Calculating the probability of an animal finding a resource

In summary, the conversation discusses the probability of a model animal finding water in a day. The chances of hitting the water in one attempt is 0.0462. However, if the animal can search over the course of a day, the probability of finding water increases. The discussion also mentions the effect of pool size and search patterns on the probability of finding water.
  • #1
killbot2000
11
0
I'd like some help working out the probability of my model animal finding water in a day.

In my 'model' there is a square landscape 17km^2
The water pool is a circle of 500m radius (so approx 0.7854km^2)
So in a one off shot the chances of hitting the water is 0.7854/17 = 0.0462 right?

But if I suppose that the animal can search over the course of a day, how can I incorporate this into increasing its prob. of finding the water?

Assume for the sake of argument that it can travel at 1m/second and has a 500m detection range then it should 'cut out' circles the same radius as the water pool every 1000 seconds. Then I think it would cut out 86400/1000 = 86.4 in day.

If this is correct how can I convert it into a probability?

I know this is a ramble, but I've been at it all morning, so any help would be much appreciated!
 
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  • #2
So in a one off shot the chances of hitting the water is 0.7854/17 = 0.0462 right?
If the animal magically appears at a random position in the landscape, this is the probability that it will appear in the water.

But if I suppose that the animal can search over the course of a day, how can I incorporate this into increasing its prob. of finding the water?
It depends on the way it searches for water.

Neglecting effects at the edges of the landscape, your model animal can search 1000m2 per second. With an ideal path, it would need roughly 17000 seconds to see the whole landscape, less than 5 hours. The probability to find the pool within a day is 1, independent of its size.

Real animals rarely walk on those ideal lines, so the probability depends on the walking algorithm.
 
  • #3
What's the probability of an animal appearing out of thin air into an area to which it's never been?
 
  • #4
mfb said:
If the animal magically appears at a random position in the landscape, this is the probability that it will appear in the water.

It depends on the way it searches for water.

Neglecting effects at the edges of the landscape, your model animal can search 1000m2 per second. With an ideal path, it would need roughly 17000 seconds to see the whole landscape, less than 5 hours. The probability to find the pool within a day is 1, independent of its size.

Real animals rarely walk on those ideal lines, so the probability depends on the walking algorithm.

Pool size radius matters: ( versus a search independant of pool radius )
Even less search time for a 500 radius water pool. Search radius would be detection radius 500m plus the water pool radius giving a total 1000m search radius ( assuming pool edge detection ). A 5km by 3.5 km grid (17.5 square km ) could be searched in 2 passes. So, not exactly, but somewhere around 9000 seconds of search required.

In fact a 5 x 4 km rectangular area could be searched in less than 10000 seconds ( again assuming edge detection of the water pool ).
 
  • #6
256bits said:
Pool size radius matters
It reduces searching time, but it does not increase the probability to find the pool.

pool edge detection
:D

If the pool is circular and fully within the search area, we can do even better. We can ignore 1km on both sides of the 5km-range, and the total travel distance is below 8.5km*.
A 3x6km-area would require at most 6km, as it can be done in a single pass.

*Edit: Below ##(6.5 + \sqrt{2})km \approx 7.9km##.
 

1. What is the importance of calculating the probability of an animal finding a resource?

The probability of an animal finding a resource is crucial for understanding the behaviors and survival strategies of different species. It also helps in predicting the impact of environmental changes on their ability to find and utilize resources.

2. How is the probability of an animal finding a resource calculated?

The probability is calculated by dividing the number of successful resource findings by the total number of attempts made by the animal. This can be further enhanced by including factors such as the animal's sensory abilities, energy expenditure, and environmental conditions in the calculation.

3. What are some factors that can affect the probability of an animal finding a resource?

Some factors that can influence the probability include the animal's physical abilities, such as speed and agility, as well as its cognitive abilities, such as memory and problem-solving skills. Other factors include the availability and distribution of resources in the environment, competition from other animals, and changes in weather or season.

4. Can the probability of an animal finding a resource change over time?

Yes, the probability can change over time as animals adapt to changing environmental conditions and learn from their experiences. For example, if a new predator is introduced into the ecosystem, the probability of finding a resource may decrease as the animal has to spend more time avoiding the predator. However, over time, the animal may develop new strategies or behaviors to increase its chances of finding a resource.

5. How can calculating the probability of an animal finding a resource benefit conservation efforts?

By understanding the factors that influence an animal's ability to find resources, conservation efforts can be tailored to provide better habitats and resources for endangered species. This can also help in predicting the impact of human activities, such as deforestation or pollution, on the ability of animals to find resources and survive in their natural habitats.

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