Spatial aggregation and optimal Spatial aggregation and optimal p p gg gg g g p p reserve number in species rich reserve number in species rich forests forests f f t t 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 on 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 b t between timber and biodiversity (forest production between timber and biodiversity (forest production ti ti b b d bi di d bi di it (f it (f t t d d ti ti 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 – Take advantage of high Take advantage of high-speed computers T k T k d d t t f hi h f hi h speed computers d d t t – Build detailed & realistic models Build detailed & realistic models – Test hypotheses concerning reserve design Test hypotheses concerning reserve design yp yp g g g g
Incorporating an Ecological Incorporating an Ecological Non Non linearity Non Non-linearity linearity linearity – Spatial Aggregation Spatial Aggregation 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 are aggregated in space. are aggregated in space. t d i t d i Habitat Factors Habitat Factors Dispersal Dispersal Dryobalanops aromatica Dryobalanops aromatica Rinorea sylvatica Rinorea sylvatica y Dryobalanops lanceolata Dryobalanops lanceolata In addition, aggregation is scale dependent. In addition, aggregation is scale dependent. , , gg gg g g p 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. • Empirical evidence suggests a power law relationship. E Empirical evidence suggests a power law relationship. E i i i i l l id id t t l l l ti l ti hi hi •
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.
Spatially implicit model of aggregation Spatially implicit model of aggregation U Urn Analogy A l 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. • leads to an elevated probability of having more or fewer l d t l t d b bilit f h i f 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 .
Example: Malaysian Timber Concession Example: Malaysian Timber Concession S Species = 1103 Species = 1103 S i i 1103 1103 Area = 10,000 ha Area = 10,000 ha • • Species abundance distribution Species abundance distribution Stem density = 600 ha -1 Stem density = 600 ha 1 • • generated using Hubbell s unified generated using Hubbell’s unified generated using Hubbell’s unified generated using Hubbell s unified Number of Stems = 6,000,000 Number of Stems = 6,000,000 neutral theory ( θ = 100). neutral theory ( = 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 ii. ii. 0.1 0 1 - scale independent 0.1 - scale independent scale independent scale independent aggregation aggregation 0.5 - scale 0 5 - scale iii iii iii. 0.1 + 0.0001A iii. 0.1 + 0.0001A 0.5 0 1 + 0 0001A 0 5 0 1 + 0 0001A scale scale dependent aggregation dependent aggregation • Species’ minimum abundance, Species’ minimum abundance, Spec es Spec es u u abu da ce, 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 p gg gg g g Reserve Number (m): Reserve Number (m):
iii. Scale dependent aggregation iii. Scale dependent aggregation p p gg gg g 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
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