Lanchester's models of attrition describe casualty rates during battles between groups as functions of the numbers of individuals and their fighting abilities. Originally developed to describe human warfare, Lanchester's square law has been hypothesized to apply broadly to social animals as well, with important consequences for their aggressive behaviour and social structure. According to the square law, the fighting ability of a group is proportional to the square of the number of individuals, but rises only linearly with fighting ability of individuals within the group. By analyzing mortality rates of fire ants (Solenopsis invicta) fighting in different numerical ratios, we provide the first quantitative test of Lanchester's model for a nonhuman animal. Casualty rates of fire ants were not consistent with the square law; instead, group fighting ability was an approximately linear function of group size. This implies that the relative numbers of casualties incurred by two fighting groups are not strongly affected by relative group sizes and that battles do not disproportionately favour group size over individual prowess.

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Inflammation is often accompanied by robust angiogenesis. Vascular endothelial cells (ECs) express erbB receptors and their ligand, neuregulin-1, and can respond to neuregulin by proliferation and angiogenesis. We hypothesized that some growth factor-like responses of ECs to inflammatory cytokines can be explained by cleavage of transmembrane neuregulin with subsequent release of its extracellular epidermal growth factor-like-containing domain and autocrine activation. Using a model of cultured human ECs, we found that interleukin-6 or interferon-gamma causes rapid cleavage and release of transmembrane neuregulin. Inhibitors of metalloproteinases abolish this effect. The addition of an inhibitor of tumor necrosis factor-alpha converting enzyme (TACE) blocks cytokine-induced neuregulin release. Silencing of TACE expression increases the amount of basal proneuregulin present in ECs but does not block neuregulin release in response to phorbol myristate acetate (PMA), suggesting that other proteinases are responsible for mediating protein kinase C-dependent cleavage. Cytokines capable of inducing neuregulin cleavage stimulated ERK activation and in vitro angiogenesis (Matrigel cord formation). This effect is blocked by inhibitors that block neuregulin cleavage, erbB protein tyrosine kinase inhibitors, or antineuregulin-neutralizing antibodies. Cytokine-activated metalloproteinase cleavage of neuregulin may play an important role in autocrine activation of EC signaling pathways, contributing to key biological effects, perhaps including inflammation-associated angiogenesis.

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