Why Only the Lightest Male Camels Can Hold Territory — And What That Reveals About Animal Societies

In the high Andes, where wind-scoured grasslands stretch for miles, a male vicuña doesn’t just fight for land — he fights for energy. And according to a new model, only males under a precise body-mass threshold can win. That threshold? $7.75\times 10^{-6}{\mu }^{1.45}$ kilograms, where $\mu$ is the energy available per unit of food. In plain terms: if you’re too heavy for the available grass, no amount of dominance or aggression will save you. You’ll lose your territory, your access to mates, and your shot at passing on your genes.

This isn’t just about camelids. It’s a demonstration that metabolic physics — not just brute strength — governs the structure of animal societies. In a world where climate change is altering vegetation patterns and body sizes are shifting across species, this model reveals a hidden rule: territory isn’t won by the strongest, but by those whose bodies are best tuned to the energy landscape.

The Science

Tomás Ignacio González, Guillermo Abramson, and María Fabiana Laguna set out to build a model that finally links three powerful forces in animal behavior: body size, energy use, and space. Their focus was camelids — wild South American relatives of llamas and alpacas, including guanacos and vicuñas. These animals live in harsh, open environments where males defend feeding areas to attract females, a strategy known as resource-defense polygyny.

But existing models of territoriality often treat animals as abstract competitors, ignoring the fact that bigger bodies cost more to move, and that cost scales predictably with mass. The researchers wanted to fix that.

They built a spatially explicit, individual-based simulation on a 50×50 grid (each cell representing 1 hectare), where 50 male camelids, each with a randomly assigned body mass between 50 and 140 kg, attempt to claim territory over 90 iterations — roughly one breeding season. The model tracks each male’s energy balance, which depends on three things:

1. Energy gained from resources in their territory (scaled by $\mu$, the energy per unit resource),
2. Energy spent patrolling the perimeter of their territory, which depends on locomotion costs derived from the allometric equation of Taylor and Heglund: $E(m,v)=10.7m^{-0.316}v+6.03m^{-0.303}$ (in W/kg),
3. Energy risked in fights, where losing costs $C$ kJ.

Territory expansion happens cell by cell. A male can claim an empty cell if the energy gain exceeds the added cost of patrolling a longer perimeter. If the cell is occupied, he weighs the odds: his probability of winning a fight depends on the relative mass difference $\delta =(m_i-m_j)/(m_i+m_j)$, with larger males more likely to win. But he only attacks if the expected payoff — $p_{ij}\Delta B_i>(1-p_{ij})C$ — is positive.

The landscape itself is generated using a “sowing” model: 20 random points of high resource richness, from which resources spread across the grid depending on a connectivity parameter $\alpha$. When $\alpha$ is low, resources are patchy and isolated; when high, they’re evenly distributed.

The model runs until territorial boundaries stabilize — or collapse.

What They Found

The results reveal three fundamental rules shaping territorial societies.

First: There’s a strict upper limit on body mass for territorial success — and it’s set by physics, not fighting.

Even in a world with no fights ($C=0$), only males below a critical mass can hold territory. That threshold scales with the 1.45th power of available energy $\mu$. When $\mu$ is low — say, 50 kJ per unit resource — only males under about 60 kg can survive. When $\mu$ rises to 185 kJ, the threshold climbs to nearly 100 kg. Above that, locomotion costs eat up all gains, and the male collapses territorially.

Maximum male mass that can hold territory vs. energy per resource (μ)

Label	Value
50	60
75	72
100	81
125	89
150	96
175	102
185	105

Data derived from Figure 5, showing the upper bound of male mass that can maintain positive energy balance.

This isn’t just theoretical. In real populations, vicuñas average around 45 kg, guanacos 90–120 kg. The model suggests that in low-productivity environments, only lighter males can sustain territories — which may explain why vicuñas, living in more extreme altitudes, are smaller and more rigidly territorial than their larger, more flexible guanaco cousins.

Second: Resource connectivity controls inequality.

When resources are scattered (low $\alpha$), males rarely meet. Territories stay small and equal — a Gini index near 0.1. But as $\alpha$ increases, resources become connected, competition intensifies, and inequality spikes. Some males grab large, rich patches; others are pushed to the margins. The Gini index peaks in mid-range $\alpha$, then drops again when resources are so abundant and uniform that no one can monopolize them.

Territorial inequality (Gini index) vs. resource connectivity (α) and energy richness (μ)

Label	Value
0.2	0.15
0.4	0.25
0.6	0.35
0.8	0.3
1.0	0.2

Data from Figure 4B, showing non-monotonic relationship between resource connectivity and territorial inequality.

This non-monotonic pattern — inequality rising and then falling — is a signature of spatial competition. It mirrors wealth inequality in human cities: moderate connectivity enables monopolies; extreme connectivity enables redistribution.

Third: Fighting isn’t destabilizing — it’s stabilizing.

Intuitively, you’d think that costly fights make territorial systems more volatile. But the model shows the opposite. When confrontation cost $C$ is zero, males fight recklessly. The strong keep expanding, the weak keep challenging, and the system never stabilizes — the fraction of territorial males keeps dropping.

But when $C$ is high, males think twice. The risk of losing energy — or worse — deters unnecessary fights. Territories stabilize. More males survive. Conflict, paradoxically, promotes coexistence.

shows this in the $(\alpha ,\mu )$ plane: when $C=0$, high resource richness and connectivity lead to near-total male exclusion. But when $C>0$, those same conditions support stable, diverse territorial systems.

Why This Changes Things

For decades, behavioral ecologists have treated territoriality as a social strategy — a way for dominant individuals to monopolize mates. But this model shows that it’s also a metabolic strategy. Territory isn’t just a stage for competition; it’s a machine for energy capture, and its efficiency depends on the physics of the body.

This reframes how we think about animal societies. In ungulates, body size is often seen as a weapon — bigger means stronger, more dominant, more successful. But this model shows that size is also a liability. There’s a sweet spot: big enough to win fights, small enough to afford patrols.

That has evolutionary consequences. If environments become less productive — due to drought, overgrazing, or climate change — the viable male mass range shrinks. Selection may favor smaller males, even if they’re less dominant. We might already be seeing this: studies show body sizes shifting in response to warming climates across mammals (Yom-Tov, 2005; Sheridan & Bickford, 2011). This model suggests that such shifts could reshape social structures, not just physiology.

It also explains differences between species. Vicuñas, in high-altitude deserts with sparse, stable resources, defend small, permanent territories. Guanacos, in more variable lowlands, are more flexible — some migrate, some defend seasonally. The model’s parameter $\alpha$ captures this: low $\alpha$ (patchy resources) favors stability and small territories; high $\alpha$ (connected resources) allows expansion but requires flexibility.

Even human land use fits this framework. Indigenous pastoralists in the Andes manage camelid grazing by rotating access to resource patches — effectively manipulating $\alpha$. By preventing overuse and maintaining spatial heterogeneity, they may be stabilizing the very social systems that govern reproduction and territory.

And beyond camelids? The same principles likely apply to red deer, elk, antelope — any species where males defend feeding areas. The allometric locomotion cost equation used here is universal across mammals. So too is the trade-off between resource access and movement cost. This model offers a template for understanding territoriality not as a behavioral quirk, but as an emergent property of energy, space, and body size.

What's Next

The model is theoretical, but its predictions are testable. Researchers could track wild guanacos with GPS collars and accelerometers, measuring actual patrol costs and energy expenditure. By combining that with vegetation maps and body mass data, they could validate the $m^{\ast }<\psi {\mu }^{1.45}$ threshold in nature.

Another step is incorporating females. The current model focuses on male competition, but females choose mates based on territory quality. Adding female movement and mate choice could reveal feedback loops: do females prefer larger territories, even if they’re energetically inefficient? Does that select for males who over-expand, risking collapse?

Climate change adds urgency. As Andean grasslands dry and warm, $\mu$ and $\alpha$ will shift. Models like this can forecast how camelid societies will respond — not just in population size, but in social structure. Will territories shrink? Will dominance hierarchies flatten? Will smaller males rise?

One limitation is the assumption of constant walking speed (1 m/s). In reality, animals adjust speed based on terrain and fatigue. Future models could make speed a variable, coupling it to energy expenditure more dynamically.

Another is the linear fight probability model. While $p_{ij}=1/2+\delta$ is simple and symmetric, real fights may depend on age, experience, or prior residency. Adding those could refine predictions about who wins — and who holds on.

But the core insight stands: animal societies are not just shaped by competition, but by the physics of energy. Territory is not just a social construct — it’s a metabolic necessity. And in a world where energy is becoming scarcer, the lightest may inherit the earth.

shows the stark contrast: at $C=0$, territories sprawl chaotically, with a few males dominating vast areas. At $C=46$ kJ, boundaries are compact, stable, and more equally distributed. Conflict, it turns out, keeps the peace.

The takeaway isn’t just for ecologists. It’s a reminder that in any system — animal, human, ecological — stability often comes not from the absence of conflict, but from the cost of losing it. Rules that make failure expensive don’t suppress competition — they make it sustainable.