Making biodiversity-friendly cocoa pay: combining yield, certification, and REDD for shade management.

The twin United Nations' Millennium Development Goals of biodiversity preservation and poverty reduction both strongly depend on actions in the tropics. In particular, traditional agroforestry could be critical to both biological conservation and human livelihoods in human-altered rainforest areas. However, traditional agroforestry is rapidly disappearing, because the system itself is economically precarious, and because the forest trees that shade traditional crops are now perceived to be overly detrimental to agricultural yield. Here, we show a case where the commonly used agroforestry shade metric, canopy cover, would indeed suggest complete removal of shade trees to maximize yield, with strongly negative biodiversity and climate implications. However, a yield over 50% higher was achievable if approximately 100 shade trees per hectare were planted in a spatially organized fashion, a win-win for biodiversity and the smallholder. The higher yield option was detected by optimizing simultaneously for canopy cover, and a second shade metric, neighboring tree density, which was designed to better capture the yield value of ecological services flowing from forest trees. Nevertheless, even a 50% yield increase may prove insufficient to stop farmers converting away from traditional agroforestry. To further increase agroforestry rents, we apply our results to the design of a sustainable certification (eco-labelling) scheme for cocoa-based products in a biodiversity hotspot, and consider their implications for the use of the United Nations REDD (reducing emissions from deforestation and forest degradation) program in agroforestry systems. Combining yield boost, certification, and REDD has the potential to incentivize eco-friendly agroforestry and lift smallholders out of poverty, simultaneously.

Acausality of massive gravity.

We show, by analyzing its characteristics, that the ghost-free, 5 degree of freedom, Wess-Zumino massive gravity model admits superluminal shock wave solutions and thus is acausal. Ironically, this pathology arises from the very constraint that removes the (sixth) Boulware-Deser ghost mode.

Quantum cosmology and conformal invariance.

According to Belinsky, Khalatnikov, and Lifshitz, gravity near a spacelike singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini, and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the Universe is the zero-energy eigenmode of the Hamiltonian, or the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models with enhanced ADE symmetry is constructed, based on the quantization of nilpotent coadjoint orbits.

Gauge invariances and phases of massive higher spins in (anti-) de Sitter space.

The (m2,Lambda) plane of spin s>1 massive fields in (anti-) de Sitter space backgrounds is shown to consist of separate phases, divided by lines of novel "partially massless" gauge theories that successively remove helicities, starting from the lowest, 0 or +/-1/2. The norms of the excluded states flip as the gauge lines are crossed and only the region containing the massive Minkowski theory is unitary. The partially massless gauge theories are unitary or not, depending on the ordering of the gauge lines. This "level splitting" of massless Minkowski gauge theories is specific to nonzero Lambda.