Humans have exceptional locomotor endurance among mammals (Carrier, 1984; Bramble and Lieberman, 2004; Pontzer, 2017; Raichlen et al., 2019). Our body seems to be tuned to perform prolonged moderate to vigorous physical activity, such as walking and running, to the extent that the absence of physical activity increases vulnerability to poor physical and mental health and contributes to diseases such as heart disease, osteoporosis, obesity, and Alzheimer's disease (Morris et al., 1953; Paffenbarger et al., 1986; Donnelly et al., 2009; Guadalupe-Grau et al., 2009; Mattson, 2012; Lieberman, 2020). Human locomotor endurance has been explained as resulting from selection for long-distance walking and running (Bramble and Lieberman, 2004). Initially, foraging by walking in hot open habitats with sparsely distributed resources might have selected for locomotor endurance (e.g., Brace and Montagu, 1965; Lieberman, 2015; Pontzer, 2017). Further increase in locomotor endurance may have stemmed from selection for endurance running used in scavenging and persistence hunting (Carrier, 1984; Bramble and Lieberman, 2004; Pontzer, 2017). The importance of endurance running in these evolutionary scenarios was based largely on observations of modern hunter-gatherer populations, some of which use running or intermittent running (alternation of running and walking) to drive their prey to exhaustion, heatstroke, or otherwise into traps or other means by which they can be killed by hunters (Liebenberg, 2006; Lieberman et al., 2020). However, other research has suggested that walking without running could also result in successful persistence hunting (Pickering and Bunn, 2007). If so, persistence hunting would not have required endurance running as a prerequisite (Nickels, 1984; Pickering and Bunn, 2007), and could have been used by hominins before the emergence of the running-related traits in Homo erectus (Nickels, 1984). Nevertheless, the records of persistence hunting by walking in modern hunter-gatherers are limited to the report of Pickering and Bunn (2007; and perhaps Bartram et al., 1991 see Discussion section), which may suggest a lower success rate compared to running. However, the relative success rates of walking and running in persistence hunting remain unclear.

Owing to differences in mechanics and energetical and thermoregulatory demands between walking and running, different aspects of locomotor endurance might be favored by selection for each gait. Locomotor endurance, defined as the maximum duration of locomotion sustainable at a given velocity (Pontzer, 2017), is determined by several factors including aerobic capacity, volume of mitochondria in muscles, locomotor economy, and heat loss capacity (for a more complex discussion of endurance see, e.g., Bassett and Howley, 2000; Hutchinson, 2018). Aerobic capacity (VO2max) determines how much oxygen can be delivered to and used by muscles active during locomotion and since one cannot operate above VO2max for extended periods, it sets the upper limit for endurance performance (Bassett and Howley, 2000). Aerobic capacity is affected by, among other factors, cardiorespiratory capacity and volume of mitochondria in active muscles, which itself is primarily a function of muscle volume, muscle fiber type (Weibel et al., 2004), and mitochondrial volume density (Hoppeler et al., 1973). Volume of mitochondria in muscles also positively affects endurance at submaximal aerobic velocities by allowing to perform at higher percentage of aerobic capacity because of slower accumulation of metabolites, lower rates of glycogen depletion, and increase of fat oxidation (Holloszy and Coyle, 1984). The need for higher aerobic capacity and mitochondrial volume would rise with intensity of the locomotion, e.g., due to challenging terrain, carried loads, and velocity. As modern hunter-gatherers usually walk relatively slowly (e.g., about 1.1 m s−1 in Hadza; Pontzer et al., 2015), foraging might not require high aerobic capacity. Similarly, persistence hunting by walking would not be expected to select for higher aerobic capacity unless it benefited from faster velocities which require higher oxygen uptake (e.g., Ralston, 1958). More intensive running-based scavenging or persistence hunting would put stronger selection pressure for increased aerobic capacity in hominins compared to walking (Bramble and Lieberman, 2004; Pontzer, 2017).

The locomotor economy is defined as the mass-specific distance traveled per unit of energy (and thus oxygen) expended (Pontzer, 2017). Keeping aerobic capacity constant, individuals with better locomotor economy would travel at lower percentage of their aerobic capacity and hence have greater endurance (Conley and Krahenbuhl, 1980; Daniels and Daniels, 1992). Although some morphological characteristics improve the economy of both walking and running (e.g., long lower limbs; Steudel-Numbers and Tilkens, 2004; Pontzer, 2005; Steudel-Numbers et al., 2007), others are relevant for only a single gait (e.g., energy storage in a long Achilles tendon and a plantar arch during running; Bramble and Lieberman, 2004). Thus, we suggest that selection for walking economy, whether due to persistence hunting or other long-distance walking foraging behaviors, could act on some of the same traits (e.g., long lower limbs) as those selected for running economy.

In hot, open environments, hyperthermia and dehydration become the key limits of locomotor endurance (Adolph, 1947; Carrier, 1984; Steudel-Numbers et al., 2007; Ruxton and Wilkinson, 2011a, b; Lieberman, 2015; Rathkey and Wall-Scheffler, 2017; Longman et al., 2019, 2021; Hora et al., 2020). Modern humans are characterized by several traits that facilitate heat loss such as high sweating capacity and loss of functional hair cover (Lieberman, 2015). It has been argued that heat loss capacity might have been under selection in hominins foraging in open habitats (Wheeler, 1992; Ruxton and Wilkinson, 2011a), especially in the middle of the day to avoid predators (Brace and Montagu, 1965; Lieberman, 2015). Persistence hunting by walking was reported in a hot open environment (Pickering and Bunn, 2007) so it would also benefit from the derived heat loss capacity. As high-intensity locomotion is more thermogenic, heat loss capacity would be more important for persistence hunting if performed at faster walking velocities and would be essential with the adoption of persistence hunting by running (Montagu, 1964; Carrier, 1984; Bramble and Lieberman, 2004; Lieberman, 2015).

There are several factors that could contribute to the optimal gait and velocity for a successful persistence hunt, including the prey sweating capacity, body size of the prey, and preferred velocity of the prey, as well as environmental factors such as air temperature and relative humidity. Although terrestrial ungulates (the typical prey in persistence hunting; Liebenberg, 2006; Lieberman et al., 2020) dissipate heat primarily by panting and many rely on panting exclusively (e.g., wildebeest, wild boar, mule deer; Taylor et al., 1969a; Ingram, 1965; Parker and Robbins, 1984), some wild ungulate species also have heat-induced sweating capacity (Robertshaw and Taylor, 1969a; Bullard et al., 1970; Robertshaw and Dmi'el, 1983; Parker and Robbins, 1984), which would provide them with an additional route to lose heat while fleeing from the hunter. In contrast to human eccrine glands which produce sweat through exocytosis of secretory granules of specific content, in ungulates, sweat is produced by apocrine glands through discharging a portion of the cell, including cell membrane, cell cytoplasm, and intracellular fragments (Farkaš, 2015). The resulting sweat ranges from highly concentrated to watery (Weiner and Hellmann, 1960). As such, the evaporative capacity of the apocrine sweat might be lower than that of the eccrine sweat. However, experiments show that cutaneous evaporation can surpass the evaporation from respiratory tract in some sweating ungulate species (Knapp and Robinson, 1954; McLean, 1963; Taylor, 1969; Taylor et al., 1969b; Finch, 1972; Robertshaw and Dmi'el, 1983) and other animals (Dawson et al., 1974) and account for up to 95% of overall evaporation (McLean, 1963), although most data come from resting animals. More data are needed from animals during physical activity when ventilation is increased and so would be the evaporation from the respiratory tract. On the other hand, cutaneous evaporation would also be enhanced during locomotion due to airflow over the body surface. Nonequid ungulates seem to lack the direct humoral control of sweating through circulating catecholamines (studied in cattle and black bedouin goat; Robertshaw and Whittow, 1966; Dmi'el et al., 1979) that can contribute to sweating during physical activity (in addition to neural control) in equids (Evans et al., 1956; Robertshaw and Taylor, 1969b) and primates (Wada, 1950; Robertshaw et al., 1973). Nevertheless, because of increased metabolic heat production, sweating should be induced by heat during physical activity also in nonequid ungulates, which is illustrated, e.g., in eland whose cutaneous evaporation “increased by 4- to 10-fold during a run and the sweat literally dripped off them after they stopped” as reported by Taylor and Lyman (1972: 116). The observed increase of body core temperature in eland during running was below 1 °C compared to the up to 4.5 °C increase in gazelle, who increased cutaneous evaporation by only 40%, which suggests that sweating is an effective route for heat dissipation in eland (Taylor and Lyman, 1972). As such, the sweating capacity of the prey could have a negative effect on the success of the persistence hunt.

Larger animals have lower body surface area to body mass ratios that limit their relative heat dissipation capacity (Bergmann, 1848; Ruff, 1994). This characteristic should make larger animals prone to overheating at lower levels of physical activity (i.e., at lower velocities). Thus, walking might be better suited for the persistence hunting of large prey. On the other hand, larger animals might have adaptations to moderate the size-induced limits of thermoregulation. Among African ungulates, larger species have been reported to have greater sweating capacity (Robertshaw and Taylor, 1969a), lower pelage depth, and lower thermal conductance of the pelage (Hofmeyr, 1985). All these characteristics would enhance heat dissipation in larger animals. Although larger-bodied animals have relatively more muscle mass compared with smaller-bodied animals (Alexander et al., 1981), their mass-specific cost of locomotion is lower (Taylor et al., 1970, 1982) and thus they should generate relatively less heat when moving.

Quadrupeds use narrow ranges of energetically optimal velocities within each gait (Hoyt and Taylor, 1981). The hunter might thus benefit from selecting velocities just above those preferred ranges to force prey to switch to a faster gait and hasten the rate of heat accumulation (Carrier, 1984). As hunting by walking would elicit lower heat production in the prey compared to running (Hoyt and Taylor, 1981), it might require a higher air temperature (which increases heat gain from the environment and limits heat loss) or higher relative humidity (which limits evaporative heat loss) to push the game to overheat. Owing to the circadian oscillation of air temperature and humidity, the success of walking in persistence hunting could also be affected by the time of day.

In this study, we simulated the success of walking and running in persistence hunting using a heat exchange model. We adjusted and validated (in humans, horses, sheep, cattle, and elands) a previously published heat exchange model (Hora et al., 2020) to simulate persistence hunts for prey of three sizes and three levels of sweating capacity by a modern human hunter at combinations of the hunter's aerobic velocity, air temperature, relative humidity, and start time. The heat exchange model was used to estimate body core temperature and water loss of the hunter and prey. The prey was modeled as fleeing from the hunter at its preferred velocity (equal or faster than the actual velocity of the hunter), stopping after reaching a certain distance from the hunter and resting in the shade until the hunter gets closer again. We identified successful simulated hunts as those in which the hunter had greater locomotor endurance (limited by hyperthermia, dehydration, and sunset) than the prey. We calculated the success rate of simulated persistence hunts by dividing the number of successful simulated hunts under given conditions by the number of simulated hunts under the given conditions, thus assuming that the hunter can track the prey at a given velocity and never loses the trail. We tested two hypotheses: 1) walking is as successful as running in persistence hunting of medium to very large prey and 2) the success of walking is greater in larger prey, in animals with low sweating capacity, at velocities that force the prey to trot, and under hot and humid ambient conditions.