An improved formal approach to demographic loop analysis.

Loop analysis is introduced to demographic analysis as a tool to compare relative contributions of different life-history types to population growth rate. In 1998, G. M. Wardle brought in basic concepts of the graph theory to demographic loop analysis and proposed a methodology to determine the loops from any life-cycle graph based on these concepts. However, the mathematics behind Wardle's methodology cannot readily be used by most population ecologists. A new methodology that is also based on graph theory concepts but both makes ecological sense in its application and is simpler to implement is proposed. Three rules of thumb serve as the basis of the proposed methodology that brings a more systematic approach to loop selection: it identifies only those loops that are ecologically meaningful (i.e., loops that are forward-flowing and with positive elasticity values). Thus, it produces a loop set that is more amenable to answer questions on comparison of different lifehistory types. It is tested on several life-cycle graphs from the literature. Three of these are presented: Vouacapoua americana, Dipsacus sylvestris, and Alcyonium sp. In each case, the methodology successfully produced a loop set that makes sense in terms of the ecology of the species. The methodology is also implemented as a couple of open-source computer codes. It is hoped that the proposed methodology will lead to wider use of loop analysis in demographic population studies.