Recently, researchers in several areas of ecology and evolution have begun to change the way in which they analyze data and make biological inferences. Rather than the traditional null hypothesis testing approach, they have adopted an approach called model selection, in which several competing hypotheses are simultaneously confronted with data. Model selection can be used to identify a single best model, thus lending support to one particular hypothesis, or it can be used to make inferences based on weighted support from a complete set of competing models. Model selection is widely accepted and well developed in certain fields, most notably in molecular systematics and markrecapture analysis. However, it is now gaining support in several other areas, from molecular evolution to landscape ecology. Here, we outline the steps of model selection and highlight several ways that it is now being implemented. By adopting this approach, researchers in ecology and evolution will find a valuable alternative to traditional null hypothesis testing, especially when more than one hypothesis is plausible.Science is a process for learning about nature in which competing ideas about how the world works are evaluated against observations . These ideas are usually expressed first as verbal hypotheses, and then as mathematical equations, or models. Models depict biological processes in simplified and general ways that provide insight into factors that are responsible for observed patterns. Hence, the degree to which observed data support a model also reflects the relative support for the associated hypothesis.Two basic approaches have been used to draw biological inferences. The dominant paradigm is to generate a null hypothesis (typically one with little biological meaning ) and ask whether the hypothesis can be rejected in light of observed data. Rejection occurs when a test statistic generated from observed data falls beyond an arbitrary probability threshold (usually P , 0.05), which is interpreted as tacit support for a biologically more meaningful alternative hypothesis. Hence, the actual hypothesis of interest (the alternative hypothesis) is accepted only in the sense that the null hypothesis is rejected. By contrast, model selection offers a way to draw inferences from a set of multiple competing hypotheses. Model selection is grounded in likelihood theory, a robust framework that supports most modern statistical approaches. Moreover, this approach is rapidly gaining support across several fields in ecology and evolution as a preferred alternative to null hypothesis testing [1,3,4]. Advocates of model selection argue that it has three primary advantages. First, practitioners are not restricted to evaluating a single model where significance is measured against some arbitrary probability threshold. Instead, competing models are compared to one another by evaluating the relative support in the observed data for each model. Second, models can be ranked and weighted, thereby providing a quantitative measure of relative sup...
Ligand binding to heme proteins is studied by using flash photolysis over wide ranges in time (100 ns-1 ks) and temperature (10-320 K). Below about 200 K in 75% glycerol/water solvent, ligand rebinding occurs from the heme pocket and is nonexponential in time. The kinetics is explained by a distribution, g(H), of the enthalpic barrier of height H between the pocket and the bound state. Above 170 K rebinding slows markedly. Previously we interpreted the slowing as a "matrix process" resulting from the ligand entering the protein matrix before rebinding. Experiments on band III, an inhomogeneously broadened charge-transfer band near 760 nm (approximately 13,000 cm-1) in the photolyzed state (Mb*) of (carbonmonoxy)myoglobin (MbCO), force us to reinterpret the data. Kinetic hole-burning measurements on band III in Mb* establish a relation between the position of a homogeneous component of band III and the barrier H. Since band III is red-shifted by 116 cm-1 in Mb* compared with Mb, the relation implies that the barrier in relaxed Mb is 12 kJ/mol higher than in Mb*. The slowing of the rebinding kinetics above 170 K hence is caused by the relaxation Mb*----Mb, as suggested by Agmon and Hopfield [(1983) J. Chem. Phys. 79, 2042-2053]. This conclusion is supported by a fit to the rebinding data between 160 and 290 K which indicates that the entire distribution g(H) shifts. Above about 200 K, equilibrium fluctuations among conformational substates open pathways for the ligands through the protein matrix and also narrow the rate distribution. The protein relaxations and fluctuations are nonexponential in time and non-Arrhenius in temperature, suggesting a collective nature for these protein motions. The relaxation Mb*----Mb is essentially independent of the solvent viscosity, implying that this motion involves internal parts of the protein. The protein fluctuations responsible for the opening of the pathways, however, depend strongly on the solvent viscosity, suggesting that a large part of the protein participates. While the detailed studies concern MbCO, similar data have been obtained for MbO2 and CO binding to the beta chains of human hemoglobin and hemoglobin Zürich. The results show that protein dynamics is essential for protein function and that the association coefficient for binding from the solvent at physiological temperatures in all these heme proteins is governed by the barrier at the heme.
We document a strong association between predation environment and life-history phenotypes in the Costa Rican livebearing fish Brachyrhaphis rhabdophora. Populations that co-occurred with piscine predators attained maturity at a smaller size, and produced more, smaller offspring relative to populations from predator-free environments. These differences persisted over 3 years and between wet and dry seasons within a year. Reproductive allotment did not differ between predation environments, but was greater in the wet season than in the dry season. We also examined the phenotypic covariance structure among life-history traits and found traits to be highly correlated. Based on life-history differences, discriminant analyses showed that populations could be neatly classified by predation category, and could be reasonably classified into wet and dry season categories. Finally, we found that the pattern of predator-associated life-history divergence in B. rhabdophora is remarkably similar to that of the taxonomically distinct Trinidadian guppy (Poecilia reticulata), possibly pointing to an evolutionary convergence between these two systems.
The kinetic properties of the three taxonomic A substates of sperm whale carbonmonoxy myoglobin in 75% glycerol/buffer are studied by flash photolysis with monitoring in the infrared stretch bands of bound CO at nu(A0) approximately 1967 cm-1, nu(A1) approximately 1947 cm-1, and nu(A3) approximately 1929 cm-1 between 60 and 300 K. Below 160 K the photodissociated CO rebinds from the heme pocket, no interconversion among the A substates is observed, and rebinding in each A substate is nonexponential in time and described by a different temperature-independent distribution of enthalpy barriers with a different preexponential. Measurements in the electronic bands, e.g., the Soret, contain contributions of all three A substates and can, therefore, be only approximately modeled with a single enthalpy distribution and a single preexponential. The bond formation step at the heme is fastest for the A0 substate, intermediate for the A1 substate, and slowest for A3. Rebinding between 200 and 300 K displays several processes, including geminate rebinding, rebinding after ligand escape to the solvent, and interconversion among the A substates. Different kinetics are measured in each of the A bands for times shorter than the characteristic time of fluctuations among the A substates. At longer times, fluctuational averaging yields the same kinetics in all three A substates. The interconversion rates between A1 and A3 are determined from the time when the scaled kinetic traces of the two substates merge. Fluctuations between A1 and A3 are much faster than those between A0 and either A1 or A3, so A1 and A3 appear as one kinetic species in the exchange with A0. The maximum-entropy method is used to extract the distribution of rate coefficients for the interconversion process A0 <--> A1 + A3 from the flash photolysis data. The temperature dependencies of the A substate interconversion processes are fitted with a non-Arrhenius expression similar to that used to describe relaxation processes in glasses. At 300 K the interconversion time for A0 <--> A1 + A3 is 10 microseconds, and extrapolation yields approximately 1 ns for A1 <--> A3. The pronounced kinetic differences imply different structural rearrangements. Crystallographic data support this conclusion: They show that formation of the A0 substate involves a major change of the protein structure; the distal histidine rotates about the C(alpha)-C(beta) bond, and its imidazole sidechain swings out of the heme pocket into the solvent, whereas it remains in the heme pocket in the A1 <--> A3 interconversion. The fast A1 <--> A3 exchange is inconsistent with structural models that involve differences in the protonation between A1 and A3.
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