Agriculture Reference
In-Depth Information
because the soil nitrification rates will more often stay within the linear response range to
available moisture.
The prevalence and magnitude of systematic and random (or unpredictable) aggrega-
tion bias of microbial processes in agroecosystems due to Jensen's inequality is largely
unknown. The opportunities for including correction factors (e.g., variance-weighted
interpolation) for systematic bias may help reconcile mass balance and interpolated esti-
mates from point process rate measurements (Webster and Oliver, 2007). When the aggre-
gation bias is unpredictable, however, it is important to minimize aggregation across the
predictor variable and perform process-based modeling on the smallest spatial and tem-
poral scales that the data allow to minimize bias (Parkin, 2008).
Jensen's inequality does not appear to be explicitly recognized in the ecological (Ruel
and Ayres, 1999), soil, or agricultural sciences. A search of ISI Web of Science for the topic
keywords “Jensen's inequality” and “soil” or “ecosystem” or “agriculture” resulted in only
3 articles (Aikio and Ruotsalainen, 2002; Kon, 2004; Benedetti-Cecchi, 2005b) compared to
251 articles with the keyword “Jensen's inequality” alone. The theory is well established,
but it is not being communicated to the natural sciences student (Ruel and Ayes, 1999).
Ruel and Ayes (1999) reported finding no mention of Jensen's inequality in several biom-
etry textbooks as of 1999. I do not report these findings as proof that Jensen's inequality is
not considered in these fields; however, it appears that this principle is used inconsistently
in agroecological research.
not uniform, conditions
A potentially significant corollary of Jensen's inequality is that soil heterogeneity should
allow microbial processes to proceed that would not occur under uniform or constant
conditions. Here, I explore the evidence for rare processes occurring in agricultural soils
despite attempts at uniformity.
One widely known illustration of soil processes occurring under field conditions at
small spatial scales that is unlikely to occur under uniform conditions is Parkin's denitri-
fying pigweed (
Amaranthus retroflexus
L.) leaf (Parkin, 1987) (
Figure 3.4
)
. Within a single
soil core (2-cm i.d. × 15 cm in length) taken from an agricultural field in Michigan, Parkin
found that about 84% of the denitrification activity (determined by the acetylene block
technique) occurring in this core was near a small pigweed leaf that had been incorpo-
rated into the soil. This was despite the disproportionately small mass of the leaf relative
to the whole soil core (less than 0.01%) and the overall aerobic soil conditions of this field.
This work demonstrated the potential for hot spots in the soil to dominate process rates.
Furthermore, this observation stimulated the hypothesis that if the components of this
leaf (e.g., sugars, proteins, etc.) were evenly dispersed throughout the soil core it would not
have provided a sufficiently concentrated resource to deplete soil O
2
concentrations to the
point at which denitrification would have been favorable.
Concurrent with Parkin's (1987) work, the role of oxygen diffusion in soils was being
investigated. For example, Sexstone et al. (1985) demonstrated that O
2
gradients within indi-
vidual soil aggregates could range from near-atmospheric concentrations (~20,000 μL L
−1
) on
the surface of the aggregate to less than 200 μL L
−1
in the interior of a soil aggregate, a dis-
tance of less than 2 mm. This novel demonstration helps explain why the products of anaero-
bic metabolism (e.g., denitrification) are produced in soils that on average were well aerated.
Search WWH ::
Custom Search