Explanation:

The Hardy-Weinberg principle is a fundamental concept in population genetics that describes the relationship between allele and genotype frequencies in a population. It is based on several assumptions, including the absence of mutation, migration, selection, and genetic drift. The principle states that under certain conditions, the frequencies of alleles and genotypes in a population will remain constant from generation to generation.

Allele Frequency Variation
One of the assumptions of the Hardy-Weinberg principle is that the allele frequencies in a population remain constant from generation to generation. This means that the relative proportions of different alleles in a population do not change over time.

However, option C states that the allele frequency varies from species, which contradicts the Hardy-Weinberg principle. In reality, allele frequencies can and do change in natural populations due to various factors such as mutation, gene flow, genetic drift, and natural selection. These factors can lead to changes in the genetic composition of a population over time, resulting in shifts in allele frequencies.

Frequency Fixation
The Hardy-Weinberg principle states that under certain conditions, the frequencies of alleles and genotypes in a population will remain constant from generation to generation. This means that there is no change in the allele frequencies over time and that the population is in genetic equilibrium.

Algebraic Equations
The Hardy-Weinberg principle can be mathematically described using algebraic equations. These equations allow us to calculate the frequencies of alleles and genotypes in a population based on the initial allele frequencies and the rules of Mendelian inheritance. The equations provide a quantitative framework for understanding how genetic variation is maintained or changed in populations over time.

Gene Pool Consistency
Another assumption of the Hardy-Weinberg principle is that the population is in genetic equilibrium, meaning that the gene pool remains constant from generation to generation. This means that there is no migration, mutation, selection, or genetic drift occurring in the population, and the population is not evolving.

In summary, the Hardy-Weinberg principle describes the relationship between allele and genotype frequencies in a population. It assumes that the allele frequencies remain constant, can be described using algebraic equations, and that the gene pool remains constant. However, it does not hold true when allele frequencies vary from species, as stated in option C.