A recent paper, ‘Productivity beyond density: A critique of management models for reindeer pastoralism in Norway’, published in Pastoralism: Research, Policy and Practice sets out to investigate the validity of the premise that there is a strong relationship between density and carcass weights in the reindeer husbandry in Norway.

In short, the paper aims to challenge the official view of overstocking and reframe reindeer herding in terms of non-equilibrium ecology.

Their focus of attack is the Røros model which, according to the authors, hinges on

“… classic ecological equilibrium models where there is a clear unequivocal relationship between animal densities, production, and carcass weights”

p. 15

As such the article fits nicely in a growing trend: rather than investigating problems currently facing pastoralists, the main point is to establish systems as non-equilibrium, and thus all issues are assumed resolved, or at least externally caused (for an excellent example from the reindeer husbandry in Norway, check out ‘Conceptualising resilience in Norwegian Sámi reindeer pastoralism‘).

In another paper, some of the same authors have, for example, argued that reindeer herding in Norway is better characterised as a non-equilibrium system

“…where herbivore populations fluctuate randomly according to external influences, [and] the concepts of carrying capacity and overgrazing have no discernible meaning”.

‘Misreading the Arctic landscape: A political ecology of reindeer, carrying capacities, and overstocking in Finnmark, Norway’, p. 223

‘Productivity beyond density’ goes at least further in attempting to quantify the relative importance of non-equilibrium factors (such as climate) and equilibrium factors (such as density).

While the paper is well-written and exciting, I find it a bit strange that in the only quantitative analysis they present the sole focus is on statistically significant effects of precipitation and temperature for the carcass weights of reindeer:

While the analysis shows indeed that climate factors (precipitation: all the daily observation in the stated period and growing degree days [GDD]) are significant, the discussion of the table completely fails to address two critical factors:

• Multicollinearity
• Effect size

They never discuss whether the variables measuring climate is correlated or not (as they are monthly based, it wouldn’t be a huge surprise if they are).

High or even moderate, collinearity is problematic when effects are weak (as the climate effect sizes indicate). If collinearity is ignored, it is possible to end up with a statistical analysis where nothing is significant, but were dropping one predictor may make others significant, or even change the sign of estimated parameters.

The point is technical; it would be interesting to see how these potential problems were accounted for.

Concerning effect size, the most substantial effect by far is that of density: -0.16 kg for calves and -0.32 kg for varit (1.5-year-old bucks).

In effect, this has a considerable impact on the carcass weights in high-density vs low-density environments

Keep in mind that they do not provide information concerning variable transformation, so I take it for granted that the intercept represents average carcass weights when every other variable is at zero. I also take for granted that all variables are continuous. Moreover, not all of the data was in the supplemental material so I couldn’t re-analyse the data properly.

In short, at density 0 average calf carcass weight is 18.52 kg and average varit carcass weight is 25.34 kg.

The paper does not indicate the range of density utilised in this analysis, but Fig. 5 presents the range for mainland districts (which are the same districts used in table) to be from 0 to 25.

Disregarding the climate parameters (since there are no interactions and the range of the climate parameters are not presented) density has a significant effect in high-density environments:

Calves: 18.52 – 0.16 X 25 = 14.52 kg

Varit: 25.34 – 0.32 X 25 = 17.34 kg

In short, the model in Table 1 predicts that the difference in varit carcass weight between a low-density environment and a high-density environment is 8 kg. For calf carcass weight, the model predicts a difference of 4 kg.

While I fully agree with the authors that an over-emphasis on density and herd size is too simplistic when modelling pastoral production, it is bizarre that the above is not communicated at all.

Part of the problem, I think, stems from the simplified representation of non-equilibrium ecology. Concerning Africa and Asia, for example, they write “…a wholesale paradigm shift from equilibrium to non-equilibrium modelling took place from the early 1990s” (p. 9).

This is in fact, only partially true.

In the chapter ‘Why are there so many animals? Cattle population dynamics in the communal areas of Zimbabwe’, Ian Scoones, for example, investigated factors affecting herd growth among Zimbabwean pastoralists.

He mainly focused on periodic events such as droughts (a density-independent factor) and more persistent factors such as herd size (a density-dependent factor)

In other words, he investigated the degree to which density-dependent and density-independent factors explained herd size fluctuations (data for 60 years).

In short, he found:

• In years with high precipitation, the population of cattle approaches a ceiling, which he terms the carrying capacity. As density increases, the birth rate drops, and mortality rates increases (although they never reach equilibrium and the cattle population never reaches its theoretical maximum).
• The cattle population never reaches a maximum because stochastic events such as droughts occur and kill off large parts. Noteworthy, the number of animals killed by these events was more substantial than what can be predicted from density-dependent factors alone.

In the long term, it thus looks like non-equilibrium factors have the most significant impacts on cattle populations. Still, equilibrium factors are essential in years without stochastic climatic effects and when the population is high.

Scoones’ investigation show what seems now to be forgotten:

It is unlikely that any system is characterised by either equilibrium or non-equilibrium factors alone, but rather that they both operate on a continuum.

This supports the predominant ecological perspective that at high population sizes, herbivores are sensitive to a combination of density-dependent and -independent factors, which has been shown for reindeer in Norway.

As I argued in the paper ‘Climate Change, Risk Management and the End of Nomadic Pastoralism’.

“To understand the effects of climate change on nomadic pastoralists, it is thus necessary to move beyond the simplistic dichotomy of characterising pastoral system as equilibrial (density dependence: livestock and pastures are regulated by grazing pressure) or non-equilibrial (density independence: livestock and pastures are limited by external factors such as climate) and look at the interplay between density dependent and density independent factors”

p. 131