Synchronized metapopulations in a coloured world What is the effect of correlated environmental variation, combined with synchrony, in spatially structured populations? Is there a difference when growth rates vary compared to variation in carrying capacity? Natural populations vary constantly. An important approach to studying population variation is the power spectrum analysis (Gao et al., 2007). When the spectral exponent is positive, the population time series is dominated by low frequencies and is therefore autocorrelated (‘red noise’). No frequencies dominate when the spectral exponent is close to zero, and the time series is not correlated (‘white noise’). Here we use fourier transform in two dimensions, for adding correlation in space (i.e. synchrony) without destroying correlation in time and keeping the overall mean and variance constant. The environmental variation is put either in the growth rate or in carrying capacity. Mean growth rate, r=[ ], and mean carrying capacity, K=[50 500]. The population is divided into ten patches. Dispersal is a mass-action mixing process, i.e. migrants from one patch can disperse to all other patches with the same probability. Local population dynamics is governed by the Ricker model: Figure 1. Extinction risk for different correlations in time and space. Variation in growth rates, mean r=0.8. Ten subpopulations. Carrying capacity, K=50 (A) and K=500 (B). Results: Correlation in both time and space (synchrony) has a great effect on extinction risk (Figure 1). Strong autocorrelation in time and high degree of synchrony results in the largest extinction risk. The lower the carrying capacity, the more increased extinction risk. Resource utilization matches extinction risk (Figure 2.). Difference between combinations decreases for increased mean growth rate, and when variation is put in carrying capacity. There is a strong correlation between environmental synchronization and the synchrony of population densities, as well as between noise colour in environmental noise and population density. A B Figure 2. Extinction risk for different correlations in time and space. Variation in growth rates (A), and in carrying capacity (B). Mean r=0.8, and mean carrying capacity, K=500. Ten subpopulations. Conclusions: The extinction risk can increase from 0% up to 85%, by just re-arranging environmental variation in time and space while keeping overall mean and variance constant. There is a strong connection between extinction risk and resource utilization. Application to empirical data: Measures of population density means and variances are misleading. An analysis of extinction risks, or any prediction of population growth, have to include synchronization between patches and noise (autocorrelation in time). Reference: Gao, M., Li, Z. and Dai, H Effects on spectral color of a spatially-structured population: Environmental noise, dispersal, spatial heterogeneity. Ecological Modelling 201:

Frida Lögdberg & Uno Wennergren, Spatiotemporal Biology IFM – Theory and Modelling, Linköping University Linköping, Sweden