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We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.

 

Abstract Understanding the connectivity of reef organisms is important to assist in the conservation of biological diversity and to facilitate sustainable fisheries in these ecosystems. Common methods to assess reef connectivity include both population genetics and biophysical modelling. Individually, these techniques can offer insight into population structure; however, the information acquired by any singular analysis is often subject to limitations, underscoring the need for a multi-faceted approach. To assess the connectivity dynamics of the red grouper (Epinephelus morio), an economically important reef fish species found throughout the Gulf of Mexico and USA western Atlantic, we utilized two sets of genetic markers (12 microsatellite loci and 632 single nucleotide polymorphisms) to resolve this species’ population genetic structure, along with biophysical modelling to deliver a spatial forecast of potential larval “sources” and “sinks” across these same regions and spatial scale. Our genetic survey indicates little, if any, evidence of population genetic structure and modelling efforts indicate the potential for ecological connectivity between sampled regions over multiple generations. We offer that using a dual empirical and theoretical approach lessens the error associated with the use of any single method and provides an important step towards the validation of either of these methodologies. 

Throughout the Galápagos, differences in coral reef development and coral population dynamics were evaluated by monitoring populations from 2000–2019, and environmental parameters (sea temperatures, pH, NO₃⁻, PO₄³⁻) from 2015–19. The chief goal was to explain apparent coral community differences between the northern (Darwin and Wolf) and southern (Sta. Cruz, Fernandina, San Cristóbal, Española, Isabela) islands. Site coral species richness was highest at Darwin and Wolf. In the three most common coral taxa, a declining North (N)-South (S) trend in colony sizes existed forPorites lobataandPocilloporaspp., but not forPavona  spp. Frequent coral recruitment was observed in all areas. Algal competition was highest at Darwin, but competition by bioeroding sea urchins and burrowing fauna (polychaete worms, bivalve mollusks) increased from N to S with declining coral skeletal density. A biophysical model suggested strong connectivity among southern islands with weaker connectivity to Wolf and even less to Darwin. Also, strong connectivity was observed between Darwin and Wolf, but from there only intermittently to the south. From prevailing ocean current trajectories, coral larvae from Darwin and Wolf drift primarily towards Malpelo and Cocos Islands, some reaching Costa Rica and Colombia. Mean temperature, pH, and PO₄³⁻declined from N to S. Strong thermocline shoaling, especially in the warm season, was observed at most sites. A single environmental factor could not explain the variability in observed coral community characteristics, with minimum temperature, pH and nutrient levels the strongest determinants. Thus, complex environmental determinants combined with larval connectivity patterns may explain why the northern Galápagos Islands (Darwin, Wolf) have higher coral richness and cover and also recover more rapidly than central/southern islands after region-wide disturbances. These northern islands are therefore potentially of critical conservation importance as important reservoirs of regional coral biodiversity and source of larvae.