title: An Effect of Landmarks on Territory Shape in a Convict Cichlid.
abstract: We determine size, shape and location for a territory that is optimal in the sense of minimizing defense costs, when a given proportion of the boundary is landmarked and its primary benefit in terms of fitness is greater ease of detecting intruders across it. Increasing the landmarked proportion of boundary causes the optimal configuration to be smaller and more elongated, and to be located with its center further from the nest, so that the nest is closer to the landmarked boundary. These predictions accord with observations in a recent study of the convict cichlid Amatitlania siquia. Our results thus confirm the consistency of the observed behavior with the hypothesis that A. siquia designs its territory to make intruders easier to spot. Our results also lead us to conjecture that moving the landmark proportionately closer to or further away from the nest would have yielded essentially the same outcome in this study, because the optimal configuration depends only on the angle subtended by the landmark at the nest and hence only on the length of the landmark relative to its distance from the nest, as opposed to its absolute value.
authors.affiliation: Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL, 32306-4510, USA. mesterto@math.fsu.edu.
authors.forename: Mike
authors.initials: M
authors.lastname: Mesterton-Gibbons
authors.affiliation: Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL, 32306-4510, USA. daiyaochina@gmail.com.
authors.forename: Yao
authors.initials: Y
authors.lastname: Dai
mesh_terms: D000818:Animals; D023681:Cichlids / Q000502:physiology*; D055641:Mathematical Concepts; D008954:Models, Biological; D013731:Territoriality
keywords: Costs of territorial defense; Intruder visibility; Optimization model