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The coexistence of cladogenesis, i.e., the branching of lineages along an evolutionary tree as observed in the fossil record, and anagenesis, which is the progressive evolution within populations, lacks a clear explanation. In this study, we examine a simple model that simulates the evolutionary changes occurring within populations inhabiting the same environment in sympatry, and driven by ecological competition. Our model characterizes populations through a set of evolving morphological traits represented by mathematical points within a two-dimensional morphospace. Such points may reproduce or die due to overcrowding, implying competition in morphospace as suggested by the ecological phenomenon of character displacement. By focusing on the morphospace rather than physical space, the model effectively captures the simultaneous evolution of coexisting populations. Central to the model is the delicate balance between the range of competition and the range of reproduction within the morphospace. Interesting patterns emerge when the ratio between the competition to reproducetion ranges, referred to as CR ratio, changes from values slightly smaller to significantly larger than unity. When competition acts over short distances relative to the reproduction range (low CR), the phylogenetic tree takes on a nearly uniform appearance, gradually transforming into a more bush-like structure for slightly higher CR values. With further increases in CR, evolutionary lineages become more discernible, and the morphogenetic pattern shifts from a bush-like shape to a more tree-like arrangement and few branches for very large CRs. At specific time sections, the synthetic phylogenetic tree appears as an assembly of clusters of individuals within the morphospace. These clusters, interpretable as simulated models of species, exhibit distinct separation within the morphospace and are subject to dynamic inter-cluster repulsion. Notably, clusters tend to be resistant to change. They maintain relatively constant abundances while gradually shifting their positions within the morphospace-a phase that aligns with the concept of phyletic gradualism. However, this predictable pattern is occasionally upset by the abrupt divisions into multiple groups, interpreted as cladogenesis events. The intricacies of the splitting process are explored, revealing that in scenarios with large CR values, the splitting can emerge much more rapidly than phyletic changes. This accelerated process of splitting is initiated by one or few individuals at the fringes of a cluster, where competition is minimal. The newly generated cluster then undergoes deformation, swiftly followed by divergence and splitting (seen as branching in the synthetic phylogenetic tree), as if an inherent "repulsion" triggered the division between species. The simple rules implied in the interacting-particle model may provide insight into the coexistence of gradualism and cladogenesis along lineages, illustrating the capacity for rapid shifts during cladogenesis and the more gradual process of anagenesis.

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There are strong propositions in the literature that abiotic factors override biotic drivers of diversity on time scales of the fossil record. In order to study the interaction of biotic and abiotic forces on long term changes, we devise a spatio-temporal discrete-time Markov process model of macroevolution featuring population formation, speciation, migration and extinction, where populations are free to migrate. In our model, the extinction probability of these populations is controlled by latitudinally and temporally varying environment (temperature) and competition. Although our model is general enough to be applicable to disparate taxa, we explicitly address planktic organisms, which are assumed to disperse freely without barriers over the Earth's oceans. While rapid and drastic environmental changes tend to eliminate many species, generalists preferentially survive and hence leave generalist descendants. In other words, environmental fluctuations result in generalist descendants which are resilient to future environmental changes. Periods of stable or slow environmental changes lead to more specialist species and higher population numbers. Simulating Cenozoic diversity dynamics with both competition and the environmental component of our model produces diversity curves that reflect current empirical knowledge, which cannot be obtained with just one component. Our model predicts that the average temperature optimum at which planktic species thrive best has declined over the Neogene, following the trend of global average temperatures.

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We present experimental results for the rolling of spheres on a granular bed. We use two sets of glass and steel spheres with varying diameters and a high-speed camera to follow the motion of the spheres. Despite the complex phenomena occurring during the rolling, the results show a friction coefficient nearly independent of the velocity (0.45-0.5 for glass and 0.6-0.65 for steel). It is found that for a given sphere density, the large spheres reach a longer distance, a result that may also help explain the rock sorting along natural stone accumulations at the foot of mountain slopes.

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Ammonoids are a group of extinct mollusks belonging to the same class of the living genus Nautilus (cephalopoda). In both Nautili and ammonoids, the (usually planospiral) shell is divided into chambers separated by septa that, during their lifetime, are filled with gas at atmospheric pressure. The intersection of septa with the external shell generates a curve called the suture line, which in living and most fossil Nautili is fairly uncomplicated. In contrast, suture lines of ancient ammonoids were gently curved and during the evolution of the group became highly complex, in some cases so extensively frilled as to be considered as fractal curves. Numerous theories have been put forward to explain the complexity of suture ammonoid lines. Calculations presented here lend support to the hypothesis that complex suture lines aided in counteracting the effect of the external water pressure. Additionally, it is suggested that complex suture lines diminished shell shrinkage caused by water pressure, and thus aided in improving buoyancy. Understanding the reason for complex sutures in ammonoids represents an important issue in paleobiology with potential applications to the problem of the resistance of hollow mechanical structures subjected to high pressure.

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We present a simple model of adaptive radiation in evolution based on species competition. Competition is found to promote species divergence and branching, and to dampen the net species production. In the model simulations, high taxonomic diversification and branching take place during the beginning of the radiation. The results show striking similarities with empirical data and highlight the mechanism of competition as an important driving factor for accelerated evolutionary transformation.

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