Substrate and Time of Day Effects on Benthic Organisms

Trawling Data Both Day and Night Data in HeckShare Folder Both Day and Night Data in HeckShare Folder Pool trawl data into per habitat for comparisons between habitats, and between day/night for sand and mud. Pool trawl data into per habitat for comparisons between habitats, and between day/night for sand and mud. i.e. Day Trawling – Trawls 2,3 combine for shell i.e. Day Trawling – Trawls 2,3 combine for shell Compare combined Day Trawls for mud with combined Night Trawls for mud Compare combined Day Trawls for mud with combined Night Trawls for mud

Similarity Calculations Compare similarity in fish/invert species composition during day between: Compare similarity in fish/invert species composition during day between: Mud-Sand; Mud-Shell; Sand-Shell (Day and Night) Mud-Sand; Mud-Shell; Sand-Shell (Day and Night) Use Jaccard similarity index: Use Jaccard similarity index: J = C / (A+B-C) J = C / (A+B-C) A = No. of spp. on substrate 1 A = No. of spp. on substrate 1 B = No. of spp. On substrate 2 B = No. of spp. On substrate 2 C = No. of spp. shared by both substrates C = No. of spp. shared by both substrates Value varies from 0 (no common spp.) to 1 (all common) Value varies from 0 (no common spp.) to 1 (all common)

Similarity Calculations MudSandShell Mud1 Sand1 Shell1 If Sand has 22 spp. Mud has 20 spp. 10 spp. overlap J = 10 / ( ) J =

Euclidean Distance Considers the distribution of individuals with species in each collection: Considers the distribution of individuals with species in each collection: Delta JK = Sqrt [ Sum (X if – X ik ) 2 ] Delta JK = Sqrt [ Sum (X if – X ik ) 2 ] Delta JK = Euclidean Distance Delta JK = Euclidean Distance X if = Number indiv’s of species “i” in collection “j” X if = Number indiv’s of species “i” in collection “j” X ij = Number indiv’s of species “i” in collection “k” X ij = Number indiv’s of species “i” in collection “k” n = Total number of species n = Total number of species

Euclidean Distance Compensate for fact that Euclidean Distance increases with number of species in a sample by calculating average distance: Compensate for fact that Euclidean Distance increases with number of species in a sample by calculating average distance: d jk = [ Sqrt ( Delta 2 jk ) ] / (n) d jk = [ Sqrt ( Delta 2 jk ) ] / (n) d jk = average Euclidean distance b/n sample j and k d jk = average Euclidean distance b/n sample j and k Delta jk = Euclidean Distance Delta jk = Euclidean Distance n = number of species in the samples being compared n = number of species in the samples being compared

Euclidean Dist. Calculations Site 1Site 2Site 3 Sp Sp Sp ED 1,2 = sqrt [ ( ) 2 + (20-10) 2 + (0-5) 2 ] ED 1,3 = sqrt [ ( ) 2 + (20-5) 2 + (0-0) 2 ] ED 2,3 = sqrt [ ( ) 2 + (10-5) 2 + (5-0) 2 ]

Questions Explain why you found the similarity values you did, using material from lecture, notes, text, observations Explain why you found the similarity values you did, using material from lecture, notes, text, observations Discuss why Jaccard and Euclidean distances showed different patterns (if they did) Discuss why Jaccard and Euclidean distances showed different patterns (if they did) Describe similarities and differences in body shape, shell thickness, and general morphology of the taxa inhabiting various substrates Describe similarities and differences in body shape, shell thickness, and general morphology of the taxa inhabiting various substrates

Predation Experiments

Methods Every 24 hours, check tethered crabs Every 24 hours, check tethered crabs Record identity and size of consumed animals Record identity and size of consumed animals Replace lost animals each day so that original density of 3 animals/tether maintained over next 2 trials Replace lost animals each day so that original density of 3 animals/tether maintained over next 2 trials Any escapes or unconfirmed predation, do not count them in analysis. Any escapes or unconfirmed predation, do not count them in analysis. In raw data, identify any escaped crabs In raw data, identify any escaped crabs

Data Analysis Compare % of mud crabs, hermits consumed on each of the two habitats using Chi-Square Compare % of mud crabs, hermits consumed on each of the two habitats using Chi-Square Also evaluate whether crab size or type of a hermit crab’s shell was correlated with percentage of prey taken by predators Also evaluate whether crab size or type of a hermit crab’s shell was correlated with percentage of prey taken by predators

Chi-Square Compares theorized predictions vs. observed data Compares theorized predictions vs. observed data Ho = no sig diff b/n theorized and exp. populations Ho = no sig diff b/n theorized and exp. populations Ha = There is a sig diff b/n theorized and exp. Pops Ha = There is a sig diff b/n theorized and exp. Pops Chi-Square (χ 2 ) = [ Sum (# observed – # expected ) 2 ] / [ # expected ] Chi-Square (χ 2 ) = [ Sum (# observed – # expected ) 2 ] / [ # expected ] Calculate χ 2 value and compare to Table 2 at p=0.05 (on page 55) Calculate χ 2 value and compare to Table 2 at p=0.05 (on page 55)

Chi-Square Contingency Tables Take observations (f) and compare to theoretical values (F) calculated from equation: Take observations (f) and compare to theoretical values (F) calculated from equation: F = RC/n F = RC/n Where, F = frequency of observations Where, F = frequency of observations R = Row frequency R = Row frequency C = Column frequency C = Column frequency n = Total number of data in all positions of table n = Total number of data in all positions of table

Chi-Square Contingency Tables Obs’d for birds in different regions of forest: Obs’d for birds in different regions of forest: Take Observed data to calculate theoretical: Take Observed data to calculate theoretical: F for birds in trees in spring = (59*43)/120 F for birds in trees in spring = (59*43)/120 F for birds in shrubs in autumn = (61*42)/120 F for birds in shrubs in autumn = (61*42)/120 In TreesIn ShrubsOn GroundTotal In Spring In Autumn Total

Chi-Square Contingency Tables Create Theoretical Table to which one may compare observations: Create Theoretical Table to which one may compare observations: In TreesIn ShrubsOn GroundTotal In Spring In Autumn Total

Chi-Square Contingency Tables Chi-Square Value calculated as: Chi-Square Value calculated as: χ 2 = ∑∑ [ (f – F) 2 / F ] χ 2 = ∑∑ [ (f – F) 2 / F ] Where ∑∑ indicates to sum values across all rows and columns Where ∑∑ indicates to sum values across all rows and columns

Chi-Square Contingency Tables In TreesIn ShrubsOn GroundTotal In Spring In Autumn Total In TreesIn ShrubsOn GroundTotal In Spring In Autumn Total χ 2 = [( ) 2 / 21.14] + [( ) 2 / 20.65] +[( ) 2 / 17.21] + [( ) 2 /21.86] + [( ) 2 / 21.35] + [( ) 2 / 17.79] χ 2 = [ ] =

Chi-Square Contingency Tables Take value of and compare to Critical Value for χ 2 at alpha = 0.05 and degrees of freedom Take value of and compare to Critical Value for χ 2 at alpha = 0.05 and degrees of freedom DF = (no. of rows – 1) * (no. of columns – 1) DF = (no. of rows – 1) * (no. of columns – 1) DF = (2-1) * (3-1) = 2 DF = (2-1) * (3-1) = 2 So, Critical value at alpha = 0.05 and DF = 2 is (pg. 55), which is < and reject null hypothesis – There is a difference So, Critical value at alpha = 0.05 and DF = 2 is (pg. 55), which is < and reject null hypothesis – There is a difference

Questions 1. Are there sig. diff’s in predation rate among habitats? Why do these exist? 1. Are there sig. diff’s in predation rate among habitats? Why do these exist? 2. Does prey size influence the results? 2. Does prey size influence the results? 3. Does the kind of shell carried by hermit crabs influence vulnerability to predation? 3. Does the kind of shell carried by hermit crabs influence vulnerability to predation? 4. Is predation likely to be an important factor in the ecology of the species studied? 4. Is predation likely to be an important factor in the ecology of the species studied?

Data Example DateHabitatCW Mud CrabConsumed?Size Hermit CrabConsumed? 6/23/2009G7N4N G8Y5N G9Y6Y S6Y5Y S7N5N S8N4Y 6/24/2009G7Y4Y G6Y5N G4N7Y S5N8Y S7Y5N S8Y3Y