Minimum Adequate Models Research Articles

Ecological correlates of the threat of extinction in Neotropical bird species

AbstractPredicting the threat of extinction aids efficient distribution of conservation resources. This paper utilises a comparative macroecological approach to investigate the threat of extinction in Neotropical birds. Data on ecological variables for 1708 species are analysed using stepwise regression to produce minimum adequate models, first using raw species values and then using independent contrasts (to control for phylogenetic effects). The models differ, suggesting phylogeny has significant effects. The raw species analysis reveals that number of zoogeographical regions occupied, elevational range and utilisation of specialised microhabitats were negatively associated with threat, while minimum elevation and body mass were positively associated, whereas the independent contrasts analysis only identifies zoogeographical regions as important. Confining the analysis to the 582 species restricted to a single zoogeographical region reveals elevational range and number of habitats occupied to be negatively correlated with threat whether the analysis is based on the raw data or on independent contrasts. Analysis of four contrasting zoogeographical regions highlights regional variation in the models. In two Andean regions the threat of extinction declines as the elevation range across which the species occurs increases. In the presence of substantial human populations on high Andean plateaus, a species with a greater elevational range may be more likely to persist at some (relatively) unsettled altitudes. In Central South America, the strongest predictor of threat is minimum elevation of occurrence: species with a lower minimum are less threatened. The minimum elevation result suggests that lowland species experiencing an ecological limit to their minimum elevation (min. elevation >0 m) may be more at risk than those not experiencing such a limit (min. elevation = 0 m). Finally, in southern Amazonia, where there is little altitudinal variation, the only weak predictors of threat are body size, larger species being more threatened, and number of habitats, species occupying more habitats being less threatened. These contrasting results emphasise the importance of undertaking extinction risk analyses at an appropriate geographical scale. Since the models explained only a low percentage of total variance in the data, the effects of human‐mediated habitat disturbance across a wide range of habitats may be important.

Diversity of native and alien plant species on rubbish dumps: effects of dump age, environmental factors and toxicity

Abstract. The flora of 96 rubbish dumps consisting of organic, inorganic and industrial wastes was studied in the Czech Republic. Some dumps contained toxic substances (heavy metals, chlorethylenes, phenols, polychlorinated biphenyls, oil hydrocarbons and biogas). Statistically significant factors explaining the number and proportional representation of native plant species, archaeophytes (introduced before 1500) and neophytes (introduced later) were determined. In total, 588 species of vascular plants were recorded, with archaeophytes (133 species) over‐represented and native species (322 species) and neophytes (133 species) under‐represented compared to their proportions in the national flora. Minimum adequate models were used to determine the effects of several factors on species numbers and proportions, independent of other factors. Dump area, human density in the region and altitude (non‐significant only in archaeophytes) were correlated positively with species numbers. Dump age, expressed as time since dump establishment, interacted with the dump toxicity; species numbers increased with dump age on non‐toxic dumps, whereas on toxic dumps no increase in numbers was noted. For neophytes, dump toxicity also interacted with human density; the increase in numbers of neophytes with human density is more pronounced on toxic than on non‐toxic dumps. The variables measured failed to explain observed differences in proportional representation of native species, archaeophytes and neophytes. This suggests that the occurrence of species growing in such extreme habitats is driven overwhelmingly by factors such as anthropogenic disturbance. A possible explanation for the positive effect of altitude on species numbers on dumps is that the effect of heating of the deposited substrate by microbiological processes, documented by previous studies, overrides the effect of altitude which was shown repeatedly to have a negative effect on species richness. Neophyte distribution is driven by an interplay of factors distinct from those influencing the distribution of native species, namely toxicity and human density (the latter we interpret as a surrogate for propagule pressure). Their distribution on studied dumps is more restricted than that of native taxa and archaeophytes, and they are more limited by toxic substrata; more intensive propagule pressure is required for their establishment at dumps with higher toxicity levels.

Social structure of the mara (Dolichotis patagonum) as a determinant of gastro-intestinal parasitism.

A one-year study of gastro-intestinal parasitism in a free-ranging population of maras at Whipsnade Wild Animal Park, UK, revealed a strong relationship between membership of social units and both intensity and prevalence of infection. The mara, a hystricomorph rodent from southern Argentina, has a social organization including both monogamy and communal denning of the young, an apparently unique combination among mammals. From October 1992 to September 1993, strongyloid parasite loads were estimated from faecal egg counts. A minimum adequate model was fitted to the data using the Genstat statistical package. This showed that family membership had a highly significant effect on the intensity of egg shedding in faeces, and a significant effect on the prevalence of infection. After controlling for both extrinsic environmental and intrinsic demographic factors, homogeneity of infection was greater within than between families and adult pairs.

A Macintosh BASIC program for fitting linear additive models to data by weighted least squares methods, with automatic elimination of redundant parameters from the model

A BASIC program for fitting linear additive models to data with weighted or unweighted least squares methods and matrix procedures is described. Written and compiled to run on Macintosh II type machines (68020/68030/68040) with coprocessor (68881/68882), the program fits the model supplied by the user as an X or design matrix and provides the option of making the model's parameters orthogonal. Predicted values plus regression and residual terms are calculated. For the weighted fit, the significance of the residual term is evaluated and redundant parameters sequentially and automatically removed until a minimum adequate model is achieved. An appropriate design matrix allows weighted fitting of models for multiway analyses of variance (e.g. factorial, nested and split plot), simple or multiple linear or curvilinear regression, combinations of these in covariance analyses, and genetic analyses (including diallel cross analyses). Sums of squares for individual parameters and orthogonal comparisons can be calculated by the program.

Comparisons of unweighted with weighted least squares methods of fitting a genetic model to a diallel cross

Data on mean seed weight from the F1 of a complete 6 by 6 diallel cross with flax (Linum usitatissimum), grown in a randomized block design, were used to evaluate the benefits of weighted compared with unweighted least squares fitting of a genetical model for this type of cross. The model examines combining abilities and reciprocal differences. Matrix methods were employed in this study for weighted and unweighted least squares solutions. These methods accommodate rapid modification of appropriate models through changes in the corresponding design matrices, the use of various types of weight, the handling of missing data, the construction of orthogonal sets of parameters, the calculation of sums of squares accounted for by one or more of the parameters in the model, and the analysis of variance of the data. Weights used here were reciprocals of variances of diallel cell means, i.e., a variance reflecting variation among replicate mean values for a given cell. Weighted fitting with sequential elimination of redundant parameters in the original model extracted the minimum adequate model. Predicted values, generated from significant parameters in weighted or unweighted fittings of the model to overall F1 and parental means, were compared. Deliberate, increasing distortion of data in one replicate of the randomized block design showed that weighted fitting of the model distinguished consistent diallel data from distorted, giving predicted values reflecting the more reliable observations.Key words: diallels, weighted versus unweighted fitting.

Genetic control of seed weight in flax (Linum usitatissimum) and possible implications

Mean seed weight data were obtained from the F1 and F2 of a six-by-six diallel cross with flax (Linum usita-tissimum L.). Pronounced reciprocal differences appeared in the F1, but had largely disappeared by the F2. The genetic control of mean seed weight was examined using two types of analysis of variance. The models underlying both analyses were fitted to the data by matrix methods supplying weighted least-squares estimates of the parameters in the models. Weights, the use of which dealt with the problem of variation in the reliability of means, were the reciprocals of the variances of individual cell (cross/self) means in the diallel data table. Elimination of redundant parameters supplied the minimum adequate models for each analysis type. Dominance was apparently masked by the large transient maternal effects in the F1, but surfaced in the F2, where dominance was towards larger mean seed weight. This may be coupled with findings elsewhere of possible advantages for larger seed weights to speculate on a role in preserving infrequent hybrid progeny among inbreeding (flax) species. Maternal effects producing larger seed size, plus dominance with the same result might be valuable, in conjunction with growth and competitive advantages conferred by larger seed, in preventing early elimination of rare hybrids.

A Pascal program for weighted least squares regression on a microcomputer

Weighted least-squares regression has been programmed in Pascal for a microcomputer. A double precision Pascal compiler and the Motorola 6809 assembler produce a fast machine-code program occupying 22 000 bytes of memory when appended to the Pascal run-time module. Large data sets fit in the remaining memory. A regression with 72 observations and 24 parameters runs in 7 min, excluding optional print out of large matrices. The maximum dimensions of the design matrix, X, can be altered by modifying two Pascal constants. Minor changes to the Pascal source program will make it compatible with other Pascal compilers. The program optionally orthogonalises the X matrix to detect linearly-dependent columns in X, and/or generate orthogonal parameter estimates. After orthogonalizing X and fitting the model, the parameter estimates for the original X can be retrieved by the program. Regressions on a repeatedly reduced model are performed through elimination of columns in X until the minimum adequate model is obtained.