Spatial asynchrony and periodic travelling waves in cyclic populations of field voles

Abstract

We demonstrate evidence for the presence of travelling waves in a cyclic population of field voles in northern Britain by fitting simple, empirical models to spatially referenced time series data. Population cycles were broadly synchronous at all sites, but use of Mantel correlations suggested a strong spatial pattern along one axis at a projection line 72 degrees from North. We then fitted a generalized additive model to log population density assuming a fixed-form travelling wave in one spatial dimension for which the density at each site was offset in time by a constant amount from a standard density-time curve. We assumed that the magnitude of this offset would be proportional to the spatial separation between any given site and the centroid of the sampling sites, where separation is the distance between sites in a fixed direction. After fitting this model, we estimated that the wave moved at an average speed of 19 km yr-1, heading from West to East at an angle of 78 degrees from North. Nomadic avian predators which could synchronize populations over large areas are scarce and the travelling wave may be caused by density-dependent dispersal by field voles and/or predation by weasels, both of which act at a suitably small spatial scale.

Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models

“…(Kielder Forest is approx. 30 km wide, while the wave speeds of 19 and 14 km yr K1 , reported by Lambin et al (1998) and Mackinnon et al (2001), respectively, correspond to wavelengths of approx. 76 and 56 km, respectively.)…”

“…Spatio-temporal patterns can be partly revealed by measuring how the synchrony between the population dynamics of different sites varies with the distance between sites. To illustrate this we present analysis of data on the field vole populations in Kielder Forest (see Lambin et al (1998Lambin et al ( , 2000, Mackinnon et al (2001) and Bierman et al (2006) for more details of this system and more detailed analysis). The raw data consist of average population density estimates from abundance indices (see Lambin et al (2000) for a methodological description) for a range of sites, over the period [1984][1985][1986][1987][1988][1989][1990][1991][1992].…”

“…3-4 years (Turchin 2003) plant-herbivore (Turchin 2003), plantherbivore-predator (Pitelka & Batzli 2007) wide-scale synchrony (Angerbjörn et al 2001) climatic forcing (Angerbjörn et al 2001) Kielder Forest field voles, Microtus agrestis 3-5 years (Turchin 2003) local environment (Ergon et al 2001), not predator-prey (Graham & Lambin 2002) TW (Lambin et al 1998;Mackinnon et al 2001;Bierman et al 2006) landscape obstacle (reservoir) grey-sided voles, Clethrionomys rufocanus 2-5 years (Stenseth et al 1996) predator-prey (Bjørnstad et al 1999;Stenseth et al 2002) regional synchrony (Bjørnstad et al 1999;Stenseth et al 2002;Haydon et al 2003) seasonal forcing (Stenseth et al 2002;Haydon et al 2003), mobile predators (Bjørnstad et al 1999) Canadian lynx, Lynx canadensis 9-11 years (Turchin 2003) plant-herbivore-predator (Krebs et al 2001;Turchin 2003), plant-herbivore (Selås 2006a) large-scale synchrony Schwartz et al 2002;Rueness et al 2003;Selås 2006a), TW climatic forcing Selås 2006a), widespread movement by lynx (Schwartz et al 2002;Rueness et al 2003) spruce needleminer, Epinotia tedella 6-7 years (Münster-Swendsen 2002) host-parasitoid (Münster-Swendsen & Berryman 2005), plant-herbivore (Selås (2006a) regional synchrony (Münster-Swendsen 2002) unknown autumnal moth, Epirrita autumnata 9-1...…”

A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations

“…There is an increasing body of evidence from ecological field studies suggesting that periodic travelling waves are a widespread spatiotemporal pattern in cyclic populations (Ranta & Kaitala, 1997;Lambin et al, 1998;Ranta et al, 2002;Johnson et al, 2004;. A thorough mathematical understanding of the dynamics underlying such patterns is crucial, in view of the considerable time and expense required for field studies.…”

“…These are the 1D version of more complicated 2D behaviours such as spiral and scroll waves and are also important in their own right. For example, periodic travelling waves have recently been identified in a number of ecological systems (Lambin et al, 1998;Moss et al, 2000;MacKinnon et al, 2001;Bjørnstad et al, 2002;Johnson et al, 2004;Bierman et al, 2006).…”