VI Southern-Summer School on Mathematical Biology
Positive effects of a primary
consumer on its resources:
Mývatn lake case
Group VIII:
Ana Paula Muche Schiavo (USP)
Ana Teresa Herrera-Reveles (UCV, Venezuela)
Eduardo Cocca Padovani (USP)
Hector Manuel Chuquillanqui Soto (SCBI, Perú)
Karen Amaral de Oliveira (UFABC)
Viviane Zulian (UFRGS)
INTRODUCTION:
Sub-artic lakes
Short growing season of algae (light and ice conditions)
Oligotrophic conditions (≈ 10 g C m-2 yr-1)
McDonald et al. 1996
INTRODUCTION:
Lake Mývatn (Iceland)
Abundant and diverse food web (Eutrophic lake ≈ 350 C m-2 yr-1)
The bottom consists of a layer of algae and larvae insects (up to
500.000 ind m-2).
INTRODUCTION:
Diatom (Algae):
Short life span (≈ 5 days), high
growth rate and benthic habitat (Lancelot
et al. 2005).
It is important as food to insect larve
and to recycling of nutrients (Lindegaard y
Jónasson 1979)
20 μm
INTRODUCTION:
Family Chironomidae (Insecta)
2 -3 days
Weeks
2–3
days
11 – 24 months
Multi-year life cycle (Welch 1976, Butler 1981)
INTRODUCTION:
Family Chironomidae (Insecta)
Populations fluctuate by several
orders of magnitude on irregular
periods of 4 to 7 years
Ives et al. 2008
QUESTIONS:
1. Is there a biological mechanism that could explain
the high anormal primary (algae) and secondary
(benthic insect larvae) productivity in this subartic
lake?
2. Are the irregular periods of fluctuations of
Chironomid populations sizes due intrinsic
interaction between two species?
MAIN GOAL:
Develop and analyze a simple mathematical model
capturing both negative and positive interactions
between chironomids larvae and the diatoms
MODEL:
Larvae
Algae
(Diatom)
5% nutrients
Space to growth
Detritus (Nutrients: Ni, P, Si)
http://voices.nationalgeographic.com/files/2014/07/P7033921.jpg
www.turbosquid.com/3d-models/protist-diatom-3d-max/573715
http://www.boldsystems.org/index.php/Public_BarcodeCluster?clusteruri=BOLD:ACD1924
Herren et al. 2017
ASSUMPTIONS OF THE MODEL:
1. The total nutrients (N & P) in the system are constant → It is a
close system
1.1. Every individual that dies remain in the system as
detritus.
2. All the biomass is linearly proportional to nutrients.
3. Environmental homogeneity.
4. “Larvae” includes all chironomids species and “Algae” all
diatoms → Two super species.
5. Larvae is the unique stage of the chironomids → Unstructured
populations.
MODEL:
MODEL:
MODEL:
RESULTS & DISCUSSION:
RESULTS & DISCUSSION:
CONCLUSIONS:
1. Is there a biological mechanism that could explain
the high anormal primary (algae) and secondary
(benthic insect larvae) productivity in this subartic
lake?
The positive feedback mechanism propoused is
enough to explain the high anormal productivity in
the lake.
CONCLUSIONS:
2. Are the irregular periods of fluctuations of
Chironomid populations sizes due intrinsic interaction
between two species?
The model propoused here can not explain the
fluctuations. So, there is another effect not considered
that causes the temporal pattern.
FUTURE EXPLORATIONS:
1. Open system:
1.1. Input of detritus and renewal water from rivers.
1.2. Emerging larvae as adults (Structured populations).
1.3. Input of biomass from photosynthesis.
2. Spatial dynamics.
3. Differences on population dynamics of Chironomids species.
4. Other interactions → Complex trophic system.
REFERENCES:
Parameters:
Based on:
1. Butler, M. 1981. Can. J. Zoo. 60, 58-70.
2,3,4. Ives, A et al.2008. Nature. 452, 84 – 87
5,6. Herren, C. et al. 2017. Ecology. 0, 1-17.
7,8,9. Lancelot, C. et al. 2005. MEPS. 289, 63-78.