The family of plants, Hydrocharitaceae, comprises some of the most economically important plants in the world, both from positive viewpoints, and negative.  For example, many communities have spent millions of dollars trying to eradicate Hydrilla verticillata from fishing lakes and municipal water supplies, whereas without Vallisneria spiralis and Egeria densa, the tropical fish industry would probably cease to exist as we know it today.  The remarkable thing about these plants, though, is that there is such a wide variety of forms within the family that even experienced aquarists might not know that they are in the same family.  
      As a group, Hydrocharitaceae comprises 15 genera, all of which are aquatic.  They
vary in form from thin stemmed, heavily branched strictly aquatic plants with short, 
narrow leaves (Hydrilla) to robust, emergent plants with rosettes of stiff, toothed leaves 
with large yellow flowers (Stratioides).   When reading a description of the family, one 
realizes that there is so much variability in the forms that it raises the questions of how 
and  why are these plants related.  
    What relates them, as with all groups of related organisms, are the basic structures of 
the individual plant parts, however modified those structures might be.  When we look 
very carefully at the various parts of the plants, we realize that they are all remarkably
similar.  
     Those structures are described in the official description of  a particular species to the 
extent that it helps to differentiate between species within a  genus, or a genus within a 
family, etc.  Such a description follows.  It describes the family, and points to all of the 
important structures within the family.  

Hydrocharitaceae:
   15 genera: cosmopolitan.  All aquatic, 3 genera (Enhalus, Thalassia, and Halophila) are marine, and thus excluded from this account.
      “Annual or perennial, dioecious or monoecious.  Leaves various, usually submerged, rarely floating or partly emergent.  Flower arranged in a bifid spathaceous bract or between 2 opposite bracts, bisexual or unisexual; when unisexual then males usually more than 1, females solitary.  Perianth segments free, 1- or 2- seriate, 3 or rarely 2 in each series; inner series when present usually showy and petal-like.  Stamens 1 to numerous, in 1 or more whorls, the inner ones sometimes staminodial.  Ovary inferior, of 2 to 15 united carpels; placentas parietal, occasionally protruding nearly to center of ovary; fruit globose to linear, dry or pulpy, indehiscent or rupturing irregularly, seeds numerous, smooth, warty or spiny.” (Water Plants of the World, C.D. K. Cook).
     
 So what does all of that mean?   What follows is a clause by clause parsing of the description above.
-- 15 genera: cosmopolitan:  There are 15 genera within the family.  They occur all over the habitable planet.
-- All aquatic, 3 genera (Enhalus, Thalassia, and Halophila) are marine, and thus excluded from this account:  All members of the family are strictly aquatic.  The 3 genera mentioned live in the ocean and so are not included in the book from which this reference was taken.
-- Annual or perennial:  Plants may be short lived or persistent over time.  Annuals depend upon seed production for year to year survival, whereas perennials might die back every year but retain a long-lived rootstock.
-- dioecious or monoecious:  Literally, “two houses”, and “one house”, respectively, from the Greek root oecium, “house”.  Dioecious plants are those that produce male and female flowers on separate plants.   Monoecious plants are those that produce flowers of both genders on one plant. 
-- Herbs:    Herbaceous plants are those that produce soft, non-woody tissue only. 
-- Leaves various:  Leaves exhibit a variety of forms.
-- usually submerged, rarely floating or partly emergent:  most species within the family are strictly aquatic, meaning that no part of them with the possible exception of flowers rises above the water line.  A few produce floating leaves under very specific conditions, and some of them even rise above the water or can survive when the water line drops.
-- Flower arranged in a bifid spathaceous bract or between 2 opposite bracts:  Bifid means split into two parts.  Spathaceous means having a sheathing lateral organ or pair of organs that usually open on one side and that enclose an inflorescence (an aggregation of flowers).   A bract is a reduced or modified leaf, particularly the scale-like leaves in a flower cluster.   So a ‘bifid spathaceous bract’ is a sheathing, made of modified leaves, and split into two parts, surrounding a flower cluster. 
-- bisexual or unisexual:  Flowers may exhibit characteristics of both genders, staminate (male) or pistilate (female). 
-- when unisexual then males usually more than 1, females solitary:  In those cases where a flower is unisexual and male, there may be as few as 1 flower present, but usually not.  When the flower is female, there is always only 1 flower present.
-- Perianth segments free:   A perianth is a nonessential appendage of a flower, situated outside of the whorl of stamens in the center of the flower.  The perianth includes both sepals (part of the Calyx, or outermost whorl of the floral envelopes) and petals or other segments homologous with them.   When the segments of the perianth are said to be ‘free’, it means that they are not fused to one another.  
-- **1 or 2- seriate:  arranged in 1 or 2 rows, or series.
-- **3 or rarely 2 in each series:  
-- inner series when present usually showy and petal-like:  In those plants that have an inner series of perianth segments, those segments are colorful and large.
-- Stamens 1 to numerous, in 1 or more whorls, the inner ones sometimes staminodial:  In staminate flowers, the stamens number from 1 to several.  They are arranged in whorls, numbering at least 1, and the inner whorl occasionally comprises what are called, ‘staminodia’.  Staminodia are sterile organs, resembling stamens, and presumably of staminal origin.  
-- Ovary inferior:  The ovary, or seed producing organ, is underneath all of the other flower parts.
-- **of 2 to 15 united carpels:  The female flower is made up of several parts, the ovary, the stigma and the style.  These combine to form the Pistil.   A carpel is one of the foliar units of which a pistil is composed.  When these are fused together, they are said to be united.  
-- placentas parietal:  The placentas are the structures upon which the ovules are arranged within the ovary.  When they are parietal, they rest on, or they arise from, the ovary wall. 
-- occasionally protruding nearly to center of ovary:  In this case they extend so far from the wall of the ovary that they nearly meet in the middle of the ovary.
-- fruit globose to linear:  Fruits are seed pods and to be globose is to be rounded., or nearly spherical.  To be linear is to be elongated so that the side of the fruit are nearly parallel.
-- **dry or pulpy:  Seeds are 
-- indehiscent or rupturing irregularly:  In reference to fruits, indehiscent ones are those that remain closed and do not shed their seeds readily, i.e., Ficus spp. (Figs).   Ones that rupture irregularly or those that explode, scattering their seeds far and wide, i.e., Wisteria chinensis are said to rupture.
-- seeds numerous, smooth, warty or spiny:  Each flower produces numerous seeds, which vary in form as the list implies.  

  
  Determining which characteristics determine whether a plant is in this family is still a 
tricky proposition.  Probably the best way is to examine the descriptions of each of the 
genera in the family and see how they compare to each other and, most importantly, to 
the general description of the family itself.   I shall take the genera in alphabetical order, 
and will parse each description as above. 

Do a statistical analysis of the various characteristics.
Leaf:form, Root form, Flower desc. other characteristics.

Description:
Blyxa: Submerged monoecious or dioecious, annuals or perennials.   Stem corm-like or up to 60cm long.  Leaves linear, spirally arranged, radical or along the stem; base sheathing the stem; margins entire or minutely serrate; apex attenuate; nerves parallel; midrib prominent.  Spathes sessile or stalked, tubular, with 6 longitudinal ribs, bifid at the apex.  1 flowered or in male spathes of dioecious plants with up to 10 flowers.  Flowers unisexual or bisexual, female and bisexual ones sessile, male ones stalked.  Sepals 3, linear or linear-lanceolate, green, persistant. Petals 3, linear, longer than sepals, white, flaccid, fringed or reduced or absent.  Stamens 3,6,or 9; filaments capillary; anthers linear or lanceolate 2-locular.  Ovary of 3 carpels, linear, with long, capillary beak; styles 3, entire, linear, united at the base; fruit linear or linear-lanceolate, membranous; seeds 10 to numerous, elliptic or fusiform, 1 to 2 mm long, smooth or spiny.  

Translation:
Submerged:  Living entirely under water
monoecious or dioecious: :  As above, dioecious plants are those that produce male and female flowers on separate plants.   Monoecious plants are those that produce flowers of both genders on one plant. 
annuals or perennials: :  Plants may be short lived or persistent over time.  Annuals depend upon seed production for year to year survival, whereas perennials might die back every year but retain a long-lived rootstock
Stem corm-like or up to 60cm long: A corm is a solid, swollen part of a stem, usually subterranean, as the so-called “bulb” of Crocus and Gladiolus.   This probably means that in some instances, i.e., shallow water, the stem becomes thickened and hard, while in other conditions, i.e., deeper water, or in situations where there are piles of soft silt on the bottom, the stem is softer, and probably more fragile.  
Leaves linear, spirally arranged, radical or along the stem:  Leaves of this plant are long and narrow, arragned on the stem spirally (if you were to look at a cross sectionof the stem, or if you were to remove the leaves, you would see that the leaf bases are arranged spirally).  Radical leaves are those that arise from the root or its crown.  In this case, then, probably depending upon the conditions in which the plant is growing, the leaves will be attached to that corm, or will be more spread out along the stem.
base sheathing the stem:  The leaf bases wrap partially around the stem for some distance before leaving the stem.
margins entire or minutely serrate:  The edges of the leaves are smooth or very finely toothed.
apex attenuate:  The end of the leaf tapers gradually. 
nerves parallel, midrib prominent: The leaf veins run parallel to one another.  The middle vein protrudes from the surface of the leaf.
Spathes sessile or stalked:  We know what spathes are from above.  Sessile means that there is no stem,  or stalk.  The organ in question, i.e., flower, leaf, spathe, etc., arises directly from the stem.  Stalked means that there is a stem of indeterminate length.  
tubular, with 6 longitudinal ribs, bifid at the apex:  Shaped like a tube, with 6 ribs that run the length of the spathe, in this case.  It is split in two at the end.  
1 flowered or in male spathes of dioecious plants with up to 10 flowers:  In most plants there is only 1 flower per spathe.   In those cases where the spathe contains male flowers, there may be as many as 10 flowers present.
Flowers unisexual or bisexual, female and bisexual ones sessile, male ones stalked:  Flowers may be male, female, or both.  All female flowers and flowers with both genders are held close to the stem, without a stalk.  All flowers that are exclusively male are stalked.
Sepals 3:  Sepals are the outer most part of the flower.  The sepals make up the flowers covering before it emerges.  In the case of all species of Blyxa, there are 3 of them per flower.
linear or linear-lanceolate:  Linear means straight and narrow.  Lanceolate means wider in the middle than at either end, with a pointed tip.  In the case of Blyxa, they may be anywhere between linear to narrowly lanceolate.  
green, persistant:  The spathes are colored green and do not fall away as the seeds mature.  
Petals 3, linear, longer than sepals, white, flaccid, fringed or reduced or absent:  Obviously, there are three petals per flower.  The petals are long and thin, reach out beyond the sepals, and are white in color.  They droop, and have a fringed edge.  Then again, the petals may be reduced to the point of insignificance. 
Stamens 3,6,or 9; filaments capillary:  Depending upon the speceis there are 3,6, or 9 stamens per flower and the stalks that they stand on are extremely thin, or hair-like.
anthers linear or lanceolate 2-locular:  The anters are long and thin to somewhat broadened in the middle, and are divided into two compartments, or cells.
Ovary of 3 carpels, linear, with long, capillary beak:  There are 3 chambers within the ovary.  The ovary itself is long and thin and possesses a long, hairlike protrusion from one end.
styles 3, entire, linear, united at the base:  The styles is a short or long, simple or branched stalk arising from the ovary and bearing the stigma or stigmas.    It is the part of the pistil that connect the ovary to the stigma.  Entire means that there are no notches, indentations, serations or anything else that would mare the surface of the style.  In this case there are three styles per flower, one per carpel, they are thin, and they are fused at the base, as opposed to arising from places so far apart that they sould anve to be separated.  
fruit linear or linear-lanceolate, membranous:  Like the ovary, the fruit, which is merely a fertilized ovary is long and thin,.  The growth of the seeds within the ovary cause it to be thickened in the middle, hence the linear-lanceolate.  In this case membranous measn that it has a thin, soft, pliable texture
seeds 10 to numerous, elliptic or fusiform, 1 to 2 mm long, smooth or spiny:  There are at least 10 seeds per fruit, often many more.  The seeds are essentially oblong with broadly rounded ends and sides.  They may be smooth in texture or covered with small spines.

Other notes:
Blyxa:  Abt 10 spp of submersed, stoloniferoue aquatic herbs, native to tropics of old world.  Lvs alt, linear, with prominent midribs, ...
B.  echinosperma Monoecious, lvs basal, sheathing, to 1 ft. or sometimes longer, dark green, flrs bisexual, white, 1 or rarely 2 in a spath, stamens 3.  Fr. Linear, to 2 ¾” long.  Phillipine I and S. and E. Asia, Ss to E India and trop Australia.