Dynamics of a stochastic population model with Allee effect and jumps

This paper is concerned with a stochastic population model with Allee effect and jumps. First, we show the global existence of almost surely positive solution to the model. Next, exponential extinction and persistence in mean are discussed. Then, we investigated the global attractivity and stability in distribution. At last, some numerical results are given. The results show that if attack rate $a$ is in the intermediate range or very large, the population will go extinct. Under the premise that attack rate $a$ is less than growth rate $r$, if the noise intensity or jump is relatively large, the population will become extinct; on the contrary, the population will be persistent in mean. The results in this paper generalize and improve the previous related results.

A Quasar-based Supermassive Black Hole Binary Population Model: Implications for the Gravitational Wave Background

The nanohertz gravitational wave background (GWB) is believed to be dominated by GW emission from supermassive black hole binaries (SMBHBs). Observations of several dual-active galactic nuclei (AGN) strongly suggest a link between AGN and SMBHBs, given that these dual-AGN systems will eventually form bound binary pairs. Here we develop an exploratory SMBHB population model based on empirically constrained quasar populations, allowing us to decompose the GWB amplitude into an underlying distribution of SMBH masses, SMBHB number density, and volume enclosing the GWB. Our approach also allows us to self-consistently predict the number of local SMBHB systems from the GWB amplitude. Interestingly, we find the local number density of SMBHBs implied by the common-process signal in the NANOGrav 12.5-yr data set to be roughly five times larger than previously predicted by other models. We also find that at most ∼25% of SMBHBs can be associated with quasars. Furthermore, our quasar-based approach predicts ≳95% of the GWB signal comes from z ≲ 2.5, and that SMBHBs contributing to the GWB have masses ≳108 M ⊙. We also explore how different empirical galaxy–black hole scaling relations affect the local number density of GW sources, and find that relations predicting more massive black holes decrease the local number density of SMBHBs. Overall, our results point to the important role that a measurement of the GWB will play in directly constraining the cosmic population of SMBHBs, as well as their connections to quasars and galaxy mergers.

Modeling CRISPR gene drives for suppression of invasive rodents using a supervised machine learning framework

Invasive rodent populations pose a threat to biodiversity across the globe. When confronted with these invaders, native species that evolved independently are often defenseless. CRISPR gene drive systems could provide a solution to this problem by spreading transgenes among invaders that induce population collapse, and could be deployed even where traditional control methods are impractical or prohibitively expensive. Here, we develop a high-fidelity model of an island population of invasive rodents that includes three types of suppression gene drive systems. The individual-based model is spatially explicit, allows for overlapping generations and a fluctuating population size, and includes variables for drive fitness, efficiency, resistance allele formation rate, as well as a variety of ecological parameters. The computational burden of evaluating a model with such a high number of parameters presents a substantial barrier to a comprehensive understanding of its outcome space. We therefore accompany our population model with a meta-model that utilizes supervised machine learning to approximate the outcome space of the underlying model with a high degree of accuracy. This enables us to conduct an exhaustive inquiry of the population model, including variance-based sensitivity analyses using tens of millions of evaluations. Our results suggest that sufficiently capable gene drive systems have the potential to eliminate island populations of rodents under a wide range of demographic assumptions, though only if resistance can be kept to a minimal level. This study highlights the power of supervised machine learning to identify the key parameters and processes that determine the population dynamics of a complex evolutionary system.

The PAU survey: measurement of narrow-band galaxy properties with approximate bayesian computation

Narrow-band imaging surveys allow the study of the spectral characteristics of galaxies without the need of performing their spectroscopic follow-up. In this work, we forward-model the Physics of the Accelerating Universe Survey (PAUS) narrow-band data. The aim is to improve the constraints on the spectral coefficients used to create the galaxy spectral energy distributions (SED) of the galaxy population model in Tortorelli et al. 2020. In that work, the model parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) data using Approximate Bayesian Computation (ABC). This led to stringent constraints on the B-band galaxy luminosity function parameters, but left the spectral coefficients only broadly constrained. To address that, we perform an ABC inference using CFHTLS and PAUS data. This is the first time our approach combining forward-modelling and ABC is applied simultaneously to multiple datasets. We test the results of the ABC inference by comparing the narrow-band magnitudes of the observed and simulated galaxies using Principal Component Analysis, finding a very good agreement. Furthermore, we prove the scientific potential of the constrained galaxy population model to provide realistic stellar population properties by measuring them with the SED fitting code CIGALE. We use CFHTLS broad-band and PAUS narrow-band photometry for a flux-limited (i < 22.5) sample of galaxies up to redshift z ∼ 0.8. We find that properties like stellar masses, star-formation rates, mass-weighted stellar ages and metallicities are in agreement within errors between observations and simulations. Overall, this work shows the ability of our galaxy population model to correctly forward-model a complex dataset such as PAUS and the ability to reproduce the diversity of galaxy properties at the redshift range spanned by CFHTLS and PAUS.

Global stability of an age-structured population model on several temporally variable patches

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number $$R_0$$ R 0 for time-independent and periodical models and establish the permanence dichotomy: if $$R_0\le 1$$ R 0 ≤ 1 , extinction on all patches is imminent, and if $$R_0>1$$ R 0 > 1 , permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.