Strategies to fit pattern-mixture models

Whereas most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years (Little, 1993, 1994). In this paper, we outline several strategies to fit pattern-mixture models, including the so-called identifying restrictions strategy. Multiple imputation is used to apply this strategy to realistic settings, such as quality-of-life data from a longitudinal study on metastatic breast cancer patients.     

Comparing alternative models to empirical data: cognitive models of western scrub-jay foraging behavior

Animals often select one item from a set of candidates, as when choosing a foraging site or mate, and are expected to possess accurate and efficient rules for acquiring information and making decisions. Little is known, however, about the decision rules animals use. We compare patterns of information sampling by western scrub-jays (Aphelocoma californica) when choosing a nut with three decision rules: best of n (BN), flexible threshold (FT), and comparative Bayes (CB). First, we use a null hypothesis testing approach and find that the CB decision rule, in which individuals use past experiences to make nonrandom assessment and choice decisions, produces patterns of behavior that more closely correspond to observed patterns of nut sampling in scrub-jays than the other two rules. This approach does not allow us to quantify how much better CB is at predicting scrub-jay behavior than the other decision rules. Second, we use a model selection approach that uses Akaike Information Criteria to quantify how well alternative models approximate observed data. We find that the CB rule is much more likely to produce the observed patterns of scrub-jay behavior than the other rules. This result provides some of the best empirical evidence of the use of Bayesian information updating by a nonhuman animal.     

Measuring the fit of sequence data to phylogenetic model: allowing for missing data

It is fundamentally important to assess the fit of data to model in phylogenetic and evolutionary studies. Phylogenetic methods using molecular sequences typically start with a multiple alignment. It is possible to measure the fit of data to model expectations of data, for example, via the likelihood-ratio (G) test or the X(2) test, if all sites in all sequences have an unambiguous residue. However, nearly all alignments of interest contain sites (columns of the alignment) with missing data, that is, ambiguous nucleotides, gaps, or unsequenced regions, which must presently be removed before using the above tests. Unfortunately, this is often either undesirable or impractical, as it will discard much of the data. Here, we show how iterative ML estimators may directly estimate the site-pattern probabilities for columns with missing data, given only standard i.i.d. assumptions. The optimization may use an EM or Newton algorithm, or any other hill-climbing approach. The resulting optimal likelihood under the unconstrained or multinomial model may be compared directly with the likelihood of the data coming from the model (a G statistic). Alternatively the modified observed and the expected frequencies of site patterns may be compared using a X(2) test. The distribution of such statistics is best assessed using appropriate simulations. The new method is applicable to models using codons or paired sites. The methods are also useful with Hadamard conjugations (spectral analysis) and are illustrated with these and with ML evolutionary models that allow site-rate variability.     

Foraging information affects the nature of competitive interactions

If animals can learn environmental cues, how might their use of information affect competitive interactions between species? I used shared‐preference isoleg theory to generate four different predictions regarding possible ways information could affect density‐dependent habitat selection. To test these predictions, I conducted field experiments on the foraging behavior of three coexisting species of hummingbirds. I studied black‐chinned (Archilochus alexandri), blue‐throated (Lampornis clemenciae), and magnificent (Eugenes fulgens) hummingbirds at the Southwestern Research Station in the Chiricahua Mts. of Southeastern Arizona, USA. Blue‐throated hummingbirds behaviorally dominate the other two species. I found that birds foraging with complete information (via learned color cues) avoid some of the negative effects from competition. Birds that foraged with complete information remained highly selective on rich feeders even with high competitor densities. When birds suffered an information deficit, however, the two subordinate species shifted their foraging preferences. The dominant species did not shift preference. Each subordinate's shift reflects its unique place in this competitively structured guild. With high competitor densities, black‐chinneds shifted from selective to opportunistic foraging when they also suffered from an information deficit. Thus, an information deficit caused black‐chinneds to cross over their first isoleg. Rather than reduce foraging efficiency, the magnificents shortened their foraging time. I use the magnificents’ response to competition and an information deficit to explore the possibility that this guild of hummingbirds is centrifugally organized. My results require us to consider the information‐gathering (e.g., learning) abilities of individual decision‐makers when we evaluate density‐dependent habitat selection. Differences in the level of usable information can alter the way coexisting species respond to competitive interactions that potentially structure communities.     

Using linear and non-linear regression to fit biochemical data

For biochemists or chemists the most common form of data analysis is likely to be regression analysis. This is a technique to find the ‘best’ values for various experimental parameters; defined as those values which, when used in an appropriate equation, result in the minimum deviation of the calculated results from the experimental data. Despite the widespread application of regression analysis, the basis of the technique and the underlying assumptions are often poorly understood or appreciated. This article describes the basics of linear and non-linear regression, the role of ‘weighting’ and the potential pitfalls of such analyses.     

Using empirical data to model transgene dispersal

One element of the current public debate about genetically modified crops is that gene flow from transgenic cultivars into surrounding weed populations will lead to more problematic weeds, particularly for traits such as herbicide resistance. Evolutionary biologists can inform this debate by providing accurate estimates of gene flow potential and subsequent ecological performance of resulting hybrids. We develop a model for gene flow incorporating exponential distance and directional effects to be applied to windpollinated species. This model is applied to previously published data on gene flow in experimental plots of Agrostis stolonifera L. (creeping bentgrass), which assessed gene flow from transgenic plants resistant to the herbicide glufosinate to surrounding non-transgenic plants. Our results show that although pollen dispersal can be limited in some sites, it may be extensive in others, depending on local conditions such as exposure to wind. Thus, hybridization under field conditions is likely to occur. Given the nature of the herbicide resistance trait, we regard this trait as unlikely to persist in the absence of herbicide, and suggest that the ecological consequences of such gene flow are likely to be minimal.     

Linking data to models: data regression

Mathematical models are an essential tool in systems biology, linking the behaviour of a system to the interactions between its components. Parameters in empirical mathematical models must be determined using experimental data, a process called regression. Because experimental data are noisy and incomplete, diagnostics that test the structural identifiability and validity of models and the significance and determinability of their parameters are needed to ensure that the proposed models are supported by the available data.     

Mathematical models for the swimming pattern of a lamprey

A significant characteristic in a swimming pattern of a lamprey is the generation of a constant phase lag along its body in spite of the wide range of undulation frequencies. In this paper, we discuss a mathematical treatment for coupled oscillators with time-delayed interaction and propose a model for the central pattern generator (CPG) of a lamprey to account for the generation of a constant phase relation, with consideration of the signal conduction time. From this model, it is suggested that the desired phase relation can be produced by long ascending connections from the tail to the neck region of the CPG.     

Influence of the uterine environment on rat sperm motility and swimming speed

The present study compared several rat sperm parameters in semen samples recovered from a natural uterine environment (i.e., intact estrous female) to those recovered from an artificially induced uterine environment (i.e., ovariectomized hormonally primed female). The sperm parameters measured were percent motile, percent exhibiting forward progressive motility, actual swimming speed, and linear swimming speed. The comparisons were conducted at four postcopulatory time points (0.25, 1.5, 3, and 6 hours) in order to detect differences as a function of residence time within the uterus. No significant differences (P less than 0.05) in the parameters were seen between the two types of uterine environments. Residence time within the reproductive tract had no significant effect on the parameters with the exception of percent motile, which was significantly increased (P less than 0.01) at the 1.5-hour postcopulatory time point.     

Details of local dispersion improve the fit of neighborhood competition models

I performed a series of greenhouse experiments to explore how patterns in the dispersion of local competitors affect the reproductive performance of Capsella bursa-pastoris, Poa annua and Senecio vulgaris. I manipulated the density and relative frequency of competitors in each of three concentric rings surrounding a central plant, thereby creating a variety patterns by which local competitors were distributed. Neighborhood competition models were used to predict the seed output of these central plants. For both Senecio vulgaris and Capsella bursa-pastoris, I found that models which incorporated the dispersion of competitors, as well as the relative emergence date of plants, performed substantially better than those that considered only the distance between the central plant and each of its competitors. I was unable to measure the seed output of Poa annua but neither emergence data nor the dispersion of competitors were important in determining its final dry-weight.Present address: Department of Biology, Box 1137, Washington University, 1 Brookings Drive, St. Louis, MO 63130, USA     

Quantification and identification of sperm subpopulations using computer-aided sperm analysis and species-specific cut-off values for swimming speed

Abstract

Motility is an essential characteristic of all flagellated spermatozoa and assessment of this parameter is one criterion for most semen or sperm evaluations. Computer-aided sperm analysis (CASA) can be used to measure sperm motility more objectively and accurately than manual methods, provided that analysis techniques are standardized. Previous studies have shown that evaluation of sperm subpopulations is more important than analyzing the total motile sperm population alone. We developed a quantitative method to determine cut-off values for swimming speed to identify three sperm subpopulations. We used the Sperm Class Analyzer^® (SCA) CASA system to assess the total percentage of motile spermatozoa in a sperm preparation as well as the percentages of rapid, medium and slow swimming spermatozoa for six mammalian species. Curvilinear velocity (VCL) cut-off values were adjusted manually for each species to include 80% rapid, 15% medium and 5% slow swimming spermatozoa. Our results indicate that the same VCL intervals cannot be used for all species to classify spermatozoa according to swimming speed. After VCL intervals were adjusted for each species, three unique sperm subpopulations could be identified. The effects of medical treatments on sperm motility become apparent in changes in the distribution of spermatozoa among the three swimming speed classes.     

Dietary fatty acid composition affects the repeat swimming performance of Atlantic salmon in seawater

Repeated critical swimming performance trials (Ucrit) were performed on Atlantic salmon (Salmo salar) to test the null hypothesis that the source of dietary lipids (fish-based, poultry-based, and plant-based) does not influence exercise and recovery performance. Four diets were prepared by extensively replacing supplemental lipid from anchovy oil (AO; 100% AO at 150 g/kg) with cold pressed flaxseed oil (FO; 25% AO, 75% FO), sunflower oil (SO; 25% AO, 75% SO), or poultry fat (PF; 25% AO, 75% PF). These diets had equivalent protein and energy concentrations, but due to the different supplemental lipid sources, varied widely in their fatty acid composition. Fish fed AO had a significantly higher (P<0.05) first Ucrit (2.62+/-0.07 body lenght s(-1)) than those fed PF (2.22+/-0.12 body lenght s(-1)) that had low muscle ratios of n-3 highly unsaturated fatty acids (n-3 HUFA) to saturated fatty acids (SFA) and arachidonic acid (AA), and high levels of oleic acid. Fish in the FO and SO diet groups swam as well as AO-fed fish in both swimming trials. The performance of fish fed AO decreased significantly (P<0.05) during the second swimming trial (i.e. Ucrit2/Ucrit1=0.92+/-0.02). No significant differences occurred between diet groups for the second swim trial. There was a positive correlation between both n-3 HUFA/SFA and n-3 HUFA/AA ratios, and Ucrit1. A negative correlation was found between dietary AA and oleic acids, and Ucrit1. The present study suggests that low dietary n-3 HUFA/ SFA and n-3 HUFA/AA ratios may negatively affect swimming performance. The former possibly can be offset by increasing linoleic acid in the presence of nutritionally adequate n-3 HUFA (e.g. SO diet). Lipid supplements consisting largely of vegetable oils did not compromise fish cardiorespiratory physiology under the conditions of this study.