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"Models of tree and stand dynamics": a differential journey through forest modelling

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Abstract

Models of trees and stands exist since many decades, what nowadays has changed is our focus towards integrated forest ecosystem functioning. Managing forests in the 21 st century requires efforts that go beyond empiricism. Annikki Mäkelä and Harry T. Valentine's new book "Models of tree and stand dynamics" (Springer Nature, Cham, 2020) shows the state-of-art for knowledge applied within forest models with useful practical applications. It is a textbook for graduates and scientists interested in process-based models of stand dynamics , growth and forest management. Models represent valuable tools for tackling issues like ecosystem carbon sequestration, helping us understand the economic implications of silvicultural interventions and providing insights on the impacts of climate change on forests. The textbook is a compendium of applied research that non-pure mathematicians can understand, interiorize and take advantage of for getting precious knowledge on forest functioning.
i
iF o r e s t
F o r e s t
Biogeosciences and Forestry
Biogeosciences and Forestry
“Models of tree and stand dynamics”: a differential journey through
forest modelling
Gina Marano (1),
Alessio Collalti (2-3)
Models of trees and stands exist since many decades, what nowadays has
changed is our focus towards integrated forest ecosystem functioning. Manag-
ing forests in the 21st century requires efforts that go beyond empiricism. An-
nikki Mäkelä and Harry T. Valentine’s new book “Models of tree and stand dy -
namics” (Springer Nature, Cham, 2020) shows the state-of-art for knowledge
applied within forest models with useful practical applications. It is a textbook
for graduates and scientists interested in process-based models of stand dy-
namics, growth and forest management. Models represent valuable tools for
tackling issues like ecosystem carbon sequestration, helping us understand the
economic implications of silvicultural interventions and providing insights on
the impacts of climate change on forests. The textbook is a compendium of ap-
plied research that non-pure mathematicians can understand, interiorize and
take advantage of for getting precious knowledge on forest functioning.
Keywords: Forest Modelling, Carbon Balance, Forest Management, Climate
Change, Forest Ecology
Mäkelä A, Valentine HT (2020). Models of
tree and stand dynamics. Springer Nature,
Cham, Switzerland, pp. 310 [ISBN: 978-3-030-
35760-3 ]. - doi: 10.1007/978-3-030-35761-0
Forests play a relevant role in the global
carbon cycle and this mitigation potential –
that lies in the accumulated stock of forest
ecosystem carbon – has dynamics we ei-
ther ignore or we are not able to predict
completely right now. Could we forecast
forest productivity on large geographical
areas, under several climate change sce-
narios? Will forests react to changing envi-
ronmental conditions? If so, how?
If these questions sound rather familiar, it
seems we are aware about the key role of
forests and what the challenges in manag-
ing forests in the 21st century are. What
some might not know, is that none of
these issues could ever be faced without
models.
Annikki Mäkelä and Harry T. Valentine’s
new book represents a gentle introduction
to the modelling of forest growth based on
ecological theory; besides, it is formulated
to be sufficiently clear and sharp lending
into practical applications. Models of Tree
and Stand Dynamics is a sound-based text-
book that addresses both early (graduate/
doctorate level) but even senior scientists,
calling upon “functional” approaches in
forest ecology, where particular attention
is drawn by reproducing mechanistically
and/or empirically eco-physiological pro-
cesses. Mäkelä & Valentine’s main intent is
to teach us, or refresh in some cases our
blear memory, to go beyond mathematical
models per se; it shows the state-of-art try-
ing at the same time to forecast the 21st
century’s quantum leap.
This is not the first book addressing for-
est modelling (see Waring & Running 2007,
Burkhart & Tomé 2012, Landsberg & Sands
2011), but is certainly the first one integrat-
ing an extensive documentation of theory
and concepts and their translation into
source codes for a prompt computer pro-
gramming and testing. Thus, this is not a
merely descriptive book and coherently
the authors stated that the description of
the plethora of existing forest models can
be found elsewhere.
As a premise, the book aims at bridging
the gap between empirical and process-
based models using mathematical tools
and numerical estimations and it perfectly
does so by covering a wide range of exam-
ples with a rich set of R-codes at the end of
each chapter (and including solutions,
which were much appreciated). The same,
the reader should not be too much con-
cerned about sinking into complex equa-
tions, but rather the logic behind is easily
comprehensible even from non-pure math-
ematicians. In this sense, it is more a hand-
book than a cookbook, because “trees and
stands are complex life systems and any at-
tempt to fully describe these systems math-
ematically is sure to fail”. The Mäkelä and
Valentine’s book is itself the compendium
of a whole career as researchers and pio-
neering modellers, a cradle of lectures ma-
terial and applied research, from which
they drawn up numerous interesting and
clarifying examples. The focus is immedi-
ately stated: the book mainly covers proc-
ess-based models that incorporate mecha-
nism, hybridisation, or optimisation, singly
or in combination. Yet why? Because our
common understanding of stand dynamics,
growth and management lacks and is gen-
erally limited by a predetermined set of
empirical data which we try to rely on.
The first four chapters represent the
book’s backbone for they provide a syn-
thetic but exhaustive overview of the main
concepts and theories, together with ele-
ments of carbon balance modelling applied
to individual trees (individual tree models),
moving then to forest stands (forest stand
© SISEF https://iforest.sisef.org/ 152 iForest 13: 152-153
(1) Department of Agriculture, University of Napoli Federico II, v. Università 100, I-80055
Portici, Naples (Italy); (2) Institute for Agriculture and Forestry Systems in the Mediterranean
(ISAFOM), National Research Council of Italy (CNR), I-87036 Rende, CS (Italy); (3) Department
of Innovation in Biological, Agro-food and Forest Systems, University of Tuscia, I-01100
Viterbo (Italy)
@
@ Alessio Collalti (alessio.collalti@cnr.it)
Received: Apr 06, 2020 - Accepted: Apr 13, 2020
Citation: Marano G, Collalti A (2020). “Models of tree and stand dynamics”: a differential
journey through forest modelling. iForest 13: 152-153. – doi: 10.3832/ifor0061-013 [online
2020-04-16]
Book Review
Book Review
doi:
doi: 10.3832/ifor0061-013
10.3832/ifor0061-013
vol. 13, pp. 152-153
vol. 13, pp. 152-153
Marano G & Collalti A - iForest 13: 152-153
models). A first insight of a real (adapted)
tree dynamics model, as synthesis from
“pipe-model” (Shinozaki et al. 1964a, Shi-
nozaki et al. 1964b) and carbon-balance
theory, is firstly presented in chapter 5,
along with the main allocation rules by
which the carbon available for growth is al-
located between the components of bio-
mass (leaf, branch, stem, coarse root, and
fine root). Chapter 6 deals with individual
tree and stand-level competition thus fo-
cusing on the challenging issue of resource
limitation to total growth and productivity.
Applications of evolutionary optimisation
to tree structure and consequent carbon
allocation are introduced in chapter 7 alto-
gether with examples of models that use
this approach to derive plant structure and
carbon allocation (e.g., optimal crown
structure, stem shape, etc).
How does forest production vary region-
ally? Is climate change going to increase or
decrease productivity and carbon seques-
tration? To tackle these issues, go to Chap-
ter 8 which outlines some general ideas
and overall accepted theories about linking
models with data, moving to input quantifi-
cation for model applications by introduc-
ing different methods of parameterisation
for a chosen model (Chapter 5).
Data assimilation is widely used in other
rather different fields such as engineering,
meteorology and physical oceanography…
but it surprisingly happens in forestry re-
search, too. In chapter 9 some basic con-
cepts – central to model calibration – are il-
lustrated, followed by some examples of
Bayesian calibration as used in ecological
modelling, in comparison with conven-
tional statistical parameter calibration. Two
examples of calibrated models for predict-
ing forest growth and estimating carbon
balance are also shown. Worth noting, a
clear definition (and distinction) of what
state variables, parameters and driving (or
forcing) variables, including model hierar-
chical organizations, is provided. What
sounds obvious in the theory not often re-
flects in the practice, and this is even a
practical textbook.
There is an increasing demand by national
forest policies to assess sustainable har-
vest levels, forest potential for climate
change mitigation, or the supply of round-
wood and biomass to the global markets
and far more. In this sense, forest model-
ling represents a valuable toolbox to in-
spect pressing issues like ecosystem car-
bon sequestration, economic implications
of different silvicultural interventions and
policies. In chapter 10 some sound applica-
tions of modelling frameworks are pro-
vided. In conclusion, we know that models
of trees and stands have existed for hun-
dreds of years, but what has changed now
is our focus towards integrated ecosystem
functioning rather than single tree growth.
Quo vadis then? Forest management rec-
ommendations in many countries are
based on economical optimization studies
that assess the impact of intervention on
economic revenue (and costs), trying to
find appropriate strategies that are benefi-
cial for the stakeholders. Consequentially,
standard optimization studies in forestry
are centred and based on empirical growth
models. When applied to standard man-
agement conditions, these models can of-
fer reliable and reassuring predictions, but
at the same time we must be aware that
they may lead to serious problems in opti-
misationwhere a solution may be found
outside the valid range of model develop-
ment data or, if restricted, on the border of
applicability”. And that is often the case in
forest management. It is crucial to bridge
empirical and process-based data assimila-
tion methods that combine research-based
ecological measurements with standard
forestry data. Another useful application of
process-based stand-level models relies on
the possibility to estimate forest productiv -
ity in areas not subject to forest inventory.
In this case, we should also consider incor-
porating air-borne measurement methods
such as LiDAR, drones, and different vari-
eties of satellite-derived vegetational in-
dexes to drive our models. Nevertheless,
the biggest challenge in nowadays forest
models – at any level of spatial and tempo-
ral resolution is to make reliable predic-
tions under climate change, especially
when not all has been (or can be) ac-
counted for. Major phenomena that de-
serve more attention here are: (i) changes
in sink-source balance due to changes in
the annual cycle, and (ii) changes in the
carbon and nitrogen (C:N) balance due to
different above-ground and below-ground
responses to environmental change (citing
Mäkelä & Valentine 2020), indeed “we
know much less about the response of for-
est soils and nutrient availability under a
changing climate”. These are our new quan-
tum leaps, hic sunt dracones.
References
Burkhart HE, Tomé M (2012). Modeling forest
trees and stands. Springer Science and Busi-
ness Media, Dordrecht, Netherlands, pp. 458. -
doi: 10.1007/978-90-481-3170-9
Landsberg J, Sands P (2011). Physiological ecol-
ogy of forest production: principles, processes
and models (Vol. 4). Elsevier/Academic Press,
London, UK.
Mäkelä A, Valentine HT (2020). Models of tree
and stand dynamics. Springer Nature, Cham,
Switzerland, pp. 310. - doi: 10.1007/978-3-030-
35761-0
Shinozaki K, Yoda K, Hozumi K, Kira T (1964a). A
quantitative analysis of plant form - the pipe
model theory. I. Basic analysis. Japanese Jour-
nal of Ecology 14: 97-105. [online] URL: http://
www.jstage.jst.go.jp/article/seitai/14/4/14_KJ00
001775220/_article/-char/en
Shinozaki K, Yoda K, Hozumi K, Kira T (1964b). A
quantitative analysis of plant form - the pipe
model theory. II. Further evidence of the the-
ory and its application in forest ecology. Japa-
nese Journal of Ecology 14: 133-139. [online]
URL: http://www.jstage.jst.go.jp/article/seitai/
14/4/14_KJ00001775220/_article/-char/en
Waring RH, Running SW (2007). Forest ecosys-
tems, analysis at multiple scales (3rd edn). Aca-
demic Press, S. Diego, CA, USA, pp. 370. - doi:
10.1093/treephys/19.2.138
153 iForest 13: 152-153
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Article
The book is designed to be a textbook for university students (MSc-PhD level) and a reference for researchers and practitioners. It is an introduction to dynamic modelling of forest growth based on ecological theory but aiming for practical applications for forest management under environmental change. It is largely based on the work and research findings of the authors, but it also covers a wide range of literature relevant to process-based forest modelling in general. The models presented in the book also serve as tools for research and can be elaborated further as new research findings emerge. The material in the book is arranged such that the student starts from basic concepts and formulations, then moves towards more advanced theories and methods, finally learning about parameter estimation, model testing, and practical application. Exercises with solutions and hands-on R-code are provided to help the student digest the concepts and become proficient with the methods. The book should be useful for both forest ecologists who want to become modellers, and for applied mathematicians who want to learn about forest ecology. The basic concepts and theory are formulated in the first four chapters, including a review of traditional descriptive forest models, basic concepts of carbon balance modelling applied to trees, and theories and models of tree and forest structure. Chapter 5 provides a synthesis in the form of a core model which is further elaborated and applied in the subsequent chapters. The more advanced theories and methods in Chapters 6 and 7 comprise aspects of competition through tree interactions, and eco-evolutionary modelling, including optimisation and game theory, a topical and fast developing area of ecological modelling under climate change. Chapters 8 and 9 are devoted to parameter estimation and model calibration, showing how empirical and process-based methods and related data sources can be bridged to provide reliable predictions. Chapter 10 demonstrates some practical applications and possible future development paths of the approach. The approach in this book is unique in that the models presented are based on ecological theory and research findings, yet sufficiently simple in structure to lend themselves readily to practical application, such as regional estimates of harvest potential, or satellite-based monitoring of growth. The applicability is also related to the objective of bridging empirical and process-based approaches through data assimilation methods that combine research-based ecological measurements with standard forestry data. Importantly, the ecological basis means that it is possible to build on the existing models to advance the approach as new research findings become available.
Article
To test the applicability of the pipe model theory to actual tree form, the frequency distribution of the thickness of woody organs in a tree was examined in 10 different species. The frequency f(D) of a certain diameter class D proved to have a definite pattern of distribution in the root, branch and trunk respectively, with only a little difference between the species. The obtained f(D)〜D curves showed that a root system could well be approximated by the assemblage of many pipes of unit thickness, a trunk by a few cones piled up one upon another, and a branch system by a geometric model intermediate between the two. The results were well consistent with the pipe model theory of tree form. As an application of the theory in forest ecology, a new method for estimating the amounts of leaves or branches of trees and stands was also proposed, based on the direct proportionality found between those amounts and the cross-sectional area of the trunk at the height just below the lowest living branch.
Book
Drawing upon a wealth of past research and results, this book provides a comprehensive summary of state-of-the-art methods for empirical modeling of forest trees and stands. It opens by describing methods for quantifying individual trees, progresses to a thorough coverage of whole-stand, size-class and individual-tree approaches for modeling forest stand dynamics, growth and yield, moves on to methods for incorporating response to silvicultural treatments and wood quality characteristics in forest growth and yield models, and concludes with a discussion on evaluating and implementing growth and yield models. Ideal for use in graduate-level forestry courses, this book also provides ready access to a plethora of reference material for researchers working in growth and yield modeling. © 2012 Springer Science+Business Media Dordrecht. All rights are reserved.