The challenge of selecting an appropriate soil organic carbon simulation model: A comprehensive global review and validation assessment.

Promotion of soil organic carbon (SOC) sequestration as a potential solution to support climate change mitigation as well as more sustainable farming systems is rising steeply. As a result, voluntary carbon markets are rapidly expanding in which farmers get paid per tons of carbon dioxide sequestered. This market relies on protocols using simulation models to certify that increases in SOC stocks do indeed occur and generate tradable carbon credits. This puts tremendous pressure on SOC simulation models, which are now expected to provide the foundation for a reliable global carbon credit generation system. There exist an incredibly large number SOC simulation models which vary considerably in their applicability and sensitivity. This confronts practitioners and certificate providers with the critical challenge of selecting the models that are appropriate to the specific conditions in which they will be applied. Model validation and the context of said validation define the boundaries of applicability of the model, and are critical therefore to model selection. To date, however, guidelines for model selection are lacking. In this review, we present a comprehensive review of existing SOC models and a classification of their validation contexts. We found that most models are not validated (71%), and out of those validated, validation contexts are overall limited. Validation studies so far largely focus on the global north. Therefore, countries of the global south, the least emitting countries that are already facing the most drastic consequences of climate change, are the most poorly supported. In addition, we found a general lack of clear reporting, numerous flaws in model performance evaluation, and a poor overall coverage of land use types across countries and pedoclimatic conditions. We conclude that, to date, SOC simulation does not represent an adequate tool for globally ensuring effectiveness of SOC sequestration effort and ensuring reliable carbon crediting.

Strong neutral sweeps occurring during a population contraction.

A strong reduction in diversity around a specific locus is often interpreted as a recent rapid fixation of a positively selected allele, a phenomenon called a selective sweep. Rapid fixation of neutral variants can however lead to a similar reduction in local diversity, especially when the population experiences changes in population size, e.g. bottlenecks or range expansions. The fact that demographic processes can lead to signals of nucleotide diversity very similar to signals of selective sweeps is at the core of an ongoing discussion about the roles of demography and natural selection in shaping patterns of neutral variation. Here, we quantitatively investigate the shape of such neutral valleys of diversity under a simple model of a single population size change, and we compare it to signals of a selective sweep. We analytically describe the expected shape of such "neutral sweeps" and show that selective sweep valleys of diversity are, for the same fixation time, wider than neutral valleys. On the other hand, it is always possible to parametrize our model to find a neutral valley that has the same width as a given selected valley. Our findings provide further insight into how simple demographic models can create valleys of genetic diversity similar to those attributed to positive selection.

Gene surfing of underdominant alleles promotes formation of hybrid zones.

The distribution of genetic diversity over geographical space has long been investigated in population genetics and serves as a useful tool to understand evolution and history of populations. Within some species or across regions of contact between two species, there are instances where there is no apparent ecological determinant of sharp changes in allele frequencies or divergence. To further understand these patterns of spatial genetic structure and potential species divergence, we model the establishment of clines that occur due to the surfing of underdominant alleles during range expansions. We provide analytical approximations for the fixation probability of underdominant alleles at expansion fronts and demonstrate that gene surfing can lead to clines in one-dimensional range expansions. We extend these results to multiple loci via a mixture of analytical theory and individual-based simulations. We study the interaction between the strength of selection against heterozygotes, migration rates, and local recombination rates on the formation of stable hybrid zones. Clines created by surfing at different loci can attract each other and align after expansion, if they are sufficiently close in space and in terms of recombination distance. Our findings suggest that range expansions can set the stage for parapatric speciation due to the alignment of multiple selective clines, even in the absence of ecologically divergent selection. This article is part of the theme issue 'Species' ranges in the face of changing environments (part I)'.

Generalized voterlike model on activity-driven networks with attractiveness.

We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity-driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity a, ruling the rate at which they generate connections, and an intrinsic attractiveness b, modulating the rate at which they receive connections. The consensus dynamics considered is a mixed voter and Moran dynamics. Each agent, either in state 0 or 1, modifies his or her state when connecting with a peer. Thus, an active agent copies his or her state from the peer (with probability p) or imposes his or her state to him or her (with the complementary probability 1-p). Applying a heterogeneous mean-field approach, we derive a differential equation for the average density of voters with activity a and attractiveness b in state 1, which we use to evaluate the average time to reach consensus and the exit probability, defined as the probability that a single agent with activity a and attractiveness b eventually imposes his or her state to a pool of initially unanimous population in the opposite state. We study a number of particular cases, finding an excellent agreement with numerical simulations of the model. Interestingly, we observe a symmetry between voter and Moran dynamics in pure activity-driven networks and their static integrated counterparts that exemplifies the strong differences that a time-varying network can impose on dynamical processes.

Effect of risk perception on epidemic spreading in temporal networks.

Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties, including complex and temporal interaction networks. Moreover, a number of recent studies have started to go beyond the assumption of an absence of coupling between the spread of a disease and the structure of the contacts on which it unfolds. Models including awareness of the spread have been proposed, to mimic possible precautionary measures taken by individuals that decrease their risk of infection, but have mostly considered static networks. Here, we adapt such a framework to the more realistic case of temporal networks of interactions between individuals. We study the resulting model by analytical and numerical means on both simple models of temporal networks and empirical time-resolved contact data. Analytical results show that the epidemic threshold is not affected by the awareness but that the prevalence can be significantly decreased. Numerical studies on synthetic temporal networks highlight, however, the presence of very strong finite-size effects, resulting in a significant shift of the effective epidemic threshold in the presence of risk awareness. For empirical contact networks, the awareness mechanism leads as well to a shift in the effective threshold and to a strong reduction of the epidemic prevalence.

Aging and percolation dynamics in a Non-Poissonian temporal network model.

We present an exhaustive mathematical analysis of the recently proposed Non-Poissonian Activity Driven (NoPAD) model [Moinet et al., Phys. Rev. Lett. 114, 108701 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.108701], a temporal network model incorporating the empirically observed bursty nature of social interactions. We focus on the aging effects emerging from the non-Poissonian dynamics of link activation, and on their effects on the topological properties of time-integrated networks, such as the degree distribution. Analytic expressions for the degree distribution of integrated networks as a function of time are derived, exploring both limits of vanishing and strong aging. We also address the percolation process occurring on these temporal networks, by computing the threshold for the emergence of a giant connected component, highlighting the aging dependence. Our analytic predictions are checked by means of extensive numerical simulations of the NoPAD model.

Burstiness and aging in social temporal networks.

The presence of burstiness in temporal social networks, revealed by a power-law form of the waiting time distribution of consecutive interactions, is expected to produce aging effects in the corresponding time-integrated network. Here, we propose an analytically tractable model, in which interactions among the agents are ruled by a renewal process, that is able to reproduce this aging behavior. We develop an analytic solution for the topological properties of the integrated network produced by the model, finding that the time translation invariance of the degree distribution is broken. We validate our predictions against numerical simulations, and we check for the presence of aging effects in a empirical temporal network, ruled by bursty social interactions.