Regression analysis of interactions between competing species

Abstract

SUMMARYThe method of investigating interactions in two-way tables by the regression analysis introduced by has been applied to data from competition diallel experiments with plant species reported by and Norrington-Davies (1968). Arithmetic and logarithmic scales were used in both experiments and the relative advantages of these are briefly discussed.Significantly high proportions of the interactions between species (row) and associates (column) effects were explained as differences between the linear regressions of individual performance on the associate values. Consequently the performance of the species in competition could largely be specified by three parameters. These were the species mean (v), the regression coefficient (b) and the mean effect of associates (a), which respectively measured the general vigour of the species, its sensitivity to competition and its aggressiveness. The parameters were used to derive formulae which provide descriptive and predictive measurements of the competitive advantage of species in particular combinations, and of the mixture performances relative to the performance of other mixtures or monocultures. The types of competition phenomena which could derive from a situation involving only general competitive abilities were shown to vary greatly and depended on the correlations between the three parameters in the experimental material.The possible types of interactions between associated genotypes (competi. tion, co-operation, antagonism, etc.) can be defined in terms of the general competitive ability parameters, or recognised as specific competitive abilities. It is thus suggested that the regression technique forms a useful approach to the discovery and classification of these effects among competing species.The second experiment (Norrington-Davies, 1968) involved competition between grass species under four different treatments. Common regression lines constructed over all treatments indicated that response to competitive stress was to some extent similar to the response to other kinds of environmental stress. This raised the concept that some aspects of general competitive abilities could be determined from general response to limitation in environmental factors. The plant breeding implications of this are briefly discussed, particularly the possibility of predicting performance under competition from performance as spaced plants.

A comparison of substitution and addition designs for the analysis of competitive interactions in Drosophila melanogaster

“…Alternatively, more general estimates of the average aggression (taken over all indicators) and the average response (taken over all associates) can be obtained (Breese and Hill, 1973). These values represent the relative competitive behaviour The data in table 3 show that, as observed previously (Eggleston, 1985), there is a significant amount of variation in both aggression and response, with generally more variation in aggression [x5=49548 and X(5)-270°7 for the characters Pa and l/ii3 respectively] than in Table 3 Estimates of the mean aggression and mean response of the six genotypes involved in the experiment for (a) character p and (b) character 1/sE All values relating to the character list' have been multiplied by 102 for ease of presentation.…”

“…The ascendancy of regression models to describe competitive interactions is primarily due to their popularity with many agricultural experimentalists (Breese and Hill, 1973;Mather and Caligari, 1981;Mather, Hill and Caligari, 1982 Baan-Hofman and Ennik, 1982; Vernon and Parker, 1983;Spitters and van den Bergh, 1982), or with the use of competitive mixing of different crops or cultivars to stabilise or improve the total yield (Chowdury and Hodgson, 1982;Spitters, 1983b;Salter et a!., 1985;Mead and Riley, 1981). These experiments generally differ both in design and analysis with the weed-crop interactions conforming more to an addition type design and the mixed cropping experiments usually being more suited to a substitution design analysis.…”

Competitive interactions in Drosophila melanogaster: recurrent selection for aggression and response

“…These competitive effects may be combined to describe how genotypes exert competitive pressure or aggression on the one hand, and respond to such aggression on the other. This distinction between aggression and response was drawn by Breese and Hill (1973) and the analytical procedure was refined by Mather and Caligari (1983). Subsequently, this model for the analysis of competitive interactions (although developed using Drosophila melanogaster as a model system) has been applied to a range of experimental and commercial material including Lolium perenne (Mather, Hill and Caligari, 1982) and Hordeum vulgare (Powell, Caligari and Thomas, 1985).…”

The competition diallel and the exploitation and interference components of larval competition in Drosophila melanogaster

“…This may be due to the closely controlled environmental conditions of these experiments which leave little opportunity for niche partitioning and interference which in turn are the major contributors to the interaction between sensitivity and pressure. Such interaction is more likely to be found in plant competition (Breese & Hill, 1973; Mather et al, 1982) and it would be interesting to know how the model behaves in these situations. The model also explains conflicting evidence from previous studies.…”

“…The diallel is formed by competing each strain with every other strain, including itself, and recording the performance of the primary (indicator) genotype in the presence of various associate competitors. However, with notable exceptions (McGilchrist & Trenbath, 1971) the analysis of such diallels has been largely empirical (Williams, 1962;McGilchrist, 1965;Norrington-Davies, 1967, 1968Breese & Hill, 1973;Mather & Caligari, 1983;Eggleston, 1985;de Miranda & Eggleston, 1987, 1988c with little regard for the biological determinants underlying the diallel. Hence, in this paper we present an analytical model for the competition diallel based on three linear biological parameters, representing both the exploitation (acquisition and utilization of a common resource) and interference (unique resources and mixture benefits) components of competition (Birch, 1957).…”