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Temporal patterns of populations in a warming world: a modelling framework

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Abstract

In this paper, we present an approach for describing the environmentally induced temporal pattern of structured populations by partial integro-differential equations. Populations are structured according to size or stage. Growth, energy allocation and stage transitions are affected by environmental conditions of which temperature, photoperiod, water depth and food supply were taken into account. The resulting modelling framework was applied to describe, analyse and predict alterations in populations with continuous development, populations with distinct state structures and interacting populations. Our exemplary applications consider populations of freshwater Amphipoda, Isopoda and Odonata. The model was capable of simulating life cycle alterations in dependence on temperature in interaction with other environmental factors: (1) population dynamics, (2) seasonal regulation, (3) water depth-dependent dispersal, (4) intraguild predation and (5) consumer-resource dynamics.

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Abbreviations

B(s, n, E):

Reproduction (mm−1 day−1)

b(s, n):

Total number of incremental offspring (day−1)

b max :

Maximum birth rate (mm−β day−1)

C :

Day length change

C crit :

Critical day length change

D :

Day length (h)

D crit :

Critical day length (h)

E :

Environmental conditions representing temperature, water depth, level of nutrition, day length, day length change

f in :

Environmental response of flow into main reach

f out :

Environmental response of flow out of main reach

f(s, n, E):

Balance (mm−1 day−1)

F :

Level of nutrition

F H :

Half-saturation level of nutrition

g(s, E):

Growth

Growth in length (mm day−1)

Growth in mass (mg day−1)

l :

Length (mm)

L :

Lag for water depth-dependent dispersal (day)

M(s, n, E):

Mortality (mm−1 day−1)

m :

Mortality rate (day−1)

n :

Population density distribution over size

… over length (mm−1)

… over mass (mg−1)

P(s, n, E):

Transition (mm−1 day−1)

p imax :

Maximum transition rate from stage i (mm−1 day−1)

Q10:

Shape parameter of temperature response (°C−1)

r max :

Maximum growth rate (day−1)

s :

Size

Body length (mm)

Head length (mm)

Body mass (mg)

s max :

Maximum size for reproduction (mm or mg)

s min :

Minimum size for reproduction (mm or mg)

s i :

Size threshold for transition from stage i (mm)

(mg)

t :

Time (day)

T :

Temperature (°C)

T max :

Maximum temperature (°C)

T min :

Minimum temperature (°C)

T opt :

Optimum temperature (°C)

w :

Body mass (mg)

W :

Water depth (cm)

α:

Shape parameter for day length control

β:

Size dependency of reproduction

γ:

Anabolic rate (mg−2/3 day−1)

κ:

Shape parameter for water depth response

λ:

Catabolic rate (mg day−1)

ν:

Shape parameter for transitions

μ:

Mortality rate (day−1)

τ:

Critical water depth (cm)

Ω:

Latitude

Π(s):

Density function of the size of hatched larvae

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Acknowledgments

We thank the Deutsche Forschungsgemeinschaft (DFG) for funding our studies within the priority programme 1162 Aquashift (Ri 534/11-1,2,3), (Mu 1464/2-1,2,3) and all members of the Running Water Cluster for fruitful cooperation. This article is in commemoration of the late Alfred Seitz.

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Authors and Affiliations

  1. Institute of Geoecology, TU Braunschweig, Langer Kamp 19c, 38106, Braunschweig, Germany

    Sylvia Moenickes, Marieke Frassl, Moritz Kupisch, Frank Suhling & Otto Richter

  2. Limnological Institute, University of Konstanz, Mainaustraße 252, 78464, Konstanz, Egg, Germany

    Marieke Frassl

  3. Department of Freshwater Conservation, BTU Cottbus, Seestr. 45, 15526, Bad Saarow, Germany

    Jeanette Schlief & Michael Mutz

  4. Institute of Crop Science and Resource Conservation, University of Bonn, Katzenburgweg 5, 53115, Bonn, Germany

    Moritz Kupisch

  5. Faculty of Life Sciences, Rhein-Waal University of Applied Sciences, 47533, Kleve, Germany

    Sylvia Moenickes

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  1. Sylvia Moenickes
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Correspondence to Sylvia Moenickes.

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Communicated by U. Sommer.

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Moenickes, S., Frassl, M., Schlief, J. et al. Temporal patterns of populations in a warming world: a modelling framework. Mar Biol 159, 2605–2620 (2012). https://doi.org/10.1007/s00227-012-1996-4

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  • DOI: https://doi.org/10.1007/s00227-012-1996-4

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