Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction

When a virus spreads, it may mutate into, e.g., vaccine resistant or fast spreading lineages, as was the case for the Danish Cluster-5 mink variant (belonging to the B.1.1.298 lineage), the British B.1.1.7 lineage, and the South African B.1.351 lineage of the SARS-CoV-2 virus. A way to handle such spreads is through a containment strategy, where the population in the affected area is isolated until the spread has been stopped. Under such circumstances, it is important to monitor whether the mutated virus is extinct via massive testing for the virus sub-type. If successful, the strategy will lead to lower and lower numbers of the sub-type, and it will eventually die out. An important question is, for how long time one should wait to be sure the sub-type is extinct? We use a hidden Markov model for infection spread and an approximation of a two stage sampling scheme to infer the probability of extinction. The potential of the method is illustrated via a simulation study. Finally, the model is used to assess the Danish containment strategy when SARS-CoV-2 spread from mink to man during the summer of 2020, including the Cluster-5 sub-type. In order to avoid further spread and mink being a large animal virus reservoir, this situation led to the isolation of seven municipalities in the Northern part of the country, the culling of the entire Danish 17 million large mink population, and a bill to interim ban Danish mink production until the end of 2021.

Exploring the potential effect of COVID-19 on an endangered great ape

The current COVID-19 pandemic has created unmeasurable damages to society at a global level, from the irreplaceable loss of life, to the massive economic losses. In addition, the disease threatens further biodiversity loss. Due to their shared physiology with humans, primates, and particularly great apes, are susceptible to the disease. However, it is still uncertain how their populations would respond in case of infection. Here, we combine stochastic population and epidemiological models to simulate the range of potential effects of COVID-19 on the probability of extinction of mountain gorillas. We find that extinction is sharply driven by increases in the basic reproductive number and that the probability of extinction is greatly exacerbated if the immunity lasts less than 6 months. These results stress the need to limit exposure of the mountain gorilla population, the park personnel and visitors, as well as the potential of vaccination campaigns to extend the immunity duration.

Distribution range and population viability of Emys orbicularis in Slovakia: a review with conservation implications

The European pond turtle (Emys orbicularis) is the only native freshwater turtle species in Slovakia. Due to watercourse regulations in the middle of the 20th century, its range became fragmented and, currently, there are only two isolated populations. From a total of 1,236 historical records in Slovakia, most observations (782 records) came from the area of the Tajba National Nature Reserve (NNR). Three of the population viability analysis models (‘baseline’, ‘catastrophe’, ‘nest protection during a catastrophe’) indicated the extinction of the population in Tajba, with the highest probability of extinction occurring during a catastrophic event (probability of extinction 1.00). We also evaluated information about the activity patterns of seven radio-tracked individuals and about the number of destroyed nests from the area. During the period 2017–2021, we recorded only two turtles leaving the aquatic habitat of Tajba. An alarming fact is the massive number of destroyed nests found in the area during the study period (Tajba 524; Poľany 56). Our results indicate that the population in the Tajba NNR require immediate application of management steps to ensure its long-term survival.

Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction

When a virus spreads, it may mutate into, e.g., vaccine resistant or fast spreading sub- types, as was the case for the Danish Cluster-5 mink, the British B.1.1.7, and the South African 501Y.V2 variants of the SARS-CoV-2 virus. A way to handle such spreads is through a containment strategy, where the population in the affected area is isolated until the spread has been stopped. Under such circumstances, it is important to monitor whether the mutated virus is extinct via massive testing for the virus sub-type. If successful, the strategy will lead to lower and lower numbers of the sub-type, and it will eventually die out. An important question is, for how long time one should wait to be sure the sub-type is extinct? We use a hidden Markov model for infection spread and an approximation of a two stage sampling scheme to infer the probability of extinction. The potential of the method is illustrated via a simulation study. Finally, the model is used to assess the Danish containment strategy when SARS-CoV-2 spread from mink to man during the summer of 2020, including the Cluster-5 sub-type. In order to avoid further spread and mink being a large animal virus reservoir, this situation led to the isolation of seven municipalities in the Northern part of the country, the culling of the entire Danish 17 million large mink population, and a bill to interim ban Danish mink production until the end of 2021.

Hybridization and the coexistence of species

It is thought that two species can coexist if they use different resources present in the environment, yet this assumes that species are completely reproductively isolated. Closely related species often interbreed, raising the question of how this might affect coexistence. We model coexistence outcomes for two sympatric species that are ecologically differentiated but have incomplete reproductive isolation. Results show that the consequences of interbreeding depend crucially on hybrid fitness. When hybrid fitness is high, just a small rate of hybridization can lead to collapse of two species into one. Low hybrid fitness can cause population declines, making extinction of one or both species likely. The intrinsic growth rate of the population has an important influence on the outcome. High intrinsic growth rates result in higher reproductive rates when populations are below carrying capacity, reducing the probability of extinction and increasing the likelihood of stable coexistence at moderate levels of assortative mating and hybrid fitness. Very strong but incomplete assortative mating can induce low hybrid fitness via a mating disadvantage to rare genotypes, and this can stabilize coexistence of two species at high but incomplete levels of assortative mating. Given these results and evidence that it may take many millions of years of divergence before related species become sympatric, we postulate that coexistence of closely-related species is more often limited by insufficient assortative mating than by insufficient ecological differentiation.

Equity and Sustainability: An Exposition

The paper is an exposition of some issues involving sustainability of equitable (stationary) plans in infinite horizon models. We consider examples of deterministic as well as stochastic models. The models provide conditions on the possibility, inevitability or probability of extinction or collapse.

Über die Wahrscheinlichkeit des Aussterbens einer Population in einer langsamen periodischen Umgebung

International audience Wir studieren die Wahrscheinlichkeit des Aussterbens eines linearen Geburts- und Todesprozesses mit mehreren Typen in einer periodischen Umgebung, wenn die Periode groß ist. Diese Wahrscheinlichkeit hängt von der Jahreszeit ab und zeigt eine Diskontinuität im Zusammenhang mit einem "Canard" in einem langsam-schnellen dynamischen System. Der Diskontinuitätspunkt wird in einem Beispiel mit zwei Typen genau bestimmt. Dieses Beispiel kommt von einem Modell für eine Krankheit, die durch Vektoren übertragen wird. We study the probability of extinction of a population modelled by a linear birth-and-death process with several types in a periodic environment when the period is large compared to other time scales. This probability depends on the season and may present a sharp jump in relation to a "canard" in a slow-fast dynamical system. The point of discontinuity is determined precisely in an example with two types of individuals related to a vector-borne disease transmission model. On s'intéresse à la probabilité d'extinction d'un processus linéaire de naissance et de mort avec plusieurs types dans un environnement périodique dans la limite d'une période très grande. Cette probabilité dépend de la saison et peut présenter à la limite une discontinuité en lien avec un canard dans un système dynamique lent-rapide. On détermine précisément le point de discontinuité dans un exemple avec deux types d'individus provenant d'un modèle de transmission d'une maladie à vecteurs.

Native trees in Nug-as forest Key Biodiversity Area, Cebu, Philippines

Lillo EP, Malaki AB, Alcazar SMT, Redoblando BR, Diaz JLB, Pinote JP, Rosales R, Buot IE Jr. 2020. Native trees in Nug-as forest Key Biodiversity Area, Cebu, Philippines. Biodiversitas 21: 4162-4167. Threatened species, by definition, have a high probability of extinction, and so each of their populations significantly contributes to their survival. This paper presents a list of threatened Native trees in Nug-as forest of the Municipality of Alcoy, Cebu. A list of indicators was used to identify the conservation status of the Native trees at the local level. A total of 135 native trees from 48 families and 105 genera were recorded. Most species belong to the families of Euphorbiaceae, Lauraceae, Moraceae, Clusiaceae, Myrtaceae, Meliaceae, Fabaceae, and Rutaceae. In this study, 62 species were categorized as threatened, and 72 species as Least Concern, while in IUCN classification 19 threatened species were recorded, and 111 taxa considered as Least Concern respectively. Using the DENR method of classification 15 threatened species were recorded, and 115 taxa considered as Not Evaluated. The Nug-as forest was degraded by illegal cutting, kaingin, hunting and charcoal making. Based from Beynen and Townsend analysis, Nug-as forest was categorized as moderately disturbed. While DENR and IUCN declaration on the status of the Philippine native trees take a very long time, threatened plant species would be gone before we know it, considering the destruction rate in the Philippines.