New Insights to Compare and Choose TKTD Models for Survival Based on an Interlaboratory Study for Lymnaea stagnalis Exposed to Cd.

Toxicokinetic-toxicodynamic (TKTD) models, as the General Unified Threshold model of Survival (GUTS), provide a consistent process-based framework compared to classical dose-response models to analyze both time and concentration-dependent data sets. However, the extent to which GUTS models (Stochastic Death (SD) and Individual Tolerance (IT)) lead to a better fitting than classical dose-response model at a given target time (TT) has poorly been investigated. Our paper highlights that GUTS estimates are generally more conservative and have a reduced uncertainty through smaller credible intervals for the studied data sets than classical TT approaches. Also, GUTS models enable estimating any x% lethal concentration at any time (LCx,t), and provide biological information on the internal processes occurring during the experiments. While both GUTS-SD and GUTS-IT models outcompete classical TT approaches, choosing one preferentially to the other is still challenging. Indeed, the estimates of survival rate over time and LCx,t are very close between both models, but our study also points out that the joint posterior distributions of SD model parameters are sometimes bimodal, while two parameters of the IT model seems strongly correlated. Therefore, the selection between these two models has to be supported by the experimental design and the biological objectives, and this paper provides some insights to drive this choice.

Necessity of chance: biological roulettes and biodiversity.

Chance plays an important role in the dynamics of biodiversity. It is largely responsible for the spontaneous processes leading to biological diversification. The mechanisms behind chance belong to two categories: on the one hand, those outside of biological systems, and thus belonging to their environment, on the other hand, those endogenous to these systems. These last mechanisms are present at all levels of the hierarchical organization of the living world, from genes to ecosystems. We propose calling them 'biological roulettes'. Like roulettes in casinos, they could be deterministic processes functioning in chaotic domains and producing results that look as though they had been generated by random processes. The spontaneous appearance and natural selection of these roulettes have led to living systems potentially adapted to new environmental conditions not encountered before. They may even have permitted some of them to survive major upheavals. Moreover, palaeontological data show that the rate of biological diversification accelerates and that living systems become more and more complex over time. That may also increase their resilience. It can be also the consequence of the appearance and the selection of 'biological roulettes' and of chance they generate. They are at the same time products and engines of the evolution. Without them, life would have disappeared from the Earth a long time ago. Thus, they are of primary importance.

By way of introduction: modelling living systems, their diversity and their complexity: some methodological and theoretical problems.

Some principles for a current methodology for biological systems' modelling are presented. It seems possible to promote a model-centred approach of these complex systems. Among present questions, the role of mechanisms producing random or quasi-random issues is underlined, because they are implied in biological diversification and in resulting complexity of living systems. Now, biodiversity is one of our societies' and scientific research's main concerns. Basically, it can be interpreted as a manner, for Life, to resist environmental hazards. Thus, one may assume that biodiversity producing mechanisms could be selected during evolution to face to corresponding risks of disappearance: necessity of chance? Therefore, analysing and modelling these 'biological and ecological roulettes' would be important, and not only their outputs like nowadays by using the theory of probabilities. It is then suggested that chaotic behaviours generated by deterministic dynamical systems could mimic random processes, and that 'biological and ecological roulettes' would be represented by such models. Practical consequences can be envisaged in terms of biodiversity management, and more generally in terms of these 'roulettes' control to generate selected biological and ecological events' distribution.

Mass extinctions, biodiversity explosions and ecological niches.

The logistic model proposed by Courtillot and Gaudemer to describe the growth of biodiversity during geological ages is more explored here and further developed. A new parameterisation is first proposed. Another expression of this model is obtained by introducing a new variable representing the number of ecological niches. It appears that the rates of increase of biodiversity during Jurassic and Cretaceous periods is quite different from other ones. The classical literature essentially focuses on possible extinction mechanisms, but explosions in biodiversity must be more precisely explored. For this purpose, on the basis of data analysis through different expressions of the logistic model, different ecological mechanisms can be assumed (e.g., qualitative and quantitative niches changes, possible appearance of new kinds of ecological relationships, such as 'niche-sharing', which involves coexistence or cooperation), even if genetic processes must also be involved. Finally, we emphasise the astonishing speed of biological diversification following a 'catastrophic' mass extinction. We could refer to this feature as 'catastrophic biological diversification'.