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Would the dynamic between soil nitrogen and plant growth be a positive or negative feedback loop

I think it is a negative feedback loop because as soil nitrogen increases then plant growth increases, and as plant growth increases, soil nitrogen decreases, is this correct? Therefore, since $+ × - = -$, it's a negative feedback loop.

Also, what about the feedback loop between temperature and soil organic matter? As temperature increases so does soil organic matter, as soil organic matter increases so does the release of CO2 thus causing more warming. A positive feedback loop.

Is this reasoning correct?

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You're on the right track, though the positive and negative aspect of feedback loops is more about dynamics of the overall system rather than just the increase or decrease of components in the feedback loop. This website offers a straight forward explanation of positive vs. negative feedback loops https://serc.carleton.edu/introgeo/models/loops.html :

Feedback Loops can enhance or buffer changes that occur in a system.

  • Positive feedback loops enhance or amplify changes; this tends to move a system away from its equilibrium state and make it more unstable.
  • Negative feedbacks tend to dampen or buffer changes; this tends to hold a system to some equilibrium state making it more stable.

In your second example, the feedback loop between temperature and soil organic matter leads to amplified changes in the system, making it more unstable. You're correct in identifying this as a positive feedback loop.

In the first example about plant available nitrogen and plant growth, there is a feedback loop there but is it positive or negative? You noted that the effect of increased plant growth would reduce available nitrogen. That isn't necessary the case, but even if it was, reduced nitrogen itself could actually be a positive feedback loop because it would lead the system out of equilibrium and into an unstable state (with the plants present no longer able to sustain themselves). However, in an undisturbed ecosystem I'd expect this to actually increase available nitrogen and also increase stability of the system over time, making this a negative feedback loop.

The relationship between soil nutrients and plants can be complex and vary between plants (e.g. leguminous plants would certainly create a negative feedback loop, enhancing the stability of the system they are thriving in). In general plants left to their own succession would increase organic matter which serves as a nutrient reservoir, further enhancing nutrient availability. In our more controlled agricultural systems, you can see this effect applied in crop rotation and allowing fields to go fallow as a means to increase available nutrients among other potential benefits.

Note that the nature of a feedback loop also depends on how the system's boundaries are defined. This is especially true looking at industrial agriculture and other systems that rely heavily on external inputs or otherwise have far-removed externalities.

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I don't think you can define a direct relationship between soil temperature and organic carbon - at least in a general sense.

As temperature increases so does soil microbial activity, which will tend to decrease soil carbon, not increase it.

However, plant growth will also increase if there is sufficient water and nutrient availability. That will tend to increase soil organic matter. So soil organic matter is dominated by factors other than temperature. Some examples: Boreal forest in northern Canada contains areas of peat bog with abundant organic matter. Much of the native soil in the moderate rainfall (~350mm/yr) areas of southeastern Australia has very low organic matter.

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