Quantitative Biology

Self-organized spatial patterns of vegetation are frequent in water-limited regions and have been suggested as important indicators of ecosystem health. However, the mechanisms underlying their emergence remain unclear. Some theories hypothesize that patterns could result from a scale-dependent feedback (SDF), whereby interactions favoring plant growth dominate at short distances and growth-inhibitory interactions dominate in the long range. However, we know little about how net plant-to-plant interactions may change sign with inter-individual distance, and in the absence of strong empirical support, the relevance of this SDF for vegetation pattern formation remains disputed. These theories predict a sequential change in pattern shape from gapped to labyrinthine to spotted spatial patterns as precipitation declines. Nonetheless, alternative theories show that the same sequence of patterns could emerge even if net interactions between plants were always inhibitory (purely competitive feedbacks, PCF). Although these alternative hypotheses lead to visually indistinguishable patterns they predict very different desertification dynamics following the spotted pattern. Moreover, vegetation interaction with other ecosystem components can introduce additional spatio-temporal scales that reshape both the patterns and the desertification dynamics. Therefore, to make reliable ecological predictions for a focal ecosystem, it is crucial that models accurately capture the mechanisms at play in the system of interest. Here, we review existing theories for vegetation self-organization and their conflicting predictions about desertification dynamics. We further discuss possible ways for reconciling these predictions and potential empirical tests via manipulative experiments to improve our understanding of how vegetation self-organizes and better predict the fate of the ecosystems where they form.

The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific Lotka Volterra (LV) equation. The link with population dynamics was obvious as logistic function and LV equation were proposed within the demography science field. Mathematical population dynamics has a history of about two centuries. The first principle and model of population dynamics can be regarded the exponential law of Malthus. In the XIX century, the Malthusian demographic model was first refined to include mortality rate by Gompertz. In the early XIX century the model was further refined by Verhulst by introducing the standard logistic function. The previous models only concern the population of a single species. In the early XX century, the American demographer Lotka and the Italian mathematician Volterra proposed a pair of state equations which describe the population dynamics of two competing species, the predator and the prey. This paper is concerned with the single and two-species fundamental equations: the logistic and LV equation. The paper starts with the generalized logistic equation whose free response is derived together with equilibrium points and stability properties. The parameter estimation of the logistic function is applied to the raw data of the US crude oil production. The paper proceeds with the Lotka Volterra equation of the competition between two species, with the goal of applying it to resource exploitation. At the end, a limiting version of the LV equation is studied since it describes a competition model between the production rate of exploited resources and the relevant capital stock employed in the exploitation.

Phylogenetic networks can model more complicated evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models that are used to model evolution on trees can also be extended to networks and similar questions, such as the identifiability of the network parameter or the invariants of the model, can be asked. In this paper we focus on finding the invariants of the Cavendar-Farris-Neyman (CFN) model on level-1 phylogenetic networks. We do this by reducing the problem to finding invariants of sunlet networks, which are level-1 networks consisting of a single cycle with leaves at each vertex. We then determine all quadratic invariants in the sunlet network ideal which we conjecture generate the full ideal.

Mediterranean ecosystems such as those found in California, Central Chile, Southern Europe, and Southwest Australia host numerous, diverse, fire-adapted micro-ecosystems. These micro-ecosystems are as diverse as mountainous conifer to desert-like chaparral communities. Over the last few centuries, human intervention, invasive species, and climate warming have drastically affected the composition and health of Mediterranean ecosystems on almost every continent. Increased fuel load from fire suppression policies and the continued range expansion of non-native insects and plants, some driven by long-term drought, produced the deadliest wildfire season on record in 2018. As a consequence of these fires, a large number of structures are destroyed, releasing household chemicals into the environment as uncontrolled toxins. The mobilization of these materials can lead to health risks and disruption in both human and natural systems. This article identifies drivers that led to a structural weakening of the mosaic of fire-adapted ecosystems in California, and subsequently increased the risk of destructive and explosive wildfires throughout the state. Under a new climate regime, managing the impacts on systems moving out-of-phase with natural processes may protect lives and ensure the stability of ecosystem services.

A novel coronavirus disease (COVID-19) is sweeping the world and has taken away thousands of lives. As the current epicenter, the United States has the largest number of confirmed and death cases of COVID-19. Meteorological factors have been found associated with many respiratory diseases in the past studies. In order to understand that how and during which period of time do the meteorological factors have the strongest association with the transmission and fatality of COVID-19, we analyze the correlation between each meteorological factor during different time periods within the incubation window and the confirmation and fatality rate, and develop statistic models to quantify the effects at county level. Results show that meteorological variables except maximum wind speed during the day 13 - 0 before current day shows the most significant correlation (P < 0.05) with the daily confirmed rate, while temperature during the day 13 - 8 before are most significantly correlated (P < 0.05) with the daily fatality rate. Temperature is the only meteorological factor showing dramatic positive association nationally, particularly in the southeast US where the current outbreak most intensive. The influence of temperature is remarkable on the confirmed rate with an increase of over 5 pmp in many counties, but not as much on the fatality rate (mostly within 0.01%). Findings in this study will help understanding the role of meteorological factors in the spreading of COVID-19 and provide insights for public and individual in fighting against this global epidemic.

We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer" model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations.

B cell receptor sequences diversify through mutations introduced by purpose-built cellular machinery. A recent paper has concluded that a "templated mutagenesis" process is a major contributor to somatic hypermutation, and therefore immunoglobulin diversification, in mice and humans. In this proposed process, mutations in the immunoglobulin locus are introduced by copying short segments from other immunoglobulin genes. If true, this would overturn decades of research on B cell diversification, and would require a complete re-write of computational methods to analyze B cell data for these species. In this paper, we re-evaluate the templated mutagenesis hypothesis. By applying the original inferential method using potential donor templates absent from B cell genomes, we obtain estimates of the methods's false positive rates. We find false positive rates of templated mutagenesis in murine and human immunoglobulin loci that are similar to or even higher than the original rate inferences, and by considering the bases used in substitution we find evidence that if templated mutagenesis occurs, it is at a low rate. We also show that the statistically significant results in the original paper can easily result from a slight misspecification of the null model.

Phylogenetic trees are important tools in the study of evolutionary relationships between species. Measures such as the index of Sackin, Colless, and Total Cophenetic have been extensively used to quantify tree balance, one key property of phylogenies. Recently a new proposal has been introduced, based on the spectrum of the Laplacian matrix associated with the tree. In this work, we calculate the Laplacian matrix analytically for two extreme cases, corresponding to fully balanced and fully unbalanced trees. For maximally balanced trees no closed form for the Laplacian matrix was derived, but we present an algorithm to construct it. We show that Laplacian matrices of fully balanced trees display self-similar patterns that result in highly degenerated eigenvalues. Degeneracy is the main signature of this topology, since it is totally absent in fully unbalanced trees. We also establish some analytical and numerical results about the largest eigenvalue of Laplacian matrices for these topologies.

Collective migration of cells and animals often relies on a specialised set of "leaders", whose role is to steer a population of naive followers towards some target. We formulate a continuous model to understand the dynamics and structure of such groups, splitting a population into separate follower and leader types with distinct orientation responses. We incorporate "leader influence" via three principal mechanisms: a bias in the orientation of leaders according to the destination, distinct speeds of movement and distinct levels of conspicuousness. Using a combination of analysis and numerical computation on a sequence of models of increasing complexity, we assess the extent to which leaders successfully shepherd the swarm. While all three mechanisms can lead to a successfully steered swarm, parameter regime is crucial with non successful choices generating a variety of unsuccessful attempts, including movement away from the target, swarm splitting or swarm dispersal.

Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g., the "tragedy of the commons"), modulate their behaviors to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Utilizing evolutionary game theory and stochastic games, we develop a game-theoretical framework that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviors can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favored over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social-ecological dilemmas, learning enables the adaptation of individuals to varying environments.