PubMed · 14833385
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J D MATTHEWS. 1951-05-12. Forest genetics.. https://doi.org/10.1038/167764a0
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Model validation is often realized as a test of how well model predictions match a set of independent observations. One would think that the burden of proof should rest with the model, to force it to show that it can make accurate predictions. Further, one would think that increasing the sample size ought to increase the model's ability to demonstrate its utility. Traditional statistical tools are inappropriate for this because they default to the case that the model and the data are no different, and their ability to detect differences increases with the sample size. These traditional tools are optimized to detect differences, rather than similarities. We present an alternative strategy for model validation that is based on regression and statistical tests of equivalence. Equivalence tests reverse the usual null hypothesis: they posit that the populations being compared are different and use the data to prove otherwise. In this sense, equivalence tests are lumping tests, whereas the traditional statistical tests are splitting tests. To date, model validation with equivalence tests has focused on comparisons of means. Our proposed test checks not only for similarity of means, but also for similarity between individual predictions and observations. The strategy is demonstrated using three case studies that differ in their modeling objectives, and for varied sample sizes. The proposed strategy provides a formal means of model validation that is superior to traditional statistical tests in each case.
In this study an economic analysis of the purification of integrated solid waste treatment facility leachates through a willow-coppice (Salix) vegetation filter in southern Sweden was carried out. Calculations were based on the use of two computer models that were initially used in estimating a pump-and-pipe irrigation system for a 36-ha willow-coppice plantation to purify an average annual quantity of 195,000 m(3) of leachate with an average nitrogen content of 24 g/m(3). Results showed that facility leachates could be purified at US dollars 0.34/m(3) compared with US dollars 0.62/m(3) for that of conventional leachate treatment at a wastewater treatment plant. Furthermore, results revealed that the increased income from willow growing and sale of the biomass chips represented only a small factor in the overall cost of the purification technique--decreasing purification costs to US dollars 0.326/m(3). Sensitivity analyses also demonstrated that, because of the large leachate holding pond expense, only a fraction of facility leachate should be treated through a vegetation filter.
We evaluated the population genetic structure of seven microsatellite loci for old growth and second growth populations of eastern white pine (Pinus strobus). From each population, located within Hartwick Pines State Park, Grayling, Michigan, USA, 120-122 contiguous trees were sampled for genetic analysis. Within each population, genetic diversity was high and inbreeding low. When comparing these populations, there is a significant, but small (less than 1%), genetic divergence between populations. Spatial distance between populations or timber harvest at the second growth site were reasonable explanations for the observed minor differences in allele frequencies between populations. Spatial autocorrelation analysis suggested that, for the old growth population, weak positive structuring at 15 m fits the isolation by distance model for a neighbourhood size of about 100 individuals. In comparison, genotypes were randomly distributed in the second growth population. Thus, logging may have decreased spatial structuring at the second growth site, suggesting that management practices may be used to alter natural spatial patterns. In addition, the amount of autocorrelation in the old growth population appears to be lower for some of the microsatellites, suggesting higher numbers of rare alleles and that higher mutation rates may have directly affected spatial statistics by reducing structure.