This document summarizes a model exploring how local negative feedbacks can influence the evolution of species diversity within metacommunities. The model shows three possible outcomes: 1) permanent generalism with one widespread species, 2) permanent specialization with many specialist species, or 3) taxon cycles where specialist species periodically go extinct and are replaced. For diversity to emerge, parameters like colonization rate and negative feedback strength must be high, while extinction rate and environmental contamination must be low. The model reproduces classical macroecological patterns like species-area relationships and species abundance distributions. This framework provides insights into how local interactions can maintain biodiversity at larger scales.

1. Nicolas Loeuille
Laboratoire Ecologie & Evolution,
Université Pierre et Marie Curie
nicolas.loeuille@upmc.fr
Effects of local negative feedbacks on
the evolution of species within
metacommunities

2. Starting with an old debate
Gause 1934
Hutchinson 1961
How do we explain the maintenance
of diversity within a group of species ?

3. Spatial components in the maintenance
of diversity
● Total « regional » diversity :
– Colinization-Competition Trade-off (Tilman 1994)
– Spatial heterogeneity and niche partitioning (Leibold
et al. 2004)
– Storage effects (Chesson 1994)
– Random speciation, ecological drift (Hubbell 2001)
● Local diversity
– Mass effects (source-sink relationships) Mouquet &
Loreau (2004)
– Janzen-Connell (Janzen 1970)

4. The puzzling diversity of tropical
forests
● Neutral dynamics
Speciation, migration,
ecological drift
(Hubbell 2001)
● Niche deterioration
Competitive hierarchy,
mediated by enemy
attraction (Janzen 1970)

5. The Janzen-Connell hypothesis
Janzen 1970

6. Local negative feedbacks
Enemy presence
Presence of
one individual
Decrease in survival, decrease in competitive ability

7. An illustrative example
Diez et al. 2010

8. Importance for community structure and
diversity
Klironomos et al. 2002

9. Consumption constraints also yield
local negative feedback (1/2)
Plant
N:P=12:1
Soil
N:P=15:1
Nutrientuptake
Nitrogenrelease
N:P in soil increases
Favors incoming competitor species with a higher N:P

10. Consumption constraints also yield
local negative feedback (2/2)
P
BA
P
B
A
Habitat becomes less suitable for predator A
An alternative predator with high affinity for B would be favored

11. Critical conditions under which
feedbacks act on diversity
1)Local environment is largely driven by the species
presence (vs, eg, external abiotic constraints): niche
construction (Laland et al. 1999, Kylafis & Loreau
2008)
2)Spatial constraints: low diffusion of enemies or
nutrient compared to the species dispersal
3)Evolutionary constraints: Evolutionary dynamics lag
behind ecological dynamics
What is the amount of diversity emerging from the
interplay of these three constraints?

12. Ecological dynamics of the model
● 30*30 patches on a torus
● Each patch i has an environmental state zi
● Each morph has a trait xi
● (a) Extinction, with probability e
● (b) Colonization from neighbor with probability c,
success if the invader j is better adapted (xj
closer to
zi
)
Initial Situation(a)
(b)
Ecological Dynamics

13. Evolutionary dynamics
● Each local population has a probabilityμ to undergo
a beneficial mutation.
● (c) If so, the new trait of the population xi
becomes
closer to environmental state zi
by less than dx
Initial Situation
(c)
Evolutionary Dynamics

14. Environmental dynamics
Local environment zi
changes :
d) Away from xi
by a fixed step
dz if the patch is full (negative
feedback)
d) Toward 0 by a step dz if the
patch is empty (global
averaging)
e) Toward the local average by
a step αdz in all instances
(contamination)
Initial Situation
(d)
(e)

15. Initial conditions and possible dynamics
● Only one population, of trait xi
=0.5
● For each patch, an environmental value z is picked at
random between 0 and 1
● One million time steps considered
Q1 Conditions for the emergence of diversity ?
Q2 Effects on the environmental structure ?
Q3 Effects on the community patterns at various
scales ?

16. Permanent generalism
One species only, generalist
(here, high e)

17. Permanent specialization
Diversification
Maintenance of specialist morphs
(here, e=0)

18. Taxon cycles
Diversification
Periodic extinction of specialist morphs
(here, intermediate e)

19. On taxon cycles
Considering the occupation
of islands by lizards :
-one lizard species on one
island
-invasion by larger lizard
species is possible
-evolution toward smaller
sizes of the ancestral
species (specialization)
-Same for the invader
-Eventual extinction of the
ancestral species
Roughgarden & Pacala 1979
Ricklefs & Bermingham 2002

20. Effects on the grain
of the environment
Permanent Generalism
Taxon cycles
Permanent specialization

21. The succession of the three patterns is
deterministic

22. Conditions for emerging diversity
● From the succession of the three patterns, it is
possible to distinguish parameters favoring diversity
(PG->TC->PS)
● Such parameters include : colonization rate c,
negative feedback dz
● Parameters that prevent the emergence of structure
and diversity : extinction rate e, mutation rate μ (or
mutation amplitude dx), contamination from
surrounding patches α

23. What is the amount of diversity
obtained ?

24. What is the amount of diversity
obtained ?

25. The succession of the three patterns is
deterministic

26. How is diversity organized in space ?
● Species-Area relationship (Preston 1962) : D=D0
As
Kodric-Brown & Brown (1993)

27. How is diversity organized in space ?

28. Species abundance distribution
From McGill et al. 2007

29. On an arithmetic scale, the model
reproduces the traditional empty curve
PGTCPS PGTCPS

30. On a logarithmic scale, multimode
distributions
PGTCPS PGTCPS

31. Conclusions
● Negative feedbacks may allow the emergence of
diversity, but not under all conditions
● Taxon cycle one possible outcome, but in fact part of
a continuum
● The model also provides classical shapes for
macroecological patterns (species abundance
distribution, species area curve)
● Associated with the temporal dynamics of diversity,
such patterns can allow more robust testing of the
model (McGill et al. 2003)

32. Acknowledgements
Mathew Leibold