# The temporal scale of energy maximization explains allometric variations in movement decisions of large herbivores

Daniel Fortin, Christopher F Brooke, Hervé Fritz, Jan A Venter

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Daniel Fortin, Christopher F Brooke, Hervé Fritz, Jan A Venter. The temporal scale of energy maximization explains allometric variations in movement decisions of large herbivores. Ecosphere, 2024, 15 (12), 10.1002/ecs2.70101. hal-05392360

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# The temporal scale of energy maximization explains allometric variations in movement decisions of large herbivores

Daniel Fortin<fnref n="1" />

<figure><img src="image_2.png" /></figure>

Christopher F. Brooke<fnref n="2" />

<figure><img src="image_3.png" /></figure>

Hervé Fritz<fnref n="3" />,<fnref n="4" />

<figure><img src="image_4.png" /></figure>

Jan A. Venter<fnref n="2" />

<figure><img src="image_5.png" /></figure>

**Correspondence**

Daniel Fortin

Email: daniel.fortin@bio.ulaval.ca

**Funding information**

Nelson Mandela University; Natural
Sciences and Engineering Research
Council of Canada; University of
KwaZulu-Natal; Fairfield Tours; Eastern
Cape Parks and Tourism Agency; Walter
Sisulu University

**Handling Editor:** Sunshine A. Van Bael

**Abstract**

Empirical testing of energy maximization models has been used to clarify the drivers of resource partitioning among large herbivores. Most studies, however, have not considered that predictions of optimal diet depend on the temporal scale of maximization. This omission can hinder the effectiveness of optimality principles in elucidating animal distributions, dietary choices, and the dynamics of species coexistence. We used movement analysis and scale-dependent energy gain modeling to study how three large herbivores share resources: red hartebeest (Alcelaphus buselaphus), a 120-kg grazing ruminant; zebra (Equus quagga), a 300-kg grazing nonruminant; and eland (Tragelaphus oryx), a 460-kg ruminant, mixed feeder. We found that resource partitioning was achieved through a synergy of spatial segregation and interspecies differences in habitat selection and in the temporal scale of energy maximization. Radio-collared individuals of the three species spent 95% of their time >850 m from one another. Hierarchical movement analysis revealed that red hartebeest and zebra selected grasslands within which they selected patches maximizing their daily energy gains. Selection was particularly strong for red hartebeest, as expected for a ruminant of relatively small size. Unlike the other species, eland avoided grasslands; when they ventured into grasslands, they selected patches offering high short-term energy gains at the expense of daily gains. This selection for rapid energy gain could reflect relatively high missed opportunity costs when foraging in grasslands due to the broad range of feeding opportunities for this large mixed feeder. This finding is also consistent with the notion that larger herbivores tend to face stronger constraints from resources availability than digestibility. Overall, differences in selection strength and foraging currencies among these large herbivores are consistent with allometric theory. Our study illuminates the drivers of resource partitioning that can promote the coexistence of large herbivore species, while also showing that, to provide a useful and robust basis to explain animal

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2024 The Author(s). *Ecosphere* published by Wiley Periodicals LLC on behalf of The Ecological Society of America.

<footnote n="1">¹Centre d'Étude de la Forêt and
Département de Biologie, Université
Laval, Quebec, Canada</footnote>

<footnote n="2">²Department of Conservation
Management, Faculty of Science, Nelson
Mandela University, George, South Africa</footnote>

<footnote n="3">³REHABS International Research
Laboratory, CNRS-Université de
Lyon1-Nelson Mandela University,
Nelson Mandela University, George,
South Africa</footnote>

<footnote n="4">⁴Sustainability Research Unit, Nelson
Mandela University, George, South Africa</footnote>
movement and resource partitioning, energetic models should be based on a relevant scale of energy maximization.

### KEYWORDS

animal movement, forage maturation hypothesis, herbivore coexistence, resource partitioning, step selection functions, temporal scale of energy maximization

## INTRODUCTION

Understanding the mechanisms allowing species to coexist has been and remains one of the most fundamental challenges of ecological sciences (Dickie & Serrouya, 2022; Scheffer & van Nes, 2006). It is now well established that stable species coexistence requires differences in niches that are sufficient to prevent competitive exclusion (Pansu et al., 2022). Evolutionary forces thus tend to promote physiological, morphological, and behavior differentiation among potential competitors (e.g., Grant & Grant, 2008). Ruminants, for example, have evolved a better capacity to digest lignocellulose than nonruminants (Terry et al., 2019). Differences in nutritional niche are such that mammalian herbivores can be classified along a continuum of diet preferences from browsers to mixed (or intermediate) feeders to grazers (Fritz & Loison, 2006; Spitzer et al., 2020). In western ecosystems of North America, white-tailed deer (*Odocoileus virginianus*) browse woody vegetation, plains bison (*Bison bison bison*) largely focus on graminoids, and elk (*Cervus canadensis*) are mixed feeders (Walter et al., 2010) that consume both food types (Fortin et al., 2003).

Diets have been described in detail for several species of multiple animal communities. Although, substantially less research has focused on the determinants of dietary choices (Spitzer et al., 2023), valuable progress has been made notably through empirical testing of foraging theory (Fortin et al., 2002; Owen-Smith & Novellie, 1982). For example, the forage maturation hypothesis (FMH) has been used repetitively to successfully explain resource selection and movements of large herbivores (Esmaeili et al., 2021; Fryxell et al., 2004; Wilmshurst et al., 1995). FMH theory uses trade-offs between digestibility and availability constraints to enlighten behavioral observations such as herbivores neglecting the richest vegetation patches in favor of patches of intermediate biomass. As plants mature, their structural fiber increases, and they become less digestible and require longer digestion time (Van Soest, 1982). By contrast, the short-term rate of vegetation intake increases as plants mature, largely because herbivores can crop larger bites. The net outcome is that maximum energy gains are

achieved when herbivores forage in patches of intermediate biomass (Fryxell, 1991).

Allometric changes in the nutritional niche of mammalian herbivores can be expected from FMH, because digestibility and availability constraints scale with animal size. Short-term rate and daily rate of vegetation intake, for example, increase with body mass (Shipley et al., 1994; Wilmshurst et al., 2000), whereas digestion rate is slower and the extraction of nutriment is greater for larger herbivores (Illius & Gordon, 1992; Murray, 1991). Because of these allometric relations and the higher metabolic requirements of larger herbivores, smaller species should be able to subsist on shorter swards. In fact, theory predicts that small grazers are more likely to be regulated by digestive constraints and large grazers by availability constraints (Hopcraft et al., 2012). While these general principles remain consistent between digestive systems, nonruminants should be able to subsist on lower-quality forage than a same-size ruminant because of their faster digestion rate (Demment & Van Soest, 1985; Esmaeili et al., 2021).

The allometry of FMH has been demonstrated in the
ory (Wilmshurst et al., 2000) and has received substantial
field support (Esmaeili et al., 2021). However, the accuracy
of FMH in predicting foraging decisions should depend on
the strength of its relation to fitness and could therefore
vary among species and habitat conditions. Food selection
is intricately linked to the foraging objective, and a funda-
mental challenge in foraging theory is to identify a cur-
rency that strongly drive the foraging strategy (Houston &
McNamara, 2014). Various foraging currencies have
been proposed, such as short-term or daily energy
gains (Fortin et al., 2002; Fryxell et al., 2004; van
Wieren, 1996), intake rate of essential nutriments
(e.g., protein, sodium, phosphorus, water; Babin
et al., 2011; Fryxell & Lundberg, 1997; McNaughton, 1988),
and trade-off between resource intake and predation
risk (Courbin et al., 2019; Latombe et al., 2014;
McNaughton, 1990; Sih, 2005). Surprisingly, relatively few
studies have provided quantitative predictions from alterna-
tive currencies, before assessing the most effective at
predicting animal movement and distribution. Fryxell et al.
(2004) conducted such a test, initially formulating
predictions across various temporal scales of energy
maximization, and subsequently showing that the movements of Thompson's gazelles (*Gazella thomsoni thomsoni*) were best predicted based on daily energy gains. By contrast, plains bison were found to select plants maximizing their short-term energy gains at the expense of daily gains (Fortin et al., 2002). This currency was then successfully used to predict the spatial distribution of plains bison reintroduced into a landscape comprised of strongly different plant communities (Babin et al., 2011). Despite the value of identifying the most relevant currency (e.g., Houston & McNamara, 2014; Lucas, 1990), few studies have tested more than a single temporal scale of energy maximization predicted by the FMH.

We studied resource partitioning among red hartebeest (*Alcelaphus buselaphus caama*), zebra (*Equus quagga*), and eland (*Tragelaphus oryx*), as a mechanism of coexistence in a predator-free reserve consisting of forests, wetlands, rocky outcrops, and a mosaic of grass patches of different stages of maturation after fire (Brooke et al., 2020). Previous studies have demonstrated that movement analysis can provide insights into how large herbivores adjust their distribution in response to energy-rich plant patches (Brooke et al., 2020; Esmaeili et al., 2021; Merkle et al., 2014). Accordingly, we assessed how each of the three species adjusted their movements to the different landcover types, and when in grasslands, if they selectively adjusted their movements to grass patches providing relatively high short-term rate ($I_{IDE}$) or daily rate ($I_{DDE}$) of digestible energy intake as predicted by the FMH. The three species exhibit strong differences in body mass and feeding strategy, with red hartebeest being a relatively small (120 kg) grazing ruminant, zebra a grazing nonruminant (hind-gut fermenters) of medium size (300 kg), and eland a large (460 kg) ruminant and mixed feeder (Venter, Prins, et al., 2014). Given the absence of natural predators, our study is set to clarify the foraging behavior and nutritional niche partitioning of herbivores primarily concerned with resource intake.

# METHODS

## Study area and animal tracking

Mkambati Nature Reserve (hereafter Mkambati, 31.26° S and 29.99° E) is a small (9200 ha) fenced nature reserve situated on the southeast coast of South Africa, bordered by natural boundaries (river gorges to the north and south and the Indian Ocean to the east) on three sides, with the only manmade boundary being a fence inland to the west (Venter, Prins, et al., 2014). High annual rainfall (1200 mm) and mild temperatures (average of 18°C in winter and 22°C in summer) give rise to a mild subtropical

climate with relatively high humidity. The vegetation is dominated by Pondoland-Ugu Sandstone Coastal Sourveld interspersed with patches of indigenous forest (scarp and southern coastal forest). Frequent fires result in a dynamic mosaic of recently burnt nutrient-rich and older more moribund grasses (Brooke et al., 2018).

Large herbivores in the reserve had no natural predators but could encounter poachers (Brooke et al., 2020). We used GPS collars (African Wildlife Tracking) to track three large herbivore species: plains zebra, red hartebeest, and eland. Collars were fitted at varying times throughout the study period (2008–2012), and GPS positions were recorded at fixed time intervals of 30 min for varying periods of time (Appendix S1: Table S1). This research was approved by and carried out in accordance with the recommendations in the approved standards protocols of the animal ethics subcommittee of the University of KwaZulu-Natal (approval number 012/09/Animal).

## Foraging currency

### Instantaneous intake of digestible energy, $I_{IDE}$

$I_{IDE}$ was estimated from the relationships that instantaneous rate of forage intake ($I$, in grams per minute) and forage digestibility ($D$) have with plant biomass ($B$, in grams per square meter). The species-specific functional responses providing $I$ came from the allometric relationships described in Brooke et al. (2020) for red hartebeest and eland, whereas it came from Okello et al. (2002) for zebra. The negative relationship between $D$ and $B$ was determined from field measurements across the study area (see Brooke et al., 2020 for details). Digestible energy of grass ($Q$, in kilojoules per gram) was estimated as $Q = M_E \times 17.1 \text{ kJ/g}$ (note that Wilmshurst et al., 2000 mistakenly reported the units as MJ/g), where the metabolizable energy ($M_E$) was considered 82% of $D$ (Wilmshurst et al., 2000). Based on this information, we calculated $I_{IDE}$ (in kilojoule per minute) as:

$$I_{IDE} = I \times Q. \qquad (1)$$

### Daily intake of digestible energy, $I_{DDE}$

We estimated $I_{DDE}$ by considering additional time or digestive constraints (cf. Fryxell, 1991). When daily forage intake is limited by time constraints, daily energy intake corresponds to $I_1 = I_{IDE} \times T_{max}$, where $T_{max}$ is the maximum time that can be spent actively foraging in a day ($T_{max}$ was set to 13 h/day following Wilmshurst et al., 2000). When daily forage intake is limited by
digestive process, daily energy intake can be estimated by $I_2 = V \times Q$, where V is the daily voluntary intake (in grams per day) of vegetation given ad libitum forage availability, which is a proxy commonly used to represent digestive constraints (Bergman et al., 2001; Wilmhurst et al., 2000). V is known to decrease with D, and we use the species-specific relationships provided in Brooke et al. (2020). Once $I_1$ and $I_2$ had been estimated, $I_{DDE}$ (MJ/day) was found as:

$$I_{DDE} = \min(I_1, I_2)/1000. \quad (2)$$

$I_{IDE}$ and $I_{DDE}$ were estimated for vegetation available specifically in grasslands.

## Statistical analysis of herbivore movement

We used step selection function (SSF; Fortin et al., 2005) to determine how foragers adjust their movements in response to habitat features, including grasslands where $I_{IDE}$ and $I_{DDE}$ were estimated. SSFs are recognized as a versatile and powerful framework for studying animal movement (Hofmann et al., 2024), and they have been used recently to test the FMH in several species of large herbivores (Esmaeili et al., 2021). SSFs contrast characteristics of observed (i.e., recorded by GPS collars) and random steps, with a step being the straight line linking two successive locations. We paired each observed step with 10 random steps sharing the same starting location but differing in length and turning angle. The endpoint locations of random steps were drawn within a species-specific distance that included 99th percentile of all step lengths observed for a species (5.4 km for red hartebeest, 6.2 km for zebra, and 7.4 km for eland), and a direction drawn uniformly over 360° (see Nicosia et al., 2017 for details). We estimated turning angles (θ) between successive steps following Fortin et al. (2005).

The endpoint locations of observed and random steps were intersected with a GIS of landcover types: forests, wetlands, rocky outcrops, and grasslands, with each type coded as a dichotomic variable and forest being used as the reference category. For every location in grasslands, we estimated plant biomass based on the number of days since it last burned (Brooke et al., 2020) and used this information to calculate species-specific $I_{IDE}$ and $I_{DDE}$ (Equations 1 and 2) expected at that grassland location. $I_{IDE}$ and $I_{DDE}$ were normalized ([x - mean]/SD) for each species to enable the comparison of SSF coefficients on a unique scale. We built a set of candidate SSFs for each season (wet season: November-April; dry season: May-October), where characteristics of observed (coded as 1) and random (coded as 0) steps were contrasted with

conditional logistic regression. The candidate SSFs were hierarchical as they tested the selection of landcover types, and when individuals were in grasslands, if they selected plant patches offering relatively high $I_{DDE}$ or $I_{IDE}$:

$$w(x) = \exp\left(\beta_{LL} \log[L_L] + \beta_L L_L + \beta_{\Phi} \cos[\theta] \right. \\ \left. + \beta_1 \text{Wetlands} + \beta_2 \text{Rocky\_outcrops} \right. \\ \left. + \beta_3 \text{Grasslands} + \beta_4 \text{Grasslands} \times \text{Currency}\right), \quad (3)$$

where Currency is either $I_{IDE}$ or $I_{DDE}$ for each species. The candidate SSFs thus assessed the interplay between animal movement and habitat covariates—including potential digestible energy intake—while accounting for fundamental movement parameters such as step length and turning angles (Courant & Fortin, 2012; Latombe et al., 2014).

The short relocation interval (30 min; Appendix S1: Table S1) created temporal autocorrelation in SSF deviance residuals. We thus estimated robust (unbiased) SEs of SSF parameters using generalized estimating equations (Craiu et al., 2008). The approach requires the creation of clusters, that is, a sequence of successive steps that can be autocorrelated within a given cluster but must be independent of the steps in other clusters. Following an analysis of autocorrelations and partial autocorrelations of SSF deviance residuals, we removed sets of 50 (eland) or 100 successive locations (hartebeest, zebra) for each individual to end up with ≥26 statistically independent clusters for each species (as recommended by Prima et al., 2017). Also, because of the autocorrelation, we assessed the relative empirical support of competing SSFs using the quasi information criterion (QIC) calculated with the same clusters (Craiu et al., 2008).

We assessed the multicollinearity of the top-ranking SSFs and found that the VIF of any covariable was <7.2, that is, below 10, as recommended by Belsley et al. (1980). SSFs should thus allow robust inferences about the foraging currency.

## RESULTS

The patch biomass providing the highest rate of digestible energy intake varied strongly with the temporal scale of maximization (Figure 1). Optimality models predicted that all three herbivores would have to feed in patches with >4.6 times more biomass to maximize $I_{IDE}$ than $I_{DDE}$. The optimal biomass maximizing a given currency
<figure><img src="image_6.png" /><figcaption>**FIGURE 1** Optimal grass biomass for the maximization of (a) short-term ($I_{IDE}$) and (b) daily rate ($I_{DDE}$) of digestible energy intake for three large African herbivore species on Mkambati Nature Reserve, South Africa.</figcaption></figure>

was also different among species, but to a lesser extent than between temporal scales (Figure 1).

The comparison of candidate SSFs (Appendix S1: Table S2) underscored differences among species in the foraging currency and land cover types that most strongly influenced their movements, as well as in basic movement characteristics (Table 1). Red hartebeest tended to make frequent reversals along their movement paths ($\beta_{Cos[\theta]}$ < 0), whereas eland had strong directional persistence ($\beta_{Cos[\theta]}$ > 0). Not surprisingly, this led to differences in daily movements, which averaged 3.4 ± 0.3 km (mean ± SE) for red hartebeest, 6.1 ± 0.2 km for zebra,

and 7.4 ± 0.6 km for eland. Relative to forests, red hartebeest and zebra selected wetlands, rocky outcrops, and grasslands in both seasons (Table 1). By contrast, eland did not select wetlands in the wet season, and never selected rocky outcrops. Eland avoided grasslands relative to forests, but when in grasslands, they displayed a stronger selection for optimal patches than the other large herbivores (Figure 2). This difference was particularly pronounced in the wet season (i.e., higher standardized coefficient; Table 1). Importantly, eland selected patches maximizing a different foraging currency than the other species (Appendix S1: Table S2). Indeed, they made
<table><caption>TABLE 1 Summary of the top-ranking step selection function (SSF) for radio-collared red hartebeest, zebra, and eland on Mkambati Nature Reserve, South Africa, during the wet and dry seasons.</caption><thead><tr><th rowspan="2">Variable</th><th colspan="2">Red hartebeest</th><th colspan="2">Zebra</th><th colspan="2">Eland</th></tr><tr><th>β ± SE</th><th>p</th><th>β ± SE</th><th>p</th><th>β ± SE</th><th>p</th></tr></thead><tbody><tr><td colspan="7"><strong>Dry season</strong></td></tr><tr><td>log(Dist)<sup>a</sup></td><td>-3.55 ± 0.47</td><td>&lt;0.001</td><td>-4.15 ± 0.13</td><td>&lt;0.001</td><td>-1.80 ± 0.43</td><td>&lt;0.001</td></tr><tr><td>Dist<sup>a</sup></td><td>0.78 ± 0.15</td><td>&lt;0.001</td><td>-0.13 ± 0.09</td><td>0.16</td><td>0.52 ± 0.25</td><td>0.04</td></tr><tr><td>Cos(θ)<sup>a</sup></td><td>-0.63 ± 0.25</td><td>0.01</td><td>1.10 ± 0.05</td><td>&lt;0.001</td><td>30.22 ± 7.34</td><td>&lt;0.001</td></tr><tr><td>Wetlands<sup>b</sup></td><td>2.06 ± 0.17</td><td>&lt;0.001</td><td>1.02 ± 0.09</td><td>&lt;0.001</td><td>0.78 ± 0.24</td><td>&lt;0.001</td></tr><tr><td>Rock<sup>b</sup></td><td>1.44 ± 0.27</td><td>&lt;0.001</td><td>0.91 ± 0.12</td><td>&lt;0.001</td><td>-0.06 ± 0.23</td><td>0.81</td></tr><tr><td>Grasslands<sup>b</sup></td><td>2.02 ± 0.16</td><td>&lt;0.001</td><td>0.93 ± 0.09</td><td>&lt;0.001</td><td>-4.30 ± 1.33</td><td>0.001</td></tr><tr><td>I<sub>IDE_Eland</sub><sup>c</sup></td><td>0.39 ± 0.06</td><td>&lt;0.001</td><td>0.22 ± 0.03</td><td>&lt;0.001</td><td>0.62 ± 0.15</td><td>&lt;0.001</td></tr><tr><td colspan="7"><strong>Wet season</strong></td></tr><tr><td>ln(Dist)<sup>a</sup></td><td>-4.02 ± 0.32</td><td>&lt;0.001</td><td>-4.24 ± 0.12</td><td>&lt;0.001</td><td>-1.29 ± 0.55</td><td>0.02</td></tr><tr><td>Dist<sup>a</sup></td><td>0.78 ± 0.22</td><td>&lt;0.001</td><td>-0.24 ± 0.16</td><td>0.14</td><td>0.57 ± 0.25</td><td>0.02</td></tr><tr><td>Cos(θ)<sup>a</sup></td><td>-0.82 ± 0.26</td><td>0.002</td><td>1.22 ± 0.03</td><td>&lt;0.001</td><td>53.38 ± 16.77</td><td>0.002</td></tr><tr><td>Wetlands<sup>b</sup></td><td>1.90 ± 0.39</td><td>&lt;0.001</td><td>0.75 ± 0.21</td><td>&lt;0.001</td><td>0.24 ± 0.20</td><td>0.25</td></tr><tr><td>Rock<sup>b</sup></td><td>1.64 ± 0.52</td><td>0.002</td><td>0.88 ± 0.18</td><td>&lt;0.001</td><td>-0.65 ± 0.19</td><td>&lt;0.001</td></tr><tr><td>Grasslands<sup>b</sup></td><td>1.98 ± 0.49</td><td>&lt;0.001</td><td>0.80 ± 0.20</td><td>&lt;0.001</td><td>-10.0 ± 2.01</td><td>&lt;0.001</td></tr><tr><td>I<sub>IDE_Eland</sub><sup>c</sup></td><td>0.28 ± 0.14</td><td>0.04</td><td>0.20 ± 0.04</td><td>&lt;0.001</td><td>1.39 ± 0.25</td><td>&lt;0.001</td></tr></tbody></table>

Note: Although the best SSFs for red hartebeest included I<sub>DDE_zebra</sub>, the model with I<sub>DDE_hartebeest</sub> is also provided for comparison.

<sup>a</sup>Dist: step length; Cos(θ): cosine of turning angle.

<sup>b</sup>Wetland, Rocky outcrop (Rock), and Grassland were dichotomic variables, and Forest was the reference category.

<sup>c</sup>Expected daily intake (I<sub>DDE</sub>, normalized values) or short-term rate of digestible energy (I<sub>IDE</sub>, normalized values) for each species.

non-random movements that were more consistent with maximizing I<sub>IDE</sub> than I<sub>DDE</sub> (i.e., lower QIC for I<sub>IDE</sub> than I<sub>DDE</sub>), while zebra and red hartebeest favored patches yielding relatively high I<sub>DDE</sub> (Figure 2).

Despite strong home-range overlap among species, individuals of different species rarely co-occurred in space. On average, GPS-collared animals monitored simultaneously spent 95% of their time >850 m apart for individuals of other species (Table 2). Evidence of spatial segregation can also be observed in their locations within the reserve (Figure 3).

DISCUSSION

We show that resource partitioning among red hartebeest, zebra, and eland resulted from a combination of spatial distancing, differences in the strength of selection of grasslands and optimal sward patches, and discrepancies in the temporal scale energy maximization. Species-specific movement rules involved a rather complex array of internal (e.g., directional persistence) and external drivers that ultimately led to non-random encounters with vegetation patches providing a high rate

of energy gains, consistently with expectations of FMH. The smallest herbivores—red hartebeest—selected most strongly patches providing high daily energy gains, whereas the largest herbivore—eland—was the only one selecting patches yielding high short-term energy gains. Our study shed light on the dietary choices of large herbivores, which is considered one of the least understood drivers of herbivore population dynamics (Staver & Hempson, 2020).

While most studies on FMH make qualitative predictions (Esmaeili et al., 2021) or considered a single temporal scale (e.g., Brooke et al., 2020; van Wieren, 1996; Wilmshurst et al., 1995, 2000), we demonstrate that behavioral expectations strongly depend on temporal scale, with at least a fourfold difference between the optimal biomass maximizing short-term rates versus daily rates of energy gains for any species. A key implication is that energy maximizers can thus be expected to use different vegetation patches and to occur in different parts of the landscape if they are driven by different scales of energy maximization. Optimal foraging models based on an incorrect scale of energy maximization can thus poorly predict the spatial dynamics of landscape use by large herbivores (Fryxell et al., 2004; Sigaud et al., 2017),
<figure><img src="image_7.png" /><figcaption>**FIGURE 2** Mean selection ratios (+SE) of post-fire sward biomass (% use/% available) for each season, based on the observed and random locations of radio-collared red hartebeest, zebra, and eland on Mkambati Nature Reserve, South Africa. The horizontal line shows a selection ratio of 1, indicating that patches are used in proportion to availability.</figcaption></figure>

making these models also less useful to inform, for example, on human–wildlife conflicts and population demography (e.g., Sigaud et al., 2017). Our study supports

<table><caption>**TABLE 2** Average ± SE (n: number of individuals) of the fifth percentile distance (in meters) between radio-collared individuals of red hartebeest, zebra, or eland and the nearest radio-collared individual of another species that was radio-tracked simultaneously on Mkambati Nature Reserve, South Africa.</caption><thead><tr><th rowspan="2">Focal species</th><th colspan="2">Distance to hartebeest</th><th colspan="2">Distance to zebra</th><th colspan="2">Distance to eland</th></tr><tr><th>Mean ± SE</th><th>n</th><th>Mean ± SE</th><th>n</th><th>Mean ± SE</th><th>n</th></tr></thead><tbody><tr><td colspan="7"><strong>Dry season</strong></td></tr><tr><td>Red hartebeest</td><td>...</td><td></td><td>992.52 ± 311.28</td><td>4</td><td>1240.65 ± 90.85</td><td>4</td></tr><tr><td>Zebra</td><td>965.52 ± 14.75</td><td>4</td><td>...</td><td></td><td>1039.09 ± 22.96</td><td>4</td></tr><tr><td>Eland</td><td>951.53 ± 25.43</td><td>3</td><td>852.81 ± 147.35</td><td>3</td><td>...</td><td></td></tr><tr><td colspan="7"><strong>Wet season</strong></td></tr><tr><td>Red hartebeest</td><td>...</td><td></td><td>997.50 ± 466.83</td><td>2</td><td>933.11 ± 54.80</td><td>4</td></tr><tr><td>Zebra</td><td>948.66 ± 212.20</td><td>5</td><td>...</td><td></td><td>1042.68 ± 281.16</td><td>4</td></tr><tr><td>Eland</td><td>853.83 ± 69.21</td><td>3</td><td>862.30 ± 65.82</td><td>3</td><td>...</td><td></td></tr></tbody></table>

Fryxell et al.'s (2004) assertion that energetic models can provide a robust foundation for developing predictive models of animal distribution—provided the appropriate temporal scales of maximization is considered. A corollary here is that energy maximization models, when grounded in the correct temporal scale, offer a more insightful framework for understanding the mechanisms of co-occurrence and coexistence of large herbivores in grazing systems.

Patch selection by both zebra (a nonruminant of 300 kg) and red hartebeest (a ruminant of 120 kg) was more closely linked to the maximization of $I_{DDE}$ than $I_{IDE}$. Although basic allometric theory predicts that the diet of a nonruminant would be more similar to that of larger ruminants (Kleynhans et al., 2011, and references therein), our predictions of optimal sward biomass were rather similar for zebra and hartebeest, just as their actual choices of vegetation patches. Nonetheless, the two herbivores faced different foraging constraints. The faster passage of ingesta and lower digestive efficiency of smaller ruminants incite them to select relatively young plants (Demment & Van Soest, 1985; Gordon & Illius, 1996; Hopcraft et al., 2012). As a hindgut fermenter, zebra does not depend on young vegetation patches (Mandlate & Rodrigues, 2020) and thus has greater latitude than hartebeest to adjust its selection of high-quality vegetation according to its physiological
<figure><img src="image_8.png" /><figcaption>**FIGURE 3** Land cover types and kernel density estimates of 50% and 95% for red hartebeest, zebra, and eland on Mkambati Nature Reserve, Eastern Cape, South Africa.</figcaption></figure>

state (Sundaresan et al., 2008) and the prevailing grazing conditions (Arsenault & Owen-Smith, 2008; Potgieter & Kerley, 2022; Venter, Nabe-Nielsen, et al., 2014). Thus, although previous studies have reported an intensive use of young vegetation patches by zebra (Arsenault & Owen-Smith, 2011; Clauss et al., 2013; Ménard et al., 2002), as we observed, their foraging decisions can differ among grazing systems. Our study took place in a system where large herbivores faced fewer constraints on their foraging decisions than in many other environments. In the reserve, there were no natural predators, and water was not a limiting resource (Venter, Nabe-Nielsen, et al., 2014). In contrast, in other systems, predation risk can reduce the focus on selecting food that maximizes energy intake. Likewise, equids often face strong constraints from the need to remain near water bodies to maintain their hydric balance (e.g., Esmaeili et al., 2021; Owen-Smith, 2008). The lack of these constraints at Mkambati appears to increase the overlap in foraging niches between zebra and hartebeest. However, the plasticity in foraging decisions and foraging strategies may prove fitness rewarding in environments where the intensity of foraging constraints varies across space and time.

Despite sharing similar patch selection and having overlapping home ranges, hartebeest and zebra spent 95% of their time ~1 km apart. Spatial distancing extended to resource partitioning with eland, where the latter typically remained >0.8 km from the other two species. Importantly, eland was the only species making movement decisions that were most consistent with the maximization of their *I*IDE. Eland avoided grasslands relative to forests, but when they were in grasslands, they were more selective than hartebeest and zebra. While eland in other systems have been reported to consume relatively high qualities of grass (Fabricius & Mentis, 1990), the herbivore can adjust its diet according to browse and grass availability and quality (Fabricius & Mentis, 1990; Nge'the & Box, 1976). The strong selection of eland for short-term energy gains when in grasslands is perhaps related to the missed opportunity costs (Stephens & Krebs, 1986) that come with the broad range of feeding opportunities in various landcover types that can benefit such a large mixed feeder. Their flexible diet should allow eland to maintain relatively low interspecific competition when resources become scarce, an advantage that could help them to outcompete other large herbivores (Venter, Prins, et al., 2014).

We can combine our observations with the limited existing research on the temporal scale of energy maximization to gain insights into potential allometric relations of foraging currencies. Thompson's gazelle (Fryxell et al., 2004) and elk (although Wilmshurst et al. [1995]
tested a single currency, the steep decline observed in the selection of patches exceeding the biomass maximizing *I*<sub>DDE</sub> makes the maximization of *I*<sub>IDE</sub> highly unlikely), together with hartebeest and zebra (current study), are all herbivores <300 kg reported to maximize their daily energy gains. By contrast, bison (Babin et al., 2011; Fortin et al., 2002) and eland (current study) are herbivores >385 kg found to maximize their short-term energy gains. *I*<sub>IDE</sub> enables herbivores to ingest the most digestible energy in the least amount of time but provides less energy at the end of the day compared to the maximization of *I*<sub>DDE</sub>. Our observations thus support the notion that larger herbivores tend to consume food of lower quality (but see Arsenault & Owen-Smith, 2008) because they require more food and low-quality vegetation tend to be available at higher biomass (Clauss et al., 2013).

Our study thus should reveal fundamental responses of these herbivores to food distribution and abundance. We show that, under these conditions, energy maximization principles can explain the movements of herbivores of different sizes and digestive and foraging strategies, but prediction accuracy can strongly depend on the temporal scale of maximization. Although the most relevant currency may vary in systems where consumers face a wider range of constraints (Houston & McNamara, 2014; Newman et al., 1995), previous research has demonstrated that the scale of maximization can remain consistent even in the face of radical changes in foraging options (Babin et al., 2011; Sigaud et al., 2017). Our research offers compelling evidence that energetic models, when appropriately scaled for maximization, can shed light on the intricate dynamics of sympatric species of large herbivores.

## AUTHOR CONTRIBUTIONS

Jan A. Venter was in charge of the research program. Jan A. Venter, Hervé Fritz, and Daniel Fortin secured research funding. Jan A. Venter and Christopher F. Brooke collected the data. Christopher F. Brooke extracted the GIS information and created the database. Daniel Fortin conceived the ideas for the article, created the optimality models, analyzed the data, and wrote the paper. All authors discussed the results, edited the manuscript text, and gave final approval for publication.

## ACKNOWLEDGMENTS

We thank the Nelson Mandela University, Walter Sisulu University, University of KwaZulu-Natal, and Fairfield Tours for funding this study. We also thank the Eastern Cape Parks and Tourism Agency for their funding as well as support of this project and their assistance in the field. The project was also supported by the Natural Sciences and Engineering Research Council of Canada.

## CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

## DATA AVAILABILITY STATEMENT

Data (Venter, 2024) are available from Mendeley Data: https://doi.org/10.17632/xrnkfwrc8.1.

## ORCID

Daniel Fortin https://orcid.org/0000-0003-1267-1891

Jan A. Venter https://orcid.org/0000-0002-4548-2571

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## SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.

> **How to cite this article:** Fortin, Daniel, Christopher F. Brooke, Hervé Fritz, and Jan A. Venter. 2024. "The Temporal Scale of Energy Maximization Explains Allometric Variations in Movement Decisions of Large Herbivores." *Ecosphere* 15(12): e70101. https://doi.org/10.1002/ecs2.70101