Final answer:
An arrow on the phase portrait pointing straight to the right indicates that there will be no change in the population sizes over a short time period, signifying zero population growth. This suggests an equilibrium point and differs from the exponential growth typical of bacteria, which would be indicated by upward pointing arrows.
Step-by-step explanation:
When an arrow on the phase portrait points straight to the right, this indicates that the population size represented by the arrow will not change over a short time period. In other words, neither the population size of the pathogenic bacteria nor the probiotic bacteria will increase. This could be due to the system being at an equilibrium point where the population growth rate is zero, often referred to as zero population growth. In a phase portrait, a horizontal arrow pointing to the right simply means that there's no change in the population size along the vertical axis that usually represents the number of individuals.
In the context of bacterial growth curves, exponential growth is typically shown as a curve where the slope continually increases, which would be represented by arrows that angle upwards to the right, not directly to the right. Exponential growth is characterized by each individual reproducing at a constant rate, thereby resulting in the population doubling at regular intervals, which is why bacterial populations can grow from 1000 to over 16 billion in just 24 hours under ideal conditions.
The logistic growth model shows a different trend where a population initially grows exponentially, but then the growth rate slows as the population reaches the carrying capacity of its environment. In a phase portrait, this would be represented by arrows that turn or bend towards a certain point (the equilibrium) and not arrows pointing directly to the right.