Microorganism growth and reproduction have been traditionally modeled independently of the direct effect of the metabolic process. The latter caused inconsistencies between the modeling results and experimental data. A major inconsistency was linked to the experimentally observed lag phase in the growth process. Attempts to associate the lag phase to delay processes have been recently proven incorrect. The only other alternative is the existence of unstable stationary states resulting from the explicit inclusion of the metabolic mass transfer process via the resource consumption and utilization. The proposed theory that accounts for the latter is presented, analyzed, and compared with experimental data both qualitatively as well as quantitatively.

1.
Malthus
,
T. R.
, 1798,
An Essay on the Principle of Population
,
Penguin
,
Harmondsworth, UK
.
2.
Verhulst
,
P. F.
, 1838, “
Notice sur la loi que la population suit dans son accroissement
,”
Corr. Math. et Phys. Publ. par A. Quetelet. T.
,
10
, pp.
113
121
.
3.
Pearl
,
R.
, 1927, “
The Growth of Populations
,”
Q. Rev. Biol.
0033-5770,
2
(
4
), pp.
532
548
.
4.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2008, “
Microbial Models
,”
Ecological Models
(
Encyclopedia of Ecology
, Vol.
3
),
S. E.
Jørgensen
and
B. D.
Fath
, eds.,
Elsevier
,
Oxford
, pp.
2369
2389
.
5.
Baty
,
F.
, and
Delignette-Muller
,
M. L.
, 2004, “
Estimating the Bacterial Lag Time: Which Model, Which Precision
,”
Int. J. Food Microbiol.
0168-1605,
91
, pp.
261
277
.
6.
Augustin
,
J. C.
, and
Carlier
,
V.
, 2000, “
Mathematical Modelling of the Growth Rate and Lag Time for Listeria monocytogenes
,”
Int. J. Food Microbiol.
0168-1605,
56
, pp.
29
51
.
7.
Baranyi
,
J.
, 2002, “
Stochastic Modelling of Bacterial Lag Phase
,”
Int. J. Food Microbiol.
0168-1605,
73
, pp.
203
206
.
8.
Vadasz
,
A. S.
,
Vadasz
,
P.
,
Abashar
,
M. E.
, and
Gupthar
,
A. S.
, 2001, “
Recovery of an Oscillatory Mode of Batch Yeast Growth in Water for a Pure Culture
,”
Int. J. Food Microbiol.
0168-1605,
71
(
2–3
), pp.
219
234
.
9.
Vadasz
,
A. S.
,
Vadasz
,
P.
,
Abashar
,
M. E.
, and
Gupthar
,
A. S.
, 2002, “
Theoretical and Experimental Recovery of Oscillations During Batch Growth of a Mixed Culture of Yeast in Water
,”
World J. Microbiol. Biotechnol.
0959-3993,
18
(
3
), pp.
239
246
.
10.
Vadasz
,
A. S.
,
Vadasz
,
P.
,
Gupthar
,
A. S.
, and
Abashar
,
M. E.
, 2002, “
Theoretical and Experimental Recovery of Oscillations During Batch Yeast Growth in a Pure Culture Subject to Nutritional Stress
,”
J. Mech. Med. Biol.
,
2
(
2
), pp.
147
163
.
11.
Pirt
,
S. J.
, 1975, “
Growth Lag
,”
Principles of Microbe and Cell Cultivation
,
Blackwell
,
London
.
12.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2005, “
Predictive Modeling of Microorganisms: LAG and LIP in Monotonic Growth
,”
Int. J. Food Microbiol.
0168-1605,
102
, pp.
257
275
.
13.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2007, “
Biological Implications From an Autonomous Version of Baranyi and Roberts Growth Model
,”
Int. J. Food Microbiol.
0168-1605,
114
, pp.
357
365
.
14.
Baranyi
,
J.
, and
Roberts
,
T. A.
, 1994, “
A Dynamic Approach to Predicting Bacterial Growth in Food
,”
Int. J. Food Microbiol.
0168-1605,
23
, pp.
277
294
.
15.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2002, “
The Neoclassical Theory of Population Dynamics in Spatially Homogeneous Environments—Part I: Derivation of Universal Laws and Monotonic Growth
,”
Physica A
0378-4371,
309
(
3–4
), pp.
329
359
.
16.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2002, “
The Neoclassical Theory of Population Dynamics in Spatially Homogeneous Environments—Part II: Non-Monotonic Dynamics, Overshooting and Oscillations
,”
Physica A
0378-4371,
309
(
3–4
), pp.
360
380
.
17.
Maier
,
R. M.
, 2000, “
Bacterial Growth
,”
Environmental Microbiology
,
R. M.
Maier
,
I. L.
Pepper
, and
C. P.
Gerba
, eds.,
Academic
,
New York
, pp.
43
59
.
18.
Swinnen
,
I. A. M.
,
Bernaerts
,
K.
,
Dens
,
E. J. J.
,
Geeraerd
,
A. H.
, and
Van Impe
,
J. F.
, 2004, “
Predictive Modeling of the Microbial Lag Phase: A Review
,”
Int. J. Food Microbiol.
0168-1605,
94
, pp.
137
159
.
19.
May
,
M. R.
, 1973, “
Time-Delay Versus Stability in Population Models With Two and Three Trophic Levels
,”
Ecology
0012-9658,
54
, pp.
315
325
.
20.
May
,
M. R.
, 1978, “
Mathematical Aspects of the Dynamics of Animal Populations
,”
S. A.
Levin
, ed.,
Studies in Mathematical Biology—Part II: Populations and Communities
(
Studies in Mathematics Vol. 16
),
The Mathematical Association of America
,
Washington, D.C.
, pp.
317
366
.
21.
May
,
M. R.
, 1981, “
Models for Single Populations
,”
Theoretical Ecology
,
Blackwell Scientific
,
Oxford
, pp.
5
29
.
22.
Vadasz
,
P.
, and
Vadasz
,
A. S.
, 2010, “
On the Distinction Between Lag and Delay in Population Growth
,”
Microb. Ecol.
0095-3628,
59
(
2
), pp.
233
245
.
23.
Ginzburg
,
L. R.
, 1986, “
The Theory of Population Dynamics: I. Back to First Principles
,”
J. Theor. Biol.
0022-5193,
122
, pp.
385
399
.
24.
Wangersky
,
P. J.
, and
Cunningham
,
W. J.
, 1957, “
Time Lag in Population Models
,”
Cold Spring Harbor Symp. Quant. Biol.
0091-7451,
22
, pp.
329
338
.
25.
O’Donovan
,
L.
, and
Brooker
,
J. D.
, 2001, “
Effect of Hydrolysable and Condensed Tannins on Growth, Morphology and Metabolism of Streptococcus gallolyticus (S. caprinus) and Streptococcus bovis
,”
Microbiology
1350-0872,
147
, pp.
1025
1033
.
26.
Gompertz
,
B.
, 1825, “
On the Nature of the Function Expressive of the Law of Human Mortality, and a New Mode of Determining the Value of Life Contingencies
,”
Philos. Trans. R. Soc. London
0962-8428,
115
, pp.
513
583
.
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