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>Stéphane
Legendre
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CNRS - UMR 8197
Ecole
Normale Supérieure
46 rue d'Ulm
75230 Paris
Cedex 05
France
Tel:
+33.1.44.32.37.01
legendre@ens.fr
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Research
team
Team
of Mathematical Eco-Evolution
Research
interests
My
work is at the interface of mathematics, computer science and ecology,
i.e., ecological modelling.
Population
dynamics
Development of the ULM computer program
(Legendre & Clobert 1995, Ferrière & al
1996;
Fig.1), widely used
by ecologists.
- The ULM
program can be
downloaded there.

Figure 1. Chaotic
attractor in population dynamics studied with the ULM software (model
from Ferrière 1992).
Conservation
biology
Small populations dynamics:
- reintroductions
(Sarrazin
& Legendre 2000)
- extinctions (Legendre & al. 1999,
Schoener & al 2003, Legendre & al 2008)
Figure 2. Probability
of extinction as a function of time for the spider Argiope argentata
in
the Bahamas: observed (initial population size = 21-50
individuals; solid squares), and simulated (initial population size =
32 individuals; open squares). ULM model incorporating demographic stochasticity,
population ceiling and
environmental stochasticity (Schoener & al. 2003).
Sexual
selection
Impact of sexual selection on small
populations:
- 2-sex demographic models (Legendre
& al 1999, Legendre
2004, Bessa-Gomes & al 2004, 2010),
- The pair formation process (Bessa-Gomes
& al 2003)
- Combinatorics (Møller &
Legendre 2001;
Fig. 3)
- Adaptive dynamics (Morlon &
Legendre 2002)
Figure 3.
The probability of one individual being mated as a function of
population size with monogamous pair formation, sex ratio 0.5, and
chance realization in the number of males and females (circles). When
each individual chooses its mate with probability 0.5, the probability
of being mated is reduced at low population sizes (squares), as
observed in captive populations (Møller &
Legendre 2001).
Evolutionary
dynamics
The ZEN computer program (Fig. 4) allows to
study ecological models in an evolutionary
perspective. The project was funded by an Action Incitative
Bioinformatique from the CNRS.
- The ZEN
program can be downloaded there
Figure 4. Adaptive
radiation
in bacteria with environmental catastrophes (mixing). Time on the
horizontal axis, position on the vertical axis. The figure
shows the positions of diversifying phenotypes adapted to different
niches along a vertical
gradient (ZEN simulation; collaboration with Andy
Gonzalez, Régis Ferrière and Nirmala Massin).
Figure 5. Evolutionary
restoration after environmental change. Distribution
of phenotypes along time in polymorphic populations. The environment is
constant over the first 21000 generations and changes gradually between
time 21000 and 22000. Only 2 branches persist. The environment is
progessively restored to its
initial state from time 31000 to 32000. Diversity recovers. Model of
cooperative evolution (Ferriere & Legendre 2013).
Allometry
Evolutionary entropy is a measure of the
life-cycle complexity introduced by L. Demetrius. We show that entropy
is in logarithmic relation with generation
time (Fig. 6), and with body
size. When
entropy is considered as a measure of fitness, this implies that along
evolutionary time, body size should increase in equilibirum species
(Cope's rule), and decrease in opportunistic species (Demetrius,
Legendre & Harremöes 2009).

Figure 6. The relation S ~ log T + b for 127 species of
mammals, with S
evolutionary entropy and T generation time (Demetrius & al.
2009). The large dot corresponds to Homo sapiens.
Ecological networks
Development
of computer programs to study ecological networks using the methods of
graph theory.
Trophic networks (food webs; Lazzaro
&
al 2009, Gauzens & al 2013, Gauzens & al 2015)
The n_w
program (Fig. 7), can be
downloaded there.
Figure 7. Representation
of the Créteil Lake food web with basal species at the
bottom
and consumer species arranged according to their trophic height . (A)
Partition into trophic
groups indicated by color circles. (B) Partition into modules indicated
by rectangles. Trophic groups and modules decompositions computed by
the n_w
program.
Bipartite ecological networks (plant-pollinator, site-species, host-parasite, male-female, ...)
The a2b program can be
downloaded there.
Figure 8. Representation of an experimental plant-pollinator network from Colin Fontaine using the a2b
program. The width and color of the links correspond to the number of visits of
plant species on the left by pollinator species on the right.
Publications
- Legendre
S & J Clobert. 1995. ULM, a software for conservation and
evolutionary biologists. Journal of Applied Statistics 22:817–834.
- Thomas-Orillard
M & S Legendre. 1996. Virus C de la Drosophile et dynamique
d'une
population hôte. Comptes Rendus de l'Académie des
Sciences de Paris
319:615–621. PDF
file
- Ferrière
R, F Sarrazin, S Legendre & J-P Baron. 1996. Matrix population
models applied to viability analysis and conservation: Theory and
practice with ULM software. Acta Oecologica 17:629–656.
- Legendre
S, J Clobert, AP Møller & G Sorci. 1999. Demographic
stochasticity
and social mating system in the process of extinction of small
populations: The case of passerines introduced to New Zealand. American
Naturalist 153:449–463. PDF
file
- Sarrazin
F & S Legendre. 2000. Demographic approach to releasing adults
versus young in reintroductions. Conservation Biology 14:488-500. PDF
file
- Barot
S, J Gignoux, R Vuattoux & S Legendre. 2000. Demography of a
savanna palm tree in Ivory Coast (Lamto): population persistence and
life-history. Journal of Tropical Ecology 16:637–655.
PDF
file
- Møller
AP & S Legendre. 2001. Allee effect, sexual selection and
demographic stochasticity. Oikos 92:27–34. PDF
file
- Barot S,
J Gignoux & S Legendre. 2002. Stage-classified matrix models
and age estimations. Oikos 96:56–61. PDF
file
- Morlon
H & S Legendre. 2002. A model of sexual selection using
adaptive
dynamics: The Fisher's runaway and its reversibility. Unpublished
manuscript. PDF
file
- Schoener
TW, J Clobert, S Legendre & DA Spiller. 2003. Life-history
models
of extinction: A test with island spiders. American Naturalist
162:558–573. PDF
file
- Bessa-Gomes
C, S Legendre, J Clobert & AP Møller. 2003. Modeling
mating
patterns given mutual mate choice: The importance of individual mating
preferences and mating system. Journal of Biological Systems
11(3):205–219. PDF
file
- Bessa-Gomes
C, M Danek-Gontard, P Cassey, AP Møller, S Legendre
& J Clobert.
2003. Mating behaviour influences extinction risk: insights from
demographic modelling and comparative analysis of avian extinction
risk. Annales Zoologici Fennici 40(2):231–245. PDF
file
- Chapron
G, P-Y Quenette, S Legendre & J Clobert. 2003. Evaluating
conservation strategies for the French Pyrenean brown bear (Ursus
arctos) population by using stage-structured population models. Comptes
Rendus Biologies 326:S174–S182. PDF
file
- Chapron
G; S Legendre, R Ferrière, J Clobert & RG Haight.
2003.
Conservation and control strategies for the wolf (Canis lupus) in
western Europe based on demographic models. Comptes Rendus Biologies
326:575–587. PDF
file
- Robert
A, F Sarrazin, D Couvet & S Legendre. 2004. Releasing adults
versus
young in reintroductions: Interactions between demography and genetics.
Conservation Biology 18:1–10. PDF
file
- Bessa-Gomes
C, S Legendre & J Clobert. 2004. Allee effects, mating systems
and
the extinction risk in populations with two sexes. Ecology Letters
7:802–812.
PDF
file
- Legendre
S. 2004. Influence of age structure and mating system on population
viability. In
Evolutionary Conservation Biology (Ferrière R,
U
Dieckmann & D Couvet eds.), Cambridge University Press, pp.
41–58. PDF
file
- Chapron
G, DG Miquelle, JG Goodrich, A Lambert, S Legendre & J Clobert.
2005. The effect of poaching on tigers in the russian far east. In
Tigers of Sikhote-Alin Zapovednik: ecology and conservation, DG
Miquelle, JG Goodrich & EN Smirnov (eds.), pp. 191–195,
chapter
25 (in Russian). PDF
file
- Legendre
S.
2008. La séparation en biologie. In De la
Séparation,
directed by C Schaeffer, L'Harmattan, Paris, pp. 55–71. PDF
file
- Legendre
S, TW Schoener, J Clobert & DA Spiller. 2008. How is extinction
risk related to population-size variability over time? A family of
models for species with repeated extinction and immigration. American
Naturalist 172:282–298. PDF
file
- Chapron
G, DG Miquelle, A Lambert, JM Goodrich, S Legendre & J Clobert.
2008. The impact on tigers of poaching versus prey depletion. Journal
of Applied Ecology 45:1667–1674. PDF
file
- Demetrius
L, S Legendre & P Harremöes.
2009. Evolutionary entropy: A predictor of body size, metabolic rate
and maximal life span. Bulletin of Mathematical Biology 71:800–818. PDF
file
- Lazzaro X, G Lacroix,
B Gauzens, J Gignoux & S Legendre. 2009. Predator foraging
behaviour drives
food-web topological structure. Journal of Animal Ecology 78:1307–1317. PDF
file
- Legendre
S.
2009. The number of crossings in a regular drawing of the
complete bipartite graph. Journal
of Integer Sequences, Vol.
12, article 09.5.5
- Bessa-Gomes
C, S
Legendre & J Clobert. 2010. Discrete two-sex models of
population dynamics:
On modelling the mating function. Acta Oecologica 36:439–445. PDF
file
- Legendre
S.
2011. La résilience des écosystèmes. In De la
Réparation,
directed by C Schaeffer, L'Harmattan, Paris, pp. 41–51. PDF
file
- Hulot F,
D Carmignac, S Legendre, C Yéprémian & C
Bernard.
2012. Effects of microsystin-producing and microsystin-free strains of
Planktothrix
agardhii on long-term population dynamics of Daphnia magna.
Annales de Limnologie - International Journal of Limnology
48:337–347. PDF
file
- Demetrius
L & S Legendre.
2013. Evolutionary entropy predicts the outcome of selection:
Competition for resources that vary in abundance and diversity.
Theoretical Population Biology 83:39–54. PDF
file
- Ferriere
R
& S Legendre.
2013. Eco-evolutionary feedbacks, adaptive dynamics and evolutionary
rescue theory. Philosophical Transaction of the Royal Society B 368
20120081. PDF
file
- Chaine
A, S Legendre & J Clobert. 2013. The co-evolution of
multiply-informed dispersal: Information transfer across landscapes
from neighbors and immigrants. PeerJ 1:e44; DOI
10.7717/peerj.44. PDF
file
- Gauzens
B, S Legendre, X Lazzaro & G Lacroix. 2013. Food-web
aggregation, methodological and functional issues. Oikos 122:1606–1615. PDF
file
- Mugabo
M, S Perret, S Legendre & J-F Le Galliard. 2013.
Density-dependent
life history and the dynamics of small populations. Journal of Animal
Ecology 82:1227–1239. PDF
file
- Edeline
E, G Lacroix, C Delire, N Poulet & S Legendre.
2013. Ecological emergence of thermal clines in body size.
Global
Change Biology 19:3062–3068. PDF
file. Supplementary information PDF
file
- Bienvenu
F, L Demetrius & S Legendre. 2013. A general formula for the
generation time. arXiv.q-bio.PE
- Gauzens B, S Legendre, X Lazzaro & G Lacroix. 2016. Intermediate predation pressure leads to maximal complexity in food webs. Oikos 125: 595-603. PDF
file
- Brom T, M
Massot, S Legendre & D Laloi. 2016. Kin competition drives the
evolution of sex-biased dispersal under monoandry and polygyny, not
under monogamy. Animal Behavior 113: 157–166. PDF
file
- Bienvenu F, E Akçay, S
Legendre & D McCandlish. 2017. The genealogical decomposition of a
matrix population model with application to the aggregation of stages. Theoretical Population Biology 115: 69–180. PDF
file
- Massot M, S legendre, P Fédérici & J Clobert. 2017. Climate warming: a loss of variation in populations can accompany reproductive shifts . Ecology Letters 20:1140–1147. PDF
file - Supp PDF file
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