note that values in bold are for plausible models where AUC-ROC Ͼ 0.7 and we show models with AUC-ROC Ͻ 0.7 in grey. Lower case ' x ' denotes an explanatory factor not included in the best fi t model but included in a next best fi t model where only limited loss of evidence of for model support was noted (Methods). Closest waterhole had a patchy ability to explain response variables among years with limited pattern apparent except an absence from most 2006 models when rainfall was highest (Table 1). Of note, in all plausible models closest water was the least important explanatory variable. In contrast, where closest water hole explained lion responses, the likelihood of a station being visited decreased with increasing distance from the closest waterhole (Supplementary material Appendix 6 Fig. A1 -A4).

Explanatory factors and relative importance (proportion)
Prey biomass was selected or indicated as important in next best fi t model in only four plausible models among years and response variables. Prey biomass explained the likelihood of a station being visited by an adult male in 2005 and 2006 and by an adult female in 2008. For adult males the relative importance of prey biomass was low, however for adult females in 2008 prey biomass was the most important explanatory variable (Table 1). For both response variables, a station was more likely to be visited where prey biomass was low (Supplementary material Appendix 6 Fig. A2, A3).
Finally, the presence of hyena was also variably important in explaining lion responses with no clear pattern apparent among years or response variables. However the presence of hyena did explain whether a call-up station was visited in at least one of the sampling years for each response variable (Table 1). Of note, where hyenas were present a call up station was considerably less likely to be visited (Supplementary material Appendix 6 Fig. A1 -A5).

2005/2006 sampling period
In this sampling period, no plausible models explained the likelihood of stations being visited by adult females or females with cubs. Similar to models for 2005, 2006 and 2008 above, sum NDVI, rainfall and latitude together explained the likelihood of a station being visited, or visited by hyenas in the combined 2005/2006 dataset. For the likelihood of a station being visited, closest waterhole was also an explanatory factor, but of considerably less relative importance (Table 1) and for the likelihood of a station being visited by hyena, distance to closest river was important. SumNDVI and rainfall together with the presence of hyenas explained the likelihood of a station being visited by adult male lions. Th e relationships between lion responses and sumNDVI, rainfall, latitude and closest rivers were complex in respective models for response variables (Supplementary material Appendix 6 Fig. A1, A2, A5), however the likelihood of a station being visited by any lions decreased with increasing distance from closest waterhole.

All years
Of most interest to our evaluation, year explained likelihood of a station being visited and being visited by females with cubs, but not whether a station was visited by adult males. Note that the best fi t model for adult females and hyenas were not plausible. Where year was selected the likelihood of a station being visited was lower in 2008 (Supplementary material Appendix 6 Fig. A1, A2, A4). SumNDVI, rainfall and latitude explained likelihood of a station being visited by any lions, by adult male lions, by hyenas, but did not additionally explain the likelihood of a station being visited by adult females with cubs. Th is was rather explained by latitude, distance to closest waterhole and the presence

2005/2006 sampling period
Our models for the 2006/2006 sampling period plausibly explained the probability of a station being visited, of adult males visiting a station and of hyenas visiting a station, but did not plausibly explain the probability of adult females or adult females with cubs visiting stations. Th e stability of the plausible models was low for probability of visiting a station and the diff erence between ROC and cvROC values for adult male lions and hyenas suggested some instability in these models. Best fi t models were negligibly better fi ts than next fi t model(s) with one to two variables removed with limited loss of evidence in support of the model fi tting the data (Table 1, Supplementary material Appendix 4).

All years
Our models for data from when all years were combined plausibly explained the probability of visiting a station, and adult males and adult females with cubs visiting stations but did not explain the visits of adult females or hyenas. Diff erences between ROC and cvROC values for visiting a station and for adult males suggested some model instability, but the model for explaining the likelihood of a female with cubs visiting a station was stable (Table 1). Best fi t models were negligibly better fi ts to the data than next fi t model(s), but diff ered mostly in terms of degrees of freedom for each variable and not in explanatory factors themselves (Table 1, Supplementary material Appendix 5).

Among sampling years and response factors
SumNDVI rainfall and latitude consistently explained whether a station was visited, was visited by adult male lions and was visited by hyenas. In general latitude was the most important factor for these response variables among all years. Secondary importance wavered between rainfall and NDVI among years. In contrast, latitude did not explain the visits of females with cubs to stations (although it was indicated as important in the next best fi t models, Supplementary material Appendix 4) but rainfall and sumNDVI did (Table 1). Of note none of these factors explained adult female visits to call-up stations in the only plausible model (2008).
Th e relationships between lion responses and sumNDVI and rainfall were complex in most models for all response variables (95% CI: 1288 -1515) lions from the percentage of females with cubs in 2008, if only a behavioural response occurred. Th is was higher than the observed estimate of 1016 (95% CI: 862 -1180) during 2008 (SANParks unpubl. data). In contrast, when we considered estimates of adult females only /2006: 415, 95% CI: 380 -450, Ferreira and Funston 2010, the response by females predicts 381 (95% CI: 349 -413) substantially lower than the observed estimate of 612 (95% CI: 556 -669).

Discussion
Reliable estimates of population size are needed to inform sound conservation management decisions (Krebs 2003). Th is is especially relevant when interpreting trends in populations of threatened carnivore species subject to multiple stressors including human induced habitat changes and mortality (Ogutu and Dublin 2002, Ogutu et al. 2005, Woodroff e and Frank 2005, Loveridge et al. 2007, Kiff ner et al. 2009, Packer et al. 2011. Our assessment of the infl uence of structural and functional landscape factors on lion responses to call-up stations strongly supports our concern that quantifying real trends in lion population size between two sampling periods (2005/2006 and 2008) in Kruger National Park, South Africa, was complicated by variation in rainfall among sampling years and its fl ow on eff ects on the spatial confi guration of resources on lion behaviour.
Call-up sampling relies on behavioural responses to an attractant stimulus (Ogutu andDublin 1998, Ferreira andFunston 2010). Behavioural responses are fl exible (Snell-Rood 2013) and therefore subject to infl uences of several intrinsic and extrinsic factors. In our assessment, the mean number of adult males as well as adult females per station did not diff er between the two sampling periods, or among the three sampling years. However, the proportion of stations visited by adult females and visited by adult females with cubs was lower in 2008 relative to 2005 and 2006 independently and combined, and the mean number of cubs was lower between the 2005/2006 and 2008 sampling periods. Put simply, while the number of adult females visiting stations did not diff er between sampling periods, the presence of cubs with them did. Our result that year explained the likelihood of a call-up station being visited by adult females with cubs when all years were combined is consistent with this interpretation.
Th e reduction of cubs appearing at call-up stations may result from lower fecundity of females and/or higher mortality of cubs, thus resulting in fewer cubs in the population to respond to call-up stations. Alternatively, females may make behavioural choices hiding young cubs when perceiving dangers such as presence of hyenas or large male lions when taking part in feeding events.
Rainfall is a primary driver of heterogeneity at the landscape scale in savannah systems and drives surface water and prey food availability for lions (Hopcroft et al. 2005, De Boer et al. 2010, Valeix et al. 2010. We knew that rainfall diff ered between the two sampling periods and our results confi rmed it also diff ered among the three sampling years. We had predicted that because lions take advantage of their prey being limited to the confi guration of available water sources and of hyena. Th e relationships between lion responses and sumNDVI and rainfall were complex in respective models for response variables, but probability of a visit consistently declined with increasing latitude (Supplementary material Appendix 6 Fig. A1, A2, A4). Th e likelihood of a station being visited by any lions decreased with increasing distance from closest waterhole and was lower where hyenas were present (Supplementary material Appendix 6 Fig. A1, A2, A4).

Variation in numbers among stations
Our models for explaining variation in the number of lions (number in group, number of males, number of females and number of cubs) were weak (low D 2 values) and unstable under cross validation (very low cvCOR values) ( Table 2). Th is held for all sampling years combined, as well as for the 2005/2006 sampling period and for when all years were combined. Hence while our structural and functional landscape factors were plausibly able to predict probability of lion occurrence, they were unable to explain variation in numbers among call-up stations.

Consequences for population estimates
Our simulations showed that population estimates (N) increased with the relative proportion of females with cubs (Pfc) following the equation  Table 2. Summaries of best fi t generalised additive models selected according to AIC for explaining variation in lion group size, number of adult males lions, number of adult female lions and number of lion cubs. D 2 represents the proportion of deviance explained, COR is the correlation of observed versus predicted values and cvCOR represent the models performance under fi vefold cross-validation (Methods). rainfall. Indeed in this dry year, distance to closest river was the most important explanatory factor most likely because lionesses prefer to hunt in riverine areas where there is cover , Loarie et al. 2013) and refuge to hide their cubs and where prey is more likely to be concentrated (Smit et al. 2007) especially during dry years (Valeix et al. 2010). Hence, the diff erence in the infl uence of explanatory variables in relation to rainfall and rivers on the probability of station being visited by adult females with cubs may refl ect on our prediction that lions were more concentrated around water sources during the dryer 2008 years and that this altered their responses. Th e eff ect of distance from water (rivers and waterholes) between years may also have been amplifi ed by call-up stations being further from rivers in 2008 than in 2006 independently, and further from waterholes in 2008 than in 2005/2006 combined. We could not isolate this eff ect from that of the other landscape factors. Given the importance of these variables in explaining adult female and adult females with cubs visiting call up stations, and the decline in likelihood with increasing distance from waterholes, it is important to ensure that sample designs for diff erent surveys keep distances to water sources from call-up stations constant. Furthermore, given that prey is concentrated about water (rivers and water sources) during dryer years (Smit et al. 2007, Valeix et al. 2010, the higher likelihood of adult females visiting stations where prey biomass is low as noted during 2008, makes sense. A lioness using areas where prey are tethered to water sources, may not respond to a prey distress calls as readily as those located where prey biomass is low. Consistent with this notion, in 2008 prey food availability was the most important landscape factor for the probability of females attending stations in 2008, noting that models were not plausible for female visits to stations in 2005 or 2006. Hence, in the dryer sampling period of 2008, when prey food availability was lower, the probability of females attending stations appears more strongly driven by this landscape factor. Notably however, prey food availability was not selected as a landscape factor for whether females with cubs visited stations in any of the sampling years.

Response
Th e inclusion of latitude into our analyses allowed us to infer diff erences between the infl uence of spatial variation and inter-annual variability in rainfall on lion responses. In Kruger National Park increasing rainfall from the north to the south of the park (Gertenbach 1980) creates an increasing north to south gradient in surface water availability. Hence the decreasing probability of adult males visiting stations with increasing latitude seems consistent with male lions attending call-up stations in association with the spatial distribution of surface water. Indeed the similarity in the inclusion and relative importance of latitude among years and combinations of years for adult males is consistent with inter-annual variability in rainfall having limited infl uence on male lion responses to call-up stations. In contrast, the complete lack of latitude as an explanatory variable for adult females and for adult females with cubs (except for inclusion in next best fi t models), but high relative importance of rainfall in wetter years and low relative important of rainfall in dry years, is consistent with the response of adult females with cubs being more sensitive to inter-annual variability rather than spatial variability in rainfall. Th e importance prey food availability, particularly in dry years (Hopcroft et al. 2005, De Boer et al. 2010, Valeix et al. 2010, lions would be patchily distributed in association with water sources during the drier sampling period of 2008. In addition, females with cubs may be less likely to respond to call up stations given that prey may be more concentrated and readily available at such water sources, but with increased chances of encountering fear agents such as other male lions and hyenas. Hence, we predicted that the relationships between structural and functional factors and lion responses should be stronger in 2008 when we noted lower rainfall. Consistent with our predictions, landscape factors infl uenced lion responses to call up stations and more so in 2008 for the response of adult females and adult females with cubs. In fact, only the 2008 model was plausible amongst those explaining adult female visits to call-up stations. Th is suggests that the infl uence of landscape factors on the response of this demographic group could only be confi rmed when conditions were dry. Moreover, distance to rivers only explained the likelihood of a station being visited by adult females and adult females with cubs during the driest sampling year (2008). Given the complete absence of this explanatory factor in best fi t or even next best fi t models for all other years for these two demographic groups, the relationships between the distribution of surface water -in this case rivers for adult females with cubs, and closest waterholes and rivers for adult females, and lion responses only became relevant when we noted low rainfall.
Th e strong ability for models to explain adult male visits to call-up stations for all sampling years and the inclusion of surface water features either in best models or next best models in all sampling years suggests that adult male responses may not be as sensitive to diff erences in conditions among years as adult females and adult females with cubs. Indeed for adult males, the relative importance and inclusion of factors explaining call-up station visits remained generally similar among sampling years and combinations of sampling years when factors from next best fi t models were also considered. Hence, the behavioural response of adult females and of those with cubs may be more strongly infl uenced by variation in rainfall than adult males and adult females alone. Th e lack of year as an explanatory factor for adult male visits when all years were combined, together with the lack of change in number of males attending stations and proportion of stations attended by males among sampling years and between 2005/2006 and 2008 sampling periods, supports this notion.
Changes in the relative importance of explanatory factors among sampling years, changes in the shapes of relationships between landscape factors and the response of adult females with cubs was also consistent with expected fl ow-on eff ects of varying rainfall among years, particularly on the response of adult females with cubs. Certainly, in the higher rainfall years of 2006 and 2005, variation in rainfall among stations was the most important landscape factor determining the probability of adult females with cubs attending call-up stations and this relationship was complex. In contrast, in the drier year of 2008, rainfall was the least important explanatory factor and the probability of adult females with cubs visiting a call-up station linearly declined with increasing when their choice to not bring cubs along to call-up stations introduced pseudo-frequencies of females without cubs. Th e lower than predicted estimate for total population size in 2008, combined with the higher than predicted estimate for adult females in 2008 suggest that the total number of adult females may actually have increased from 2005/2006 to 2008, but that substantially fewer cubs were present during 2008 compared to 2005/2006. Hence, lion attendance to call-up stations diff ered between sampling periods, and some of these diff erences may be a result of real population changes.
Quantifying real diff erences, however, was constrained by fl ow-on eff ects of inter-annual variability in rainfall among sampling years that determined the importance of proximity to rivers and spatial variation in rainfall to whether adult females and adult females with cubs responded to call-up stations. Th e reduction in relative importance of rainfall in 2008 from 2006 and replacement by rivers and waterholes as explanatory variables strongly support this notion. Adult females eff ectively make decisions for their cubs and their reduced probability of visiting stations and bringing cubs to stations impacted on the ability to calculate comparable population estimates between surveys. As a matter for further attention, we note that the estimated number of adult females did not change between surveys, but that their visitation of stations and decisions to bring cubs with them did. Because variability in fecundity and cub survival is a feature that results from lion ' s resilient population demographic capabilities (Whitman et al. 2007), there may be a good argument to consider trends in lion abundances according to stable reproductive units -being number of adult females, as opposed to total population size.
In summary, our results suggest the need for caution when interpreting results from population estimates for lions that rely on behavioural responses that may be modifi ed by variability in structural and functional landscape factors among sampling occasions. Th is is especially the case for population estimators that are sensitive to changes in demographic components of the population most likely to be aff ected by variable conditions. Our analyses demonstrate that the fl ow-on eff ects of variation in landscape factors on lion behavioural responses to the confi guration of resources are diffi cult to unravel from real changes in population size. Th is was especially the case for adult females with cubs, an important demographic component in calculating population estimates. Hence, further to the above suggestion, we advocate the exploration of methods to evaluate trends in lion populations according to the number of adult females and the complementary use of other non-invasive sampling methods that do not rely on behavioural responses to estimate population size. Furthermore, we suggest that behavioural responses to prey distress calling, particularly the decision/ability to bring cubs by females, could be more directly tested by conducting experimental, repeated, calling targeting prides of known composition (including numbers of young), among contrasted areas and years.
Acknowledgements -Th e South African National Parks are thanked for the opportunity to conduct this research in Kruger National Park. For their eager support and of latitude as explanatory factor in the model for all years combined is not inconsistent with this suggestion. When total variation in rainfall is only considered spatially and not specifi c to a set of conditions temporally, then spatial variation in rainfall refl ected best by latitude is relevant.
Th e lack of ability of landscape factors to plausibly explain variation in lion numbers for any of our demographic groups in any year is not surprising. Like most carnivores lion distribution is non-uniform and associate with the patchy distribution and dynamics of their prey species (Valeix et al. 2011). Hence, the large prevalence of non-visited stations makes predicting variation in numbers for such species diffi cult. Nevertheless, this patchiness combined with lower visitation rates most likely amplifi ed the fl ow-on eff ects for estimating population size. Lionesses operate and make decisions as a pride (Mosser and Packer 2009). Th e lack of a visit by adult females with cubs, or failure to bring cubs to the station could mean that a whole pride of individuals of adult females and cubs may not be counted with large fl ow-on eff ects for calculating population estimates.
Th e explanatory factors and their relative importance among years for explaining hyena visits to stations were similar to those of adult male lions and thus consistent with the notion that the distribution of hyenas and lions overlap according to the distribution of surface water and other landscape factors. Indeed, we had expected that hyenas would modulate the behaviour of lions and in particular adult lionesses with cubs given that hyenas are a competitor of lions (Owen-Smith and Mills 2008). Certainly, we found that the probability of a station being visited by adult female lions with cubs and adult male lions was markedly higher when hyenas did not visit stations in the higher rainfall year of 2006. Perhaps in periods of high rainfall, when prey concentrates less around water sources, competition between lions and hyenas weakens. Alternatively, when surface water is more restricted and prey more concentrated, lions may be able to exercise more discretion over their behavioural responses to a prey distress call and choose not to attend stations where hyena are present. Either reason, hyenas infl uenced lion responses to call-up stations and this relationship diff ered among sampling years with stronger infl uence occurring during higher rainfall years.
Our inability to defi nitively conclude that population estimates for 2008 were the result of landscape factors on the behaviour of lions is a limitation of this study. Th is is because the one-off surveys that we employed, do not provide the ability to estimate detection error (Ferreira and Funston 2010), thus it is diffi cult to empirically separate non-detection and behavioural responses from real absence. We had anticipated that reduction in the number of cubs was unlikely because lion cub survival is typically higher during relatively dry years compared to relatively wet years (Eloff 1980) when lionesses may take advantage of prey clustering and concentrations associated with reduced surface water availability (Smit et al. 2007, Valeix et al. 2010. We had thus reasoned that lion cub survival was most likely higher during 2008 when rainfall was markedly lower compared to that recorded during 2005/2006 and 2005 and 2006 independently. By contrast, however, our simulation outcomes compensated for potential female behavioural responses participation, we thank all the section rangers and camp managers in Kruger who assisted us so willingly during the fi eldwork. For fi nancial assistance, we gratefully acknowledge Mr John Jackson from Conservation Force, and additional fi nancial contributions from Mr Rodney Fuhr, and the Tshwane Univ. of Technology (Dept of Nature Conservation and Faculty Research Committee). Andrei Snyman, Hennie de Beer, Grant Beverley, Margo Mathee and Vuyi Matokazi (deceased) assisted with fi eldwork. We are particularly grateful to Simon Chamaill é -Jammes for substantial comments which greatly improved the manuscript.