Comparison of Populations Based on Attribute Data,when Covariance Matrices are Unequal

Mahalanobis—like distance indices B² and G² of BALAKRISHNAN and SANGHVI (1968) are employed to compare multinomial populations of proportions in human data. Recently, BOWERING and MISRA (1982) employed these methods, with modifications, in a different field viz. to compare fish stocks, based on meristic characters. The method of BALAKRISHNAN and SANGHVI (1968), however, assumes equality of covariance matrices, which is doubtful with multinomial populations of proportions. In this paper a statistical method for comparing such populations (where covariance matrices are not equal) is presented. Also, a feature of the G² method of BALAKRISHNAN and SANGHVI (1968) is discussed, which makes its statistical status a little more clear.     

A Multivariate Procedure for Linear Comparisons of Mean Vectors when Residual Covariance and Regression Coefficient Matrices are Unequal

A multivariate procedure for testing linear comparisons of vectors of adjusted group means of response (dependent) variables when groups differ in residual covariance and regression coefficient matrices is presented. Such disparities have been observed in investigations of trends in contaminant levels in fish. Application of the procedure is illustrated with data on Atlantic cod (Gadus morhua). The procedure is quite general and can be employed to test any linear comparisons.     

Measuring the structural similarity of two communities composed of the same species

Summary The primary purpose of this paper is to propose empirical measures of the structural differences between two communities of plants or animals composed of the same species. Structure is defined to consist of; 1) the species in the community, 2) the pattern of interactions as represented by the covariance or correlation matrix of successive observations on each species, and 3) the mean abundances of each species in each of the two communities. Statistical tests are proposed for testing whether the covariance matrices and the vectors of mean densities for each community are equal and empirical measures of the differences between the covariance matrices and mean vectors are proposed. Given unequal covariance or correlation matrices the factor analysis model is used to derive empirical measures of the degree to which each variable of the ecosystem is responsible for the observed defferences in the pattern of interactions in each community. These tests and measures were applied to data gathered byHunter (1966) on the abundances of six species ofDrosophila censused monthly over a period of approximately two and a half years in two adjacent, but different habitats near Bogota, colombia. The two covariance matrices were significantly different indicating different patterns of interactions in the twoDrosophila communities.     

Effects of Hatchery Rearing on Brain Structures of Rainbow Trout, Oncorhynchus mykiss

In this study, we contrast brain morphology from hatchery and wild reared stocks to examine the hypothesis that in salmonid fishes, captive rearing produces changes in brain development. Using rainbow trout, Oncorhynchus mykiss, as a model, we measured eight regions of the salmonid brain to examine differences between wild and hatchery reared fish. We find using multiple analysis of covariance (MANCOVA), analysis of covariance (ANCOVA) and discriminant function analysis (DFA) that the brains of hatchery reared fish are relatively smaller in several critical measures than their wild counterparts. Our work may suggest a mechanistic basis for the observed vulnerability of hatchery fish to predation and their general low survival upon release into the wild. Our results are the first to highlight the effects of hatchery rearing on changes in brain development inbreak fishes.     

A note on simulating null distributions for G matrix comparisons

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G . We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti‐conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.     

A Multivariate Procedure for Comparing Mean Vectors for Populations with Unequal Regression Coefficient and Residual Covariance Matrices

In fisheries research there is a need to compare vectors of means of continuous random response variables adjusted for concomitant variations of covariables for populations that have unequal regression coefficient and residual covariance matrices. A multivariate procedure that provides an extended comparison of vectors of adjusted means is presented. An example is presented using a real data set. The procedure is quite general and applicable to many other fields of research.     

One-Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations

When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, SRIVASTAVA and AWAN (1982) develop one-way ANOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, KABE (1965), (1974).     

THE COVARIANCE STRUCTURE OF LIFE-HISTORY CHARACTERS IN DAPHNIA PULEX

The genetic covariance structure for life-history characters in two populations of cyclically parthenogenetic Daphnia pulex indicates considerable positive correlation among important fitness components, apparently at odds with the expectation if antagonistic pleiotropy is the dominant cause of the maintanence of genetic variation. Although there is no genetic correlation between offspring size and offspring number, present growth and present reproduction are both strongly positively correlated genetically with future reproduction, and early maturity is genetically correlated with larger clutch size. Although the ubiquity of antagonistic pleiotropy has been recently questioned, there are peculiarities of cyclical parthenogenesis that could lead to positive life-history covariance even when negative covariance would be expected in a similar sexual species. These include the influence of nonadditive gene action on evolution in clonally reproducing organisms, and the periodic release of hidden genetic variance within populations of cyclical parthenogens. Examination of matrix similarity, using the bootstrap for distribution-free hypothesis testing, reveals no evidence to suggest that the genetic covariance matrices differ between the populations. However, there is considerable evidence that the phenotypic and environmental covariance matrices differ between populations. These results indicate approximate stability of the genetic covariance matrix within species, an important assumption of many phenotypic evolution models, but should caution against the use of phenotypic in place of genetic covariance matrices.     

The Method of Random Skewers

Ecological and evolutionary studies are often concerned with the properties of covariance matrices. The method of random skewers (RS method) has been used compare a matrix to an a priori vector or to compare two matrices. The method involves multiplying a matrix by many random vectors drawn from a uniform distribution over all possible vector directions. The comparisons are usually made using the average angle (or cosine) of the response vectors to an a priori vector or to the response vectors corresponding from another matrix. Angles are usually constrained to the interval 0°–90° because the distribution of response vectors is bipolar bimodal. The size of the average angle or cosine depends strongly on the relative sizes of the eigenvalues (especially the first). The distribution of angles between pairs of response vectors from two covariance matrices is more complicated because it depends on the differences in orientation of the eigenvectors and the relative sizes of the eigenvalues of the both matrices. The average absolute value of the angles between these pairs of response vectors depends on the relative sizes of the eigenvalues of the matrices making it difficult to interpret its meaning without knowledge of the eigenvalues and eigenvectors of the two matrices. Thus, it is simpler to just directly compare matrices in terms of these quantities.     

Discriminant functions for linear comparisons of means when covariance matrices are unequal

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.     

Changes in the lower trophic levels as a consequence of the level of fish manipulation in the ponds

Cyprinid fish of different mature age classes (3+ -4+) and stocks (100, 300 and 500 kg/ha) were introduced into each of three experimental ponds with area of 0.3 ha (average depth ca 1.7 m) while the fourth pond was left free of fish. Bream (Abramis brama L.), white bream (Blicca bjoerkna L.) and roach (Rutilus rutilus L.) made up 75% of the total cyprinid biomass, with wild carp (Cyprinus carpio L.) as the remaining 25%. The introduced fish spawned successfully. The high (above 300 kg/ha) planktivorous and benthivorous fish stocks resulted in several qualitative and quantitative alterations of the food chain structure in our simulation pond experiments. These alterations must primarily be assigned to changes caused by both the zooplanktivory and benthivory nature of the stocked fish populations. At the higher levels of fish biomass, Secchi depth was influenced significantly by chlorophyll-a concentration. Most of the variance in suspended solids concentration could be explained by the biomass ratio of the mature benthivorous fish. There was a clear shift in algal cell size in the ponds with the higher fish stocks: ponds with more fish had larger cells later in the summer. The relative influence of young cyprinid fish on crustaceans species composition and biomass, and mature populations on benthic fauna abundance and biomass, was sufficiently greater at higher (300–500 kg/ha) fish stock rates.     

Stock discrimination and connectivity assessment of yellowfin seabream (Acanthopagrus latus) in northern South China Sea using otolith elemental fingerprints

Connectivity between fish stocks is fundamental to the understanding of population dynamics and the implementation of sustainable fisheries management. Otolith microchemistry is a promising tool as it can provide information on the continuous growth of otoliths and the environmental effects on otolith composition. Such elemental fingerprints can help distinguish different stocks or life history stages, identify the origins or nursery areas of fish, and assess population structure. In this study, we examined the stock discrimination and spatial connectivity of cage-cultured and wild stocks of yellowfin seabream (Acanthopagrus latus) from the coastal waters of Shantou, Yangjiang, and Zhanjiang in China southern province Guangdong during 2012–2014, based on otolith trace-elemental signatures using multivariate statistical analysis and machine learning approaches. The concentrations of 13 elements (⁷Li, ²³Na, ²⁴Mg, ⁴⁰Ca, ⁵⁵Mn, ⁵⁶Fe, ⁵⁹Co, ⁵⁹Ni, ⁶⁴Cu, ⁶⁵Zn, ⁸⁸Sr, ¹²²Sb, and ¹³⁷Ba) in the natal spot of fish otoliths, representing the embryonic and paralarval stages of fish, were analyzed using laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Stepwise discriminant analysis and random forests were used to distinguish the cultured and wild stocks of yellowfin seabream, and non-metric multidimensional scaling (NMDS) and cluster analysis were used to determine the spatial variation and connectivity of yellowfin seabream stocks. Overall, the cultured and wild stocks of yellowfin seabream could be identified with classification accuracy of 80.7% and 99.2% by using stepwise discriminant analysis and random forests respectively. When we compared site difference between cultured and wild stocks (site × stock interactions), the classification success was 60.4% for stepwise discriminant analysis and 85.7% for random forests. The misclassification of cultured and wild stocks within the three sites suggested the spatial connectivity between stocks and among sampling locations. Our findings suggested that the three wild stocks of yellowfin seabream from Guangdong coastal waters could be considered as one unit for management, and the difference between cultured and wild stocks was significant for yellowfin seabream from Shantou and Yangjiang, but less significant for yellowfin seabream from Zhanjiang. This study demonstrated that otolith elemental fingerprints can help improve our knowledge on the spatial connectivity, population structure, and life history of fish stocks, and random forests can be a useful tool for identifying cultured and wild stocks compared to the traditional stepwise discriminant analysis.     

Synchronous patterns of fluctuations in two stocks of anchovy Engraulis ringens Jenyns, 1842 in the Humboldt Current System

Most of the studies investigating synchrony in fluctuations of abundance of small pelagic fish have been based on catch data only, which do not describe the dynamics of populations as a relative abundance index. In this paper, catch, biomass, recruitment and recruitment rate, were used to compare synchronous changes for two stocks of anchovy (Engraulis ringens) from 1982 to 2004. One is the North Central Peru stock (NCP) and the other is the shared South Peru‐Northern Chile stock (SPNC). Correlation analysis demonstrated a significant association between population time series, particularly during the growing phase of the stocks. Thus, the synchronous fluctuation pattern of the two stocks is due to the recovery phase and probably driven by density‐independent effects of simultaneous favorable environmental conditions occurring in the two regions. The conclusions were: (i) both NCP and SPNC anchovy stocks are in an overall positive phase of synchrony, (ii) higher correlations in the synchronous pattern of fluctuations occurred during simultaneous increase of biomass, and (iii) short‐term fluctuations were negative when the abundance of the stock was lower and/or impacted by El Niño events.     

Patterns of phenotypic covariation and correlation in modern humans as viewed from morphological integration

Proportionality of phenotypic and genetic distance is of crucial importance to adequately focus on population history and structure, and it depends on the proportionality of genetic and phenotypic covariance. Constancy of phenotypic covariances is unlikely without constancy of genetic covariation if the latter is a substantial component of the former. If phenotypic patterns are found to be relatively stable, the most probable explanation is that genetic covariance matrices are also stable. Factors like morphological integration account for such stability. Morphological integration can be studied by analyzing the relationships among morphological traits. We present here a comparison of phenotypic correlation and covariance structure among worldwide human populations. Correlation and covariance matrices between 47 cranial traits were obtained for 28 populations, and compared with design matrices representing functional and developmental constraints. Among-population differences in patterns of correlation and covariation were tested for association with matrices of genetic distances (obtained after an examination of 10 Alu-insertions) and with Mahalanobis distances (computed after craniometrical traits). All matrix correlations were estimated by means of Mantel tests. Results indicate that correlation and covariance structure in our species is stable, and that among-group correlation/covariance similarity is not related to genetic or phenotypic distance. Conversely, genetic and morphological distance matrices were highly correlated. Correlation and covariation patterns were largely associated with functional and developmental factors, which probably account for the stability of covariance patterns.     

The host‐specific parasite Nippotaenia mogurndae confirms introduction vectors of the fish Perccottus glenii in the Volga river basin

Two alternative hypotheses about aquarium vs fish‐farm vectors of non‐native distribution of the fish rotan, Perccottus glenii (Odontobutidae), within the Volga River Basin were assessed using a parasitological approach. Three separate locations were studied where rotan populations were assumed to have different introduction histories: (i) vicinities of Tarakanovo pond, Moscow province (aquarium release in 1950), (ii) Ilev fish farm, Nizhniy Novgorod province (unintentional transportation together with stocking of commercial fish in 1970), (iii) the lower Volga River, Saratov province (unknown origin; first record in 1983). The odontobutid‐specific tapeworm Nippotaenia mogurndae was the most informative species because it has a complex life cycle and therefore does not persist in aquarium conditions. Absence of this tapeworm in the rotan populations in the first locality and presence in the second location are in agreement with the available information about appropriate vectors of introduction. Populations of rotan in the lower Volga (third locality) where N. mogurndae occurs could originate from individuals unintentionally transported to fish farms together with commercial fish species or have mixed origins. Thus, the presented parasitological data are in agreement with information concerning introduction vectors of P. glenii and confirm that the specific parasite N. mogurndae is a valuable biological tag for analysing vectors and pathways of geographical dispersal of rotan, P. glenii.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

The non-linear relationship between body size and function in parrotfishes

Parrotfishes are a group of herbivores that play an important functional role in structuring benthic communities on coral reefs. Increasingly, these fish are being targeted by fishermen, and resultant declines in biomass and abundance may have severe consequences for the dynamics and regeneration of coral reefs. However, the impact of overfishing extends beyond declining fish stocks. It can also lead to demographic changes within species populations where mean body size is reduced. The effect of reduced mean body size on population dynamics is well described in literature but virtually no information exists on how this may influence important ecological functions. The study investigated how one important function, scraping (i.e., the capacity to remove algae and open up bare substratum for coral larval settlement), by three common species of parrotfishes (Scarus niger, Chlorurus sordidus, and Chlorurus strongylocephalus) on coral reefs at Zanzibar (Tanzania) was influenced by the size of individual fishes. There was a non-linear relationship between body size and scraping function for all species examined, and impact through scraping was also found to increase markedly when fish reached a size of 15–20 cm. Thus, coral reefs which have a high abundance and biomass of parrotfish may nonetheless be functionally impaired if dominated by small-sized individuals. Reductions in mean body size within parrotfish populations could, therefore, have functional impacts on coral reefs that previously have been overlooked.     

Genetic variability, population size and isolation of distinct populations in the freshwater fish Cottus gobio L.

Analysis of allozyme data of the European freshwater fish Cottus gobio showed marked genetic differentiation across drainage basins in northeastern Bavaria, which points to the existence of at least two cryptic taxa. Genetic variability within populations differed significantly between these two taxa, which could be due to historical (bottlenecks) or ecological reasons (population size). To distinguish between these two hypotheses we sampled 12 distinct populations from Rhine, Elbe and Danube drainages. Using allozyme data we examined the influence of population size and isolation on genetic variability within populations. We used spatial extent of populations (patch size) as a measure for population size. To estimate isolation we calculated a compound measure which took into account patch size and distance to all neighbouring populations. Both patch size and isolation were highly correlated with genetic variability, explaining ≈95% of the variance of genetic variability within populations. Furthermore, analysis of covariance suggests that the difference in genetic variability between taxa may be explained by differences in population size.     

Genetic population structure in flatfishes and potential impact of aquaculture and stock enhancement on wild populations in Europe

Marine fish wild stocks are known to be heavily depleted by overfishing and flatfish species are no exception. Wild catches being soon insufficient for responding to consumer demand, the cultivation of marine species appeared as a logical response to the need of seafood. Nevertheless, fish aquaculture also entails major impacts on wild populations from which genetic ones are now better known. The hybridization between domestic and native strains potentially have a genetic impact on recipient populations as long as 1) domestic populations are distinct from native wild ones (through domestication process, genetic improvement of captive stocks) and/or 2) the native wild populations are structured (metapopulation structure, local adaptation). Some of the flatfish species exhibit population differentiation and even local adaptation and the release of domestic genetically modified fishes (selected, transgenic) could threaten their survival in case of introgression. The impact of aquaculture on flatfishes is probably still low as land-based farms and low production levels guaranty low rates of escapes and therefore limited contacts between wild and farmed strains. However, flatfish aquaculture is regarded by experts as a rapidly growing domain that will greatly develop soon. In our opinion, this perspective, added to the quite good performances of farmed flatfishes when released into the wild, fully justifies a stronger interest from the scientific community to the conservation of their wild stocks.