Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations.

Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters' contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude.

Evolutionary games under incompetence.

The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

Spring constant calibration techniques for next-generation fast-scanning atomic force microscope cantilevers.

As a recent technological development, high-speed atomic force microscopy (AFM) has provided unprecedented insights into dynamic processes on the nanoscale, and is capable of measuring material property variation over short timescales. Miniaturized cantilevers developed specifically for high-speed AFM differ greatly from standard cantilevers both in size and dynamic properties, and calibration of the cantilever spring constant is critical for accurate, quantitative measurement. This work investigates specifically, the calibration of these new-generation cantilevers for the first time. Existing techniques are tested and the challenges encountered are reported and the most effective approaches for calibrating fast-scanning cantilevers with high accuracy are identified, providing a resource for microscopists in this rapidly developing field. Not only do these cantilevers offer faster acquisition of images and force data but due to their high resonant frequencies (up to 2 MHz) they are also excellent mass sensors. Accurate measurement of deposited mass requires accurate calibration of the cantilever spring constant, therefore the results of this work will also be useful for mass-sensing applications.