To determine which statements are correct regarding the relationships between organisms and their life cycles, let's analyze each statement one by one.
### Step-by-Step Solution:
1. **Statement I**: "The human liver fluke, a nematode parasite, depends on two intermediate hosts (snail and pig) to complete its life cycle."
- This statement is **correct**. The human liver fluke (Fasciola hepatica) indeed requires a snail as the first intermediate host and a pig (or other mammals) as the second intermediate host to complete its life cycle.
2. **Statement II**: "The malaria parasite needs a vector (mosquito) to spread to other hosts."
- This statement is also **correct**. The malaria parasite (Plasmodium spp.) is transmitted through the bite of infected female Anopheles mosquitoes, which act as vectors for the disease.
3. **Statement III**: "The female mosquito is not considered a parasite; however, it needs our blood for reproduction."
- This statement is **correct** as well. Female mosquitoes require blood meals to obtain the necessary nutrients for developing their eggs, but they are not classified as parasites in the same way that organisms like flukes or lice are.
4. **Statement IV**: "In case of brood parasitism, the eggs of parasitic birds (e.g., cuckoo) are not detected and ejected from the nest because the parasite's eggs resemble the host's eggs in morphology and color."
- This statement is **correct**. Brood parasitism, as seen in cuckoos, involves the parasitic bird laying eggs that closely mimic the appearance of the host's eggs, which helps them avoid detection and ejection.
5. **Statement V**: "A population of frogs protected from all predators would increase indefinitely."
- This statement is **incorrect**. While removing predators may initially lead to an increase in the frog population, other factors such as competition for resources (food, habitat) and environmental carrying capacity would limit indefinite growth. Eventually, the population would stabilize at a certain level due to these factors.
### Conclusion:
The correct statements are I, II, III, and IV. Therefore, the answer is that statements 1, 2, 3, and 4 are correct.
---