Latitudinal Gradients in Species Diversity

Latitudinal Gradients in Species Diversity

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

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 speciesPrimary 2. Ecological time Degree of unsaturation with speciesPrimary 3. Climatic stability Mean niche breadthPrimary 4. Climatic predictability Mean niche breadthPrimary or 5. Spatial heterogeneity Range of available resourcessecondarySecondary 6. Productivity Especially mean niche breadth, but

also range of available resourcesSecondary 7. Stability of primary Mean niche breadth and range of

production available resourcesTertiary 8. Competition Mean niche breadthPrimary, 9. Disturbance Degree of allowable niche overlapsecondary, and level of competitionor tertiaryTertiary 10. Predation Degree of allowable niche

overlap

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Intermediate Disturbance Hypothesis

Tree Species Diversity in

Tropical Rain Forests

Seed Predation Hypothesis

Nutrient Mosaic Hypothesis

Circular Networks Hypothesis

Disturbance Hypothesis

(Epiphyte Load Hypothesis)

Sea Otter (Enhydra lutris)

Amchitka ShemyaSea Otters 20-30 km2 only

vagrants

Kelp dense mats heavily

grazed

Sea Urchins 8/m2, 2-34mm 78/m2,

2-86mm

Chitons 1/m2 38/m2

Barnacles 5/m2

1215/m2

Mussels 4/m2 722/m2

Greenling abundant

scarce or absent

Harbor Seals 8/km l.5-2/km

Bald Eagles abundant

scarce or absent

Community Stability

Traditional Ecological Wisdom

Diversity begats stability

(Charles Elton)

More complex ecosystems with more

species have more checks and

balances

Types of Stability Point Attractors <——> Repellers Domains of Attraction, Multiple Stable States Local Stability <——> Global Stability Types of Stability 1. Persistence 2. Constancy = variability 3. Resistance = inertia 4. Resilience = elasticity (rate of return, Lyapunov stability) 5. Amplitude stability (Domain of attraction) 6. Cyclic stability, neutral stability, limit cycles, strange attractors 7. Trajectory stability

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

Edward Lorenz

Strange Attractor

Generalized Lotka-Volterra Equations:

dNi/dt = Ni (bi + aij Nj)

Jacobian Matrix

Partial Derivatives ∂Ni / ∂Nj , ∂Nj / ∂Ni

Sensitivity of species i to changes in density of species jSensitivity of species j to changes in density of species i

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

Robert MacArthur

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 wereAssembled 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!

May varied three aspects of community complexity:

1.Number of species (dimensionality of the Jacobian matrix)

2. Average absolute magnitude of elements (interaction strength)

3.Proportion of elements that were non-zero (connectedness)

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 10764 possible networksof which only about 10500 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 31.513 random systems produced, there is a 95% expectation of never encountering even one realistic ecological system!

Latitudinal gradients in species diversityTropical tree species diversitySeeding ringsNutrient mosaicCircular networksDisturbance (epiphyte loads)Connectance and number of speciesSea otters as keystone species, alternative stable statesTypes of stabilityConstancy = variabilityInertia = resistanceElasticity = resilience (Lyapunov stability)Amplitude (domain of attraction)Cyclic stability (neutral stability, limit cycles, strange attractors)Trajectory stability (succession)Traditional ecological wisdom: diversity begats stabilityMay’s challenge using random model systemsReal systems not constructed randomly