Resource partitioning is a phenomenon in ecology where different species coexist in the same habitat by utilizing different resources or occupying different niches. This allows for the reduction of competition and promotes species diversity. In the given options, resource partitioning is most likely to occur between sympatric populations of species with similar ecological niches and between sympatric populations of two strong competitor species.

1. Sympatric populations of species with similar ecological niches:
- Sympatric populations refer to populations of different species that inhabit the same geographic area.
- Species with similar ecological niches have similar resource requirements and occupy similar habitats.
- When these species coexist in the same area, they are likely to compete for the same resources.
- In order to reduce competition, they may evolve to occupy different niches or utilize different resources.
- For example, two species of birds that feed on insects may partition their feeding grounds by feeding at different times of the day or foraging in different areas of the habitat.

2. Sympatric populations of two strong competitor species:
- When two species have similar ecological requirements and are strong competitors for the same resources, they may undergo resource partitioning to coexist in the same habitat.
- This can involve the division of resources such as food, nesting sites, or territory.
- Each species may specialize in utilizing certain resources or occupy different microhabitats within the larger habitat.
- This reduces direct competition and allows both species to persist in the same area.
- For example, two species of predatory cats may partition their hunting territories, with one species specializing in hunting small prey while the other focuses on larger prey.

3. Allopatric populations of species with similar ecological niches:
- Allopatric populations refer to populations of different species that inhabit separate geographic areas.
- If these populations have similar ecological niches, they are not likely to directly compete for resources since they are not sharing the same habitat.
- Therefore, resource partitioning is less likely to occur between allopatric populations with similar niches.

4. Allopatric populations of the same animal species:
- Allopatric populations of the same animal species are geographically isolated from each other.
- Since they belong to the same species, they have similar ecological requirements and niches.
- However, without direct competition, there is no need for resource partitioning between these populations.

In conclusion, resource partitioning is most likely to occur between sympatric populations of species with similar ecological niches and between sympatric populations of two strong competitor species. These scenarios involve direct competition for resources, which drives the evolution of niche differentiation and resource partitioning to promote coexistence.