Spatial correlation as leading indicator of catastrophic shifts

Generic early-warning signals such as increased autocorrelation and variance have been demonstrated in time-series of systems with alternative stable states approaching a critical transition. However, lag times for the detection of such leading indicators are typically long. Here, we show that increased spatial correlation may serve as a more powerful early-warning signal in systems consisting of many coupled units. We first show why from the universal phenomenon of critical slowing down, spatial correlation should be expected to increase in the vicinity of bifurcations. Subsequently, we explore the applicability of this idea in spatially explicit ecosystem models that can have alternative attractors. The analysis reveals that as a control parameter slowly pushes the system towards the threshold, spatial correlation between neighboring cells tends to increase well before the transition. We show that such increase in spatial correlation represents a better early-warning signal than indicators derived from time-series provided that there is sufficient spatial heterogeneity and connectivity in the syste

Making connections: Using skill theory to recognize how students build and rebuild understanding

In this companion to Marc Schwartz and Kurt Fischer's article, Patricia King and JoNes VanHecke describe how student affairs educators can help students become sophisticated thinkers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50666/1/155_ftp.pd

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Community Partnership Through Transformative Justice: the Healing Project at the Oregon State Penitentiary

In the Foreword to Gerard Robinson and Elizabeth English Smith’s Education for Liberation volume on educational initiatives in prison, Newt Gingrich and Van Jones note that educational programs “do something powerful: they give hope and dignity to the incarcerated.” The authors wholeheartedly agree and while they recognize the importance of higher education programs that confer degrees and therefore credentials out in the free world, they find that education can be broadly understood in prison in ways that greatly enhance the hope and dignity of the incarcerated. In this chapter, they explore the creation of a Japanese-style healing garden at the Oregon State Penitentiary (OSP), a maximum security, 2,000-person male prison in Salem, Oregon. This prisoner-led initiative was a resounding success, despite all the odds against it, because it was animated by a philosophy of transformative justice that both prison administration and prisoners could believe in, and it embraced the need for meaningful and inclusive community partnerships