We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions amongst large numbers of components, leading to ecosystems that possess the prototypical characteristics of complex systems. We argue that statistical mechanics is at present the best methodology available to obtain a quantitative description of complex systems, and that ecology is in urgent need of ``integrative'' approaches that are quantitative and non-stationary. We describe examples where combining statistical mechanics and ecology has led to improved ecological modelling and, at the same time, broadened the scope of statistical mechanics.
NEMF is a novel network-based ecosystem modelling framework. It is a flexible and easy-to-use tool for modelling ecosystems with low- to intermediate complexity. It is designed around the idea of visualizing an ecosystem through a network that implicitly defines a set of differential equations. These equations are then solved numerically and can also be inverse modelled. The framework offers the functionality to handle non-equilibrium, non-linear interactions.
The concentration of the population in coastal regions, in addition to the direct human use, is leading to an accelerated process of change and deterioration of the marine ecosystems. Human activities such as fishing together with environmental drivers (e.g. climate change) are triggering major threats to marine biodiversity, and impact directly the services they provide. In the South and Southwest coasts of Portugal, the deep-water crustacean trawl fishery is not exemption. This fishery is recognized to have large effects on a number of species while generating high rates of unwanted catches.…
In this paper we provide a model to describe the dynamics of the species of the ecosystem after it has been raided by a bad competing specie. The competing specie invades the native plants for nutrition, carbon dioxide and space. This affects the population of the native species of the ecosystem. The effect of the bad biomass on the ecosystem is examined by considering it's equilibrium points as well as its stability. An optimal control system is developed by using Pontryagin's maximum principle to construct a Hamiltonian function which minimizes the spread of the bad biomass. Numerical simula…
Collective motion is an intriguing phenomenon, especially considering that it arises from a set of simple rules governing local interactions between individuals. In theoretical models, these rules are normally \emph{assumed} to take a particular form, possibly constrained by heuristic arguments. We propose a new class of models, which describe the individuals as \emph{agents}, capable of deciding for themselves how to act and learning from their experiences. The local interaction rules do not need to be postulated in this model, since they \emph{emerge} from the learning process. We apply this…
The state of the art of epidemic modelling in terrestrial ecosystems is the compartmental SIR model and its extensions from the now classical work of Kermack-Mackendrick. In contrast, epidemic modelling of marine ecosystems is a bit behind, and compartmental models have been introduced only recently. One of the reasons is that many epidemic processes in terrestrial ecosystems can be described through a contact process, while modelling marine epidemics is more subtle in many cases. Here we present a model describing disease outbreaks caused by parasites in bivalve populations. The SIRP model is…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births and deaths are negligible. This phenomenon is particularly prevalent in populations of larger, vertebrate animals who often reproduce only once per year or less. To understand spatial arrangements of animal communities on such timescales, we use a class of diffusion-taxis equations for modelling inter-population movement responses between $N \ge…
Statistical averaging and asynchronous population dynamics as portfolio mechanisms are considered as the most important processes with which biodiversity contributes to ecosystem stability. However, portfolio theories usually regard biodiversity as a fixed property, but overlook the dynamics of biodiversity altered by other ecosystem components. Here, we proposed a new mechanistic food chain model with nutrient-diversity feedback to investigate how dynamics of phytoplankton species diversity determines ecosystem stability. Our model focuses on nutrient, community biomass of phytoplankton and z…
While much has been learnt about the impacts of specific stressors on individual marine organisms, considerable debate exists over the nature and impact of multiple simultaneous stressors on both individual species and marine ecosystems. We describe a modelling tool (OSIRIS) for integrating the effects of multiple simultaneous stressors. The model is relatively computationally light, and demonstrated using a coarse-grained, non-spatial and simplified representation of a temperate marine ecosystem. This version is capable of reproducing a wide range of dynamic responses.Results indicate the deg…
The vulnerability to trawling on a species level is determined by a species' individual combination of biological traits that is related to the ecosystem functions. Trait-based indices of physical resistance RI and reproductive potential RPI were developed and combined into an overall vulnerability index on a species level, the RRI or Resistance and Reproductive Potential Index. The indices are used to explore how resistance and reproductive potentia change over a trawling gradient. The RRI allows for dividing the benthic community into groups expressing different levels of vulnerability that …
Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief overview of our recent effort that investigated various aspects of such morphogenetic collective systems. We first propose a theoretical classification scheme that distinguishes four complexity levels of morphogenetic collective systems based on the nature of their components and interactions. We conducted a series of computational experiments using a self-…
