Density as an explanatory variable of movements and calf survival in savanna elephants across southern Africa

Authors


Correspondence author. E-mail: rjvaarde@zoology.up.ac.za

Summary

1. Southern Africa’s ‘elephant problem’ is often attributed to an overabundance of elephants (Loxodonta africana) in conservation areas. Paradoxically, the African elephant is listed as ‘vulnerable’ (IUCN Redlist) despite occupying a large geographical range and numbering about 600 000. How densities influence elephant populations is therefore important for conservation management decisions, particularly because a move towards non-equilibrium management of savannas implies a need for elephant populations to fluctuate in response to variation in intrinsic (demographic) and extrinsic (resource) factors.

2. A study on one of the world’s largest elephant populations demonstrated that population regulation is driven by a spatial response to water availability, environmental stochasticity and density. The challenge remains to identify the demographic and behavioural variables that drive density dependence.

3. We evaluated whether the movements of elephant family groups from 13 populations across a wide resource gradient were explained by variability in primary productivity, rainfall and population density. We then assessed whether density-related movements explained variability in juvenile survival, hence inferring a spatially driven behavioural mechanism that may explain density-dependent population growth. We also analysed whether management actions modified this mechanism.

4. In the dry season, daily-displacement distances (DDDs) increased non-linearly with density, and declined with increased vegetation productivity and previous wet season rainfall. In the wet season, DDDs were primarily explained by vegetation productivity.

5. The survival of weaned calves (4–7 years) decreased with increasing dry season DDDs, but this did not hold for suckling calves (1–3 years) or sub-adults (8–11 years).

6. Fences and supplementary water modified the shape and strength of relationships between DDDs and densities, vegetation productivity and rainfall and negated the relationships between DDDs and weaned calf survival.

7. We suggest that density dependence in weaned calf survival is driven by the response of dry season roaming activities of family groups to variations in density, rainfall and the distribution of food. Fences and supplementary water that alter this mechanism may contribute to the relatively high population growth rates of some populations.

Introduction

Density-dependent regulation is an accepted population phenomenon (Sibly, Hone & Clutton-Brock 2003 and references therein). Determining how extrinsic (environmental) and intrinsic (density-dependent) drivers of variation in population abundance interact through time, however, continues to challenge ecologists (Bradshaw 2008). Density feedback responses have been difficult to establish for elephants, both in theory (e.g. Woolley et al. 2008), and in practice (e.g. van Aarde, Whyte & Pimm 1999; Gough & Kerley 2006; Owen-Smith et al. 2006; van Aarde et al. 2008). However, a study on part of one of the world’s largest elephant populations demonstrated that density dependence in population growth rates, is apparently mediated by the relationship between surface water and local densities (Chamaillé-Jammes et al. 2008). The challenge now is to address ‘which demographic rates (survival, fertility) and behavioural processes (immigration, emigration) operating on which age-classes drive the strength and form of broad density regulation features’ (see Bradshaw 2008, p. 3). We combined demographic (density-related) and mechanistic (resource-related) approaches (Krebs 2003; Sibly et al. 2003) to explore these questions for elephant populations across a wide resource and rainfall gradient. This is important because a move towards non-equilibrium management (Gillson & Lindsay 2003; van Aarde & Jackson 2007) implies the need for populations to fluctuate in response to both intrinsic and extrinsic factors. Hence, identifying the mechanisms that regulate elephant populations is relevant for management. This may particularly be the case given predicted changes to climatic conditions in savanna ecosystems (Chamaillé-Jammes et al. 2008).

Elephant populations may be regulated by bottom-up processes (Sinclair 2003), but population responses to forage availability can be delayed by the buffering effects of large body size and long generation times. Consequently, high population growth rates may be maintained to the point where resources are depleted (Fowler & Smith 1973) before negative feedback mechanisms on population growth are induced (Whyte, van Aarde & Pimm 2003; Gough & Kerley 2006; van Aarde et al. 2008). In addition, the provision of supplementary water and impedence of movement by fences in some conservation areas may compound this concern (Chamaillé-Jammes, Valeix & Fritz 2007a; van Aarde et al. 2008; Loarie, van Aarde & Pimm 2009). Therefore, although density feedback must inevitably influence population growth (van Aarde et al. 1999; Chamaillé-Jammes et al. 2007a), it is uncertain at which stage this occurs in different systems (Owen-Smith et al. 2006).

Density-related regulation of elephant population growth rates includes depressed female conception (Dobson 1993; Sinclair 2003; Wittemyer, Rasmussen & Douglas-Hamilton 2007a), density-promoted immigration and emigration (van Aarde et al. 1999; Chamaillé-Jammes et al. 2008) and changes in age-specific mortality (Dudley et al. 2001; Moss 2001; van Aarde et al. 2008). Changes in adult survival have a disproportionate effect on overall population growth rates (Woolley et al. 2008). However, adult survival is highly elastic and buffered against temporal variation in limiting resources (Gaillard, Festa-Bianchet & Yoccoz 1998; Gaillard et al. 2000). In contrast, juvenile elephants are more susceptible to mortality during harsh conditions (Dudley et al. 2001; Moss 2001; Foley, Pettorelli & Foley 2008), particularly in arid savannas (see Trimble, Ferreira & van Aarde 2009). For example, all calves died during a drought in Namibia between 1991 and 1993 (Leggett 2003) and 20% of calves died during a drought in Tanzania in 1993 (Foley et al. 2008). Thus, consistent with Eberhardt’s (2002) prediction for long-lived vertebrates of a sequential response to limited resource availability, under certain conditions (see Trimble et al. 2009) juvenile survival may be more susceptible to density-related competition for resources (Gaillard et al. 1998, 2000).

The relationship between population growth rates and density may primarily be determined by the spatial response of individuals to increasing densities (see Sibly et al. 2003; Wang et al. 2006) as demonstrated by Chamaillé-Jammes et al. (2008). Although elephants display limited territorial behaviour, they are subject to intra-specific competition because of their feeding requirements and the patchy distribution of resources in savanna ecosystems (Wittemyer & Getz 2007). Hence, aggregations of individuals at key resources should generate heterogeneity in densities across landscapes and may invoke the ‘crowding’ effect, which appears to intensify the strength of density dependence (see Chamaillé-Jammes et al. 2008). Indeed, large aggregations of elephants in the proximity of waterholes and rivers, particularly during the dry season, can deplete local food resources (de Beer et al. 2006; Chamaillé-Jammes et al. 2008). Therefore, at high densities and during the dry season family groups with juveniles may travel large distances between water and forage (Loveridge et al. 2006; Chamaillé-Jammes et al. 2008; Jackson et al. 2008) because of their regular (often daily) drinking requirements (Stokke & du Toit 2002; Redfern et al. 2005) and selective feeding behaviour (see Stokke 1999). If the daily distances moved by family groups increase with density in response to resource depletion close to water, calves may dehydrate, be abandoned and even risk predation (see Loveridge et al. 2006). Weaned calves in particular may be more susceptible to abandonment and dehydration because of a weakened bond with their mother and lack of milk for hydration (Lee & Moss 1986).

We evaluated whether density explained variability in the distances moved by elephant family groups, thus inducing density dependence in juvenile survival, and hence a spatially driven mechanism for density dependence in population growth rates. We used daily-displacement distances as a measure of daily movements of elephant family groups and tested two related hypotheses. First, that DDDs increased with increasing density. Second, that calf survival decreased with increasing DDDs.

Because density dependence is likely to be more intense during harsh than during favourable conditions (Saether 1997; Chamaillé-Jammes et al. 2008) we expected that the possible effect of elephant densities on movement would differ between seasons. Food and surface water are more abundant and more evenly distributed during the wet than dry season (e.g. Wittemyer et al. 2007b) and hence, elephant movements are less limited by the availability of surface water in the wet season (see Wittemyer et al. 2007b; Young, Ferreira & van Aarde 2009a). Consequently, in the wet season the relationship between DDDs and densities may be less pronounced than in the dry season. In addition, rainfall influences the distribution and quantity of surface water and food availability (Scholes, Bond & Eckhardt 2003; Wittemyer et al. 2007b; Chamaillé-Jammes et al. 2008). Thus, we also expected that the relationship between elephant densities and DDDs might be stronger during harsh conditions (low rainfall periods) when elephant numbers at remaining waterholes increases (Chamaillé-Jammes et al. 2008).

Furthermore, the availability and distribution of food varies among conservation areas (Trimble et al. 2009; Young et al. 2009a). Where food is more abundant and/or of higher quality, family groups may not need to travel as far from water to access adequate food. We therefore expected that the relationship between density and DDDs would weaken with increasing vegetation productivity.

Finally, management actions such as fencing and provision of supplementary water may confound the effects of resource limitations on population growth rates (see van Aarde et al. 2008). First, the provision of water may release elephants from the limitation of natural surface water sources and facilitate access to otherwise inaccessible areas (Owen-Smith 1996; Owen-Smith et al. 2006; Chamaillé-Jammes et al. 2007a,b; van Aarde et al. 2008; Loarie et al. 2009). This may reduce daily roaming distances (see Harris et al. 2008). Second, fences that surround some southern African conservation areas may limit intra- and inter-seasonal movement within, among and beyond protected areas (Owen-Smith et al. 2006; Loarie et al. 2009). Therefore, we also tested whether fences and supplemented water modified the relationship between density and DDDs.

We used concurrent location specific data for elephant movements and densities, rainfall and vegetation productivity from 13 conservation areas across southern Africa and employed model selection procedures to determine support for our expectations that: (1) the relationship between DDDs and densities may be less pronounced in the wet than in the dry season; (2) the relationship between densities and DDDs may be stronger during low than during high rainfall spells; and (3) the relationship between density and DDD weakens with increasing vegetation productivity. We then tested whether lower than predicted proportions of suckling calves, weaned calves and sub-adult elephants in populations, as indices of age-specific juvenile survival, were explained by increasing DDDs. We undertook all analyses for all 13 sites grouped, and then separately for managed sites and for non-managed sites.

Materials and methods

Study area

The movements of elephant cows from 13 conservation areas (study sites) in six countries across a rainfall and vegetation productivity gradient in southern Africa were studied. For each site concurrent satellite location, density, NDVI and rainfall data was available (Fig. 1 and Table 1). The study area spanned a west to east rainfall gradient that during our study period (2001–2007) ranged from 260 to 870 mm mean annual precipitation. Our study sites included Etosha National Park (Etosha), Khaudum Game Reserve (Khaudum), Ngamiland 11 (NG11), Linyanti Wildlife Reserve (Linyanti), Kafue National Park (Kafue), Lower Zambezi National Park (Lower Zambezi), South Luangwa National Park (South Luangwa), North Luangwa National Park (North Luangwa), Kasungu National Park (Kasungu), Vwasa Marsh Game Reserve (Vwasa), Limpopo National Park (Limpopo), Maputo Elephant Reserve (Maputaland) and Tembe Elephant Park (Tembe) (Fig. 1). These sites ranged in size from 300 to 22 400 km2 and elephants ranged freely across each of the sites. In addition to rainfall, study sites differed in landscape types, vegetation structure and management. Boreholes in Etosha, Khaudum and Tembe provided supplementary drinking water. Kafue and Vwasa were situated beside large artificial lakes. Etosha, Khaudum, Kasungu, Vwasa and Tembe were fenced or partially fenced; however, fences in Kasungu and Vwasa were in poor condition at the time of our study and elephants therefore could have moved beyond the boundaries of these conservation areas.

Figure 1.

 Locations and resource gradients across study sites. (a) Locations of study sites, (b) annual rainfall of study sites, and (c) representative wet season (January 2004), and (d) representative dry season (September 2004) NDVI values.

Table 1.   Study site details
Study sites (conservation areas)CountryCentroidPopulation estimates (number of elephants)Area (km2)Density (elephants per km2)Management factorsSeason studied and number of elephants tracked (in brackets)Population estimate correction (years)
FencedSupplemented waterWetDry
  1. Management actions (fencing and provision of supplementary water) are shown along with season and number of elephant cows tracked per study site (in brackets), and temporal correspondence of population estimates with elephant locations (population estimate correction). Population estimates are from Blanc et al. (2007) (see Methods), with the exception of Ngamiland 11 from Jackson et al. (2008).

  2. Population correction is the number of years the population estimates were adjusted according to Caughley (1977).

EtoshaNamibia19°00′S, 16°00′E2057185510·11FullyYes2002/03 (5)2003 (6)−1
KhaudumNamibia19°00′S, 20°40′E3787104850·51PartiallyYes2005/06 (2)2006 (6)2
Ngamiland 1 1Botswana18°40′S, 22°40′E357967950·53NoNo2004/05 (3)2005 (3)2
LinyantiNamibia17°96′S, 23°68′E8725179430·58NoNo2006/07 (3)2007 (3)3
KafueZambia15°20′S, 25°40′E1510224000·07NoNo2003/04 (3)2004 (3)0
Lower ZambeziZambia15°30′S, 29°30′E147740840·42NoNo2005/06 (5)2005 (5)2
North LuangwaZambia11°42′S, 32°10′E323546880·64NoNo2004/05 (2)2005 (3)2
South LuangwaZambia13°00′S, 31°30′E445984480·59NoNo2005/06 (4)2006 (7)4
Vwasa MarshMalawi10°54′S, 33°33′E2709760·28PartiallyNo2005/06 (2)2005 (2)0
KasunguMalawi13°0′S, 33°11′E5824630·02PartiallyYes2005/06 (2)2005 (2)0
LimpopoMozambique31° 9′S, 23° 3′E630100000·06NoNo2003/04 (4)2004 (2)−2
MaputalandMozambique32°7′ S, 26° 6′ E2009000·21NoNo2001/02 (2)2002 (2)0
TembeSouth Africa32°5′ S, 26°9′ E1673000·45FullyYes2001/02 (3)2002 (3)−3

Elephant movements

Daily-displacement distances were calculated for 40 and 47 elephant cows during the wet and dry seasons, respectively. Data came from daily locations from a satellite collar fitted to each cow and locations whose date did not immediately follow that of the previous day were discarded so that no DDD represented more than one day’s movement. Core wet and core dry seasons were respectively defined as the periods from the beginning of December to the end of March and the beginning of June to the end of September. Because elephants were collared in different study sites during different times, the study period extended from December 2002 to September 2007 (Table 1). Each cow lived in a breeding herd and her movements were therefore assumed to represent those of her family group (e.g. Wittemyer et al. 2007b).

Rainfall

An estimate of daily rainfall from the NOAA climate prediction centre http://www.cpc.noaa.gov/products/fews/data.shtml was downloaded for the study period and was extracted for each elephant- and season-specific set of locations. With these the following rainfall measures were calculated: (i) core dry season rainfall – the mean of the sums of daily rainfall for each location from the beginning of June to the end of September; (ii) core wet season rainfall – the mean of the sums of daily rainfall for each location from the beginning of December to the end of March; and (iii) previous extended wet season rainfall – the mean of the sums of daily rainfall for each location from the beginning of December to the end of May inclusive.

Vegetation productivity

The Normalized Difference Vegetation Index (NDVI) served as a measure of vegetation productivity and therefore food availability. We downloaded NDVI data for each month of the study period from http://free.vgt.vito.be/. Data were at the resolution of 1 km2, with NDVI values calculated from 10-day composites of remotely sensed images from the VEGETATION sensor aboard SPOT4 and SPOT5 satellites. The mean monthly value for each elephant- and season-specific set of locations was calculated from our 10-day composites. From these we calculated: (i) core dry season vegetation productivity – the mean of the sums of NDVI for each location from the beginning of June to the end of September; and (ii) core wet season vegetation productivity – the mean of the sums of NDVI for each location from the beginning of December to the end of March.

Elephant densities

Density was the estimated population size divided by the size of the study site. Population estimates published in Blanc et al. (2007) were used where the aerial survey reliability was greater than 2 and where more than 20% of the conservation area had been surveyed [see Blanc et al. (2007) for data; and Junker (2008) for explanation]. For Vwasa an informed guess published in Blanc et al. (2007) was used, and for Ngamiland 11 an estimate from Jackson et al. (2008) was used. Where population estimates were not concurrent for the years for which we had elephant locations we used the closest published estimate in Blanc et al. (2007) and calculated population size from growth rates based on consecutive population estimates according to the method described in Caughley (1977) (Table 1).

Calf survival

Deviations in observed proportions of individuals in age-classes from predicted proportions in a smoothed model of age-classes served as a measure of variation in age-specific calf survival for each conservation area (see Trimble et al. 2009). In this predictive model, proportional age-class frequencies declined by a constant fraction with increasing age when age-specific mortality was constant and age distribution was stable. Following Trimble et al. (2009), observed age-classes were smoothed using data from REPA surveys [described and validated by Ferreira & van Aarde (2008) and undertaken in each study site (CERU, Unpublished Data)] into an age frequency function according to the log-polynomial regression (Caughley 1977) (but not for Kasungu as no REPA survey was available). Standardized residuals of observed versus predicted proportional frequency data were then calculated for juveniles belonging to yearly age-classes from 0 to 11 years for each conservation area. For each conservation area, the residual proportion of suckling calves (0–3 years), weaned calves (4–7 years) and sub-adults (8–11 years) were then summed. These residual sums represented deviations from predicted proportions of suckling calves, weaned calves and sub-adults for each conservation area.

Analyses

Elephant movements

For each cow and season, a mean daily-displacement distance was calculated and candidate generalized additive models (using GRASP, Lehmann, Overton & Leathwick 2002) were developed to identify the relative importance of density, rainfall and vegetation productivity for mean DDDs. Separate models were developed for cows from all 13 conservation areas, for cows from managed conservation areas (where fences and supplementary water existed, see Table 1), and for cows from non-managed conservation areas. We calculated the Akaike’s Information Criterion corrected for small sample sizes (AICc) (Burnham & Anderson 2002). We also calculated AICc differences (Δi) (AICc (Δi)) to assess support for each model where for the best model AICc (Δi) = 0; values from 0 to 2 indicate substantial support; values of 4–7 less support and values > 10 no support (Burnham & 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. Finally, we calculated the correlation coefficient (COR) and stability of each model (cvCOR) under cross-validation to predict correct values from a subset of values not included in the model building procedure. The model with the lowest AICc (Δi) and the highest AIC(wi) was selected in the first instance. Where two or more models were plausible, the one with the highest cvCOR value was selected as the most stable and most likely model.

Elephant movements and calf survival

To test our second hypothesis, site specific dry season mean DDDs were regressed against the residual proportions of suckling calves, of weaned calves and of sub-adults. We did this separately for all conservation areas grouped, managed areas grouped and non-managed areas grouped. In a further set of analyses we excluded the Lower Zambezi because a steep gradient limited elephant movements to a narrow belt parallel to the Zambezi river (see Loarie et al. 2009). Hence, the constant availability of surface water may have altered relationships between DDDs and calf survival.

For each model we calculated the AICc, AICc (Δi) and AIC(wi). In this analysis, AIC(wi) showed the strength of evidence for the regression model including an intercept and a slope, relative to the null model containing only the intercept.

Results

Daily-displacement distances

Dry season

Normalized Difference Vegetation Index and density were the most important explanatory factors for dry season mean DDDs of elephant cows grouped from all 13 sites. This model explained 49% of the variance in dry season mean DDDs, and was the most stable of all models under cross-validation (cvCOR = 0·56) (Table 2). In non-managed sites, NDVI, density and rainfall during the previous wet season explained 79% of the variation in dry season mean DDDs and the model was highly stable under cross-validation (cvCOR = 0·74; Table 2). The model that included only NDVI and density was also plausible for non-managed sites, but this model was less stable under cross-validation (cvCOR = 0·54) and was therefore not selected. In managed sites, density alone explained 51% of the variability in dry season mean DDDs and for managed sites this model was the most stable under cross-validation (cvCOR = 0·54; Table 2).

Table 2.   Selection parameters of candidate generalized additive models explaining dry season daily-displacement distances of elephant cows
Study sites groupNumber of elephantsCandidate modelKD2AICCAICc(Δi)AIC(Wi)CORcvCOR
  1. For each model the number of parameters (K), amount of variation explained (D2), corrected AIC (AICc), delta AICc(Δi), AIC weights (AIC(wi)), correlation coefficient (COR) and cross-validation correlation coefficient (cvCOR) are shown. For each group of sites, the most plausible model selected according to our selection criteria (see Methods) is shown in bold text. Models are listed in order of decreasing AIC(wi) and then decreasing cvCOR.

All sites47Density + NDVI20·49675·300·000·740·710·56
Density + wet rain + NDVI30·55678·843·530·130·750·52
NDVI10·34679·574·260·090·580·50
Density + dry rain + NDVI30·52681·636·320·030·730·27
Wet rain + NDVI20·38685·029·720·010·620·45
Global40·57685·5210·210·000·760·47
Density + wet rain20·31689·8614·560·000·580·41
Density10·20688·3613·060·000·490·38
Density + dry rain20·32689·6814·380·000·640·31
Density + wet rain + dry rain30·42690·6915·390·000·690·30
Wet rain + dry rain + NDVI30·39693·0217·710·000·630·29
Dry rain + NDVI20·36686·6511·340·000·600·18
Wet rain + dry rain20·23695·5120·210·000·520·11
Wet rain10·10693·9218·610·000·320·11
Dry rain10·11693·5318·220·000·430·08
Managed sites19Density10·51279·230·000·510·740·54
Dry rain10·47280·851·620·230·70−0·16
NDVI10·43282·243·010·110·660·32
Density + dry rain20·65282·743·510·090·82−0·18
Density + NDVI20·58286·437·200·010·760·55
Wet rain10·29286·417·180·010·550·15
Density + wet rain20·55287·608·370·010·75−0·11
Wet rain + dry rain20·54287·808·570·010·75−0·11
Density + wet rain + NDVI30·68292·3113·080·000·830·49
Wet rain + NDVI20·52288·949·710·000·720·39
Global40·73303·4224·190·000·850·13
Wet rain + dry rain + NDVI30·58297·6718·440·000·760·07
Density + wet rain + dry rain30·70290·9011·680·000·850·05
Density + dry rain + NDVI30·65294·0614·830·000·810·00
Dry rain + NDVI20·51289·099·860·000·72−0.31
Non-managed sites28Density + NDVI20·71390·920·000·440·850·54
Density + wet rain + NDVI30·79391·150·220·390·890·74
NDVI10·57393·092·170·150·770·69
Global40·81399·108·170·010·900·66
Density + dry rain + NDVI30·73398·697·770·010·860·54
Wet rain + NDVI20·59400·819·880·000·780·52
Density + wet rain + dry rain30·55412·8421·910·000·750·51
Wet rain + dry rain + NDVI30·59410·0119·090·000·780·48
Dry rain + NDVI20·57401·6210·690·000·770·47
Density + wet rain20·51405·5314·610·000·720·43
Density10·21409·8918·960·000·470·19
Wet rain10·16411·5620·640·000·420·19

In the selected models for all sites and for non-managed sites, mean DDDs initially decreased with increasing densities and then increased with increasing densities (Fig. 2). In managed sites this relationship was more complex. After an initial increase mean DDDs decreased and then increased again with increasing density (Fig. 2). Mean DDDs decreased with increasing dry season NDVI in the selected models for all sites and non-managed sites, and decreased with increasing wet season rainfall in the selected model for non-managed sites (Fig. 2).

Figure 2.

 Partial dependence of dry season daily-displacement distances on explanatory factors in selected generalized additive models for (a) all sites combined (b) non-managed sites and (c) managed sites. Partial dependence plots show the relationship of the response variable (dry season daily-displacement distances) to a given explanatory factor as averaged over the distribution of the values of the other explanatory factors. Plots are centered to have zero means, and it is the trend, rather than the actual values, that describes the patterns of the dependence of daily-displacement distances on explanatory factors. Dashed lines are standard errors of the smoothed relationship. The short bars on the inside of the x-axis represent the distribution of the data.

Wet season

Normalized Difference Vegetation Index was the most important explanatory variable for wet season mean DDDs for all sites grouped together, for managed sites and for non-managed sites (Table 3). However, the explanatory power of NDVI in all sites grouped and non-managed sites grouped was low (38 and 25% respectively), with the latter being relatively unstable under cross-validation (cvCOR = 0·30). In contrast, in managed sites NDVI explained 68% of the variation in wet season mean DDDs and was relatively stable under cross-validation (cvCOR = 0·67). In the selected models for all sites and for managed sites, wet season mean DDDs decreased with increasing wet season NDVI (Fig. 3). However, in non-managed sites this relationship was convex (Fig. 3).

Table 3.   Selection parameters of candidate generalized additive models explaining wet season daily-displacement distances of elephant cows
Study sites groupNumber of elephantsCandidate modelKD2AICcAICc(Δi)AIC(wi)CORcvCOR
  1. For each model the number of parameters (K), amount of variation explained (D2), corrected AIC (AICc), delta AICc(Δi), AIC weights (AIC(wi)), correlation coefficient (COR) and cross-validation correlation coefficient (cvCOR) are shown. For each group of sites the most plausible model or models selected according to our selection criteria is shown in bold text. Models are listed in order of decreasing AIC(wi) and then decreasing cvCOR.

All sites40NDVI10·38581·310·000·740·630·53
Density + NDVI20·54583·731·610·220·740·47
Global30·27588·584·400·020·780·59
Wet rain + NDVI20·33588·812·660·020·620·22
Density + wet rain20·33600·346·370·000·620·28
Density10·18592·509·200·000·490·18
Wet rain10·03599·483·920·00−0.220.17
Managed sites14NDVI10·68207·830·000·640·830·67
Density10·65209·309·200·300·820·64
Density + NDVI20·78214·061·610·030·880·45
Wet rain + NDVI20·77214·332·660·020·880·53
Density + wet rain20·73216·996·370·010·860·56
Global30·80227·604·400·000·890·58
Wet rain10·12222·033·920·000·36−0.17
Non-managed sites26Density10·29382·129·200·580·590·29
NDVI10·25383·390·000·310·510·30
Density + NDVI20·40386·681·610·060·640·31
Density + wet rain20·36388·516·370·020·620·26
Wet rain + NDVI20·32389·982·660·010·570·13
Wet rain10·04389·723·920·010·23−0.30
Global30·50391·844·400·000·710·22
Figure 3.

 Dependence of wet season daily-displacement distances on NDVI as the only explanatory factor in selected generalized additive models for (a) all sites combined (b) non-managed sites and (c) managed sites. Plots are centered to have zero means, and it is the trend, rather than the actual values, that describes the pattern of the dependence of wet season daily-displacement distances on NDVI. Dashed lines are standard errors of the smoothed relationship. The short bars on the inside of the x-axis represent the distribution of the data.

Dry season elephant movements and calf survival

Dry season mean DDDs did not explain variability in the survival of suckling calves or of sub-adults (Table 4 and Fig. 4). In contrast, the survival of weaned calves decreased with an increase in dry season mean DDDs for all sites grouped and for all sites grouped with Lower Zambezi removed (Table 4 and Fig. 4). This relationship did not hold for managed sites, but did so for non-managed sites when we excluded the Lower Zambezi (Table 4 and Fig. 4).

Table 4.   Parameters of least squares regression models calculated for survival of juvenile elephants (suckling calves, weaned calves and sub-adults) as functions of DDDs for site groupings as shown
Age-class site groupingRegression equationr2FAICc(Δi)AIC (Wi)
  1. For each model the regression equation, amount of variation explained (r2), F, delta AICc(Δi) and AIC weights (AIC(wi)) are shown. Models supported by AICc(Δi) values (see Methods) are shown in bold.

Suckling calves
 All sitesy = 0·00000129x − 0·01438r2 = 0·013F1,10 = 0·13754·440·00
 All sites with Lower Zambezi  removedy = 0·00000357x + 0·014016r2 = 0·093F1,9 = 0·92028·130·00
 Managed sitesy = 0·00000247x − 0·01889r2 = 0·156F1,2 = 0·37018·750·00
 Non-managed sitesy = 0·00000032x − 0·01098r2 = 0·001F1,6 = 0·00363·900·00
 Non-managed sites with Lower  Zambezi removedy = 0·00000632x + 0·024372r2 = 0·087F1,5 = 0·47420·690·00
Weaned calves
 All sitesy = −0·00000833x + 0·06342r2 = 0·302F1,10 = 4·3370·870·39
 All sites with Lower Zambezi  removedy = −0·00001186x + 0·0793r2 = 0·561F1,9 = 11·5000·000·95
 Managed sitesy = −0·00001 069x + 0·07209r2 = 0·608Fl,2 = 3·10710·240·01
 Non-managed sitesy = −0·00000636x + 0·05664r2 = 0·152F1,6 = 1·07417·500·00
 Non-managed sites with Lower  Zambezi removedy = −0·00001293x + 0·0848r2 = 0·544F1,5 = 5·9742·950·19
Sub-adults
 All sitesy = −0·000001 14x + 0·0004349r2 = 0·008F1,10 = 0·08460·330·00
 All sites with Lower Zambezi  removedy = 0·00000120x + 0·000624r2 = 0·007F1,9 = 0·06856·750·00
 Managed sitesy = 0·00000553x + 0·02053r2 = 0·214F1,2 = 0·54517·200·00
 Non-managed sitesy = 0·000001916x − 0·01200r2 = 0·022F1,6 = 0·13833·940·00
 Non-managed sites with Lower  Zambezi removedy = 0·000003320x − 0·01804r2 = 0·050F1,5 = 0·26424·780·00
Figure 4.

 Survival of suckling calves, weaned calves and sub-adults (mean residual proportion of individuals) in managed and non-managed conservation areas as functions of daily-displacement distances (m). Solid lines indicate support for least squares regression models according to AICc(Δi) (see Methods). ‘All sites’ included managed and non-managed sites.

Discussion

In large herbivores, densities in combination with the spatial and temporal heterogeneity in resources regulate populations (e.g.Owen-Smith, Mason & Ogutu 2005; Wang et al. 2006, 2009; Chamaillé-Jammes et al. 2008; Bonenfant et al. 2009). However, while several studies have identified the influence of density and resource availability on demographic rates (see Bonenfant et al. 2009 and references therein), the mechanisms underlying how, when and where density-dependent processes operate remain elusive (see Coulson et al. 2001; White 2008; Bonenfant et al. 2009). Our study was prompted by Bradshaw’s challenge to address demographic and behavioural processes that may induce density-related population regulation in elephants (see Bradshaw 2008, p. 3). Our detection of a behaviourally mediated spatial response to increasing densities, which had consequences for juvenile survival in elephants, advances the understanding of density induced mortality mechanisms that could regulate elephant populations. Similar mechanisms may operate in other large, wide ranging herbivores.

To date only a few studies have found a relationship between behavioural responses and density for elephant populations. For instance in the Kruger National Park, elephants apparently redistributed themselves in response to reduced local densities following culling (van Aarde et al. 1999). More recently, we (Young, Ferreira & van Aarde 2009b) showed that an increase in population size following the cessation of culling in Kruger induced an increased occupation of areas with relatively low vegetation productivity. These areas may be marginal and thus impinge on demographic variables that drive the regulation of population numbers. In Hwange National Park, aggregations of elephants at waterholes increased during years of low rainfall only at those waterholes where aggregations were previously low (Chamaillé-Jammes et al. 2008). Finally, in Etosha National Park, as well as Khaudum Game Reserve, home range sizes decreased with an increase in water point densities (de Beer & van Aarde 2008). Elephants therefore do respond to changes in resource availability induced by rainfall and by water provisioning, or mediated through culling that reduces local densities. However, how these behavioural responses may influence demography is unclear. In this study we therefore hypothesized that reduced juvenile survival because of density-related increases in foraging ranges provides a behavioural mechanism that can regulate population growth.

We considered the daily-displacement distances of family groups as a surrogate for foraging effort and assumed that an increase in DDDs denoted an increase in effort to obtain sufficient resources (food and water). We therefore expected DDDs would be greater during periods of resource scarcity (i.e. yearly dry seasons) than during periods of resource abundance. The increased cost associated with increased foraging effort may be especially stressful for infants and juveniles (Lee & Moss 1986; Loveridge et al. 2006). Consistent with our expectations, our model selection analyses identified density as an important explanatory factor for DDDs of elephant family groups during the dry season. We showed that dry season DDDs in elephants were concavely related to increasing density and negatively related to vegetation productivity (as indexed by NDVI). However, management actions such as the provisioning of water and the establishment of fences that limit natural movement patterns (see de Beer & van Aarde 2008; Loarie et al. 2009) modified this relationship. Our modelling exercise suggests that at such sites density was the main explanatory factor of dry season DDDs and the relationship between DDDs and density was more complex than in non-managed sites. In sites where management did not take place, dry season DDDs were best explained by density and vegetation productivity, and were also negatively related to previous wet season rainfall. Saturation at waterholes during the dry season may limit local elephant densities (see Chamaillé-Jammes et al. 2008). Hence, the concave relationship between dry season DDDs and density may be consistent with the abrupt onset of density dependence (see Getz 1996) in elephants because of the ‘crowding effect’ at waterholes and/or the depletion of food in the areas that surround waterholes (Chamaillé-Jammes et al. 2008; also see de Beer et al. 2006).

During the wet season, food and water are more abundant and uniformly distributed across the landscape than during the dry season (Wittemyer et al. 2007b; Young et al. 2009a). Hence, we expected that the relationship between elephant densities and DDDs would be weaker during the wet season when resources are less limiting than in the dry season. This was indeed the case and vegetation productivity alone explained variation in wet season DDDs.

Resource depletion should first decrease juvenile survival, then decrease reproductive rates, and finally decrease adult survival (Eberhardt 2002). Hence, high densities should reduce calf survival and therefore population growth rates. However, in areas of high rainfall, variability in rainfall explains variation in reproductive rates in elephants (Owen-Smith 1988; Wittemyer et al. 2007a; Trimble et al. 2009), at the same time in areas of low rainfall, decreased juvenile survival results from decreased rainfall (Trimble et al. 2009). The drivers of density dependence on population growth rates may therefore differ among populations and with rainfall.

Our results supported our second hypothesis that variation in dry season DDDs explained variation in calf survival among conservation areas. We expected reduced survival in weaned calves because a decreased bond between mother and calf makes them more susceptible to dehydration and abandonment than suckling calves, whilst being less independent than sub-adults (e.g. Conybeare & Haynes 1984; Lee & Moss 1986). Consistent with our expectations, no relationships existed between the survival of suckling calves or sub-adults and dry season DDDs. In contrast, the survival of weaned calves declined with increasing DDDs when all sites were grouped and in non-managed sites.

Elephant densities thus explained the daily distances travelled by elephant family groups in relation to the availability of resources during the dry season. Although Woolley et al. (2008) found that 37% of either suckling or weaned calves would need to die annually to reduce elephant population growth rates to zero in a hypothetical closed population with an unlikely conception probability of one, decreased juvenile survival nevertheless contributes to overall population growth rates and therefore population sizes.

We have identified a mechanism for how density-dependent regulation operates on at least one of the demographic factors that determine elephant population growth rates. Elephant densities influenced the dry season daily distances travelled by elephant family groups to meet food and water requirements. This had negative consequences for the survival of individuals in the age group most vulnerable to the density induced spatial response. Because fencing and supplementary water altered the relationship between density and dry season DDDs, and the relationship between dry season DDDs and calf survival, these relationships warrant further investigation in conservation areas where fences exist and/or supplementary water is provided. Indeed, our results may support the suggestion that managing the number and distribution of waterholes provides a mechanism for utilizing the influence of density dependence as a management tool (Chamaillé-Jammes et al. 2008, 2007a; but also see Smit, Grant & Whyte 2007).

For elephants, as for other large herbivores, the spatial heterogeneity in resources modifies the influence of densities on population growth rates (see Wang et al. 2009). Furthermore, juvenile survival in other large herbivores also decreases with increasing densities during harsh conditions (e.g. Coughenour & Singer 1996; Coulson et al. 2004; Owen-Smith et al. 2005; Bonenfant et al. 2009). Moreover, consistent with our results, a recent review of density-dependent responses in large herbivores found that nine out of sixteen studies reported decreased survival of post weaning juveniles with increasing densities (Bonenfant et al. 2009). Thus, in large herbivores, juveniles and in particular weaned juveniles, appear highly vulnerable to intraspecific competition for scarce and heterogeneously distributed resources with increasing densities.

Differences in life histories among large herbivores, however, are likely to generate different density-related behavioural responses to resource scarcity (see Clutton-Brock et al. 2002). Our study therefore highlights the need to identify the species-specific spatial and temporal factors which intensify competition for scarce resources and the behavioural responses to these which most likely contribute to decreased juvenile survival in response to increased densities. In addition, because management actions such as supplementation of water and fencing may negate the influence of density on elephant calf survival, such factors also need to be accounted for in similar studies on other large, wide ranging herbivores.

Acknowledgements

This study was funded through research grants to R. J. van Aarde from the Conservation Foundation Zambia, the Conservation International’s southern Africa’s Wilderness Programme, the International Fund for Animal Welfare, the Mozal Community Development Trust, the Peace Parks Foundation, the US Fish and Wildlife Services, the University of Pretoria, the Walt Disney Grant Foundation and the Wildlifewins Lottery. The Ministry of the Environment & Tourism of Namibia, the Department of Wildlife and National Parks, Botswana, the Zambian Wildlife Authority, the National Directorate for Conservation Areas, Mozambique, the Department of National Parks and Wildlife, Malawi and Ezemvelo KZN Wildlife, South Africa, sanctioned and supported our research. Sam Ferreira made valuable comments on the draft manuscript. Jake Overton assisted with all GRASP modelling and interpretation. Angel Bennett (NOAA Climate Center) provided rainfall data. James Sheppard (Landcare Research NZ) kindly converted all NDVI data to ARCGIS format.

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