10 Laws Of Abundance

[Charo Lemucchi]

TheInteragency Appraisal and Evaluation Guidelines clearly spell out when a lien is taken in an abundance of caution. This carries through to Call Report classification, affects CRA reporting, and other limited circumstances. In many cases, the fact that a lien is taken in an abundance of caution does not eliminate the need to comply with other regulations such as flood insurance requirements, Regulation Z and RESPA.

An institution may take a lien on real estate and be exempt from obtaining an appraisal if the lien on real estate is taken by the lender in an abundance of caution. This exemption is intended to have limited application, especially for real estate loans secured by residential properties in which the real estate is the only form of collateral. In order for a business loan to qualify for the abundance of caution exemption, the Agencies expect the extension of credit to be well supported by the borrower's cash flow or collateral other than real property. The institution's credit analysis should verify and document the adequacy and reliability of these repayment sources and conclude that knowledge of the market value of the real estate on which the lien will be taken as an abundance of caution is unnecessary in making the credit decision.

An institution should not invoke the abundance of caution exemption if its credit analysis reveals that the transaction would not be adequately secured by sources of repayment other than the real estate, even if the contributory value of the real estate collateral is low relative to the entire collateral pool and other repayment sources. Similarly, the exemption should not be applied to a loan or loan program unless the institution verifies and documents the primary and secondary repayment sources. In the absence of verification of the repayment sources, this exemption should not be used merely to reduce the cost associated with obtaining an appraisal, to minimize transaction processing time, or to offer slightly better terms to a borrower than would be otherwise offered.

In addition, prior to making a final commitment to the borrower, the institution should document and retain in the credit file the analysis performed to verify that the abundance of caution exemption has been appropriately applied. If the operating performance or financial condition of the company subsequently deteriorates and the lender determines that the real estate will be relied upon as a repayment source, an appraisal should then be obtained, unless another exemption applies.

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Often, we have a detailed understanding of which environmental factors affect community variability1,2,3,4 and, sometimes, the genetic drivers determining the response to different environmental conditions5,6. This qualitative understanding of the correlates, and potential causes, of the observed variation does not parallel with a mechanistic understanding of its fundamental and general properties7,8,9.

Recent experiments allowed to document the existence and quantify the effect of several ecological mechanisms driving diversity in vitro10,11,12,13,14. Sometimes, with counter-intuitive results. For instance, many species can coexist on a single supplied resource thanks to widespread cross-feeding13. Environmental modification can lead to ecological suicide when one species, in the absence of other ones, modify pH to such a degree that lead to extinction of the whole population14. These growing body of fundamental results in microbial ecology are made possible by the simplified nature of the experimental communities, which typically consist of an handful of interacting species. It is challenging to upscale the experimental setups to match the complex spatio-temporal conditions of natural communities, in order to characterize the processes shaping the variation of many coexisting species.

Environmental fluctuations, competition, cross-feeding, environmental modification, demographic stochasticity, migration, and many other ecological forces shape microbial communities over time and space. The existence of such forces is not in doubt. Their quantitative strength and relative relevance in determining composition and variation in natural communities are unknown. It is in fact extremely challenging to disentangle the effect of multiple mechanisms in communities with thousands of species interacting. In such complex communities, mechanisms and microscopic forces manifest in emergent, macroscopic, properties. Macroecology, the study of ecological communities through patterns of abundance, diversity, and distribution15, is therefore a promising approach to study quantitatively variation in microbial communities16,17,18, and to provide quantification of mechanisms that are shaping them.

The most studied pattern in (macro)ecology is the species abundance distribution (SAD)19,20, which is defined as the fraction of species with a given abundance. Multiple functional forms, and consequently multiple mechanisms, have been proposed to describe the empirical SAD in microbial communities17. While SADs are highly studied and characterized, it is often neglected that three distinct and independent sources of variation influence their shape: sampling noise, fluctuation of abundances of individual species, and variability in abundance across species. This work disentangles these sources of variation in three macroecological laws.

Here, I show that three macroecological laws describe the fluctuations of abundance and diversity. These three ecological laws hold across biomes and for both cross-sectional and temporal data, and are fundamental, as they suffice to predict, without fitting any additional parameters, the scaling of diversity and other commonly studied macroecological patterns, such as the SAD. These laws allow to generate in silico ecological communities, providing a statistically sophisticated ground truth, that allows to test ecological theories, models, and mechanisms.

Macroecological patterns are the bridges from uncharacterized variation to ecological processes and mechanisms. I show that the stochastic logistic growth model, which is based on environmental stochasticity, reproduces the three macroecological laws, as well as dynamic patterns in temporal data. Both data and model show that, at the taxonomic resolution commonly used, competitive exclusion is rare and variation of species presence and abundance is mostly due to environmental fluctuations.

The probability that a Gamma-distributed variable is exactly equal to zero vanishes. A direct consequence of the first macroecological law (a Gamma AFD) is that all instances in which a species is absent should be imputed to sampling error. This surprising prediction is directly tested in two ways. If the absence is caused by sampling error, one can predict the occupancy of a species, defined as the fraction of communities where it is present, from the AFD. Assuming a Gamma AFD, the expected occupancy of species i is given by (see Methods and Supplementary Note 4 for the full derivation)

where Ns is the total number of reads in sample s and T is the total number of samples. Since absence is predicted to be due to sampling errors, as sampling error reduces (i.e., when the total number of reads Ns increases) occupancy is predicted to tend to 1. Figure 2 shows that Eq. (2) predicts the occupancy from the first two moments of species abundance fluctuations (Supplementary Fig. 3). Note that the fact that a Gamma AFD reproduces this pattern is also an indirect test of the hypothesis that the AFD is Gamma. Supplementary Fig. 4 shows that a Lognormal AFD fails in reproducing the observed occupancy.

a Relationship between fluctuation in abundance and the absence of species. The fluctuations of species abundances across communities (AFD) are Gamma distributed (Fig. 1), which implies that species are absent only because of finite sampling. b Tests the prediction, by comparing the occupancy of species (the fraction of communities where a species is presence) in different biomes with what expected from independent sampling from Gamma distributed relative abundances (Supplementary Note 4 and Supplementary Fig. 3).

Further evidence to the claim that most instances where a species is absent are due to sampling error is provided using Bayesian model selection. A Gamma AFD is compared with a zero-inflated Gamma distribution, which explicitly includes species absence. The Gamma AFD is statistically superior to the zero-inflated Gamma distribution (see Methods and Supplementary Fig. 6).

This result strongly suggests that, at the taxonomic resolution used in this study, competitive exclusion is absent or, at least, statistically irrelevant. Importantly, this result clarifies the relation between abundance and occupancy21, which has been reported in multiple microbial systems18,22,23 but has never been quantitatively characterized and explained.

The mean abundance distribution (MAD) describes how the average abundance is distributed across species. Figure 1d shows that the MAD is Lognormally distributed for all the data sets considered in this work (Supplementary Figs. 9 and 10): if a species is picked at random, the probabily of observing an average abundance \(\barx\) is

The parameter σ characterizes the variability of the logarithm of the mean abundance across species. Since in a finite number of samples rare species are likely to be never sampled, the empirical MAD displays a lower cutoff which is determined by sampling. In fact, if a species is rare enough (i.e., if \(\barx_i

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