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Synchronization and noise colour: a threat to endangered species?
F. Lögdberg1 and U. Wennergren 1
1
Dep. of IFM, Biology – Linköping University, SE-581 31 Linköping, Sweden.
e-mail: [email protected]
Introduction
It is known that variation in growth rate will increase the extinction risk. Synchronized
variation will also influence the risk of local and global extinctions (Heino et al. 1997,
Palmqvist & Lundberg 1998, Engen et al. 2002). We test how the combined effect of these
two features effect the extinction rates in a landscape. Most models deal with an independent
stochastic variation, so called white noise. Here we also use positively and negatively
autocorrelated variation (red and blue noise respectively) by using 1/f-noise.
Synchrony and variation in space and time
Model and Result
A global growth rate for each time step constitute the mean of a normal distribution, from
which all local growth rates are picked at random. The variance of these distributions sets the
level of synchrony among the local populations. A high variance gives a low level of
synchrony, and vice versa. We start with a spatial null model where all local populations are
equally connected. Then we introduce landscapes with more or less aggregation, by using
Fourier transform. We investigate the extinction risk when combining different levels of
synchrony and stochastic variation patterns (noise colours). The local dynamic is described
by either a density dependent or a density independent discrete function.
Our results show that synchrony, noise colour and impact of density dependence all have
a great influence on the extinction risk. A white noise model will underestimate the extinction
risk if the true variation is a reddish noise. It is important to be aware of synchrony among
local populations and synchronizing factors. A high degree of synchrony, in a reddish
environment, will increase the extinction risk even more. Together with high impact of
carrying capacity this will really be a threat to endangered species, especially when the
landscape configuration and composition affect the dispersal success.
Application
This general model will then be applied on the ecosystem of old oaks in pastures. Old,
hollow oak is a species-rich environment. Due to changed agricultural management the
amount of old oaks has decreased and many oak-dependent species, for example
Osmoderma eremita, are threatened today (Ranius, 2002). By analysing the landscape
characteristics as above, we identify areas with oak stands where the oak-dependent
species can or can not survive in a long-term perspective.
References
Engen, S; Lande R. & Sæther, B.E. (2002) The spatial scale of population fluctuations and quasiextinction risk. The American Naturalist 160: 439-451.
Heino, M; Kaitala, V; Ranta E. & Lindström, J. (1997) Synchronous dynamics and rates of extinction
in spatially structured populations. Proceedings of the Royal Society of London - Series B:
Biological Sciences 264: 481-486.
Palmqvist, E. & Lundberg, P. (1998) Population extinctions in correlated environments. Oikos 83:
359-367.
Ranius, T. (2002) Influence of stand size and quality of tree hollows on saproxylic beetles in Sweden.
Biological Conservation 103: 85-91.