Marine Biology

, Volume 159, Issue 11, pp 2605–2620

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

  • Sylvia Moenickes
  • Marieke Frassl
  • Jeanette Schlief
  • Moritz Kupisch
  • Michael Mutz
  • Frank Suhling
  • Otto Richter
Original Paper

DOI: 10.1007/s00227-012-1996-4

Cite this article as:
Moenickes, S., Frassl, M., Schlief, J. et al. Mar Biol (2012) 159: 2605. doi:10.1007/s00227-012-1996-4

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.

List of symbols

B(s, n, E)

Reproduction (mm−1 day−1)

b(s, n)

Total number of incremental offspring (day−1)

bmax

Maximum birth rate (mm−β day−1)

C

Day length change

Ccrit

Critical day length change

D

Day length (h)

Dcrit

Critical day length (h)

E

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

fin

Environmental response of flow into main reach

fout

Environmental response of flow out of main reach

f(s, n, E)

Balance (mm−1 day−1)

F

Level of nutrition

FH

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)

pimax

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

Q10

Shape parameter of temperature response (°C−1)

rmax

Maximum growth rate (day−1)

s

Size

Body length (mm)

Head length (mm)

Body mass (mg)

smax

Maximum size for reproduction (mm or mg)

smin

Minimum size for reproduction (mm or mg)

si

Size threshold for transition from stage i (mm)

(mg)

t

Time (day)

T

Temperature (°C)

Tmax

Maximum temperature (°C)

Tmin

Minimum temperature (°C)

Topt

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

Supplementary material

227_2012_1996_MOESM1_ESM.pdf (840 kb)
Supplementary material 1 (PDF 840 kb)

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Sylvia Moenickes
    • 1
    • 5
  • Marieke Frassl
    • 1
    • 2
  • Jeanette Schlief
    • 3
  • Moritz Kupisch
    • 1
    • 4
  • Michael Mutz
    • 3
  • Frank Suhling
    • 1
  • Otto Richter
    • 1
  1. 1.Institute of GeoecologyTU BraunschweigBraunschweigGermany
  2. 2.Limnological InstituteUniversity of KonstanzKonstanz, EggGermany
  3. 3.Department of Freshwater ConservationBTU CottbusBad SaarowGermany
  4. 4.Institute of Crop Science and Resource ConservationUniversity of BonnBonnGermany
  5. 5.Faculty of Life SciencesRhein-Waal University of Applied SciencesKleveGermany