To be clear by negative EROEI I mean negative vs the needs of the society. This happens well before EROEI drops to 1:1 or less I'd suggest it depends on the complexity of the society at what level it enters a situation that it can no longer sustain itself.

Simpler societies can probably get away with very low EROEI's since simplicity simply means most members of society are themselves involved in energy/food procurement. Then net gain or complexity level is trivial to determine its the amount of food/energy they produce in excess of what they can consume. More complex societies both make the required net gain larger and make it more difficult to calculate the minimum. I've tried using the concept of the typical support pyramid for a core industry to calculate the minimum EROEI. The idea is that you take a key industry say for example farmers and determine how many people are needed to directly support the modern farmer. The simple calculation of how many people are involved in actually planting and harvesting that leads to and assertion that 1-2% of the population are farmers is simply bullshit. It does not include the gene engineers at monsanto or the fertilzer or tractor manufactures nor does it include the prepared food industry needed to process the centralized food stores etc etc etc. My best guess is at least 30% of the population is indirectly involved in the food industry from frozen foods to actual farming. We changed the nature of the work but I'd argue it has not really fallen from its low of 40% just the work has changed from direct planting. On top of this you have additional support industries such as housing for those in the food industry and cars and doctors etc every modern person uses a very generic set of services regardless of what the core industry is that creates the initial wealth. I make a WAG that this adds 10-20% to the total bring the number of people that make a living off of food up close to 50% of the population.

So if everyone else supported the energy and other commodity industries like metals you need at least a 2:1 EROEI to break even. Of course outside of food the rest of the various core industries have their own support pyramids just guess that they are 10% each.
This leads to a ballpark figure of 10:1 for the minimum energy industry direct EROEI before the society structure as a whole is negative. You can cut down my estimate for food but I worked pretty hard at it and was surprised how much of the worlds economy is directly then indirectly related to supplying food. And I don't think its wrong. And even if I'm off its easy to imagine that other industries can certainly command a bigger part of the economic pie then I've allocated bottom line is you can come up with about 10:1 or 15:1 repeatedly using various estimates of our support pyramid for our modern economies.

If right and your paper is right and we have dropped into the 3-5:1 range then one would expect that the economy would fall into a collapse rivaling the Great Depression in magnitude.

Ohh wait ..