Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information

Abstract

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory, and exobiology. Many measures of these quantities, either rely on a statistical notion of information, are difficult to compute, or can only be applied to strings. Based on assembly theory, we propose the notion of a \textit{ladderpath}, which describes how an object can be decomposed into a hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origins of life. The ladderpath approach provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

Stability of multi-layer ecosystems

“…Next, we show the effect of connectance on the stability of multi-layer ecosystems when interactions within the same layer ( C w ) are competition (figure 3 a – c ) or between different layers are competition ( C b ) (figure 3 d , e ). For interactions with I w and I b , the corresponding overall percentages f w , f b of the ratio of interaction within each and between different layers arefnormalw=S−12S−1Cnormalw1emand1emfnormalb=S2S−1Cnormalb.Note that there are various angles to characterize the ‘complexity’ of ecosystems [32–34], here the ‘complexity’ portrays the network connectance in our model [1,2]. Thus the increase of C b makes the system more complex (the connectance of the whole ecosystem increases).…”