Evolution by natural selection requires specific conditions to operate within a population. Understanding these conditions helps differentiate between essential and non-essential elements.
For natural selection to drive evolution, the following are generally considered essential:
The question asks what is NOT essential for evolution by natural selection. Let's evaluate the options:
Conclusion: Sexual reproduction is not a prerequisite for natural selection to occur.
There are two species, X and Y, with abundances $x$ and $y$, respectively. Species X has growth rate $\alpha$, and species Y has growth rate $\beta$. Assume that the sum of the species abundances is constant over time, i.e., $x + y = 1$. Let $x$ and $y$ follow the rate equations:
$$\frac{dx}{dt} = \alpha x - \varphi x,$$
$$\frac{dy}{dt} = \beta y - \varphi y,$$ where $\varphi$ is the average species fitness.
Which one of the following options correctly represents the expression for $\varphi$?
The figure illustrates the soil zinc tolerance of the grass species Anthoxanthum along a transect from inside a mine to the middle of a pasture outside the mine.

Which one or more of the following processes explain(s) the observed pattern of zinc tolerance in this grass species?
From an original population \(P\) of a butterfly species, two experimental populations \(X\) and \(Y\) were established. In \(X\), males and females were maintained in standard conditions, and females were allowed to mate and lay eggs. Only eggs from females laying small clutches (i.e., \(S\) eggs or fewer) were allowed to hatch and the rest were not utilized. In \(Y\), males and females were maintained in standard conditions and females were allowed to mate and lay eggs. From each female, \(S\) eggs were randomly selected and allowed to hatch, and the rest were not utilized. After 20 generations of these experimental conditions, relative to the original population \(P\), and assuming that clutch size is under genetic control, we expect clutch size to be ______________________in \(X\) and ___________________ in \(Y\).