Related papers: Modelling proportionate growth
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the…
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally…
We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model ecosystem in which the species are characterized by…
We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another object. The objects we consider…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish…
Nature uses elongated shapes and filaments to build stable structures, generate motion, and allow complex geometric interactions. In this Review, we examine the role of biological filaments across different length scales. From the molecular…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In…
Biological systems are modular, and this modularity affects the evolution of biological systems over time and in different environments. We here develop a theory for the dynamics of evolution in a rugged, modular fitness landscape. We show…
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
Protein evolution underpins life, and understanding its behavior as a system is of great importance. However, our current models of protein evolution are arguably too simplistic to allow quantitative interpretation and prediction of…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
A hypothesis of singleness of the growth equation for biological objects on different organizational levels and dimensional analysis are used in order to substantiate Schmalhausen's model of ontogenetic growth (the mass of a growing…
Recently, West et al. claimed to derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass, and in addition claimed to…
Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…