Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behavior of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions.

Evolution has traditionally been a historical and descriptive science and predicting future evolutionary processes has long been considered impossible. However, evolutionary predictions are increasingly being developed and used in medicine, agriculture, biotechnology and conservation biology. Evolutionary predictions may be used for different purposes, such as to prepare for the future, to try and change the course of evolution or to determine how well we understand evolutionary processes. Similarly, the exact aspect of the evolved population that we want to predict may also differ, for example we could try to predict which genotype will dominate, the fitness of the population, or the extinction probability of a population. In addition, there are many uses of evolutionary predictions that may not always be recognized as such. The main goal of this review is to increase awareness of methods and data that are used to make these predictions in different research fields by showing the breadth of situations in which evolutionary predictions are made. We describe how diverse evolutionary predictions share a common structure described by the predictive scope, time scale and precision. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation in biotechnology, we discuss the methods for predicting evolution, the factors that affect predictability, and how predictions can be used to prevent evolution in undesirable directions or to promote beneficial evolution (i.e. evolutionary control). We hope that this review will stimulate collaboration between fields by creating a common language for evolutionary predictions.

Evolution has traditionally been a historical field of study and predicting evolution has long been considered challenging or even impossible. However, evolutionary predictions are increasingly being made and used in many situations in medicine, agriculture, biotechnology and conservation biology. Because every field uses their own language and makes predictions from their background, researchers are not always aware of the breadth of evolutionary predictions. Evolutionary predictions may be used for several purposes such as to prepare for the future, to try and change the course of evolution or simply to determine how well we understand an evolutionary system. Exactly what aspect of an evolving population we want to predict, such as the most common genotype, average or individual fitness, or population size, depends on the situation. There are many uses of evolutionary predictions that may not be recognized as such. Therefore, the main goal of this review is to increase awareness of methods and data that are used to make these predictions in different fields, by showing the breadth of situations in which evolutionary predictions are made. We describe how evolutionary predictions are highly diverse, but nevertheless share a common structure described by the predictive scope, horizon, precision and risk. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation by microorganisms, we discuss the methods for predicting evolution, factors that affect the predictability, and how predictions can be used to prevent unwanted evolution or promote beneficial evolution. We hope that this review will increase collaboration between fields by creating a common language for evolutionary predictions.

Crime data provides information on the nature and location of the crime but, in general, does not include information on the number of criminals operating in a region. By contrast, many approaches to crime reduction necessarily involve working with criminals or individuals at risk of engaging in criminal activity and so the dynamics of the criminal population is important. With this in mind, we develop a mechanistic, mathematical model which combines the number of crimes and number of criminals to create a dynamical system. Analysis of the model highlights a threshold for criminal efficiency, below which criminal numbers will settle to an equilibrium level that can be exploited to reduce crime through prevention. This efficiency measure arises from the initiation of new criminals in response to observation of criminal activity; other initiation routes -via opportunism or peer pressure -do not exhibit such thresholds although they do impact on the level of criminal activity observed. We used data from Cape Town, South Africa, to obtain parameter estimates and predicted that the number of criminals in the region is tending towards an equilibrium point but in a heterogeneous manner -a drop in the number of criminals from low crime neighbourhoods is being offset by an increase from high crime neighbourhoods.

Mutational meltdown describes an eco-evolutionary process in which the accumulation of deleterious mutations causes a fitness decline that eventually leads to the extinction of a population. Possible applications of this concept include medical treatment of RNA virus infections based on mutagenic drugs that increase the mutation rate of the pathogen. To determine the usefulness and expected success of such an antiviral treatment, estimates of the expected time to mutational meltdown are necessary. Here, we compute the extinction time of a population under high mutation rates, using both analytical approaches and stochastic simulations. Extinction is the result of three consecutive processes: (1) initial accumulation of deleterious mutations due to the increased mutation pressure; (2) consecutive loss of the fittest haplotype due to Muller’s ratchet; (3) rapid population decline towards extinction. We find accurate analytical results for the mean extinction time, which show that the deleterious mutation rate has the strongest effect on the extinction time. We confirm that intermediatesized deleterious selection coefficients minimize the extinction time. Finally, our simulations show that the variation in extinction time, given a set of parameters, is surprisingly small.