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We present a simple and efficient microeconomic model incorporating generic components for trade of cattle at the level of agricultural holdings, using supply-and-demand processes as a basis for animal movements. By combining within-node dynamics of stocks with stochastic jumps describing animal exchanges between nodes, our model reproduces the dynamical network of animal trade between holdings. Variants of the model, either closely calibrated on the data, or based on mechanistic economical assumptions, are considered. In addition to mathematical investigation of the average dynamical behaviour, model performances are assessed on three datasets (including or not intermediary trade operators such as marketplaces and assembly centres), covering 5 years of cattle movement in the d'epartement of Finistère (France), as a case study. Model outputs are compared with data regarding the average size of traded batches per holding and the length of temporal trade chains with the potential to transmit disease across the market. We observe an overall good agreement with the data, with variations between models, depending on the criteria (aggregated or time-varying) and datasets considered. These findings highlight the impact of highvolume nodes such as markets and assembly centres on trade flows, as well as the importance of correctly reproducing temporal features of dynamical trade networks. Our study represents one of the first attempts of building dynamical models of livestock trade networks, incorporating simple economic mechanisms, proving to be useful for analysing and predicting cattle trade movements. Future work in this direction might lead to a more detailed analysis of the subnetworks (e.g. beef, dairy) of this complex market, as well as a better understanding of the economic drivers underlying cattle movement, allowing the improvement of predictions of its temporal features, especially in the context of outbreaks. [ABSTRACT FROM AUTHOR]

We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on Lévy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height, using a spinal decomposition of the tree, similar to the classical Bismut and Williams decompositions. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process. [ABSTRACT FROM AUTHOR]

A variety of methods based on coalescent theory have been developed to infer demographic history from gene sequences sampled from natural populations. The 'skyline plot' and related approaches are commonly employed as flexible prior distributions for phylogenetic trees in the Bayesian analysis of pathogen gene sequences. In this work we extend the classic and generalized skyline plot methods to phylogenies that contain one or more multifurcations (i.e. hard polytomies). We use the theory of Λ-coalescents (specifically, Beta (2 - α , α) -coalescents) to develop the 'multifurcating skyline plot', which estimates a piecewise constant function of effective population size through time, conditional on a time-scaled multifurcating phylogeny. We implement a smoothing procedure and extend the method to serially sampled (heterochronous) data, but we do not address here the problem of estimating trees with multifurcations from gene sequence alignments. We validate our estimator on simulated data using maximum likelihood and find that parameters of the Beta (2 - α , α) -coalescent process can be estimated accurately. Furthermore, we apply the multifurcating skyline plot to simulated trees generated by tracking transmissions in an individual-based model of epidemic superspreading. We find that high levels of superspreading are consistent with the high-variance assumptions underlying Λ-coalescents and that the estimated parameters of the Λ-coalescent model contain information about the degree of superspreading. [ABSTRACT FROM AUTHOR]