### Field survey and laboratory analyses

The study area comprised neritic waters of the southern Gulf of Mexico, between 18°–22°N and 91°–95°W. Zooplankton sampling was carried out during two periods, May and November 1995, over a sampling grid including 28 oceanographic stations (Fig. 1). Five vertical strata were sampled (0–6, 6–12, 12–18, 45–55 and 95–105 m), and a total of 187 samples were collected during the day and night using a multiple opening–closing net equipped with 75-cm-diameter and 505-μm-mesh-size nets. Day (night) period ranged from 7 am to 6 pm (7 pm to 6 am). A flowmeter was placed on the mouth of each net to estimate the amount of water filtered by nets. Samples were preserved in a 4 % formaldehyde seawater solution neutralized with sodium borate. Salinity and temperature measurements were also taken with a CTD probe at each sampling station. In the laboratory, zooplankton biomass, taken as a measure of food availability, was estimated as displaced volume and standardized to 100 m^{3} of water (ml 100 m^{−3}). All pelagic molluscs were separated from samples and identified to the genus level. Abundance values of the five genera considered in this study were expressed as ind 100 m^{−3}.

### Data analysis

Mean monthly wind speeds (3.8 m s^{−1} for May and 6.1 m s^{−1} for November; Anonymous 1999) were used to estimate the turbulent kinetic energy (*k*), the dissipation rate of kinetic energy \( \left( \varepsilon \right) \) and the length (*η*) and velocity (*v*
_{
t
}) Kolmogorov scales. Wind speed values were used for the calculations of the significant wave height (*H*
_{1/3}) and the period (*T*) of waves, as the JONSWAP Spectrum stated (Hasselmann et al. 1973):

$$ H_{1/3} = 4\left[ {1.67 \times 10^{ - 7} \frac{F}{g}} \right]^{1/2} $$

(1)

$$ \omega = \frac{2\pi }{T} = 22\left( {\frac{{g^{2} }}{{U_{10} F}}} \right)^{1/3} $$

(2)

where *F* = fetch length, here taken as 300 km; *g* = acceleration of gravity; *U*
_{10} = wind speed at a height of 10 m; *ω* = wave frequency.

The values of *H*
_{1/3} and *T* were used to estimate the wave length (*L*) and the horizontal and vertical velocities (*u* and *w*) of the water particles (SPM 1977):

$$ L = \frac{{gT^{2} }}{2\pi }\tanh \left( {\frac{2\pi d}{L}} \right) $$

(3)

$$ u = \frac{{H_{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} gT}}{2L}\frac{{\cosh \left( {{\raise0.7ex\hbox{${2\pi \left( {z + d} \right)}$} \!\mathord{\left/ {\vphantom {{2\pi \left( {z + d} \right)} L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)}}{{\cosh \left( {{\raise0.7ex\hbox{${2\pi }$} \!\mathord{\left/ {\vphantom {{2\pi } L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)}}\cos \left( {\omega t} \right) $$

(4)

$$ w = \frac{{H_{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} gT}}{2L}\frac{{\sinh \left( {{\raise0.7ex\hbox{${2\pi \left( {z + d} \right)}$} \!\mathord{\left/ {\vphantom {{2\pi \left( {z + d} \right)} L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)}}{{\cosh \left( {{\raise0.7ex\hbox{${2\pi }$} \!\mathord{\left/ {\vphantom {{2\pi } L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)}}\sin \left( {\omega t} \right) $$

(5)

where *H*
_{1/3} = significant wave height (the average height of the largest one-third of the waves); *t* = time (varying from 0 to *T*); *z* = water column depth (negative); and *d* = bottom depth (positive, here equal to 100 m).

Based on the previous calculations, the fluctuations from the horizontal and vertical mean velocities were computed:

$$ \tilde{u}^{2} = \frac{4}{T}\int\limits_{0}^{T/4} {\left( {\bar{u} - u} \right)^{2} } {\text{d}}t\quad \tilde{w}^{2} = \frac{4}{T}\int\limits_{0}^{T/4}{\left( {\bar{w} - w} \right)^{2} } {\text{d}}t $$

The mean values (\( \bar{u} \) and \( \bar{w} \)) of these velocities were estimated, taken sin(*ωt*) and cos(*ωt*) equal to \( \frac{2}{\pi } \), since \( \frac{4}{T}\int_{0}^{T/4} {\sin \omega t\begin{array}{*{20}c} {{\text{d}}t = \frac{4}{T}\int_{0}^{T/4} {\cos \omega t{\text{d}}t = } \frac{2}{\pi }} \\ \end{array} } \) in Eqs. 4 and 5.

The turbulent kinetic energy (*k*) is a measure of the turbulence intensity. It is defined as the kinetic energy per unit mass (J kg^{−1}) of the horizontal \( \left( {\tilde{u}^{2} } \right) \) and vertical \( \left( {\tilde{w}^{2} } \right) \) velocity variances (Burchard 2002):

$$ k = \frac{1}{2}\left( {\tilde{u}^{2} + \tilde{w}^{2} } \right) $$

Kolmogorov theory states that a turbulent flow is formed by eddies that decrease in diameter with depth. The dissipation rate of the turbulent kinetic energy through the spectrum of eddies in the water column is related to the turbulent velocities \( \left( {\sqrt k } \right) \) and the diameter of eddies \( \left( \ell \right) \), with units of velocity squared per second (m^{2} s^{−3}) (Tennekes and Lumley 1972):

$$ \varepsilon = \frac{AU}{\ell } $$

where *A* = constant near to one; *U* = root-mean-square velocity fluctuations, equal to \( \sqrt k ;\ell \) = diameter of the gyre.

At the superficial waters, ℓ is equal to *H*
_{1/3}; at deeper waters, ℓ is twice the amplitude \( \left( \zeta \right) \) of the waves, defined as:

$$ \zeta = \frac{{H_{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0pt} 3}}} }}{2}\frac{{\sinh \left[ {{\raise0.7ex\hbox{${2\pi \left( {z + d} \right)}$} \!\mathord{\left/ {\vphantom {{2\pi \left( {z + d} \right)} L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right]}}{{\sinh \left( {{\raise0.7ex\hbox{${2\pi d}$} \!\mathord{\left/ {\vphantom {{2\pi d} L}}\right.\kern-0pt} \!\lower0.7ex\hbox{$L$}}} \right)}} $$

The dissipation of energy mainly occurs at the smallest turbulence scales, that is, at the so-called Kolmogorov microscales. At this point, the driving energy is finally overcome by the viscosity \( \left( {\upsilon \approx 1 0^{ - 6} \begin{array}{*{20}c} {{\text{m}}^{ 2} \, {\text{s}}^{ - 1} } \\ \end{array} } \right) \), and the size of the smallest eddy (*η*) and its characteristic velocity (*v*
_{
t
}) are defined as (Tennekes and Lumley 1972) follows:

$$ \eta \equiv \left( {{\raise0.7ex\hbox{${\upsilon^{3} }$} \!\mathord{\left/ {\vphantom {{\upsilon^{3} } \varepsilon }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\varepsilon $}}} \right)^{1/4}$$

$$ v_{t} \equiv \left( {\upsilon \varepsilon } \right)^{1/4}$$

These Kolmogorov microscales are crucial to understanding the interactions of planktonic organisms with their microdistribution patterns in the water column (Rothschild and Osborn 1988).

A spatial segregation index (*D*) was also calculated between all possible pairs formed by the most abundant genera. This index is (White 1983):

$$ D = \frac{1}{2}\sum\limits_{i = 1}^{n} {\left| {\frac{{N_{1i} }}{{N_{1} }} - \frac{{N_{2i} }}{{N_{2} }}} \right|} $$

where *N*
_{1i
} = number of individuals of genus 1 at station *i*; *N*
_{2i
} = number of individuals of genus 2 at station *i*; *N*
_{1} = total number of individuals of genus 1; *N*
_{2} = total number of individuals of genus 2.

The values of *D* range from 0, in the case of the maximum spatial co-occurrence between the two genera, to 1, which indicates a perfect spatial segregation. The level of significance of an observed index value was estimated through the use of null models (Manly 1991). This procedure consists of the following: (1) estimation of the observed index Do from two vectors, (2) random reallocation of one vector (genera 1 or 2), (3) the repetition of the second step a large number of times (1,000 in this case) to estimate new random values (Dr) in order to find the null distribution of *D* and (4) the comparison of the Do value within the null distribution: If Do represents a typical value within the *D* distribution, then the spatial pattern of the two genera seems to be random. In contrast, if Do is on one of the extremes of the distribution, the conclusion is that the two genera are spatially associated (lower tail) or segregated (upper tail). In this study we tested the level of spatial segregation among the genera, and the *P* value was considered to be the proportion of the Dr values higher than or equal to Do. A MATLAB procedure was developed for these calculations.