The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.     
Plasma testosterone levels display circadian variation, peaking during sleep, and reaching a nadir in the late afternoon, with a superimposed ultradian rhythm with pulses every 90 min reflecting the underlying rhythm of pulsatile luteinizing hormone (LH) secretion. The increase in testosterone is sleep, rather than circadian rhythm, dependent and requires at least 3 h of sleep with a normal architecture. Various disorders of sleep including abnormalities of sleep quality, duration, circadian rhythm disruption, and sleep-disordered breathing may result in a reduction in testosterone levels. The evidence, to support a direct effect of sleep restriction or circadian rhythm disruption on testosterone independent of an effect on sex hormone binding globulin (SHBG), or the presence of comorbid conditions, is equivocal and on balance seems tenuous. Obstructive sleep apnea (OSA) appears to have no direct effect on testosterone, after adjusting for age and obesity. However, a possible indirect causal process may exist mediated by the effect of OSA on obesity. Treatment of moderate to severe OSA with continuous positive airway pressure (CPAP) does not reliably increase testosterone levels in most studies. In contrast, a reduction in weight does so predictably and linearly in proportion to the amount of weight lost. Apart from a very transient deleterious effect, testosterone treatment does not adversely affect OSA. The data on the effect of sleep quality on testosterone may depend on whether testosterone is given as replacement, in supratherapeutic doses, or in the context abuse. Experimental data suggest that testosterone may modulate individual vulnerability to subjective symptoms of sleep restriction. Low testosterone may affect overall sleep quality which is improved by replacement doses. Large doses of exogenous testosterone and anabolic/androgenic steroid abuse are associated with abnormalities of sleep duration and architecture.