Introduction
The existence of a diversity gradient, where the maximums are present in
equatorial regions and the minimums in polar regions, is observed in
many groups of organisms(Willig, Kaufman, and Stevens 2003; Hawkins et
al. 2003) This gradient seems to be explained by the Energetic,
Water-Energy, Altitude, Climatic Heterogeneity, Primary Productivity,
and Metabolic hypotheses(Wright 1983; Hawkins and Porter 2003a; Colwell
and Lees 2000). The Water-Energy hypothesis presents the greatest causal
effect on species richness distribution(Hawkins et al. 2003) and
predicts richness as a product of evapotranspiration and quantity of
water available on the considered place(O’Brien and Road 1998).
The relationship between species richness and the variables that
represent each of these hypotheses is considered linear and
stationary(Angermeier and Schlosser 1989; Wylie and Currie 1993; Tedesco
et al. 2005). Stationary relationships are characterized by an equal
relation of cause and effect throughout the whole geographical extension
of the data considered (Osborne et al. 2007). In this way, the global
model (obtained utilizing all the data) is the same as local models
(obtained from a subgroup of the data). In fact, stationarity is an
assumption for the application of global models(Zar 2010). In many cases
this assumption is neither tested nor observed in diversity gradients
(Foody 2004; Cassemiro et al. 2007), consequently producing imprecise
global models with few representatives of local estimates(Foody 2004).
An example of a non-stationary relationship is assumed by the
Water-Energy hypothesis, that is, in lower latitudes the quantity of
water available in the system is the limiting factor of diversity,
whereas in higher ones, energy (evapotranspiration) determines the
richness gradient (Gaston 2000; Hawkins and Porter 2003b; Eiserhardt et
al. 2011). This occurs because areas of low latitudes suffer little
influence from Earth’s precession movements, because of they are located
near the equator. Consequently, the energy input (from the Sun) occurs
in a uniform way throughout the year, making water the limiting factor
of diversity. On the other hand, areas located at high latitudes suffer
greater influence from Earth’s precession, so there are periods of the
year when the hemispheres receive grater or smaller amounts of energy.
Non-stationarity is the main cause of non-significative
relationships(Osborne et al. 2007), since the variation of regression’s
coefficients is ignored and the relationships are described by their
average along the geographic space (Foody 2004). Morphological terrain
variations and environmental heterogeneity conditions, at the spatial or
temporal level, are the main causes of non-stationarity in the
relationships of diversity with the environmental variables considered
by each hypothesis(O’Brien and Road 1998; Bickford and Laffan 2006).
Modifications of the topographical relief can isolate or connect
isolated populations, promoting or even avoiding speciation.
Heterogeneity of environmental conditions also creates an environment
with high habitat diversity, allowing the coexistence of
species(Bickford and Laffan 2006). Therefore, a non-stationarity
relationship between species richness and environment is a
characteristic that cannot be overlooked in studies about diversity
gradients(Foody 2004).
For tropical stream fishes it was shown that diversity distribution is a
product of the interactions of three hypotheses: (i) Water-Energy; (ii)
Terrestrial Primary Productivity and (iii) Climatic Temporal
Heterogeneity(Vieira et al. 2018). Despite this, the Brazilian
geographical area presents high morphologic and climatic heterogeneity,
possessing regions with elevated temperatures and pluviosity
(north/northeast regions), regions with low temperatures and high
pluviosity (south and part of the southeast regions) and regions with
elevated temperatures and long dry periods (midwest and northeast
regions(Marengo and Valverde 2007)). Therefore, our objective is to
quantify the stationarity of the relationship between stream fish
richness and the following hypotheses: (i) Water-Energy; (ii)
Terrestrial Primary Productivity and (iii) Climatic Temporal
Heterogeneity.