The growth of the human population and its standard of living leads to overexploitation of land and oceans, disrupting the global climate and leading species to extinction. The ecological responses to these disturbances are inevitably complex and require measures which allow them to be accurately described. Collectively, these measures assess the overall "stability" of ecological systems. Both disturbances to natural systems and the concept of stability are multidimensional. On the other hand, our understanding of these is not. This means that we have a remarkably poor understanding of the effects of different characteristics of the ongoing planetary changes on ecological stability.

The fragmented and one-dimensional approach adopted by environmentalists has led to ambiguities about the nature of stability as well as a clear disconnection between the theoretical and empirical literature on the subject (Donohue et al. 2016). Most of the theoretical work in ecology has been interested in the local asymptotic stability of ecological systems in the vicinity of an equilibrium and generally quantified this form of stability by the “resilience” of a system (Donohue et al. 2016, Kéfi et al. al. 2019), i.e. by the speed of its asymptotic return to equilibrium as given by the dominant value of the community matrix (May 1973). Most empirical studies, on the other hand, have used more practical measures of stability, such as the inverse of the coefficient of variation over time of the variables studied (Tilman et al. 2006, Hector et al. 2010).

A first question that arises is that of the relationship between the different stability measures used in ecology (Donohue et al. 2013): which metrics are redundant between them and which ones contain different information? In recent years, work has started to elucidate the relationships between certain stability metrics (Arnoldi et al. 2016, 2018, Arnoldi and Haegeman 2016, Dominguez-Garcia et al. 2019).

Another question is that of the relationships between biodiversity and different measures of stability, as well as the mechanisms responsible for these relationships. Recent empirical research has shown that biodiversity can indeed increase or decrease stability, depending on the measure of stability considered (e.g., resistance and variability) (Pennekamp et al. 2018).

The disturbances are also multidimensional. A recent study has shown that the type of disturbance can modify the relationship between biodiversity and stability. For example, even considering a single metric of stability, a change in biodiversity can increase or decrease the temporal invariability depending on whether the disturbance mainly affects the most abundant or least abundant species within a community (Arnoldi et al. 2019). Likewise, the type of habitat loss that affects food webs can increase or decrease their stability, as measured by the temporal variability of populations (McWilliams et al. 2019). If habitat is contiguously or correlated (i.e., large portions of habitat are lost while others remain intact), population variability increases. On the contrary, if habitat is lost at random in a given landscape, the variability of populations decreases.

In addition, most of the research on the relationships between biodiversity and ecosystem stability has been conducted primarily at the local level. However, the loss of biodiversity considerably reduces a number of ecosystem services by altering the functioning and stability of ecosystems at large temporal and spatial scales, which are most relevant for conservation and management (Gonzalez et al. In press, Isbell et al. 2015). A new theoretical study shows that biodiversity is becoming increasingly important for the functioning of ecosystems at larger spatial scales (Thompson et al. 2018). Likewise, the sign and intensity of the relationships between biodiversity and ecological stability change from one spatial scale to another. In particular, the temporal stability of a population or an ecosystem increases with the spatial scale (Wang and Loreau 2016, Wang et al. 2017, Delsol et al. 2018).

The objective of this GDR on this subject is threefold:
(1) establish the theoretical links between the different dimensions of stability in the face of different types of disturbances;
(2) develop theoretical models to study and better understand the relationships between the stability of ecosystems and their biodiversity;
(3) link this new theory to the experiments underway in France.

The concepts and models linking local dynamics and regional dynamics are defined by means of the prefix “meta-”, by analogy with the first of them, metapopulation (population of populations). A metapopulation (Levins 1970) is a spatial network where each node can host a population of an organism (Hanski and Gilpin 1997). By extension, a metacommunity designates a spatial network where each node can host a community (Leibold et al. 2004). When these species are structured, either as a food web, or more generally as an ecosystem, we will also speak of a meta-network or a metaecosystem (Loreau et al. 2003, Massol et al. 2011). The "meta" approach aims to answer classic questions such as the stability or coexistence of species within communities, but also more applied questions, such as the functioning of ecosystems, the emerging topology of interaction networks. and conservation biology. The concepts of metacommunity and meta-ecosystem have produced great advances in the understanding of the structuring of ecological systems at different spatial scales and are able to generate predictions of testable patterns in natura (Leibold et al. 2004, Logue et al. 2011).

Over the past five years, the "Metacommunities" working group within the GDR TheoMoDive has regularly brought together a highly active community, particularly around new approaches and interfaces with other disciplines (e.g. use of qualitative models for predict the possible states of communities on a dynamic landscape). The scope of the "meta" approach has greatly diversified, exploring the fields of the spatial ecology of food webs, ecosystem functioning and biogeography. A spatial approach to the functioning of ecosystems based on theories and concepts related to metacommunities and meta-ecosystems has thus found its place in the landscape of scientific ecology. For example, considering the dynamics of nutrient recycling no longer at the local scale, but at the scale of a meta-ecosystem, taking into account the flows of detritus and nutrients, leads to more theories and predictions. rich on the dynamics of these systems (Gravel et al. 2010a, 2010b, Gounand et al. 2014, Marleau et al. 2015), as well as the integration of food webs in a spatially structured system (Rooney et al. 2008, Gravel et al. 2011, Calcagno et al. 2011, Pillai et al. 2011). In addition, metacommunity approaches are beginning to integrate the genetic evolution of species (Urban et al. 2008). For example, the evolution of species can affect local competitive hierarchies and therefore niche effects according to the “monopolization” hypothesis (De Meester et al. 2002), or even modulate the effects of climate change on biodiversity via an evolution of the niche of competitively interacting species (Norberg et al. 2012).

The objective of this working group for the next five years will be to coordinate and stimulate theoretical research carried out in France in the field of metacommunities and meta-ecosystems in order to improve understanding of the spatial dynamics of biodiversity, food webs, ecosystem functioning, species evolution and the effects of global change. More specifically, we plan to support two particularly significant questions in the ecology of spatialized systems.

1. The effects of processes at work in meta-ecosystems on the structure and functioning of landscapes subjected to anthropogenic disturbances

In the context of global change, ecosystem transformations and the destruction of natural habitats have progressed considerably over the past three centuries. These changes in the environment are major factors in the current biodiversity crisis and the decline in ecosystem services (Fahrig 2003, Gonzalez et al. 2009). The spatially implicit framework proposed by "meta" approaches makes it possible to address the dynamics of such changes in fragmented habitats and thus to produce methodological tools adapted to conservation issues. For example, the ecology of metapopulations has allowed the emergence of concepts of minimum size and capacity for the viability of metapopulations (Lande 1987, Ovaskainen and Hanski 2001). The objective of the working group will thus be to bring out new theoretical work extending this approach to meta-ecosystems and taking into account a spatially explicit framework, e.g. via ecosystem networks or via continuous space approaches (partial differential equations); this extension of spatial ecology to the ecosystem level will make it possible in particular to explore how the dynamics of biological communities interact with the spatial heterogeneity of nutrients, how this interaction contributes to the maintenance of biodiversity, and how it modulates the response of biodiversity to anthropogenic disturbances.

2. The effects of planetary changes (in particular, climate change) on the distribution of interacting species, at ecological and evolutionary time scales.

The combination of ecological and evolutionary forces that determine the local coexistence of species and extrinsic limits to dispersal shape the present and future distribution of species. Classical approaches (SDM) predict changes in the distribution of species based on their niche and climate projections, but neglect the dynamics of interaction with other species (e.g: predation, facilitation, co-evolution) and with the environment (ex: niche construction, adaptation). The integration of these aspects in biogeography via the meta-ecosystem approach and the incorporation of evolutionary dynamics in meta-ecosystems will make it possible to refine these predictions by identifying the main mechanisms of the extinction-colonization dynamics at the borders of the distributions of species.

Ecology and evolution have long remained separate disciplines. The study of the dynamics of communities or food webs is often complex enough not to add an evolutionary component; conversely, in evolutionary biology, the dynamics of populations and communities are often ignored or simplified, in particular, in the case of theoretical models, to allow a mathematical analysis.
Recently, however, connections between ecology and evolution have multiplied. In France, in particular, this thematic merger has resulted in a visible rapprochement of communities of researchers in ecology and evolution through the change of the French Society of Ecology (sfe) into the French Society of Ecology and Evolution (sfe2) and a series of workshops, such as the Symposium `` At the border between ecology and evolution '', organized by Sfe2 and LabEx CeMEB in Montpellier.

The role of evolving ecology and the role of evolution in ecology are therefore increasingly taken into account, in line with historical models in evolutionary ecology. These models were particularly interested in feedbacks between demography and evolution (single-species models), the effect of spatial structure, but also interactions between species (competition, predation, parasitism, mutualism) and between communities (Govaert et al. 2019). Models explicitly representing interactions with the environment can also include eco-evolutionary dynamics (e.g. Estrela et al. 2019).

These models, however, are most often fairly simple and include little biodiversity (often only two or three species are modelled by a system of ordinary differential equations), although there are exceptions (Govaert et al. 2019). It is therefore high time to ask in a more concrete way the question of how evolution affects the dynamics of biodiversity. This question is particularly relevant since most of the global changes that directly threaten biodiversity and the functioning of ecosystems are also important selective forces.
It is therefore necessary to develop powerful approaches that allow us to understand the functioning of ecosystems in an evolutionary context. In their review article, Govaert et al. (2019) recommend in particular integrating more realism into eco-evolutionary models (for example, to consider the effect of plasticity or the structure of populations), but also to adopt mechanistic approaches, in particular by explicitly considering interactions between individuals (instead of phenomenological approaches). Another methodological challenge is to consider eco-evolutionary dynamics occurring on comparable time scales, instead of the temporal decoupling (useful for mathematical analysis) traditionally assumed.

The aim of the GDR is to coordinate theoretical developments, to create a network of researchers and to organize workshops on this topic. This theme can also be considered as cross-cutting within the GDR, with development issues affecting all subjects.

The coupling of theoretical models and empirical data makes it possible to strengthen our understanding of ecological processes by contrasting alternative ecological hypotheses formalized mathematically and by proposing a theoretical framework for the interpretation of ecological data. Nevertheless, although the first ecological theories relied heavily on empirical data (Kingsland 1995), a divide between theory and data has developed over the years, particularly during the second half of the last century. This has led to a specialization and a gap between theoretical ecologists, living in a world of Lotka-Volterra models and others, and specialists in field or experimental studies. Overcoming this cleavage would enrich models and theories by making them more realistic and strengthen empirical approaches by providing them with a theoretical framework with hypotheses to be tested. Faced with this observation, efforts have been made and the cleavage has been greatly reduced in recent years (Kendall 2015), which offers substantial opportunities for theorists to make more predictive theoretical models (Dietze et al. 2018) and thus increase our ability to falsify theoretical predictions. Moreover, beyond the production of hypotheses explaining the phenomena, the theory plays an important role in the clarification of the concepts and the meaning of the measured quantities, i.e., the theory makes it possible to verify that what one measures is what we want to measure (e.g Berlow et al. 2004). As part of the GDR, it is therefore natural to focus on approaches that allow better coupling between theory and data.


A promising approach is the development of methods for estimating the parameters of mechanistic models from experimental data such as time series (Ionides et al. 2006, Rosenbaum et al. 2019, Pennekamp et al. 2019). These approaches make it possible to calibrate theoretical models in order to then test their predictive power or to contrast various hypotheses on the functioning of a system, for example to explain fluctuations in the abundance of species (e.g. Kendall et al. 2005). Inference methods are used to fit systems of differential equations to time series derived from laboratory experiments or empirical data (Ellner et al. 2002, Rosenbaum and Rall 2018). The use of these methods is facilitated by the increase in the digital computing power of computers and opens up real prospects for theory-data coupling. Nevertheless, many questions remain, in particular on:
- the ability of the methods to recover the parameters of the theoretical models (i.e., identifiability);
- the type of data to be collected in the field;
- the architecture of the models to be adjusted to the data.
A particularly relevant project is the development of methods which make it possible to combine the non-linearity of ecological processes with stochasticity, which is omnipresent in ecology (e.g., Ionides et al. 2006).

As part of the study of the coexistence of competing plant species, a use of theory well connected to the data has shown both which quantities to measure in the field (Hart et al. 2018), which mechanistic models to adjust data to contrast ecological hypotheses (Adler et al. 2010), and how to reconcile the apparently contradictory results of experiments with those of in situ measurements (Tuck et al. 2018).

These few examples show that the links between theory and data apply to a set of thematic fields, hence the transversal aim of this axis in the GDR. The thematic working group devoted to this theme intends to focus its reflection on the issues of connection to empirical data, beyond the simple data-model adjustment, in particular through discussions and review articles. By bringing together ecologists of different backgrounds around the use of data in theoretical ecology, this activity of the GDR will make it possible to seek the consensus on which ecologists can agree and to explore the approaches which make it possible to strengthen the links between theory and data.

It is not common to question the laws of ecology; Yet this is exactly what this working theme is proposing within the GDR. What do we mean by that? A detour through neighbouring disciplines can enlighten us. With at least four centuries of hindsight, physics has a long tradition of perfecting laws, making it possible to explain in a reliable and universal way (by definition, proven and without exception) its phenomena (Barberousse et al. 2000, Hartmann and Frigg 2005). This is not the case with ecology and evolutionary sciences, and even with proven principles (by definition, which are not questioned) of theories (sets of principles) such as natural selection or Mendelian laws are still much debated (Mayr 2004, Morange 2017). Of course, models regularly challenge accepted principles and test their associated hypotheses (Israel 1996, Hartmann and Frigg 2005).

Biology is readily quite reductionist, ecology, more holistic, sometimes seeks universal laws (Hubbell 2001, Brown et al. 2002, Gaucherel 2013) and continually questions the reliability of the principles that it brings to light, even on the universality of the theories which could result from it. Whether or not it is believed that there are laws in ecology or not, several interesting corollary questions emerge from this question. For example, one is entitled to ask whether a law should relate to mechanisms (processes) or reasons (patterns)? Because while physical laws are generally based on mechanisms, some of them (e.g. gravitation) often resemble patterns and retain a phenomenological flavour (e.g. fractals and allometries). Some even question what the mechanisms are and what any causal explanation is worth (Israel 1996, Barberousse et al. 2000). And when ecology highlights allometric laws, it is part of this same tradition (Brown et al. 2002, Hatton et al. 2015). In addition, some laws are purely statistical (e.g. law of large numbers), far from any mechanism (Frank 2009).

And if ecologists highlighted a law in their field, would it have ecological specificities? In particular, biology and ecology all know the importance of scales and levels of organization in living things. Would an ecological law be affiliated with a particular level of organisation? Certain laws well known to ecologists attempt to explain the distribution of species, either by chance (Hubbell 2001) or by other observed regularities (Neill and Gignoux 2008, Tilman 2011). Several of them link several ecological compartments or several levels of organisation between them (Hardin 1960, MacArthur and Wilson 1963, Tilman 2011). Can these principles be considered as laws? We can guess that the status of such laws will not be similar to that of physical laws which appear, in the eyes of biologists, much more robust and universal (Putnam 1975, Gaucherel 2013). What exceptions, what variations, in these ecological laws, are we ready to accept? And further, how to manage the contradictions or the possible interactions between ecological laws?



Ecology does not have to follow the path of physics or chemistry, but it is entitled to be inspired by them. It can also be inspired by all related disciplines, from physics (Brown et al. 2002, Neill and Gignoux 2008), to economics, including linguistics (Gaucherel 2019). Several recent attempts go in this direction, and a field of research illustrates this growing interest in laws in ecology. Indeed, it would be daring to claim that ecological objects and phenomena violate physical laws, such as thermodynamics, or biological laws, such as natural selection (Harte 2002). Beyond the laws themselves, it is the history of neighbouring disciplines, particularly biology, that can prove to be a source of innovation in ecology (Morange 2017). The old debates on evolution, a field which made a noticeable irruption in ecology, show that it is interesting to seek laws where, previously, one still had only a list of processes and a classification. objects.
Still, the more pragmatic would question: What would be the use of such laws? Would they be there for the sole intellectual pleasure of theorists? Or would they have a real daily utility for managers, farmers or geneticists? Would such laws help to make predictions? Many think so, and claim that a better knowledge of the mechanisms and principles associated with central objects, such as the ecosystem or the population (Hardin 1960, Tilman 2011), would undoubtedly provide assistance to those who have to manage these objects on a daily basis. still poorly understood (Gaucherel 2019). Even if it turned out that ecology does not have laws, reflecting on this question would contribute as much to basic ecology as it does to applied ecology.
As part of this transversal axis we will interact with philosophers of science and we want to design a first list of general laws by doing an online survey.


Complementarity with the GDR Statistical Ecology

The GDR Statistical Ecology aims to develop and disseminate statistical methodologies adapted to the various fields of ecology, including in particular the algorithmic aspects of the fit to data (maximum likelihood, Markov Chain Monte Carlo), data management (data citizen, ...) and conceptual of applied statistics (e.g, frequentist vs Bayesian philosophy). The GDR Theory and Modeling of Biodiversity addresses questions upstream and downstream of the use of these methodologies: which data to seize for which questions? Which statistical models also make theoretical sense / how to theoretically interpret their parameters? Are there classical empirical analyses that the theory can prove are uninterpretable? How to reduce the complexity of theoretical models to fit them to necessarily limited data? Are there ecological questions of importance to the theory that currently escape empirical analysis?