Time series forecasting is of fundamental importance for a variety of domains including the prediction of earthquakes, financial market prediction, and the prediction of epileptic seizures. We present an original approach that brings a novel perspective to the field of long-term time series forecasting. Nonlinear properties of a time series are evaluated and used for long-term predictions. We used financial time series, medical time series and climate time series to evaluate our method. The results we obtained show that the long-term prediction of complex nonlinear time series is no longer unrealistic. The new method has the ability to predict the long-term evolutionary trend of stock market time series, and it attained an accuracy level with 100% sensitivity and specificity for the prediction of epileptic seizures up to 17 minutes in advance based on data from 21 epileptic patients. Our new method also predicted the trend of increasing global temperature in the last 30 years with a high level of accuracy. Thus, our method for making long-term time series predictions is vastly superior to existing methods. We therefore believe that our proposed method has the potential to be applied to many other domains to generate accurate and useful long-term predictions.

The origin of species remains one of the most controversial and least understood topics in evolution. While it is being widely accepted that complete cessation of gene-flow between populations owing to long-lasting geographical barriers results in a steady, irreversible increase of divergence and eventually speciation, the extent to which various degrees of habitat heterogeneity influences speciation rates is less well understood. Here, we investigate how small, randomly distributed physical obstacles influence the distribution of populations and species, the level of population connectivity (e.g. gene flow), as well as the mode and tempo of speciation in a virtual ecosystem composed of prey and predator species. We adapted an existing individualbased platform, EcoSim, to allow fine tuning of the gene flow's level between populations by adding various numbers of obstacles in the world. The platform implements a simple food chain consisting of primary producers, herbivores (prey) and predators. It allows complex intra-and inter-specific interactions, based on individual evolving behavioural models, as well as complex predator-prey dynamics and coevolution in spatially homogenous and heterogeneous worlds. We observed a direct and continuous increase in the speed of evolution (e.g. the rate of speciation) with the increasing number of obstacles in the world. The spatial distribution of species was also more compact in the world with obstacles than in the world without obstacles. Our results suggest that environmental heterogeneity and other factors affecting demographic stochasticity can directly influence speciation and extinction rates.

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The forces promoting and constraining speciation are often studied in theoretical models because the process is hard to observe, replicate, and manipulate in real organisms. Most models analyzed to date include pre-defined functions influencing fitness, leaving open the question of how speciation might proceed without these built-in determinants. To consider the process of speciation without pre-defined functions, we employ the individual-based ecosystem simulation platform EcoSim. The environment is initially uniform across space, and an evolving behavioural model then determines how prey consume resources and how predators consume prey. Simulations including natural selection (i.e., an evolving behavioural model that influences survival and reproduction) frequently led to strong and distinct phenotypic/genotypic clusters between which hybridization was low. This speciation was the result of divergence between spatially-localized clusters in the behavioural model, an emergent property of evolving ecological interactions. By contrast, simulations without natural selection (i.e., behavioural model turned off) but with spatial isolation (i.e., limited dispersal) produced weaker and overlapping clusters. Simulations without natural selection or spatial isolation (i.e., behaviour model turned off and high dispersal) did not generate clusters. These results confirm the role of natural selection in speciation by showing its importance even in the absence of pre-defined fitness functions.

We analyze the results of a large simulation of an evolving ecosystem to evaluate its complexity. In particular, we are interested to know how close to a stochastic or a deterministic behavior our simulation is. Four methods have been used for this analysis: Higuchi fractal dimension, correlation dimension, largest Lyapunov exponent, and P&H method. Besides, we use a surrogate data test to reach a final decision about analysis. As we expect, our results show that there is a deterministic and chaotic behavior in ecosystem simulation.