2. Latitudinal Gradients in Species Diversity

5. Latitudinal Gradients in Species Diversity

10. Regional<—>Local <—> Point diversity
Four ways two systems can differ in diversity
Saturation with species, MacArthur’s foliage height diversity vs. birds
Latitudinal gradients in diversity, primary vs. secondary mechanisms
Time theories
Climatic stability and climatic predictability
Spatial heterogeneity
Productivity and stability of productivity
Competition —> specialization, narrow niches, higher diversity
Disturbance, intermediate disturbance hypothesis
Predation-induced diversity

11. of Species Diversity and Their Proposed Modes of Action
Various Hypothetical Mechanisms for the Determination
of Species Diversity and Their Proposed Modes of Action
__________________________________________________________________
Level Hypothesis or theory Mode of action
Primary 1. Evolutionary time Degree of unsaturation with species
Primary 2. Ecological time Degree of unsaturation with species
Primary 3. Climatic stability Mean niche breadth
Primary 4. Climatic predictability Mean niche breadth
Primary or 5. Spatial heterogeneity Range of available resources
secondary
Secondary 6. Productivity Especially mean niche breadth, but
also range of available resources
Secondary 7. Stability of primary Mean niche breadth and range of
production available resources
Tertiary 8. Competition Mean niche breadth
Primary, 9. Disturbance Degree of allowable niche overlap
secondary, and level of competition
or tertiary
Tertiary 10. Predation Degree of allowable niche overlap __________________________________________________________________

13. Intermediate Disturbance Hypothesis

17. Tree Species Diversity in Tropical Rain Forests Seed Predation Hypothesis Nutrient Mosaic Hypothesis Circular Networks Hypothesis Disturbance Hypothesis (Epiphyte Load Hypothesis)

22. Sea Otter (Enhydra lutris)

24. Amchitka Shemya
Sea Otters km2 only vagrants
Kelp dense mats heavily grazed
Sea Urchins 8/m2, 2-34mm 78/m2, 2-86mm
Chitons 1/m /m2
Barnacles 5/m /m2
Mussels 4/m /m2
Greenling abundant scarce or absent
Harbor Seals 8/km l.5-2/km
Bald Eagles abundant scarce or absent

26. Community Stability. Traditional Ecological Wisdom
Community Stability Traditional Ecological Wisdom Diversity begats stability (Charles Elton) More complex ecosystems with more species have more checks and balances

27. Types of Stability Point Attractors <——> Repellers Domains of Attraction, Multiple Stable States Local Stability <——> Global Stability Types of Stability Persistence Constancy = variability Resistance = inertia Resilience = elasticity (rate of return, Lyapunov stability) Amplitude stability (Domain of attraction) Cyclic stability, neutral stability, limit cycles, strange attractors Trajectory stability

29. Types of Stability Point Attractors <——> Repellers Domains of Attraction, Multiple Stable States Local Stability <——> Global Stability Types of Stability Constancy = variability Resistance = inertia Resilience = elasticity (rate of return, Lyapunov stability) Amplitude stability (Domain of attraction) Cyclic stability, neutral stability, limit cycles, strange attractors Trajectory stability

31. Edward Lorenz
Strange
Attractor

32. Generalized Lotka-Volterra Equations: dNi/dt = Ni (bi + S aij Nj)
Jacobian Matrix
Partial Derivatives ∂Ni / ∂Nj , ∂Nj / ∂Ni
Sensitivity of species i to changes in density of species j
Sensitivity of species j to changes in density of species i

33. Traditional Ecological Wisdom:
Diversity begats Stability
MacArthur’s idea
Stability of an ecosystem should increase with both the number of different trophic links between species and with the equitability of energy flow up various food chains

34. Robert MacArthur

35. Robert May challenged
conventional ecological
thinking and asserted that complex ecological systems
were likely to be less stable
than simpler systems
May analyzed sets of randomly assembled Model Ecosystems. Jacobian matrices were
Assembled as follows: diagonal elements were defined as – 1. All other interaction terms were equally likely to be + or – (chosen from a uniform random distribution ranging from +1 to –1). Thus 25% of interactions were mutualisms, 25% were direct interspecific competitors and 50% were prey-predator or parasite-host interactions. Not known for any real ecological system!

36. May varied three aspects of community complexity:
Number of species
(dimensionality of the Jacobian matrix)
2. Average absolute magnitude of elements
(interaction strength)
Proportion of elements that were non-zero
(connectedness)

37. Real communities are far from random in construction, but must obey various constraints.
Can be no more than 5-7 trophic levels, food chain loops are disallowed, must be at least one producer in every ecosystem, etc.
Astronomically large numbers of random systems : for only 40 species, there are possible networks
of which only about are biologically reasonable — realistic systems are so sparse that random sampling is unlikely to find them. For just a 20 species network, if one million hypothetical networks were generated on a computer every second for ten years, among the resulting random systems produced, there is a 95% expectation of never encountering even one realistic ecological system!

38. Latitudinal gradients in species diversity
Tropical tree species diversity
Seeding rings
Nutrient mosaic
Circular networks
Disturbance (epiphyte loads)
Connectance and number of species
Sea otters as keystone species, alternative stable states
Types of stability
Constancy = variability
Inertia = resistance
Elasticity = resilience (Lyapunov stability)
Amplitude (domain of attraction)
Cyclic stability (neutral stability, limit cycles, strange attractors)
Trajectory stability (succession)
Traditional ecological wisdom: diversity begats stability
May’s challenge using random model systems
Real systems not constructed randomly