In the following sections the data are reanalysed through LM and GLM for a new spatial subdivisions - 7 latitudinal zones - and an exploratory statistical technique, the PCA, was also used to visualise the trends in franciscana diet with respect to spatial location.
4.4.1 Refining the study area: the latitudinal zones
The variation in the franciscana diet between the two major areas, northern and southern, of the study region was analysed in the previous sections. The northern and southern areas were defined according to the fishing areas utilised by the fishing vessels of Tramandai/Imb´e and Rio Grande/Barra, respectively (see section 4.2.1). However, the location of franciscanas within each area is expected to vary continuously along the coast (capture events), and it is possible to divide the study region into more detailed zones.
According to the fishing vessels, the information on captures were given according to cities and light house references, and occurred in depths less than 50m. Hence in the midst of the limit of the 50m isobath, and according to the distances of the cities and light houses, the study area was further subdivided into 7 latitudinal zones (figure 4.26) as follows:
• Zone 1 = 29o 11’ to 30o 01’ S (Torres city to Tramandai city);
• Zone 2 = 30o 01’ to 30o 41’ S (Tramandai city to Solidao lighthouse);
• Zone 3 = 30o 41’ to 31o 09’ S (Solidao lighthouse to Mostardas lighthouse);
• Zone 4 = 31o 09’ to 31o 40’ S (Mostardas lighthouse to Conceicao lighthouse);
• Zone 5 = 31o 40’ to 32o 07’ S (Conceicao lighthouse to Barra);
• Zone 6 = 32o 07’ to 32o 35’ S (Barra to southern Sarita lighthouse);
• Zone 7 = 32o 35’ to 33o 05’ S (southern Sarita lighthouse to Albardao lighthouse).
Tramandai 100m Torres Barra Chui Albardao Sarita Conceicao Mostardas Solidao 7 6 5 4 3 2 1 50m Tramandai South America 46 Wo 29 So 34 So
Figure 4.26: Map corresponding to the new subdivisions - 7 latitudinal zones - for further analysis of franciscana diet along the study area. In the previous analysis,
the northern area dol- phins belonged to the
zones 1, 2, and 3,
whereas for the southern franciscanas were from the zones 4, 5, 6, and
7. Except for one an-
imal from the northern coast which belonged to the zone 4. The francis- cana specimens sampled, which contained stomach contents, for each zone were: N= 30 (zone 1), N= 34 (zone 2), N= 26 (zone 3), N= 12 (zone 4),
N= 52 (zone 5), N= 72 (zone 6), and N= 18 (zone 7).
4.4.2 Linear and Generalized Linear Models and the latitudinal zones
Following the methodology described on section 4.2.4, the relationships between franciscana prey species frequency (GLM), prey lengths and weights (LM), were analysed according to the latitudinal zones. Temporal variation (season) was considered as well. The values of degrees of
freedom, residuals, F,p, and the estimated effects, are demonstrated in the variance/deviance tables.
According to the results of sections 4.3.3 and 4.3.4, for further analysis of LM and GLM the
prey species with low numbers or occurrences were discarded. They are: the fishes Cteno-
sciena gracilicirrhus, Pomatomus saltatrix, Mugil sp., Stromateus brasiliensis, Licengraulis grossidens, Raneya fluminensis, Prionotus sp., Syacium papillosum, Paralichtys isosceles, and Pagrus pagrus; and the cephalopods Octopus tehuelchus, Eledone sp., and Semirrosia tenera.
For the prey taxa, the crab species Loxopagurus loxocheles and Dardanus insignis, the infra-
order Brachiura, and the suborder Pleocyemata were not included because the correct iden- tification was only possible for the southern franciscanas (see section 4.3.2). Similarly, the
shrimp species (Artemesia longinaris, Pleoticus muelleri, Loxopagurus loxocheles, Dardanus
insignis), the family Penaidae, superfamily Penaeoidea, and the suborder Dendrobranchiata were not considered. However, they are again treated as the ”shrimp specimens” group.
4.4.3 Principal Component Analysis (PCA) and the latitudinal zones
Principal component analysis (PCA) is a well-known technique which reduces the information of many variables into fewer, orthogonal dimensions. PCA finds a set of standardized linear combinations (SLCs), called the principal components, which are orthogonal and taken to- gether can explain all the variance of the original data. The first principal component explains the largest variance among all SLCs of x. Similarly, the second principal component explains the largest variance among all SLCs of x uncorrelated with the first principal component, and so on. In general, there are as many principal components as variables. However, because of the way they are calculated, it is usually possible to consider only a few of the principal components, which together explain ”most” of the original variation. An important aspect of PCA, as opposed to discriminant analysis, is that it does not use any information on group membership and, thus, only accounts for the variation observed in the data (Venables and Ripley, 1997).
We used PCA to analyse the 7 latitudinal zones (figure 4.26) according to the franciscana diet. The variables were standardised to their means prior to conducting the PCA. The variables entered were: (a) ”prey numbers” (numerical abundance of prey species ingested in the area/total number of franciscanas analysed in the area)(n= 39 prey species), and (b)
”prey occurrence” (number of franciscanas in which a prey taxon occurred/total number of franciscanas analysed in the area)(n= 39 prey species). Furthermore, the means of (c) ”estimated prey lengths” and ”estimated prey mass” of the prey species for each zone were also investigated within PCA. The last two data are physical measurements, so the strategy was to work on a log scale (as in section 4.3.4). The prey species (n= 31) used for the analysis are listed in the tables 4.2 and 4.3. The covariance estimation function was chosen to perform the principal components analysis, when the original observations were on a equal measure, as in the case of prey numbers and prey occurrence, and were unscaled data. The correlation estimation function was used for the prey lengths and mass because they are observations of different types, and also because they are scaled data.
The percent of variance in each data set explained by each principal component (PC) is re-
ported (e.g. PC1 (89%)). Furthermore, the principal component loadings were calculated.
The principal component loadings are the coefficients of the principal components transfor- mation. They provide a convenient summary of the influence of the original variables on the principal components, and thus a useful basis for interpretation. A graphic plotted of the loadings allows one to see at a glance which variables are best explained by each component (S-PLUS 6 for Windows Guide to Statistics, Volume 2,Insightful Corporation, Seattle, WA).
To finish this section analyses, another graphical representation of the loadings was explored. The biplot (Gabriel, 1971) is a method to represent both the cases and variables. It allows representation of both the original variables and the transformed observations on the major principal components axes. By showing the transformed observations, one can easily interpret the original data in terms of the principal components. By showing the original variables, one can view graphically the relationships between those variables and the principal compo- nents (PC1 and PC2). In short, the biplot gives a comprehensive view of both the principal components and the original data.