Spatial aggregation and optimal Spatial aggregation and optimal p - - PowerPoint PPT Presentation

Spatial aggregation and optimal Spatial aggregation and optimal p gg g p p gg g p reserve number in species rich reserve number in species rich f t f t forests forests

Matthew D Potts & Jeffrey Vincent Matthew D Potts & Jeffrey Vincent Matthew D. Potts & Jeffrey Vincent Matthew D. Potts & Jeffrey Vincent University of California, San Diego University of California, San Diego

Reserve Site Selection Problem Reserve Site Selection Problem

For a fixed total reserve area ( For a fixed total reserve area (r), find the number of reserves ), find the number of reserves (m) that maximizes biodiversity. ) that maximizes biodiversity.

• What is the effect of

What is the effect of r on

• n m?

m? How does species spatial aggregation affect How does species spatial aggregation affect m?

• How does species spatial aggregation affect

How does species spatial aggregation affect m?

• Does it lead to non

Does it lead to non-

• convexities in the tradeoff

convexities in the tradeoff b t ti b d bi di it (f t d ti b t ti b d bi di it (f t d ti between timber and biodiversity (forest production between timber and biodiversity (forest production sets)? sets)?

History of the Reserve Site Selection History of the Reserve Site Selection Problem Problem

SLOSS Debate SLOSS Debate SLOSS Debate SLOSS Debate

– Single Large (SL) Or Several Small (SS) Single Large (SL) Or Several Small (SS) – Application of the theory of island biogeography to reserve Application of the theory of island biogeography to reserve design design design design – Politicized debate Politicized debate

Decision Theory Context Decision Theory Context Decision Theory Context Decision Theory Context

– Compare multiple objectives Compare multiple objectives – Set covering problem Set covering problem – Maximal convergence problem Maximal convergence problem

Modeling of Complex Systems Modeling of Complex Systems

T k d t f hi h T k d t f hi h d t d t – Take advantage of high Take advantage of high-speed computers speed computers – Build detailed & realistic models Build detailed & realistic models – Test hypotheses concerning reserve design Test hypotheses concerning reserve design yp g g yp g g

Incorporating an Ecological Incorporating an Ecological Non Non linearity linearity Spatial Aggregation Spatial Aggregation Non Non-linearity linearity – Spatial Aggregation Spatial Aggregation Approach Approach

• Build a spatially implicit model of aggregation

Build a spatially implicit model of aggregation

Hypotheses: Hypotheses: Hypotheses: Hypotheses:

• Under random tree placement, one large

Under random tree placement, one large reserve is always optimal reserve is always optimal reserve is always optimal. reserve is always optimal.

• Under aggregated placement, multiple small

Under aggregated placement, multiple small reserves are optimal reserves are optimal reserves are optimal. reserves are optimal.

Empirical Example Empirical Example

• Malaysian timber concession

Malaysian timber concession

The vast majority of tropical tree species The vast majority of tropical tree species t d i t d i are aggregated in space. are aggregated in space.

Dispersal Dispersal Rinorea sylvatica Rinorea sylvatica Habitat Factors Habitat Factors Dryobalanops aromatica Dryobalanops aromatica y Dryobalanops lanceolata Dryobalanops lanceolata

In addition, aggregation is scale dependent. In addition, aggregation is scale dependent. , gg g p , gg g p

• At small scales, dispersal effects drive aggregation,

At small scales, dispersal effects drive aggregation, leading to clumping. leading to clumping.

• At larger scales, aggregation

At larger scales, aggregation is related to heterogeneity in the landscape. is related to heterogeneity in the landscape. E i i l id t l l ti hi E i i l id t l l ti hi

• Empirical evidence suggests a power law relationship.

Empirical evidence suggests a power law relationship.

Aggregation affects species area curves Aggregation affects species area curves Aggregation affects species area curves Aggregation affects species area curves

Aggregation affects community similarity Aggregation affects community similarity by distance relationships by distance relationships

Spatially implicit model of aggregation Spatially implicit model of aggregation

Urn Analogy

Random Random -

• Binomial distribution

Binomial distribution

• the probability of occurrence of an individual in a

sample is independent of the occurrence of another individual.

U A l

Spatially implicit model of aggregation Spatially implicit model of aggregation

Urn Analogy

Aggregated – Negative binomial distribution Aggregated Negative binomial distribution

• the probability of occurrence of an individual in a sample

is not independent of the occurrence of another is not independent of the occurrence of another individual. l d t l t d b bilit f h i f

• leads to an elevated probability of having more or fewer

individuals of a particular species in a sample, depending on whether or not a clump of individuals is depending on whether or not a clump of individuals is encountered

The parameter ( The parameter (k) of the negative binomial ) of the negative binomial controls the degree of aggregation controls the degree of aggregation.

S i 1103 S i 1103

Example: Malaysian Timber Concession Example: Malaysian Timber Concession

• Area = 10,000 ha

Area = 10,000 ha

• Stem density = 600 ha

Stem density = 600 ha-1

1

• Species = 1103

Species = 1103

• Species abundance distribution

Species abundance distribution generated using Hubbell’s unified generated using Hubbell’s unified

• Number of Stems = 6,000,000

Number of Stems = 6,000,000 generated using Hubbell s unified generated using Hubbell s unified neutral theory ( neutral theory (θ = 100). = 100). Species Abundance Distribution Species Abundance Distribution

Key Parameters Key Parameters

Scale Dependent Aggregation

• Examined three cases of k:

Examined three cases of k: i.

• i. ∞

∞ -

• random placement

random placement ii ii 0 1 0 1 - scale independent scale independent ii.

• ii. 0.1

0.1 - scale independent scale independent aggregation aggregation iii iii 0 1 + 0 0001A 0 1 + 0 0001A0 5

0 5 - scale

scale iii.

• iii. 0.1 + 0.0001A

0.1 + 0.0001A0.5

0.5 - scale

scale dependent aggregation dependent aggregation

• Species’ minimum abundance,

Species’ minimum abundance, Spec es u abu da ce, Spec es u abu da ce, a.

• a. 100

100 b.

• b. 1000

1000

• i. Random Placement
• i. Random Placement

Reserve Number (m): Reserve Number (m):

• ii. Scale independent aggregation
• ii. Scale independent aggregation

p gg g p gg g

Reserve Number (m): Reserve Number (m):

• iii. Scale dependent aggregation
• iii. Scale dependent aggregation

p gg g p gg g

Reserve Number (m): Reserve Number (m):

Conclusions Conclusions Conclusions Conclusions

• Due to aggregation, the species

Due to aggregation, the species-

• maximizing

maximizing reserve number is scale dependent. reserve number is scale dependent.

• Decide total area to be protected

Decide total area to be protected

• Determine optimal number of reserves

Determine optimal number of reserves

Conclusions Conclusions

• Impact on forest management systems

Impact on forest management systems

• Optimality of segregated vs. integrated forest

Optimality of segregated vs. integrated forest

• Optimality of segregated vs. integrated forest

Optimality of segregated vs. integrated forest management differs with scale. management differs with scale.

Production Possibility Frontier Production Possibility Frontier