spatial

Spatial Relationships

BSC 2011 Lab

Spatial Ecology

1. Ecology

   • Definition: The study of interactions between organisms and their environment.

2. Spatial Ecology

   • Definition: The study of spatial patterns of organisms and their relationships with ecological phenomena.

Dispersion

1. Dispersion

   • Definition: The distribution of individuals within a population (how they are arranged in space).

2. Types of Dispersion

   • Three types are typically recognized:
     a. Clumped
     b. Uniform/Even
     c. Random

Clumped Dispersion

1. Characteristics

   • Distance between neighbors is minimized.

   • Most common type of dispersion.

   • Influenced by: a. Environmental conditions

     • Patchy physical environmental conditions.

     • Patchy resources.
       b. Dispersal limitations

     • Limited dispersal of juveniles (seeds, larvae, baby animals).
       c. Social factors

     • Herding animals and family groups (e.g., wolves).

     • Avoiding predation (protection).

Uniform/Even Dispersion

1. Characteristics

   • Distance between individuals is maximized.

   • Occurs when there is strong competition for resources.

   • Example:

     • GPS tracked wolves in Voyageurs Wolf Project demonstrating territorial behavior.

Random Dispersion

1. Characteristics

   • The location of one individual bears no relationship to the locations of other individuals.

   • Rarely found in nature.

   • May occur in:
     a. Homogeneous environments.
     b. Situations where individuals neither attract nor repel one another.
     c. Instances when there hasn’t been sufficient data collected.

Changes in Dispersion Patterns

1. Temporal Changes

   • Over time: e.g., birds may flock in winter but behave territorially when nesting.

2. Spatial Changes

   • Across space: Competition may be high in one area but not another.

3. Interpretation Influences

   • Both spatial and temporal scales greatly influence interpretations.

   • Example: Small spatial scale may show Uniform Dispersion, but a larger scale may reveal a different type of dispersion.

Quantifying Spatial Relationships

1. Methods to Determine Dispersion Type

   • Clark-Evans Nearest Neighbor Method

   • Variance/Mean Ratio

2. Methods to Determine Species Association

   • Interspecific Association (quantified using the Chi-squared Test).

Species Under Investigation

1. Species A: Ranunculus

2. Species B: Geranium

Data Collection Outside

1. Setup

   • Use four flags and a meter stick to box off an area of ground.

2. Measurement Instructions

   • Measure the distance (in centimeters) to the nearest neighbor of five (5) Ranunculus within the square.

3. Hoop Toss Method

   • Toss a hoop to random locations throughout the study area.

   • Count the number of Ranunculus and mark the presence or absence of Geranium inside the hoop.

   • Collect data for five tosses, noting that zeros are valid data entries.

Clark-Evans Nearest Neighbor Method

1. Procedure

   • Measure the mean distance between an individual and its nearest neighbor.

   • Compare this to the expected mean distance if the dispersion were random.

2. Specific Focus

   • Study will only involve Ranunculus.

   • Aim to obtain 50 distance measurements - 5 per group (actual specimens may not be Ranunculus, e.g., Taraxacum).

Variance/Mean Ratio Method

1. Counting Individuals

   • Count the number of individuals in a sample plot and compare it with an expected randomly dispersed sample.

2. Data Collection

   • As the hoop is tossed, count and record the indicated number of Ranunculus.

   • Collect data for interspecific association analysis simultaneously.

Interspecific Association

1. Key Question

   • Do the two species (A: Ranunculus, B: Geranium) tend to occur in the same place?

2. Data Collection Notes

   • Record presence (1) or absence (0) of Geranium during the previous test.

3. Chi-squared Test

   • Complete a chi-squared test based on the gathered data.

Determining Statistical Significance

1. Example Values

   • Alpha-value ($ ext{α}$) = 0.05

   • Degrees of freedom ($v$) = 49

   • t-value = 2.61

2. Finding p-value Range

   • Assess your t-value (or $ ext{X}^2$ value) against the degrees of freedom to deduce the p-value range.

3. Statistical Decision

   • If p-value > $ ext{α}$, fail to reject the null hypothesis.

   • If p-value < $ ext{α}$, reject the null hypothesis.

   • Check that inequality signs (< >) are correct!

   • Example range: $0.02 > p > 0.01

Data Recording

1. Input Data

   • Input results into the designated spreadsheet.

Sample Data Spreadsheet