Number of Source Patches Required for Population Persistence in a Source-Sink Metapopulation with Explicit Movement

The Poultry Red Mite, Dermanyssus gallinae, travels far but not frequently, and takes up permanent residence on farms

Management of Dermanyssus gallinae, a cosmopolitan hematophagous mite responsible for damage in layer poultry farming, is hampered by a lack of knowledge of its spatio-temporal population dynamics. Previous studies have shown that the circulation of this pest between farms is of strictly anthropogenic origin, that a mitochondrial haplogroup has been expanding on European farms since the beginning of the 21st century and that its local population growth may be particularly rapid. To refine our understanding of how D. gallinae spreads within and among farms, we characterized the genetic structure of mite populations at different spatial scales and sought to identify the main factors interrupting gene flow between poultry houses and between mitochondrial haplogroups. To this end, we selected and validated the first set of nuclear microsatellite markers for D. gallinae and sequenced a region of the CO1-encoding mitochondrial gene in a subsample of microsatellite-genotyped mites. We also tested certain conditions required for effective contamination of a poultry house through field experimentation, and conducted a survey of practices during poultry transfers. Our results confirm the role of poultry transport in the dissemination of mite populations, but the frequency of effective contamination after the introduction of contaminated material into poultry houses seems lower than expected. The high persistence of mites on farms, even during periods when poultry houses are empty and cleaned, and the very large number of nodes in the logistic network (large number of companies supplying pullets or transporting animals) undoubtedly explain the very high prevalence on farms. Substantial genetic diversity was measured in farm populations, probably as a result of the mite's known haplodiploid mode of sexual reproduction, coupled with the dense logistic network. The possibility of the occasional occurrence of asexual reproduction in this sexually reproducing mite was also revealed in our analyses, which could explain the extreme aggressiveness of its demographic dynamics under certain conditions.

The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models

Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.

A hierarchical intervention scheme based on epidemic severity in a community network

As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ([Formula: see text]) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how [Formula: see text] affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of [Formula: see text] on infectious disease transmission by establishing a four-dimensional [Formula: see text] edge-based compartmental model with two communities. The basic reproduction number [Formula: see text] is explicitly obtained subject to [Formula: see text] [Formula: see text]. Furthermore, according to [Formula: see text] with zero [Formula: see text], epidemics spread could be classified into two cases. When [Formula: see text] for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when [Formula: see text] for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to [Formula: see text] is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.

Nonlinear diffusion in multi-patch logistic model

We examine a multi-patch model of a population connected by nonlinear asymmetrical migration, where the population grows logistically on each patch. Utilizing the theory of cooperative differential systems, we prove the global stability of the model. In cases of perfect mixing, where migration rates approach infinity, the total population follows a logistic law with a carrying capacity that is distinct from the sum of carrying capacities and is influenced by migration terms. Furthermore, we establish conditions under which fragmentation and nonlinear asymmetrical migration can lead to a total equilibrium population that is either greater or smaller than the sum of carrying capacities. Finally, for the two-patch model, we classify the model parameter space to determine if nonlinear dispersal is beneficial or detrimental to the sum of two carrying capacities.

Synchronized Tick Population Oscillations Driven by Host Mobility and Spatially Heterogeneous Developmental Delays Combined

We consider a coupled system of delay differential equations for a single-species tick population dynamics, assuming feeding adult ticks are distributed by their hosts in a spatially heterogeneous environment consisting of two patches where egg ticks produced will complete their life cycles with different, normal and diapause, developmental delays. We show that the mobility of adult tick host and the diapause developmental delay combined drive a synchronized oscillation in the total tick populations around a uniquely defined positive equilibrium, and this synchronization makes the oscillatory patterns much simpler in comparison with multi-peak oscillations exhibited in the absence of host mobility.

Stability switching and hydra effect in a predator-prey metapopulation model

A metapopulation model is investigated to explore how the spatial heterogeneity affects predator-prey interactions. A Rosenzweig-MacArthur (RM) predator-prey model with dispersal of both the prey and predator is formulated. We propose such a system as a well mixed spatial model. Here, partially mixed spatial models are defined in which the dispersal of only one of the communities (prey or predator) is considered. In our study, the spatial heterogeneity is induced by dissimilar (unbalanced) dispersal rates between the patches. A large difference between the predator dispersal rates may stabilize the unstable positive equilibrium of the model. The existence of two ecological phenomena are found under independent harvesting strategy: stability switching and hydra effect. When prey or predator is harvested in a heterogenious environment, a positive stable steady state becomes unstable with increasing the harvesting effort, and a further increase in the effort leads to a stable equilibrium. Thus, a stability switching happens. Furthermore, the predator biomass (at stable state) in both the patches (and hence total predator stock) increases when the patch with a higher predator density is harvested; resulting a hydra effect. These two phenomena do not occur in the non-spatial RM model. Hence, spatial heterogeneity induces stability switching and hydra effect.

Perturbation drives changing metapopulation dynamics in a top marine predator

Metapopulation theory assumes a balance between local decays/extinctions and local growth/new colonisations. Here we investigate whether recent population declines across part of the UK harbour seal range represent normal metapopulation dynamics or are indicative of perturbations potentially threatening the metapopulation viability, using 20 years of population trends, location tracking data (n = 380), and UK-wide, multi-generational population genetic data (n = 269). First, we use microsatellite data to show that two genetic groups previously identified are distinct metapopulations: northern and southern. Then, we characterize the northern metapopulation dynamics in two different periods, before and after the start of regional declines (pre-/peri-perturbation). We identify source-sink dynamics across the northern metapopulation, with two putative source populations apparently supporting three likely sink populations, and a recent metapopulation-wide disruption of migration coincident with the perturbation. The northern metapopulation appears to be in decay, highlighting that changes in local populations can lead to radical alterations in the overall metapopulation's persistence and dynamics.

Mathematical epidemiology in a data-rich world

I discuss the acquisition and use of “background” data in mathematical epidemiology models, advocating a proactive approach to the incorporation of said data. I illustrate various mechanisms for acquiring data, mainly from open data sources. I also discuss incorporating this data into models.