Fig. 1-3: The long run growth rate for the entire population, for different numbers of subpopulations. Fig. 1: high level of growth rate synchrony among subpopulations. Fig. 2: low level of synchrony. Fig. 3: medium level of synchrony. Fig. 1Fig. 2 Fig. 3 Result and discussion: With a population growth rate over 1 there is no extinction risk in a long term perspective. The different levels of synchrony show a similar pattern. When the amount of subpopulations decreases to five the growth rates are one for a low and a medium level of synchrony. For a high level of synchrony the long run growth rate is slightly under one when the number of subpopulations is five. There is thus just a small difference between the three scenarios and just when the amount of subpopulations is very small. The small difference can be explained by a too small difference in standard deviation (or variance) for the growth rates (both the first and the second value), which sets the level of synchrony in this model. On the other hand a higher standard deviation will probably make the populations fluctuate too much and the number of individuals in the subpopulations can be unrealistic high. That is already a problem, and may be the explanation why I can’t get growth rate values for the three higher amount of subpopulations in fig. 1. With a high migration between subpopulations there will be a lower probability for the entire population to go extinct. The migration in my model is density independent and also independent of distance to other subpopulations and there will probably be an underestimation of the extinction risk, because of too much migration. I will continue by adding density dependent growth rate and dispersal, and could then probably increase growth rate standard deviation. The dispersal will also be regulated by the spatial pattern, i.e. the dispersal will reflect either a clumped landscape or a more homogenous distribution of subpopulations. I will also filter the variation of growth rate between time steps, which will reflect either a red noise or a blue noise. Effects of synchronization among subpopulations Frida Wall, Dep. of Biology – IFM, Linköping University, 2004 When decreasing the amount of habitat the extinction risk will increase, and there seem to be a threshold value where there is a sudden decline in number of individuals (or in other ecological responses) 1. A subdivided population will decrease the extinction risk just because one subpopulation can survive while another one will go extinct. When the number of subpopulations becomes smaller the extinction risk for the entire population will be higher. If the survival or population growth rate is synchronized among the subpopulations the extinction risk will be even higher. Heino et al. 2 show that there is a high correlation between synchrony (caused by global variation) and global extinction risk, and that the synchronization will increase with increasing migration. What is the effect on extinction risk if there is a synchronization disregarded from global environmental variation and migration? Such an underlying synchronous dynamics could be important in a management perspective. My aim is to investigate the effect of synchronization (not set by global variation and/or migration) among subpopulations, on the extinction risk for the entire population, when decreasing the amount of subpopulations at start. Model: I use a subdivided population model with non-density dependent growth rate and non- density dependent dispersal (Eq. 1). N i is the number of individuals in subpopulation i. The dispersal, d ij and d ji, are picked at random from a normal distribution (mean 0,02 and variance 0,02 (d<0 is set to d=0)) each time step. The growth rate, λ, is picked two times. The first value is picked at random from a normal distribution (mean=1) for each time step. This first value becomes then the mean of the normal distribution for the second growth rates, that are picked for every subpopulation that time step (i.e. every subpopulation gets its own λ). For a high level of synchrony the second normal distribution for λ has a low variance, and a low level of synchrony has a high second variance. The total variance, for the first and second normal distributions for λ, is always 0,5. The simulation runs for 200 time steps and for 500 replicate. The result is presented by the long run growth rate of the entire population (Eq. 2) against the amount of subpopulations at start. Eq. 1 Eq. 2 1 pers. comm., K. With, Dep. of Biological Sciences, Bowling Green State University 2 M. Heino, V. Kaitala, E. Ranta and J. Lindström Synchronous dynamics and rates of extinction in spatially structured populations. Proc. R. Soc. Lond. B, 264 ( ).