Alternative Stable States and Human-Environment Interactions in Forest Mosaics and Ecotones

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Alternative stable states and human-environment interactions in forest mosaics and ecotones

by Kirsten Henderson

A Thesis presented to The University of Guelph

In partial fulﬁllment of requirements for the degree of Doctor of Philosophy in Environmental Sciences

Guelph, Ontario, Canada

c Kirsten Henderson, September, 2016 ABSTRACT

ALTERNATIVE STABLE STATES AND HUMAN-ENVIRONMENT INTERACTIONS IN FOREST MOSAICS AND ECOTONES

Kirsten Henderson Advisor: Professor Madhur Anand University of Guelph, 2016 Co-Advisor: Professor Chris Bauch

Alternative stable states result in drastic vegetation shifts, without much ad- vanced warning. Although common in theory, they are often more difficult to observe in ecological systems and the mechanisms responsible for shifts remain largely unknown. The fragility of bistable systems when faced with large external forces, such as human influence or climate, provides a plausible explanation for the elusiveness of alternative stable states. The work presented here aims to provide quantifiable mechanisms for threshold responses in forest mosaic and ecotone systems. First, a model of tree-grass recruitment is parameterized with empirical data to gain an understanding of mechanisms driving vegetative shifts. The following chapter uses climate moisture index to model vegetation structure and stability in a boreal/temperate forest/non-forest system. In addition to climate, anthropogenic land-use change is considered to be one of the greatest stresses on natural ecosystems. Landowner behaviour, from questionnaire data, is incorporated into a human-environment coupled model to determine the influence of conservation and economic values on landscape dynamics. In both human and environment driven tree-grass systems, recruitment is a limiting factor and as such has a fundamental role in characterizing vegetative state shifts. After reviewing multiple tree-grass dynamical models and calibrating the model with empirical data, we find that soil moisture content acts as a proxy for fire and precipitation regimes, providing a simple, yet descriptive, recruitment function. The findings from the boreal/temperate climate model support an alternative framework for conceptualizing alternative stable states and suggest that future climate regimes may eclipse bistability. Likewise, human influences disrupt the natural bistable characteristic of forest-grassland mosaics. Generally, strong human influence precludes bistability. However, long-term conservation behaviour reintroduces bistability, driven by rarity-based conservation rather than natural processes. Ecosystem interactions are intricate and the presence of alternative stable states often adds to the complexity. This thesis highlights the fragility of bistable systems, particularly under strong environmental and human forces. Therefore, models that include empirical data and mechanistic processes, which enhance our understanding of biological processes, are key to determining what triggers shifts in states and assessing the vulnerability of a system to change. Contents

List of Figures ...... vii List of Tables ...... ix Preface ...... x Chapter 1: General Introduction ...... 1 1 Alternative stable states ...... 2 1.1 Alternative stable states in ecology ...... 2 1.2 Modelling alternative stable states ...... 4 2 Subtropical tree-grass mosaics ...... 4 2.1 Landscape patterns ...... 4 2.2 Socio-ecological drivers in landscape shifts ...... 5 3 Boreal/temperate forest and grassland ecotones ...... 6 3.1 Landscape patterns ...... 6 3.1.1 Boreal forest ...... 6 3.1.2 Sub-boreal ...... 6 3.1.3 Subalpine ...... 6 3.2 Socio-ecological drivers in landscape shifts ...... 7 4 Influence of climatic conditions ...... 7 5 Human Influence ...... 9 5.1 Human-environment interactions ...... 9 5.2 Human behaviour and perception ...... 9 5.3 Human activity in forest-grassland mosaic ...... 10 6 Thesis outline ...... 10 Chapter 2: Modelling bistability in tree-grass ecosystems: the recruitment function revisited ...... 25 1 Introduction ...... 26 2 Materials and Methods ...... 28 2.1 Model Review ...... 28 2.2 Recruitment Models ...... 29 2.2.1 Phenomenological fire-driven recruitment ...... 29 2.2.2 Empirically calibrated recruitment function . . . . . 30

iv 2.3 Tree-grass cover model ...... 38 2.4 Analysis ...... 40 3 Results ...... 40 4 Discussion ...... 43 Chapter 3: Bistability or fragility: the inﬂuence of climatic conditions on vegetation shifts in a managed forest ...... 54 1 Introduction ...... 55 2 Methods ...... 58 2.1 Case Study ...... 58 2.2 Model ...... 60 2.3 Analysis ...... 62 2.3.1 Current Forest Composition in the Face of Climate Change ...... 63 2.3.2 Alternative Reforestation Strategies ...... 63 3 Results ...... 64 3.1 Equilibrium Forest Cover ...... 64 3.1.1 Current Forest Composition in the Face of Climate Change ...... 66 3.1.2 Alternative Stable States ...... 68 3.1.3 Alternative Reforestation Strategies ...... 69 4 Discussion ...... 70 S1 Supplementary Information Text ...... 79 S1.1 TACA seedling survival ...... 79 S1.2 Mortality function ...... 80 S1.3 Converting evapotranspiration to temperature ...... 81 S2 Supplementary Figure ...... 84 Chapter 4: Landowner perceptions of the value of natural forest and natural grassland in a mosaic ecosystem in southern Brazil ...... 85 1 Introduction ...... 86 2 Methods ...... 89 2.1 Study area ...... 89 2.2 Sampling and analysis of land use ...... 90 3 Results ...... 91 3.1 Composition and Preference ...... 91 3.2 Composition and preference change ...... 92 3.3 Land use inﬂuence ...... 93 3.4 Regional composition ...... 93 3.5 Restoration ...... 94

v 4 Discussion ...... 94 5 Conclusion ...... 99 Chapter 5: Seeing the Forest for the Grasslands and the People: Sustain- ability of Coupled Human-Environment Mosaic Ecosystems ...... 119 1 Introduction ...... 120 2 Materials and Methods ...... 123 2.1 Study System ...... 123 2.2 Environment (Land-Use & Natural Dynamics) Model . . . . . 124 2.3 Human Behaviour Model ...... 125 2.4 Analysis ...... 127 3 Results ...... 127 3.1 Base Case ...... 127 3.2 Changing Conservation Values ...... 128 3.3 Changing Economic and Conservation Discount Rates . . . . . 130 3.4 Changing Economic and Conservation Discounting Time Hori- zons ...... 130 3.5 Extent of Human Influence ...... 133 4 Discussion ...... 134 S1 Supporting Information: Materials and Methods ...... 143 S1.1 Environment (Land-Use & Natural Dynamics) Model . . . . . 143 S1.2 Human Behaviour Model ...... 144 S1.3 Parameter Selection ...... 146 S1.3.1 Base Case Study ...... 146 S1.3.2 Changing Conservation Values ...... 147 S1.3.3 Changing Economic and Conservation Discount Rates 148 S1.3.4 Discounting Economic and Conservation Time Horizons148 S1.3.5 Weak, Moderate and Strong Human Influence . . . . 148 Chapter 6: General Conclusions ...... 151 A1 MATLAB Code ...... 159 A1.1 Forest cover: climate moisture index ...... 159 A1.2 Forest cover: human influence ...... 164

vi List of Figures

1.1 Shift in equilibrium state...... 3 1.2 Forest-grassland mosaic southern Brazil...... 5 2.1 Comparing recruitment functions: phenomenological, empirical and mechanistic ...... 37 2.2 Soil moisture content increases recruitment...... 41 2.3 The modiﬁed recruitment function (r(T )) decreases the region of bistability, when comparing analogous parameters from phenomenological and mechanistic models...... 42 2.4 Comparing tree cover over a range of potential natural disturbance rates (v)...... 43 2.5 Comparing tree cover over a range of potential maximum recruitment rates (α and c)...... 44 2.S1 Fermi-Dirac distribution in tree-grass systems...... 52 2.S2 Intersection of recruitment and disturbance dynamics...... 53 2.S3 Parameter plane showing decreased region of bistability over a range of α and v parameters ...... 53 3.1 Conceptual framework of alternative stable states through changes in variables and changes in parameters...... 57 3.2 Map of Tree Farm Licence 48 (TFL 48). Distributed along the Alberta Plateau and in the Rocky Mountains in northeastern British Columbia. 59 3.3 Simpliﬁed conceptual diagram of forces and feedbacks on forest cover in our study region (BC boreal/temperate forests)...... 60 3.4 Forest equilibrium over a range of climate moisture indices...... 66 3.5 Parameter plane demonstrating forest cover over a range of potential temperature and precipitation values ...... 67 3.6 Comparing region of bistability between forest cover modelled with climate change and without climate change...... 69 3.7 Alternative reforestation strategies shift the threshold response of forest cover under varying climatic conditions...... 70 3.S1 Logistic regression curves for each drought class species...... 80

vii 3.S2 he rate at which forest is replaced with planted (α) or natural (β) forest shifts the threshold response of forest cover (F) to climate moisture index (CMI)...... 84 4.1 Location of the study site.Map showing the 30 properties surveyed in the S˜aoFrancisco de Paula region...... 90 4.2 Required incentive to convert cropland to native vegetation...... 95 5.1 Human-environment coupling. The negative relationship between humans and natural ecosystems is driven primarily by competition with agricultural land (a). Alternatively, sustainable human behaviour (i.e., valuation of natural ecosystem services) leads to positive changes in natural ecosystems when natural ecosystems are rare (b), whereas the perception of abundant natural ecosystems results in a decreased desire to conserve natural ecosystems...... 121 5.2 Bistability in forest-grassland-silviculture system. The above image (a) depicts a natural mosaic in southern Brazil without human in- ﬂuence, where dominant Araucaria forest (F ) or dominant Campos grassland (G) are alternative stable states. The image below (b), is an example of bistability in a mosaic of natural forest (F ) and natural grassland (G) with converted land (agriculture, A). The alternative stable states are dominant converted land (agriculture and/or silviculture, F GA) and dominant forest (FG)...... 122 5.3 Conceptual diagram of model. Land states in our study region include: forest (F ), grassland (G), or converted land (agriculture and/or silviculture, A). Green arrows represent environmental drivers (natural disturbance (ν), recruitment (r(F,G)) (eq.(4)) and abandonment

(aF , aG) in eqns.(1,2,3) and black arrows represent human drivers (penal-

ties (pB, eq.(8)), proﬁts (pF ,pG,pA, eqns.(7,8)) and conservation values

(qF , qG, eq.(7))...... 124 5.4 Time-series showing base case landscape dynamics over 100 years. . . 128 5.5 Parameter plane for vegetation cover over a range of conservation values.129 5.6 Parameter plane for vegetation cover over a range of discount rates. . 131 5.7 Parameter plane for vegetation cover over a range of discount time horizons...... 132

viii List of Tables

2.1 Review of woody vegetation recruitment...... 31 2.2 Parameter description, with potential range and source...... 39 3.1 Parameter values. Parameters are obtained from Ministry guidelines for TFL 48 or calculated from studies on drought-induced mortality across western North America ...... 65 3.S1 Climate variables from ClimateNA for three regions in TFL 48. . . . 83 4.1 Correlation between past landscape composition preference and current composition using the Spearman correlation test...... 93 5.S1 Model parameters from empirical data and questionnaire results. Pa- rameter selection and calibration is described in the the supplementary text (SI1)...... 150

ix Preface

The following chapters are prepared for journal contributions, focusing on a central theme of alternative stable states in forest/non-forest systems. The first manuscript (Chapter 2)1, reviews possible mechanisms responsible for vegetative shifts in subtropical and tropical tree-grass mosaics, namely the recruitment of trees. Kirsten Henderson parameterized and analysed model simulations and led the writing of Chapter 2. Madhur Anand and Chris Bauch contributed to model development. All authors reviewed the manuscript. Chapter 3 focuses on how changes in temperature and precipitation alter threshold responses and the coexistence of alternative stable states in boreal and temperate forests. This model applies concepts of threshold responses driven by fire and moisture regimes, in addition to the framework of a mechanized recruitment function, from Chapter 2, to determine seedling establishment probability in boreal/temperate systems. The work in Chapter 3 is a collaborative project with the Canadian Forest Service at the Pacific Forestry Centre. The resulting publication2 will be co-authored by Elizabeth Campbell, Chris Bauch and Madhur Anand. Eliza- beth Campbell and Kirsten Henderson conceived the research in Chapter 3. Kirsten Henderson conducted the model simulations, analysed the results and led the writing of the manuscript. All authors contributed to model development, analysis and reviewed the manuscript. The following two chapters (Chapter 4 and Chapter 5) contribute to a limited body of literature describing the influence of landowner behaviour on vegetation shifts. In collaboration with researchers in Brazil (Mateus Reis, Carolina Blanco, ValérioPillar and Rodrigo Printes), landowner behaviours and perceptions are quantified using a questionnaire, detailing changes in land composition and landowner preferences (Chapter 4)3. Kirsten Henderson led the writing and analysed questionnaire responses for Chapter 4. Mateus Reis conducted the questionnaire interviews. Carolina Blanco, Madhur Anand, Chris Bauch and Rodrigo Printes created the questionnaire and conceived the project. All authors reviewed the manuscript. The questionnaire responses are used to parameterize a coupled human-environment model of

1Henderson KA, Anand M, Bauch C (in preparation) Modelling bistability in tree-grass ecosystems: the recruitment function revisited. Ecological Modelling 2Henderson KA, Campbell EM, Bauch C, Anand M (in preparation) Bistability or fragility: the inﬂuence of climatic conditions on vegetation shifts in a managed forest. Climate Change Biology. 3Henderson KA, Reis M, Blanco CC, Pillar VD, Printes RC, Bauch CT, Anand M (2016) Landowner perceptions of the value of natural forest and natural grasslands in a mosaic ecosystem in southern Brazil. Sustainability Science 11(1): 321-330.

x tree-grass dynamics (Chapter 5)4. Kirsten Henderson parameterized, analysed model simulations led the writing of Chapter 5. Madhur Anand and Chris Bauch conceived of the project and contributed to model development and analysis.

4Henderson KA, Anand M, Bauch C (in preparation) Seeing the Forest for the Grasslands and the People: Sustainability of Coupled Human-Environment Mosaic Ecosystems. Proceedings of the National Academy of Sciences.

xi Chapter 1

General Introduction

1 1 Alternative stable states

Environmental change is a phenomenon common to all ecosystems. Some changes may occur slowly over a longer time period, whereas others cause sudden large-scale changes to the ecosystem states – known as catastrophic regime shifts [1, 2]. These catastrophic events are generally the result of bistability, a term that describes the co-existence of alternative stable states in ecosystems [3,4]. In addition to occurring rapidly, these shifts are difficult to predict, which can threaten the integrity of ecosystems and the services they provide to humans [2, 5–8]. However, communities with greater diversity also tend to exist as alternative stable states and may be essential in maintaining some ecosystems [4,9,10]. The notion of alternative stable states was first introduced in the 1960s by Lewon- tin [11]. Alternative stable states imply that there are multiple stable equilibria coexisting under the same conditions, which require a direct change in variable (e.g. large perturbation) to shift the dominant stable state from one to another [1, 12]. Furthermore, the stability of the state is determined by initial conditions [13]. Al- ternatively, changes to parameters that manipulate system variables may force the system into an alternative state. Characteristically, dominant states remain stable over long periods, as populations tend to fluctuate around an equilibrium when faced with small perturbations [3]. The size of perturbation required to shift between states is determined by the strength of the basin of attraction and in some cases, external conditions (Fig. 1.1). These systems can easily transition, from one state to the alternative, once the critical threshold of bifurcation is passed. In such cases, very small environmental changes can result in catastrophic events [14, 15]. Gener- ally, positive feedbacks between consumers and limiting resources trigger catastrophic shifts [1, 3, 4, 13]. Positive feedbacks accelerate the shift between alternative states, resulting in unstable transient intermediate states.

1.1 Alternative stable states in ecology

In ecological systems, the abrupt shift in vegetation at ecotones and pockets of distinct vegetation types in mosaics are most commonly associated with alternative stable states [16]. However, alternative stable states have been described in aquatic, terrestrial, climatic and complex socioeconomic systems [1,17]. The co-existence of trees and grasses, under the same environmental conditions and a lack of intermediate states, has long puzzled ecologists and lends itself to the theory of alternative stable states [18]. Savanna systems represent a classic example of bistability, mediated by positive feedbacks between ﬁre and vegetation [19], in addition to rainfall patterns [20]. There exists a threshold response between ﬁre and tree

2 Figure 1.1: The diagram depicts stability landscapes over a range of external conditions. The stability dynamics can vary with perturbations to the system itself or changes in conditions, as external conditions can alter the resilience of equilibrium state. The diagram is reproduced from Scheffer et al. [1] cover, such that distinct states – a tree state and a grass state – are maintained under the same environmental conditions, despite occupying different ecological niches. The concept of alternative stable states in tropical/subtropical tree grass systems is generally accepted, although mechanisms responsible for transitions remain con- tended [21]. The proportion of trees and grasses varies among savanna types, which contributes to uncertainty in specific mechanisms responsible for vegetation distribution patterns [18]. The stability dynamics of boreal/temperate forest-parkland-grassland ecotones are obscure compared to tropical/subtropical tree-grass mosaics, however there is an increased interest in the determining whether the system exhibits alternative stable states and predicting how much stress these forests can tolerate [22–25]. Chapin and colleagues [26] suggest that the boreal forest is stable and remains so over long periods of time as a result of its resilience; however, climate warming trends and/or intensification of forest management may lead to abrupt changes and the potential for vegetation to shift into an alternative stable state. Past vegetation shifts occurred rapidly, as a result of changing fire regimes and climate change. The climate and forest cover in British Columbia’s boreal/temperate forest has been relatively consistent for 8000 years [27, 28]. Therefore, unprecedented changes in temperature could

3 threaten boreal forest resilience [23]. Loss of resilience makes a system more sensitive to changes and can be forced into an alternative state by stochastic events or small perturbations [1].

1.2 Modelling alternative stable states

Numerous models have highlighted the role fire plays in the bistability of tree-grass ecosystems [19, 20, 29–36]. Through extensive data collection and modelling, it has been suggested that the spread of fire has a threshold response to fuel availability, resulting in a positive feedback and thus enables bistability in savanna ecosystem [35]. Grass cover is maintained by fire, which in turn increases the fuel load and promotes fire (positive feedback) [36]. Small trees and bushes are killed by fire, however once a critical threshold is crossed, flammability is reduced and trees proliferate (positive feedback) [37]. The steep threshold response of fire frequency to grass cover is assumed to be a sigmoidal function and provides a phenomenological basis for dynamical models [33, 34]. Rainfall seasonality is strongly interconnected with fire frequency and severity, which provides an alternative mechanism for modelling shifts on tree-grass cover. Previous studies demonstrate tree-grass coexistence in the presence of fire [19,33,34,38,39] and rainfall patterns [10,18,19,33,38,40–42]. Few models delve into the interactions of alternative stable states and environmental or human drivers, in boreal or temperate forests. Scheffer et al. [22] demonstrate multimodality in the boreal forest biome over similar environmental conditions. The variation in tree cover state, across the biome, lacks an intermediate state, which can indicate the existence of alternative stable states. However, these findings alone do not substantiate the existence of alternative stable states. The study also finds that tree cover states vary strongly with temperature, which suggest a threshold response to temperature. Given the limited modelling work and empirical data on this system, there remain large gaps in our knowledge of mechanisms responsible for vegetation shifts and possible alternative states within boreal and temperate biomes.

2 Subtropical tree-grass mosaics

2.1 Landscape patterns

As mentioned above, naturally occurring tree-grass mosaics exemplify the phenomenon of alternate stable states. There are numerous examples of bistable tree-grass systems around the world [18–20, 30]. The forest-grassland mosaics of southern Brazil encompass high plant diversity and endemism, in addition to many threatened species

4 [43, 44], as such there is a wealth of literature describing this system. The combination of well-documented vegetation changes and well-supported assumptions stability dynamics, makes the forest-grassland mosaics of Brazil an ideal case study. The forest-grassland mosaics (Fig. 1.2) occur on an elevated plateau (900m above sea level) in southeatern Brazil, where the climate is characterized by high precipitation (annual mean 2252 mm) and moderate temperatures (annual mean 14.5◦C) [45]. Grasslands dominate the southern Pampa biome, while subtropical forests are the dominant vegetation in northern Rio Grande do Sul [46]. At present, forests form is- lands at the boundary of the Pampa and Atlantic forest biomes, although many studies suggest that the forest is encroaching onto the neighbouring grassland [36,47–49]. Historically, the dominant vegetation has flipped between forest and grassland. Pollen records indicate that grasslands have dominated Southern Brazil since the Early Holocene [47]. There was a significant expansion of Araucaria forests approximately 900 years ago, as a result of the climate becoming warm and very humid climate. The warm and moist conditions, typical of a subtropical climate, are favourable for forest development. Natural and human-influenced forest expansion has continued, leaving 13.7 million hectares of grassland [44].

Figure 1.2: The interface between Atlantic forest and Pampa biomes, in Rio Grande do Sul, forms a mosaic of ecologically-rich Araucaria forest and Campos grassland. The photo is reproduced from Silva & Anand [48].

2.2 Socio-ecological drivers in landscape shifts

The key factors responsible for altering landscape composition are fire and anthropogenic land management [50]. In the absence of fire and anthropogenic activity, the dominant ecosystem state is determined by water availability [46]. Water budgets may prevent the development of forest directly through insufficient water for sapling growth or indirectly by influencing fire regimes. Anthropogenic land management consists primarily of cattle ranging, in addition to agricultural practices and afforestation of grasslands with pine plantations [51]. Policy implementation, including the ban of fire for management purposes, quotas

5 for maintaining native land and incentives for silvicultural activities have also had a signiﬁcant inﬂuence on land cover [44,52,53]

3 Boreal/temperate forest and grassland ecotones

3.1 Landscape patterns 3.1.1 Boreal forest

The extent of forest and vegetation dynamics of British Columbia (BC) are characterized by climate and edaphic conditions [54]. BC is composed of 14 biogeoclimatic (BEC) zones, with a diverse array of species and driving factors. The boreal forest and adjacent BEC zones are of particular interest to forest managers and ecologists because of predicted climate changes, ecosystem services and forest productivity for lumber, among other reasons [23,55]. The boreal forest in BC is composed of two BEC zones, the Boreal White and Black Spruce zone (BWBS) and the Spruce-Willow-Birch zone (SWB). The Boreal White and Black Spruce (BWBS) is one of the largest ecoregions in BC, covering approximately 16 percent of BC, from the Alberta Plateau in the northeast and the Tatshenshini in the west [54]. The BWBS is dominated by black spruce, white spruce, lodgepole pine and aspen and forms an ecotone with plains grassland [27,56]. The colder temperatures and limited precipitation act as a biophysiological barrier for forest expansion [57].

3.1.2 Sub-boreal

The Sub-Boreal Spruce zone (SBS) and the Sub-Boreal Spruce-Pine zone (SPBS) comprise the two BEC zones south of the boreal forest zone, from 50◦ to 59◦N latitude [54]. The two zones occupy valleys and mountainous regions (at elevations of 850- 1500) m. Grasslands or shrub-steppes occupy warm and dry sites at low elevations [58], while lodgepole pine dominates the region. In recent years, the lodgepole pine forests have been experienced declines from mountain pine beetle [56].

3.1.3 Subalpine

The Engelmann Spruce Subalpine Fir (ESSF) zone comprises the greatest forested area at high elevations (900 to 2300 m), in southeastern BC [54]. As the biogeoclimatic classiﬁcation suggests, the region is occupied by engelmann spruce and subalpine ﬁr, in addition to a mosaic of trees interspersed between meadows at higher elevations [56]. The trees occupy microsites with higher moisture availability and

6 wind protection. The greater diversity of species, compared to the BEC zones described above, is attributed to a milder climate.

3.2 Socio-ecological drivers in landscape shifts

The most important drivers of ecosystem dynamics include climate, fire, insects and disease. These drivers form complex interactions that influence the structure and function of ecosystems directly and indirectly [23, 59, 60]. Many studies report that climate (i.e. precipitation and temperature) is a major determining factor in succession and distribution in boreal regions [23,59–62]. Environmental stress are common limiting factors in biophysical processes and species ranges [63], including boreal and temperate forest distribution. Forest-grassland boundaries in western Canada follow an isoline of climatically similar moisture regimes [64]. Grasslands occur where precipitation is consistently less than potential evapotranspiration. Furthermore, Scheffer and colleagues [22] found that the percentage of tree cover in the boreal forest varies strongly with temperature and precipitation. Fire is responsible for creating mosaic patterns of vegetation in the boreal forest [62] and rapid changes to new landscape compositions [65]. Insect outbreaks are common in boreal forest [66] and are compounded by drought [61,67,68]. Vegetation, insects and fire regimes are influenced by warmer temperatures and length of growing season . Fire initiation and spread depend on the amount and frequency of rainfall, as drought reduces decomposition process and increase fuel for fire. Disturbance regimes are linked to moisture, either directly or indirectly through long-term changes in vegetation and soils [62,64,67]. The forests of northern British Columbia are extensively managed, with the majority of forests being harvested and reforested annually [69]. The current guidance on species selection and stocking standards may not support seedling establishment and growth for changing biogeoclimatic zones [55,70]. Data analysis on species resilience and vulnerability to climate change presents useful information for forest managers looking to mitigate the risk of climate change on reforestation. Adaptive management can have an influence on spatial and temporal changes resulting from climate change. The ultimate goal of adaptive management will be to maintain genetic diversity and resilience of forest ecosystems.

4 Inﬂuence of climatic conditions

Climate has an overwhelming inﬂuence on vegetation patterns [71–73]. The availability of soil water, rates of decomposition and nutrient cycling, productivity, frequency

7 and severity of disturbance, and regulation of biological processes are all determined in part by climate [74]. The predicted changes in climate are likely to have a significant influence on species range expansion and contraction [75]. Many biological systems are thought to have already experienced climate-induced changes [76–80], for which meta-analyses confirms the emergence of a clear pattern between changes in biotic trends and climate [81]. Global temperatures are expected to increase, while precipitation changes are expected to be proportionally less – increasing the likelihood of drought [82]. Climate projections show shifts in future distributions of ecosystem climate niches [83–86]. As a result, the northern limit of tree species ranges is shifting northward as temperatures increase [87]. The greatest warming effects are predicted to occur in northern regions, which constitute large areas of boreal and temperate forests. The boreal and temperate forests of British Columbia provide many ecosystem services and as such the resilience of forests to changes in temperature and precipitation remains a topic of concern for forest managers and ecologists. In the last two decades, drought has caused widespread forest die-off in regions across western North America and Europe [16, 88–94]. Drought alters regional fire cycles, insect and pathogen outbreaks, transpiration rates and photosynthetic rates, resulting in carbon starvation, hydraulic failure, seedling desiccation and adult tree mortality [68, 94–96]. Increases in tree mortality vary across a spectrum of severity, from persistent increases in annual mortality [97], to increases in pest-related mortality [98–100] and finally, massive die-off events [77,88,101]. The impact of drought-induced mortality is compounded by limitations forest regeneration in water-stressed environments [94]. Under drought conditions, seedlings and saplings are the first to die [102]. Conversely, sporadic increases in seedling establishment are often associated with favourable changes in temperature and precipitation for seedling establishment [22,103]. The majority of forests experiencing drought-related mortality form ecotones with grassy biomes or woody vegetation, where there are theoretically multiple underlying equilibria states and critical tipping points [16]. However whether forest die-off is the result of perturbations in the landscape state, itself, or whether changes in parameters force the landscape into an alternative stable has yet to be determined [12,25].

8 5 Human Inﬂuence

5.1 Human-environment interactions

Regional vegetation transitions are the result of interactions between humans and nature [104]. Human-environment interactions are complex and often have unforeseen feedbacks [31,105]. Changes in the environment successively alter human behaviour, creating a feedback loop. Feedback loops can be negative (i.e. rarity-based conservation behaviour) or positive (i.e. economic incentives) [106,107]. The exploitation of land and resources for human consumption and population expansion is not a novel concept [108,109], however there has never been a time when humans have had such a dominant inﬂuence on the environment [110]. Historically, humans have had a deleterious impact on natural ecosystems, operating close to local or regional boundaries. In turn, the degradation of natural systems impacts humans, creating a less hospitable environment and resource constraints. In some cases, the consumptive patterns and land-use practices of society have lead to the collapse of the entire civilization [111]. Anthropogenic activities often make ecosystems more vulnerable to disturbance and cause sudden regime shifts [112]. The human-environment relationship is not limited to negative interactions; humans also demonstrate rarity- based conservation, which promotes the maintenance of threatened or endangered species [104,113]. Human behaviour has the ability to subvert many seemingly straightforward interactions [105]. Furthermore, Innes et al. [34] suggest that bistability of forest-grassland ecosystems can be removed by strong human inﬂuence. Therefore, sustainable ecosystem management requires an understanding of human behaviour and perception.

5.2 Human behaviour and perception

Landscape management behaviour is guided by the perceived value of an ecosystem, causing shifts in vegetation type [114]. Often preservation of an environment or type of vegetation is rarity-based. The scarcity hypothesis describes the valuation of an ecosystem through the rarity of species or resources. When species or resources become rare and prices rise, individuals are encouraged to protect the resources or species [106]. This process leads to instability when forests regenerate quickly, promoting cycles of deforestation and forest regeneration. Alternatively, the ecosystem service hypothesis states that the environmental degradation associated with native vegetation losses cause the value of services provided by the ecosystem to decline. A

9 positive feedback ensues, prompting the further degradation of ecosystems [106]. Im- itation behaviour amplifies the influence of value-based decision making. Individuals often imitate the decisions of those closest to them [115–119]. Economic theory suggests that humans are short-sighted and make decisions with the greatest immediate financial return [120, 121]. However, this leaves landowners vulnerable to market shifts and leaves future generations to deal with the consequences of unsustainable practices [122]. Therefore, a negative feedback in the system prevents the total collapse of resources (i.e. scarcity theory) [106].

5.3 Human activity in forest-grassland mosaic

Human activity in past millennia has contributed to forest expansion and contraction in forest-grassland mosaics of Brazil. Humans have long since occupied these regions (for approximately 7000-8000 years) [51], contributing to altered fire frequen- cies and changes in forest cover [123]. The Campos grasslands have been extensively used for cattle ranching since the early 18th century [50, 51], which may have indirectly increased forest cover through decreased fuel for fire. Recent land-use trends – harvesting timber, fire management and agricultural expansion – have led to a substantial decline in forests [43]. One of the greatest threats to natural ecosystems is a result of land-use change for agricultural purposes [124]. As the global population continues to grow, there is an increased demand for land to accommodate the needs of the population, particularly in the tropics and the subtropics. Grasslands are most likely to be disturbed for agriculture development, which further contributes to the degradation and underval- uation of grassland ecosystems [52,125]. The majority of land in this area is individually owned and subject to economic conditions, social norms and politics [107]. The financial gains from grassland (natural pasture for grazing) far exceed that of native forest in the region. In addition, large areas of the South Brazilian natural grasslands are being converted into pine plantations and agricultural production areas [126, 127]. Economy and policy are often related and together are key factors driving land use change, more so than cultural, demographic or technological factors [128].

6 Thesis outline

This thesis is centered around the theme of alternative stable states in forest-grassland or shrubland ecotones and mosaics. The following chapters examine the impact of natural processes and human inﬂuence on these ecotonal and mosaic systems. The

10 aim of Chapter 2 is to gain a better understanding of natural processes governing transitions in tree-grass systems of tropical and subtropical regions. The complex dynamics of tropical/subtropical systems represent classic examples of multi-stable systems and as such are the focus of many models describing alternative stable states. Previous models generally fall into two categories: simple phenomenological models or detailed dynamic vegetation models. Chapter 2 combines the two techniques to provide a mechanistic approach to modelling tree-grass vegetation transitions, using soil moisture content as a proxy for fire and precipitation patterns. In Chapter 3, the concept of forest/non-forest transitions driven by moisture availability is applied to boreal/temperate forests in British Columbia, at the interface between forest and grasslands or shrublands. Similar to Chapter 2, the model in Chapter 3 describes recruitment driven by moisture availability and, additionally, moisture limited mortality. The aim of this chapter is to determine the potential impacts of future climatic conditions on managed forests in northern latitude forests of British Columbia. The the first two chapters demonstrate the sensitivity of ecotonal and mosaic systems to natural processes, whereas the following two chapters (Chapter 4 and 5) look at the influence of humans on mosaic ecosystems. Chapter 4 describes a questionnaire detailing landowner preferences and changes in land-use and landscape dynamics within the last three decades in the forest-grassland mosaics of southern Brazil. The questionnaire data is then used in Chapter 5 to parameterize a coupled human-environment model. Chapter 5 builds on the recruitment model described in Chapter 1 by incorporating landowner preferences, in addition to fire and precipitation, as a driving factor of land cover change.

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24 Chapter 2

Modelling bistability in tree-grass ecosystems: the recruitment function revisited

Kirsten A Henderson, Chris T Bauch, Madhur Anand

To be submitted to Ecological Modelling

Key Words: tree-grass, bistability, recruitment, demographic, model, soil moisture content, empirically calibrated

25 Abstract

Tree-grass coexistence is a long-standing puzzle, and global encroachment of woody vegetation over grassland and savanna due to climate change and anthropogenic influence demands a better understanding of these systems. We review tree-grass interaction models, finding that most employ phenomenological representations of recruitment functions, thereby limiting their ability to distinguish important mechanisms. We introduce an empirically calibrated recruitment function and tree-grass interaction model based on well-studied biophysiological processes, using Brazil’s forest-grassland mosaics as a case study. The model explicitly includes soil moisture content–which strongly determines landscape dynamics–and implicitly includes fire- driven tree-grass shifts. We compare the model to a phenomenological model, finding that the empirically calibrated model better captures observed tree-grass vegetation regimes. Predicted tree cover can differ up to 90% between the two models as a result of bistability in tree-grass systems. Including soil moisture in recruitment functions supplements a wide class of tree-grass interaction models and provides future avenues for modelling vegetation as climate changes.

1 Introduction

Grasslands and savannas form landscape mosaics with patches of trees throughout large parts of the tropics and subtropics [1–4]. In addition to being biologically diverse and the most common vegetation type in tropical and subtropical regions, the mosaics exhibit coexistence between grass and trees [5]. The coexist of trees and grasses have long puzzled ecologists, as grasses and trees develop in areas with markedly diﬀerent environmental conditions. Despite the advances in modelling tree- grass systems and the wealth of research describing driving forces and feedbacks in these systems, there remain many contrasting theories and uncertainties explaining the dynamics of coexistence. Some have suggested that the persistence of tree-grass mosaics can be attributed to competitive interactions (i.e. competition for resources), while others argue that demographic factors are responsible for vegetation distribution (recruitment processes) [6]. Furthermore, whether the mixed-plant community is unstable, sustained by disturbance, or stable, resulting from alternative states has yet to be determined. There is strong support for the paradigm of coexistence, as a result of alternative stable states in grasslands and savannas, such that savannas are often described as a classic example of bistability [7,8]. There is little doubt that vegetation distribution in savannas and tree-grass systems is the result of multiple interacting factors, such as grazing, ﬁre, anthropogenic

26 activities, climate, resource-competition and soil characteristics [3,5,9,10]. However, to what extent each factor determines vegetation distribution remains uncertain. Tree cover in tropical and subtropical grassy biomes is greatly influenced by fire intensity and severity, as well as rainfall patterns [6–8,11–15]. Both fire and prolonged periods without precipitation limit the recruitment of trees, which has been suggested as a key determinant in the expansion of tree cover [11]. The interaction between fire and grass cover is best described as a positive feedback loop, for which grass cover increases the flammability of the system and fire increases grass cover [8, 13, 14, 16–19]. In systems with prolonged dry seasons, the initial increase in precipitation allows grass biomass to accumulate, which ultimately leads to fuel for dry season fires [12, 20]. In addition fire suppresses woody vegetation recruitment, which further contributes to the maintenance of grass cover. This same positive feedback, can also be explained in terms of tree cover. Forests (tree cover > 55%) generally occur in regions with intermediate to high annual rainfall and short dry seasons [12,13,15]. Once tree cover surpasses a critical threshold (40% tree cover), the system is more resilient to fire and seedlings are allowed to develop, further increasing tree cover. These amplifying feedbacks maintain two distinct states, which lends support to the alternative stable state theory [7,21–23]. Above or below the threshold, the positive feedback leads to rapid transitions between tree cover and grass cover, resulting in an unstable intermediate state [24]. In addition to fire, hydrological variation has an important role in determining vegetation distribution [25, 26]. Rainfall seasonality has the greatest influence on vegetation distribution in savanna biomes, as it directly influences sapling death [27] and indirectly increases fire frequency [28]. Under dry conditions (arid savannas) grasses can outcompete trees, especially seedlings, which are vulnerable to desiccation [29]. Under mesic conditions, with a short dry season, fire severity is reduced and conditions are favourable for tree recruitment [30]. Although arid and mesic savanna biomes have different processes driving vegetation transitions and vary considerably across the continents, in both systems, rainfall patterns are predictors of savanna presence [31]. Soil moisture content acts as a proxy for fire propagation [15, 32], in addition to directly limiting seedling establishment [33]. Therefore, soil moisture content may be a useful indicator of vegetation distribution among both mesic and arid savannas. The global trend describes tree encroachment into grasslands and savannas, as a result of changes in environmental conditions and land management [2, 34–36]. Sa- vannas are expected to experience further changes as temperature, precipitation and

CO2 change [37], which highlights the need for models that can apply observations

27 and empirical studies to theoretical frameworks. The positive feedbacks, threshold responses and unstable intermediate states, briefly described here, are characteristic of savanna systems and form the framework for many dynamical model interpretations. We focus our attention on the recruitment process, as recruitment responds to multiple-driving factors (i.e. fire and rainfall patterns). Many previous models use recruitment as the basis for modelling vegetation shifts in tree-grass systems [8, 10, 13–15, 21, 38–49]; yet, most models are incomplete in their understanding of the mechanisms responsible for shifts in ecosystems, focusing on broad concepts. Here we explicitly parameterize components from existing models with empirical data. Our objectives are to 1) review existing tree-grass interaction models with particular attention to recruitment functions, 2) modify existing model equations and parameters to better fit model output to observations and 3) determine how assumptions about the impact of soil moisture content on the recruitment function alter predicted patterns at the population level. We explicitly model recruitment rates as a function of soil moisture content to predict changes in tree cover in tree- grass systems. We calibrate the model for fire-driven tree-grass shifts and make comparisons to hydrologically-driven systems. We use the forest-grassland mosaics of southern Brazil as a case study, but explain how our approach is generalizable.

2 Materials and Methods

2.1 Model Review

We compiled a review of mathematical models exploring tree-grass interactions in tropical and subtropical regions (Table 2.1). Search terms included a combination of ’tree recruitment’, ’model’, ’mathematical model’, ’dynamic system’, ’tree-grass systems’, ’tropical/subtropical vegetation change’, ’landscape transition’, ’threshold response’, ’ﬁre’ and ’ecohydrological’ input into Google Scholar and Primo search engines. Models included in Table 2.1 were selected for the explicit representation of tree recruitment or vegetation change in the form of mathematical equations (i.e., ode models, cellular automata models, probability distribution) or functional form descriptions (e.g., sigmoidal threshold response [8]). Niche models and bioclimatic envelop models were not included in this review. The review focused on process- based models, however some statistical models, demonstrating probability of tree recruitment, were included for comparison. Models of tree-grass interactions generally fall under two categories: competitive interaction models and demographic bottleneck models [6], with the latter generating

28 greater attention in recent years. Demographic bottleneck models consider disturbance and/or climatic variability to be the main factors driving landscape dynamics, and in doing so have demonstrated tree-grass coexistence controlled by fire regimes and hydrologic conditions [8, 10, 14, 39, 40, 48]. An overwhelming number of studies have shown that fire affects tree cover by limiting recruitment – rather than killing adult trees [8,10,14,40,48,50]. In our review of 29 models of tree-grass interactions, 21 models emphasize the threshold response of demographic processes (i.e., regeneration or mortality) with respect to tree cover and/or hydrological conditions. In 10 of the models fire is implicit within the modelled dynamics (threshold response), 12 model fire explicitly (constant) and 7 models ignore fire and focus explicitly on hydrological factors. Vegetation dynamics are a function of water availability, soil moisture content or rainfall in 18 of the models, while 11 models do not account for hydrological conditions. Existing models of tree-grass interactions that are based on fire-response threshold and omit hydrological conditions, incompletely distinguish critical components responsible for driving tree-grass transitions. Although, such models provide a simple method of describing the fundamental characteristics of tree-grass systems, the parameters used to determine the functional form of recruitment are often unavailable in the literature or not easily measured [6]. The common functional form of the tree recruitment function is the Fermi-Dirac distribution, which generates the sigmoidal shape (i.e. threshold response). The Fermi-Dirac function is borrowed from physics and calculates the probability of being in a given energy state [51], however can be modified to calculate the probability of being in a given vegetation state (Fig. 2.S1). A change in environmental conditions or human behaviours may force the system past the critical tipping point (Fig. 2.S1), which results in transitions between alternative stable states [7,8,10,21].

2.2 Recruitment Models 2.2.1 Phenomenological ﬁre-driven recruitment

Many argue that the fire-grass feedback is responsible for determining vegetation in tree-grass systems [8, 12, 13, 30]. We let w(T ) represent the phenomenological recruitment rate of trees, where T is the proportion of tree cover. Fire has been observed to limit the growth of young or developing trees [9]. In the absence of fire, saplings are able to expand into non-woody areas via dispersal, thus G = 1 − T represents available space for tree encroachment. As a tree matures, the thicker bark provides protection from fire. A greater abundance of mature tree cover decreases the frequency and severity of fires, flame length and rate of spread [17]. Flammability

29 decreases drastically when tree cover exceeds 40% [28], which provides a reference for the fire threshold response point. The recruitment rate transitions sharply once the specific threshold in tree cover is achieved [13], hence w(T ) is assumed to be sigmoidal [10]. The functional form of w(T ) is a mathematical representation of the fire threshold response, characteristic of tree-grass systems (Fig. 2.1a), given by

c w(T ) = , (1) T 1 + exp − k( (1−T ) + b) where c, b and k are positive parameters and k controls the sharpness of the transition. Equation (1) provides an example of a ﬁre-only phenomenological recruitment model. In the following section, we formulate a recruitment curve using processes and data from many studies listed in Table 2.1, with particular reference to [40]. The recruitment is expressed as a threshold response in terms of ecological factors such as soil moisture, to gain a better understanding of processes responsible for driving tree-grass transitions.

2.2.2 Empirically calibrated recruitment function

The Higgins et al. [40] model of tree-grass coexistence in savannas uses empirical data and phenomenological assumptions of demographics to estimate the probability of seedling establishment. Arid savannas are limited in the seedling establishment stage by desiccation, whereas mesic savannas are limited in the recruitment stage by ﬁre [6, 39, 40, 52]. The authors’ work suggests that savannas in the absence of wet season droughts have a similar threshold response to ﬁre as forest recruitment. This allows us to parameterize the recruitment rate of trees described by Staver and colleagues [8], Staver and Levin [14] and Innes et al. [10] with ecological determinants. Higgins et al. [40] equation for the probability of seedling establishment in the absence of wet season drought (pe(i,j)) is given by

1 pe(i,j) = , (2) 1 + exp Gsc(i,j)−Gsc0.5 ve where Gsc(i,j) is the grass standing crop at location (i, j). The grass standing crop with a probability of 50% seedling establishment is represented by Gsc0.5. An essential component of woody vegetation recruitment models is the ﬁre threshold response, for which increased grass cover reduces tree cover; for values of Gsc(i,j) > Gsc0.5, seedling establishment is very low. ve represents the rate at which the probability of establishment changes with grass standing crop. The values for Gsc0.5 and ve are 2500 kg ha−1 and 400 kg ha−1, respectively [40].

30 Table 2.1: Review of woody vegetation recruitment.

SOURCE MODEL RECRUITMENT FUNCTIONAL FORM OR CONSTANT RANGE STUDY DESCRIPTION DESCRIPTION OR SYSTEM VALUE

[45,47] Ecohydrological ode Colonization rate of γF 0.15–2.5 Dry and model (competitive) trees (yr−1) moist savannas

[53] Fire disturbance and Rate of recruitment gl 0.2 Savannas water competition (yr−1) ode model 31 (competitive)

[42,44,46] Fire-driven logistic Intrinsic rate of rf 0.08– Savanna growth ode model increase in forest 0.09 systems (competitive) biomass (yr−1)

[54] Logistic growth and Inertia of the system α 0.12 Savannas ﬁre-driven Poisson (yr−1) distribution model (competitive)

s−sw,T [49] Ecohydrological ode Colonization rate for cT (s) = Cmax,T 0-2 Arid and smc,T −sw,T model (competitive) trees (yr−1) semi-arid savannas [55] Dynamic vegetation Sapling E = EmaxDI CI GI 0-17 Brazilian model establishment cerrado (demographic)

−1 [56] Fire-driven logistic Birth rate rb (yr ) Savannas growth ode model (competitive)

[40] Fire and rainfall Probability of pei,j)= 1 0-1 South Gi,j −G0.5 1+exp −1 spatial vegetation seedling ve (yr ) African simulation model establishment savannas (demographic) 32 xb [43] Compartmental Biomass f(x; a, b) = ab+xb 0-1 Savanna model (competitive, consumption (yr−1) systems demographic)

[50] Fire and resource Growth rate g = 1 0-1 African 1+ g˜ competition R (yr−1) savannas dynamic vegetation model (competitive, demographic)

c [10] Fire-driven ode Recruitment rate of w(F ) = 0-1 Forest- 1+exp −k( F )+b model forest 1−F (yr−1) grassland (demographic) systems [39] Rainfall, ﬁre and Probability of Pe(Mt,Ms) = 0–0.6 Semiarid 2 2 grazing distributed establishment Pe(max)exp[−It(3 − Mt) − Is(3 − Ms) ] savannas cellular automaton model (demographic)

[57] Fire-driven logistic Rate of shrub β 0.5 Chihuahuan growth ode model biomass growth (yr−1) desert (competitive) grasslands

[58,59] Spatial Seed production and (g m−2) Semi-arid W R 2 −2|x−x‘| resource-driven pde seed dispersal Rc gs fS(x‘, t) 2 (x‘)exp( )dx‘ systems, W +kl Ω πL L 33 model (competitive) arid savannas

F d [29] Deterministic Shoot biomass WS = (1 − F d+cd )WS 0–1 Savannas diﬀerential model post-ﬁre (yr−1) (competitive)

[48] Fire-driven Tree establishment ω(p )dt := [ θ(pt) Ω(θ(p ))+(1− θ(pt) )Ω(0)dt] 0–1 Savannas t pt t pt square-lattice and (yr−1) ode model (demographic) [8,14] Fire-driven ode Recruitment rate of ω(G) 0–1 Savannas model saplings (yr−1) (demographic)

[21] Precipitation-driven Frequency of cells f(p) = √1 exp( −1 [ p−µ ]2) 0–1 Tropical σ 2π 2 σ cellular automaton supporting forest savanna- model establishment forest (demographic) systems

[60] Resource-driven Rate of change plant r (yr−1) Grazing logistic growth ode standing crop systems model (competitive) 34 [15,38] Logistic growth, ﬁre Expansion rate of r(P ) = p r 0.3 Tropical hp+p m and climate ode trees (yr−1) tree systems model (competitive, demographic)

s∗−s q [33] Hydrologic Plant water stress ∗ 0–1 Tree-grass s −sw vegetation systems distribution cellular automata model (competitive) [41,61] Fire and water Rate of woody r [ wtuW + w ] (g m−2 Semi-arid w H+uW =pws s uptake ode model biomass increase yr−1) savannas (competitive) 35 The seedling establishment model from Higgins et al. [40] is on a yearly scale, thus we can substitute pe(i,j) (Eq. (2)) from Higgins et al. [40] in place of w(T ) (Eq. (1)) from phenomenological models of tree-grass interactions. We assume that the probability of seedling establishment at location (i, j) is the same for all i and j, thus we remove the location term (i, j) and ignore the spatial component of seedling establishment. Furthermore, our model describes rates of change in a tree-grass system by the proportion of tree cover, instead of grass standing crop (kg ha−1). To estimate the parameters in the function w(T ) from equation (1), we convert the grass standing crop to the proportion of grass cover (1 − T ) and scale Gsc0.5 and ve accordingly. The probability of 50% seedling establishment in reference to the proportion of grassland is represented by ψ and ve is scaled to ﬁt grass standing crop as a proportion, denoted by ω.

−1 Gsc0.5kgha ψ = −1 , (3a) Gsc100%kgha

v ω = e . (3b) Gsc100%

Grass as a proportion of land cover (G), rather than biomass (Gsc), is determined Gsc −1 by G = . Gsc100% is the biomass of grass (in kg ha ) that inhibits tree Gsc100% encroachment and therefore results in 100% grass cover. Gsc100% is ecosystem speciﬁc. Furthermore, we assume the landscape is either covered by trees or grasses, thus for the remainder of the paper we refer to tree cover as T and grass cover (G) as 1 − T . The probability of seedling establishment in terms of tree cover is given by

1 p = (4) e (1−T )−ψ 1 + exp ω where ψ = Gsc0.5 and ω = ve . The modified probability of establishment described G100% G100% in equation (4) also has a sigmoidal shape, representative of the threshold response in tree-grass interactions (Fig. 2.1b). The grass standing crop variable, in Higgins et al. [40], is calculated from the annual rainfall. Mesic savannas and forest-grassland mosaics have little to no marked dry season [13,62]. Without seasonality, we assume that greater annual rainfall results in higher fuel moisture and less intense fires [12,18,28]. We incorporate soil moisture content (S) as an indicator of annual rainfall and fuel moisture in the probability of establishment (pe), similar to Jeltsch et al. [39]. Thus, as S increases we expect to see a larger (pe) term. The probability of establishment modified to include hydrologic conditions is therefore given by

1 pe = , (5) β(0.5−S)(1−T )−ψ 1 + exp β(0.5−S)ω where β is a scalar multiple of the soil moisture content (S). We assume that the soil moisture content alters the grass cover (1 − T ) and the rate at which the probability

36 Figure 2.1: Comparison between Innes et al. [10] phenomenological forest recruitment function (a), modiﬁed Higgins et al. [40] seedling establishment (b) and the empirically calibrated tree recruitment function (c). Parameters: (a) ve = 400, Gsc0.5 = 2500, Gsc100% = 6000; (b) c = 0.2, b = 11, k = 15; (c) ψ = 0.417, ω = 0.0667, β = 2.8, α = 0.2, S = 0.2, Savg = 0.2

37 of establishment (ω) changes with grass cover. We assume that soil moisture content does not exceed 0.5 (0 ≤ S < 0.5), based on global averages of volumetric soil moisture content in tree-grass systems [63–66]. Furthermore, we assume the risk of ﬁre decreases as S → 0.5. Finally, seedling establishment (pe) refers to the transition of seed to seedling, whereas recruitment (w(T )) refers to the seedling to adult transition. However, seedling establishment in a mesic savanna system is comparable to sapling recruitment, therefore we assume pe is equivalent to w(T ). As such, the calibrated recruitment (r(T )) can be used to describe regeneration, as a result of ﬁre or desiccation in tree-grass ecosystems. The empirically formulated tree recruitment function is given by α r(T ) = ψ . (6) (1−T )− β(0.5−S) 1 + exp ω

We let α represent an empirical estimate of the maximum recruitment rate, based on resource availability, herbivory and other competition factors [67–69]. The modified recruitment rate, r(T ), models fire suppression implicitly through soil moisture content in tree-grass ecosystems. Water budgets may prevent the development of trees directly through insufficient water for sapling growth or indirectly by influencing fire regimes [9, 70]. Grazing, resource availability and edaphic conditions also determine the recruitment rate of trees [2,9,41]. Hence, in the absence of fire, we still expect the recruitment rate of trees to be limited, increasing to the maximum recruitment rate (α). We compare the empirical estimate of seedling establishment from equation (2) to the phenomenological recruitment rate of trees from (Eq. (1)) and the empirically calibrated recruitment rate of trees (Eq. (6)) in Fig. 2.1.

2.3 Tree-grass cover model To model shifts in tree grass cover we use a simplified differential equation describing the rate of change in tree cover. The state of tree-grass mosaics can be expressed as a single equation for the proportion of tree cover, since we assume grass cover is 1 − T . We incorporate the modifications made to the recruitment function (Eq. (6)) into the model for tree-grass interactions in the following equation: dT = r(T )T (1 − T )S0 − vT, (7) dt where T represents the proportion of tree cover. The term r(T ) modifies the rate of succession from grasses to trees and v is the rate at which trees revert to grass through natural processes, such as disturbance and mortality. From Innes et al. [10] it is assumed that trees expand at a rate proportional to the product of existing tree cover (T ) and existing grass cover (1 − T ), hence the term r(T )T (1 − T ). Recruitment is a critical component in the analysis of population ecology; in the absence of sufficient recruitment, populations are vulnerable to local extinction [69]. Finally, the recruitment function is multiplied by a scaled soil moisture content parameter, S0 = S , Savg such that when S = 0 there is no recruitment and when S → 0.5 recruitment is enhanced. Savg is the average annual soil moisture content.

38 Table 2.2: Parameter description, with potential range and source.

Param- Description Simu- Range Source eter lated Value α Maximum 0.2 0.1-0.5 [67,68] potential yr−1 recruitment rate ψ Threshold grass 0.417 0.17-1 [40,71,72] cover S Soil moisture 0.2 0-0.5 [64–66] content m3m−3 β Soil moisture 2.8 0-8 Calibrated from [10,28,40] coeﬃcient ω Recruitment 0.0667 0.027- [40,71,72] parameter 0.16 Savg Average soil 0.2 0.07-0.3 [64,66] moisture content, m3m−3 under trees and grasses v Natural 0.02 0-0.15 [69,73] disturbance rate yr−1

39 2.4 Analysis In our analysis of the model, we examine the influence of soil moisture content on recruitment rates of trees and compare r(T ) to previously modelled tree-grass interactions, specifically w(T ) (Eq.(1)), and observations of population dynamics at tree- grass ecotones. We use data from the forest-grassland mosaics of southern Brazil to parameterize the model (Table 2.2) and validate our assumptions about the influence of soil moisture content on recruitment rates of trees. The Campos grasslands of Brazil (between latitudes 24◦ and 30◦S) form a mosaic with native Araucaria Atlantic forests and non-native plantations [2]. Grasslands are the dominant vegetation of southern Brazil, but as the climate becomes warmer and moister, providing a favourable environment for forest development, neighbouring patches of forest are encroaching over the grasslands [16]. The key factors preventing forest encroachment and maintaining grasslands are fire and grazing [74]. In the absence of fire and grazing, the state of the ecosystem is determined by the soil water budget [9]. Annual grass production in the Campos ranges between 2500 kg ha−1 and 4000 kg ha−1 [71] and Fidelis et al. [72] measured fuel loads between 3900 kg −1 −1 ha to 14 400 kg ha ; therefore, we estimate that 100% grass cover (G100%) occurs when G ≥ 6000 kg ha−1. Mortality rates are low for adult trees, Nazareno and Reis [69] observed annual mortality rates between 0.2% and 2% in Butia eriospatha of southern Brazil. Similarly, Beckert and colleagues [73] found an average mortality rate of 2.11%/yr in Araucaria forest, therefore empirical estimates give an average natural disturbance rate of 0.002 < v < 0.02. The threshold response of recruitment driven by fire, for which T < 0.4 results in seedling mortality and limited recruitment and T ≥ 0.4 provides favourable conditions for tree recruitment [28]. Therefore, we chose our parameter β to have the value of 2.8, since this allows our recruitment function to match this result.

3 Results

There exists a trivial equilibrium at T ∗ = 0 and two interior equilibria from the equation: v r(T ∗) = (8) (1 − T ∗)S0

The equilibrium points are determined numerically, given by the intersections of recruitment under various soil moisture conditions (r(T )S0) and natural disturbance (v) (Fig. 2.S2). There are interior equilibrium points at T ∗ = 0.4 and T ∗ = 0.9. The stability of the equilibrium is given by

r(T ∗)(1 − T ∗)S0 − r(T ∗)T ∗S0 + r(T ∗0 )T ∗(1 − T ∗)S0 − v < 0 (9)

The system is bistable, as T ∗ = 0 and T ∗ = 0.9 are both stable, but depend on the ∗ initial tree cover to establish which equilibrium persists. When T0 < 0.4, T = 0 ∗ and when T0 ≥ 0.4, T = 0.9. This exempliﬁes the alternative stable state paradigm through changes in variables [75].

40 We ﬁnd that higher soil moisture contents increase recruitment rates (Fig. 2.2). As expected, r(T ) → α when soil moisture increases (S → 0.5). Soil moisture content alters the steepness of the threshold response and shifts the threshold point in r(T ),

Figure 2.2: Soil moisture content increases recruitment rate. Increasing S shifts the threshold response to the left and increases the recruitment rate of trees significantly. In our model simulations, we use S = 0.2 (black line) to represent average soil moisture content in the Campos region. Less tree cover (T ) is required to increase the recruitment term (r(T )S0) at higher soil moisture contents. Other parameters: ψ = 0.417, ω = 0.0667, α = 0.2, β = 2.8, Savg = 0.2 while β amplifies or dampens the influence of S on the recruitment rate of trees. As β → 0, the recruitment curve shifts to the left, for all S – creating a dampening effect. As β increases, the influence of S is amplified and the recruitment curve shifts to the left or the right depending on S. When S → 0 the threshold point shifts to the right; therefore, greater proportions of tree cover are required for recruitment (r(T )) to outpace natural disturbance (v). When S → 0.5 the opposite occurs. Simulations of the model system indicate that the current tree cover in the region (T = 0.35) is unsustainable for long-term annual soil moisture content (under both tree and grass) below the regional average, Savg = 0.2 [66]. In such cases, mortality is always greater than recruitment, resulting in a rapid decline in tree cover. Consistent with previous studies and observations, there is a positive feedback between tree cover and recruitment rates. When the recruitment rate (r(T )), under favourable soil moisture conditions (S0), exceeds the rate of natural disturbance (v), the fire response threshold is crossed and trees dominate. Conversely, if r(T )S0 < v, tree cover is suppressed by fire and grass dominates. However, contrary to half the models reviewed, both hydrological factors and fire limit tree cover, which provides greater flexibility in the model, in terms of parameter manipulation. In previous models, the maximum recruitment rate (α) is 1, however empirical studies show that seedling establishment is significantly impeded by herbivory and other non-fire related disturbances [41, 67, 69], resulting in a maximum recruitment rate that is 10 to 50% of the original recruitment potential. Assuming that maximum recruitment is between 0.1 and 0.5 (α = 0.1 − 0.5) increases the region of pure grassland for greater than average disturbance rates (v > 0.05) (Fig. 2.S3). This reduced region of bistability is carried through to changes in other parameters, such as ω (Fig. 2.3b) and β (Fig. 2.3d), which are analogous parameters to k and b, from the phenomenological recruitment function (Eq.(1)). The b in equation (1) (Fig. 2.3c)

41 ψ is expressed by the threshold grass cover term β(0.5−S) , both shift the threshold point. The sharpness of the curve is controlled by k in equation (1) and ω (Eq. (6)).

A) B) Phenomenological Model Empirical Model 30 0.1

25 0.08

20 0.06 k 15 0.04

10 0.02

5 0 0.05 0.1 0.15 0 0.05 0.1 0.15 v v C) D) Phenomenological Model Empirical Model 15 8

6 b 10 5

5 2 0 0.05 0.1 0.15 0 0.05 0.1 0.15

v v

Figure 2.3: The modiﬁed recruitment function (r(T )) decreases the region of bistability, when comparing analogous parameters from phenomenological and mechanistic models. The upper subpanels compare the sharpness of the transition from T ∗ = 0 and T ∗ = 0.9 between the phenomenological model (a) and the empirical model (b). ω is analogous to the inverse of k from the phenomenological model. The bottom subpanels compare b from the phenomenological model (c) to β from the empirically calibrated model (d, Eq. (6)). Other parameters: (a) c = 0.2, b = 11; (b) ψ = 0.417, ω = 0.0667, α = 0.2, S = 0.2, Savg = 0.2; (c) c = 0.2, k = 15; (d) ψ = 0.417, α = 0.2, S = 0.2, β = 2.8, Savg = 0.2

Shifts in predicted tree cover in our empirically calibrated recruitment function are determined by rates of disturbance (v) and maximum potential recruitment rates (α), in addition to initial tree cover (Fig. 2.4). In contrast, the predicted tree cover in the phenomenological model (Eq. (1)), is driven by the initial tree cover only, hence the greater region of bistability over a wide range of conditions in the phenomenological model (Fig. 2.3). Using Campos grassland to illustrate the influence of natural disturbance (v) and recruitment (α) on tree cover, we show that the tree cover can expand or decline rapidly depending on v (Fig. 2.4a,b) and α for our empirically derived recruitment (Fig. 2.5a,b), yet has little to no effect on phenomenologically derived tree cover predictions (Fig. 2.4c,d, Fig. 2.5c,d). At high initial tree cover values, the phenomenological and empirically calibrated models predict the same proportion of tree cover over time, for changes in both natural disturbance rates (Fig. 2.4b,d) and maximum recruitment rates (Fig. 2.5b,d). While it is clear that threshold response and positive feedback between trees and fire have an important role in determining vegetation patterns in tree-grass system; we suggest that small changes in demographics, such as natural disturbance (v) and maximum potential recruitment (α), are also important and should not be ignored.

42 A) B) 1

0.8 0.95 v=0.01 v=0.02 0.9 0.6 v=0.03 v=0.04 T v=0.05 0.85 0.4 0.8 0.2 0.75

0.7 0 100 200 300 400 500 0 100 200 300 400 500 time time C) D) 0.4 1

v=0.01 0.95 0.3 v=0.02 v=0.03 0.9 v=0.04 v=0.05 T 0.2 0.85

0.8 0.1 0.75

0 0.7 0 100 200 300 400 500 0 100 200 300 400 500 time time

Figure 2.4: Comparing tree cover over a range of potential natural disturbance rates (v). The empirically calibrated model (a) can generate dominant tree cover for low initial tree cover values (T0 = 0.35) when natural disturbance rates (v) are below average (v < 0.02). Comparatively, the phenomenological model (c) is not as sensitive to changes in disturbance rates at low initial tree cover (T0 = 0.35). Once the ﬁre threshold is crossed (T0 = 0.9), the empirically calibrated model (b) and phenomenological model (d) have the same output for changes in natural disturbance rates. Other parameters: (a) ψ = 0.417, ω = 0.0667, α = 0.2, S = 0.2, Savg = 0.2; (b) ψ = 0.417, ω = 0.0667, α = 0.2, S = 0.2, Savg = 0.2; (c) c = 0.2, k = 15, b = 11; (d) c = 0.2, k = 15, b = 11

4 Discussion

Our model calibration is based on findings that hydrologic conditions, both directly and indirectly, have an overwhelming influence on vegetation patterns in tropical and subtropical tree-grass systems [8, 9, 12–15, 31]. Our model shows that soil moisture content significantly influences tree cover in our study region, by decreasing the tree cover required to suppress fire and increasing the maximum recruitment rate. Here we suggest that tree expansion into grass systems can be modelled simply by using soil moisture as an indicator of fire frequency and rainfall patterns, combining modelling techniques described in Table 2.1 into a single recruitment function. Thus, the inclusion of soil moisture content in the recruitment function is essential and provides greater grounding for phenomenological demographic models of tree- grass interactions; these findings are in agreement with recent work from Staal and colleagues [15]. We use empirical data to parameterize the recruitment function according to hydrologic conditions and obtain results similar to those found in nature. Notably, that tree cover greater than 40% reduces fuel flammability and further increases forest cover [28], which is reflected in our model by larger sapling recruitment rates for T > 0.4 (Fig. 2.1c). Consistent with other empirical studies [12, 13], higher precipitation, thereby soil moisture content, promotes tree cover. Using the Campos as an example, we were able to show that greater than average natural disturbance rates result in declining tree cover and maximum recruitment rates limit the potential tree cover. Additionally, data on vegetation distribution in forest-grassland mosaics

43 A) B) 1 1

0.8 0.95

0.6 0.9 T T 0.4 0.85

0.2 0.8

0 0.75 0 100 200 300 400 500 0 100 200 300 400 500 time time C) D) 0.35 1 0.3 c=0.1 0.95 0.25 c=0.2 c=0.3 0.2 c=0.4 0.9 T c=0.5 T 0.15 0.85 0.1 0.8 0.05

0.75 0 100 200 300 400 500 0 100 200 300 400 500 time time

Figure 2.5: Comparing tree cover over a range of potential maximum recruitment rates (α and c). The empirically calibrated model (a) is more sensitive to changes in maximum recruitment rates at lower initial tree cover (T0 = 0.35) than the phenomenological model (c). The empirically calibrated model (b) and phenomenological model (d) have the same output for changes in maximum recruitment at higher initial tree cover values (T0 = 0.9), which shows the strong influence of the fire- response threshold. Other parameters: (a) ψ = 0.417, ω = 0.0667, v = 0.02, S = 0.2, Savg = 0.2; (b) ψ = 0.417, ω = 0.0667, v = 0.02, S = 0.2, Savg = 0.2; (c) v = 0.02, k = 15, b = 11; (d) v = 0.02, k = 15, b = 11 in Brazil and underlying soil moisture content find that average soil moisture content below trees is 0.26 m3 m−3 and below grasses is 0.16 m3 m−3, consistent with our results that indicate tree cover would decrease in areas with soil moisture content below 0.2 m3 m−3. Exceptionally low soil moisture content reduces the positive feedback effect between tree cover and fire. Instead, the system is controlled by water availability, as in semi-arid savanna systems. This would not be accounted for in models that only model fire. Which could explain why the fire hypothesis fails to explain grass/forest boundaries [11]. The model presented here can be calibrated for mesic and arid tree-grass systems by varying the influence of soil moisture (β). The presence of alternative stable states is considered to be a key component in tree-grass landscape dynamics. This model maintains bistability, feedbacks and the fire threshold response, however demonstrates how changes in demographics (i.e. natural disturbance rates and maximum recruitment rates) can increase the presence of grass cover. When disturbance rates exceed double the normal range, the system tends to pure grassland, which coincides with findings from van Langevelde et al. [41] and reflects that disturbance, with respect to adult tree mortality, is a major determinant of tree-grass coexistence [11,76]. In Staver and Levin [14], changing the rate at which trees establish in grasses changes the stability dynamics of the system via Hopf bifurcations. Similarly, we show that small changes in demographics (i.e. natural disturbance rates and maximum recruitment rates) can be enough to shift the ecosystem across the critical threshold from one stable state to an alternative state. Our model is more sensitive to small changes in demographic processes, which can generate differences in forest cover up to 90% when compared to previous phe-

44 nomenologically derived models (Fig. 2.4, 2.5). When modelling ecotone ecosystems, the ability to represent small changes is critical in predicting future vegetation states. As such, we conclude that the inclusion of soil moisture content in tree recruitment functions, in addition to empirical estimates for tree mortality and maximum seedling establishment rates, provide a simple mechanistic approach to modelling vegetation transitions at tree-grass ecotones. The model calibration described here gives a more accurate depiction of tree-grass mosaic systems and complements previous phenomenological models describing tree- grass ecotone interactions. We incorporate the findings from our extensive review of tree expansion, with a focus on climate and fire, into the recruitment function of our model to gain a better understanding of the mechanisms responsible for tree-grass transitions. Although our model focuses on the forest-grassland mosaics of southern Brazil, the recruitment function described here has broader applications. The modified recruitment function is relevant to all tree-grass interactions governed by fire or precipitation regimes. Furthermore, changing the time scale and varying soil moisture content, accordingly, can incorporate rainfall seasonality and a range of rainfall patterns (low, intermediate, high). The parameter values can easily be found in the literature or obtained from field studies and the resulting output more accurately reflects tree-grass interactions. This work provides a framework for future modelling of tree-grass systems. To simplify our model, we exclude landscape transitions due to human influence and ignore spatial variability, both of which can contribute to vegetation shifts [10, 19, 77, 78]. Human influence significantly alters land composition, and future work on vegetation shifts should include human behaviour. The introduction of hydrologic conditions facilitates the modelling of climate change impacts on tree-grass ecosystem coexistence with few required modifications to the current model.

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Supplementary Figures

1 a

0.8

0.6 b f(X) 0.4

0.2

c 0 0 5 10 15 20 X

Figure 2.S1: Fermi-Dirac distribution. Transition to an alternative state (a → c) occurs when the threshold point (b) is crossed. The black line represents the threshold response of the function to X and the grey line represents linear changes with respect to X.

52 Figure 2.S2: Intersection of recruitment (r(T )T (1 − T )S0) and disturbance dynamics (vT ). There exist three potential equilibrium points for a given set of conditions, at T ∗ = 0, T ∗ = 0.4 and T ∗ = 0.9. S0 = S Savg

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 0 0.05 0.1 0.15

Figure 2.S3: Empirical estimates for maximum potential recruitment (α) increase the likelihood of being in a pure grass state (black) when natural disturbance (v) is high. Therefore, region bistability (white) also decreases.

53 Chapter 3

Bistability or fragility: the inﬂuence of climatic conditions on vegetation shifts in a managed forest

Kirsten A Henderson, Elizabeth M Campbell, Madhur Anand Chris T Bauch, Craig R Nitschke

To be submitted to Climate Change Biology

Key Words: tree-grass, bistability, recruitment, demographic, model, soil moisture content, empirically calibrated

54 Abstract

Climate-induced shifts in vegetation are among the top concerns of foresters and ecologists. Western North America has experienced large-scale forest die-oﬀ, following unprecedented drought conditions. Future changes in climatic conditions are predicted to be much the same, perhaps hotter and drier still. The areas most vulnerable to climate-induced vegetation shifts are forest ecotones, which brings about questions related to alternative stable states and tipping points. Particularly, how much stress can the forests tolerate and is there a critical tipping that will force a shift from forest to non-forest? This model uses threshold responses in seedling establishment and adult tree mortality as a function of climate moisture index to explore potential vegetation shifts in boreal and temperate forests, using managed forests in British Columbia as a case study. As to be expected, our results indicate that precipitation and temperature have an overwhelming inﬂuence on vegetation dynamics; to the extent that if alternative stable states do exist, it is only over a very small range of climatic conditions. As such, the predicted changes in temperature and precipitation will likely force the system into a forested or non-forested state.

1 Introduction

In recent years, the vulnerability of forests dynamics to climate change has been at the forefront of research in the field of forest ecology and management. Tempera- ture increases have many direct and indirect effects on forest structure and function, including expansion and contraction of species distribution [1–7], increased and decreased growth [8], reduction in leaf area [9], altered carbon assimilation [10], in addition to increased pest invasion and increased risk of fire [11–14]. Temperature rarely acts alone in determining vegetation patterns, proportional increases in precipitation may buffer the effects of increased temperature, however when changes in temperature greatly exceed those of precipitation, many tree species become drought-stressed, and in severe cases drought conditions result in widespread forest die-off [13]. Globally, the impact and severity of drought-related changes in forest cover is well-documented [13, 15–20]. In many cases, trees adapt to drought conditions or shift northward and towards higher elevations [1, 5, 7]. In other cases, forest regeneration is limited by drought conditions, as seedlings are most vulnerable to desiccation, requiring greater moisture regimes to survive [21–23]. Drought indirectly influences fire regimes and insect/pathogen invasion, which have direct impacts on forest structure and function [11–14,24]. Furthermore, there are abundant records of

55 increased mortality, both gradual increases in mortality [25] and rapid massive die- offs. The majority of studies demonstrating widespread climate-induced mortality are from western North America. Among the observations of increased mortality are trembling aspen (Populus tremuloides) in Alberta and the southern Rocky Moun- tains [26–29], pinus species in southwestern North America [30] and high elevation whitebark pine (Pinus albicaulis) [31]. The trend of drought-stressed forests is likely to continue, as global temperatures are expected to increase between 0.3 and 6◦C by the end of the 21st century [32], with northern regions experiencing the greatest warming effects. The most extensive climate-induced changes are likely to occur in regions with abrupt transitions between states, such as ecotones [33], especially those driven by climatic conditions. Earlier work on boreal threshold responses to biome transitions [34], highlights the importance of changing climatic conditions on vegetation distribution in the boreal forest. The multimodality distribution frequency of the boreal forest is considered to be the result of non-linear responses of vegetation to environmental conditions (i.e. precipitation and temperature). At intermediate temperatures non-forested states coexist with boreal forest and open woodlands, whereas higher temperatures result in steppe grassland and lower temperatures result in tundra. Vegetation transitions at ecotones as a result of drought form a large component of recent climate-induced mortality observations [27,30,33,35–38], which suggests that further research is needed on the cumulative influence of alternative stable states and changing climatic conditions on vegetation dynamics. In the case of bistability (i.e. alternative stable states), the system may shift from one stable state to an alternative state following a catastrophic event (i.e. large-scale disturbance), or once a critical threshold is crossed. From a modelling perspective, alternative stable states can be described in terms of variables – in which multiple potential equilibria exist for a given condition and the stability dynamics are the result of direct perturbations to the variable (Fig. 3.1 model 1) – or parameters, such that parameter changes force alternative stable states (Fig. 3.1 model 2) [39]. Although the two model frameworks exist (model 1 and model 2), the alternative stable state paradigm focuses on four main conditions, 1) there often exists a tipping point, for which small perturbations lead to a change in state of the system, 2) the transition lacks a stable intermediate stage, such as the transition from forest to grassland, 3) the alternative stable states exist under the same ecological conditions and climatic conditions, 4) the system is self-replacing, often through positive feedbacks between states or driving factors [40–43]. The use of thresholds and positive feedbacks to identify multiple stable states is contentious [43,44]; however, positive feedbacks between driving forces and the system intensify and/or speed up transitions, which may lead

56 Figure 3.1: Conceptualizing alternative stable states. Model 1 shows shifts in variable, as the system shifts between coexisting alternative stable states following direct changes to the variable. Model 2 demonstrates a shift to an alternative stable state caused by parameter changes that alter the system dynamics. to a lack of resilience and a transition to an alternative stable state. This cumulative effect is exemplified by drought-induced mortality in temperate forests of Spain, where drought-stressed trees are less resilient and more susceptible to widespread tree mortality once the tipping point is crossed [45]. Given the complexity of ecosystems – with multiple interacting biotic and abiotic factors, such as temperature, pathogens, precipitation, pH, carbon, fire, wind and insects – it is more likely than not that positive feedbacks exist in a given system [46]. However, whether the positive feedback is strong enough to shift ecosystems from one state to another is case specific. Thus, the occurrence of positive feedbacks is not sufficient to infer bistability. Since the seminal work by Lewontin in 1969 [47], the theoretical application of alternative stable states has been widely used throughout the literature, although the availability of empirical findings to support such claims of tipping points and alternative stable states are limited [48,49]. In recent years, when faced with rapid climate changes, forests respond through massive dieback and mortality, but whether this constitutes a tipping point remains uncertain. Further work is needed to quantify changes in vegetation dynamics in response to drought conditions and find mechanisms of die-off. Boreal and temperate forests in North America are generally resilient forests and serve many ecological, industrial and societal purposes [50]. Indeed, past work and historical records suggest that the boreal forest is stable and remains so over long periods of time, as a result of its resilience; however, climate warming trends and/or

57 intensification of forest management may lead to abrupt changes and the potential for vegetation to shift into an alternative stable state [51]. In the past, vegetation shifts in the boreal forest have occurred rapidly, as a result of changing fire regimes and climate change. Fossil and pollen records indicate warmer conditions 10 000 BP, which restricted forest growth and supported grassland ecosystems [52,53]. The predicted changes in climatic conditions, biotic and abiotic disturbances are expected to match or exceed those of the past [54], which may lead to extensive changes in forest cover. Shifts in climatic conditions are predicted to occur at speeds faster than trees can migrate, therefore forests will be forced to acclimate, adapt or die [55]. Adap- tive forest management is proposed to mitigate the impact of increased temperature and drought conditions on forest ecosystems and society. What triggers vegetation change is of particular interest to forest managers and ecologists, alike. The main question refers to how much stress can be tolerated before forest health and persistence are threatened [56]. In the substantial collection of literature related to forest die-off, threshold responses to climatic conditions and ecotonal transitions, there are few studies that offer quantitative indices for water-stress and tree mortality [57,58]. Millar and Stephenson [14] emphasize the need for tools to study disturbance thresholds and forest vulnerability to cumulative stresses. Given the abundance of research on drought-induced mortality and regime shifts in recent years, it is surprising that most current forest and vegetation models do not simulate tipping points or feedbacks [59]. The aim of this study is to model changes in managed forests over the next century in the face of changing climatic conditions (precipitation and temperature). We use the boreal, sub-boreal and subalpine regions of British Columbia to parameterize our model, as the North American boreal forest demonstrates multimodality between dense forest cover, open woodland and steppe/tundra [34] and forms a boundary with temperate forest. We explore the potential occurrence of alternative stable states in managed forests of British Columbia with changes in precipitation and temperature. Finally, we compare reforestation strategies to manage for drought conditions and potential regime shifts.

2 Methods

2.1 Case Study

The boreal forest and adjacent biogeoclimatic zones are of particular interest to forest managers and ecologists because of predicted climate changes and in turn the impact on forest productivity for lumber and ecosystem services. The extent and

58 Figure 3.2: Map of Tree Farm Licence 48 (TFL 48). The study region is located in eastern British Columbia, south of the Peace River. Topographically, TFL 48 lies partially on the Alberta Plateau and in the Rocky Mountains, which generates a diversity of vegetation - grassland at low elevations near Peace River (yellow area on map) and subalpine forest in the mountains (purple area on map). vegetation dynamics of British Columbia are characterized by climate and edaphic conditions. Disturbance, such as fire, drought and insect invasion, is common in boreal and temperate forests and as such the forests have adapted and are resilient to change. However, in the last century droughts, across North America and Europe, have reached unprecedented levels of severity [20,60]. Tree Farm Licence 48 (TFL 48) is located northeast of Prince George (between 54◦N and 56◦N latitude, 120◦W and 122◦W longitude)(Fig. 3.2). Presently, the region is classified in three biogeoclimatic zones: Boreal White and Black Spruce (BWBS), which makes up approximately 25%, Sub-Boreal Spruce (SBS) and Engel- mann Spruce-Subalpine Fir (ESSF), which make up approximately 25% and 50% of TFL 48, respectively. The variation in species and climate creates ecotones between boreal/temperate and boreal/parkland/grassland. Forest covers 88% of the 643,238 ha, of which 56% is productive forest, used for harvest, and 32% is productive forest left intact [61]. The remaining 12% is non-forested land or non-productive forest. The study system is composed of white spruce (32%), lodgepole pine (29-34%), subalpine fir (13-22%), and trembling aspen (12%) [61, 62], which we use to calculate seedling establishment probabilities and adult mortality based on drought characteristics of tree species. The species are classified as drought intolerant (I), moderately drought

59 Figure 3.3: Simplified conceptual diagram of forces and feedbacks on forest cover in our study region (boreal/temperate forests of British Columbia). The main driver in vegetation cover is climate moisture index (CMI), which impacts the rate of seedling establishment and disturbance. The mechanisms responsible for feedbacks between forest cover and processes are unknown, however forest can have both positive and negative effects on disturbance [34]. Increased forest cover increases the rate of seedling establishment, either through reduced fire or favourable conditions for development [46, 63]. tolerant (M) and drought tolerant (D).

2.2 Model

To explore changes in forest cover over the next century, with respect to changes in temperature and precipitation, we use a simple model of forest cover (F ) dynamics, applying a threshold response paradigm to forest transitions similar to our previous work in tropical/subtropical systems [64] and Henderson et al. unpub (Chapter 2). However, the biotic and abiotic factors responsible for driving vegetation changes and creating thresholds in the boreal/temperate system are markedly different. Cli- matic conditions are the primary driving forces in the boreal/temperate system, as precipitation and temperature have a role in determining the fire regime, seedling establishment probability, frequency and severity of insect outbreaks and tree growth patterns (Fig. 3.3) [14,65]. The change in forest cover (F ) is expressed in terms of annual reforestation and harvesting practices, in addition to natural regeneration and disturbance. Our study region is composed of boreal and temperate managed forest (F ), which forms an ecotone with parkland and grassland (1 − F ). The distribution of vegetation can be determined along a gradient of climate moisture indices [66]. The climate moisture index (C) describes the difference between precipitation and evapotranspiration, as such C can be negative or positive. When the value is negative, forest is absent, however when precipitation greatly exceeds evapotranspiration, a moist forest persists. The landscape dynamics can be simplified to a single equation to express vegetation changes in the region, as a function of forest cover (F ) and climate moisture index

60 (C): dF = (α + β)p (F,C)F (1 − F ) − ν(C)F − hF. (1) dt e The forest in our study region is partially-managed with an annual harvest rate (h) of approximately 1% [61]. Reforestation eﬀorts must replace the harvested forest, hence the term α. The probability of planted seedlings becoming ’free-to-grow’ trees

(trees>1-2m high) is constrained by the probability of establishment (pe(F,C)). Re- forestation efforts assume some natural regeneration, approximately 40-90% of harvested land can be left to regenerate on its own [67]. Although, the majority of managed forests in British Columbia are replanted post-harvest, an estimated 75% of the harvested forest is restocked with seedlings [68]. Therefore, if h = 0.01, we set α = 0.0075 and introduce a natural regeneration parameter β, which yields significantly more seedlings than planting alone. We set β = 0.03, from work on potential natural tree regeneration [67]. Increases in seedling establishment are often associated with favourable changes in temperature and precipitation [34, 69]. Therefore we model the probability of seedling establishment in terms of the climate moisture index (C). Adult tree mortality (ν(C)) is also a function of C; from Hogg et al. [66] we assume that adult tree mortality (ν(C)) increases as C decreases, either directly or indirectly from water deficit (see section below). We use TACA (tree and climate assessment) output [70] for seedling establishment probability on edaphic amplitude sites, S1 (dry) to S5 (wet), and the corresponding climate conditions (temperature, precipitation and potential evapotranspiration) to generate the probability of seedling establishment (pe(F,C)) using regression analysis (supplementary information). We ignore the possibility of direct competition for resources between grasses/shrubs and seedlings, as desiccation is the primary cause of seedling mortality [21]. The probability of seedling establishment is given by: 1 1 pe(F,C) = , (2) −C+CMIδ+mT (1 − F )γ 1 + exp η where CMIδ is the threshold climate moisture index for which the probability of seedling establishment is 50%, in combination with mean annual temperature (T ). Higher temperatures shift the threshold to the right, as higher temperatures require greater moisture availability to sustain forest cover. We let m represent the temperature-dependence coefficient. The sharpness of the threshold response is controlled by η, dictating the sharpness of the transition from forest to non-forest. The temperature dependence of seedling establishment (m), climate moisture index threshold (CMIδ) and rate of seedling establishment (η) are related to tree-specific characteristics, such as drought-tolerance. We assume a positive feedback between

61 the proportion of forest cover and seedling establishment, using a simple non-linear pe relationship between forest cover and seedling establishment (1−F )γ , such that when F is large seedling establishment is maximal. The mechanisms responsible for the positive feedback in the forest/non-forest system are uncertain [34], but the balance of evidence supports the presence of positive feedbacks [46, 59, 63]. We also experi- mented with the Hill function to generate positive feedbacks, however the results are similar. Mortality of adult trees as a result of changing climatic conditions could have greater implications on landscape structure and function than regeneration [16]. The relationship between C and the probability of adult tree mortality (ν(C)) is derived from ﬁeld observations of tree die-oﬀ following severe drought years across western North America [25, 26]. We use data from outside our study region, as there is no drought-induced mortality data from TFL 48. We apply a linear regression similar to Hogg et al. [26] to generate adult mortality (supplementary information). We represent the annual rate of adult mortality in terms of C, in the following equations:

ν(C) = a − bC, (3) where a and b are mortality and water-deficit mortality coefficients, respectively. The values assigned to a and b depend on the drought tolerance characteristics of tree species and thus are determined from empirical data for drought class species (I,M,D). Mechanisms of mortality are uncertain, whether it be from carbon starvation, hydraulic failure, reduced resistance to pests (i.e. fungi, pathogens, insects), increased fire severity, however, all such mechanisms are related to water-stress ( [14, 16, 19, 71]). Therefore, b reflects increased likelihood of adult mortality under water-stressed conditions. As C decreases the mortality of adult trees (ν(C)) increases. If a − bC < 0.001, we let ν(C) = 0.001 to reflect average mortality rates for adult trees. Currently, our study region experiences very low rates of mortality (approximately 0.1% on average), as C is high throughout most of the productive forest in TFL 48, and associated disturbances are infrequent (Permanent Sample Plot inventory for TFL 48).

2.3 Analysis

We determine the equilibrium forest and non-forest states and threshold responses to changes in climate moisture index (C) from the above equations. Climate moisture index is the diﬀerence between precipitation, P , and potential evapotranspiration, E,(C = P − E), however climate change is generally discussed relative to changes in precipitation and temperature, thus we simplify evapotranspiration in terms of

62 temperature (T ). The calculation of E is based on Hargreaves’ method [72] and linear regression analysis (supplementary information). Our calculated E shows a strong positive correlation (r = 0.9429) with potential evapotranspiration climate data from ClimateNA [73]. We use a parameter plane to determine the landscape composition over a range of potential T and P conditions to explore the presence of bistable alternative stable states currently and in the future, amid changing climatic conditions. For the purpose of our study, we separate tree species into three categories based on drought tolerance characteristics (drought tolerant (D), moderately drought tolerant (M) and drought intolerant (I)), as such 18% are drought intolerant species

(pI ), 50% are moderately drought tolerant species (pM ) and 34% are drought tolerant species (pD). We let pe(F,C) equal the sum seedling establishment for each drought class species. We apply the same principle3 to mortality of adult trees ν(C).

pe(F,C) = pI peI (F,C) + pM peM (F,C) + pDpeD (F,C), (4)

ν(C) = pI νI (C) + pM νM (C) + pDνD(C). (5) The possible forest states and non-forested states include full forest cover for F ≥ 0.7, open forest (0.4 < F < 0.7), woodland (0.05 < F ≤ 0.1), aspen parkland which is between woodland and open forest (0.1 < F ≤ 0.4) and ﬁnally grass/shrubland which constitutes less than 5% tree cover [34,74].

2.3.1 Current Forest Composition in the Face of Climate Change

Using TFL 48 as a case study, we systematically select three regions (54.77◦N, 120.894◦W; 55.832◦N, 122.151◦W; 56.130◦N, 120.894◦W) and three elevations (600m, 900m, 1200m) for a total of 9 sites covering potential ranges of climate, vegetation and topographic conditions, to explore which regions are most vulnerable to changes in temperature and precipitation. The highest latitude point at low elevations is the only region in TFL 48 currently occupied by grassland and aspen parkland, the other regions exhibit full forest cover (F = 0.88). ClimateNA [73] predictions from three models (CanESM2, CNRM CM5, HadGEM2-ES) for 2085 climatic conditions are used to predict changes in vegetation through to the next century and establish which species of tree should be reforesting the region. The model parameters determined by data analysis and observations are given in Table 3.1.

2.3.2 Alternative Reforestation Strategies

Tree Farm Licence 48 (TFL 48) is predicted to experience considerable shifts in climate supporting current vegetation. The climatic conditions are projected to shift

63 from those supporting Engelmann Spruce-Subalpine Fir (ESSF) to conditions that favour Sub-Boreal Spruce (SBS) species by 2050s. Furthermore, the southern extent of the boreal forest is predicted to shift from full forest cover (e.g. Boreal White and Black Spruce) to non-forested grassland or parkland/open forest (i.e. Interior Douglas Fir) over the next century [4,75,76]. We explore two alternative reforestation strategies, in which we increase the proportion of moderately drought tolerant and drought tolerant species, to compare with the current reforestation strategy (pI = 18%, pM = 59%, pD = 32%). The alternative strategies fall within the reforestation guidelines for preferred and acceptable species, so to avoid issues with seed zone transfer and other potential unforeseen complications of altering the biogeoclimatic subzones beyond current guidelines [77]. The ﬁrst alternative strategy involves reforestation in the absence of drought intolerant species

(pI = 0%, pM = 55%, pD = 45%). The second alternative strategy reforests the sites with the maximum possible proportion of drought tolerant species (pI = 15%, pM = 25%, pD = 60%), estimated from British Columbia forestry guidelines and TFL 48 biogeoclimatic zone composition.

3 Results

The proportion of forest cover is highly dependent on the precipitation regime (P ) and temperature (T ) in the region. The equilibrium forest cover (F ∗) and stability depend on all parameters modelled, with the probability of seedling establishment

(pe(F,C)) and mortality (ν(C)) having the greatest impacts.

3.1 Equilibrium Forest Cover

Our study region has two potential equilibria, including a trivial equilibrium at F ∗ = 0. The non-trivial equilibrium is given by the following equation:

2 2 γ 2 2 2 2 ∗ α pe(C) + 2pe(C) αβ + β pe(C) − h − 2hν − ν F = 2 2 (6) pe(C) (α + β) The equilibrium curve for forest cover (F ) with respect to climate moisture index (C) is shown in Fig. 3.4. The minimum forest cover is F ∗ = 0 and the maximum forest ∗ ∗ dF ∗ cover is F = 0.91. The stability of F is determined from dt = f(F ), for which F is stable when f 0(F ∗) < 0. The stability condition for forest cover is given by

64 Table 3.1: Parameter values. Parameters are obtained from Ministry guidelines for TFL 48 or calculated from studies on drought-induced mortality across western North America

Symbol Parameter Definition Range Unit Source C Climate moisture index -40–80 cm [73] T Mean annual temperature 0–7 ◦C [32,73] ◦ Td Mean temperature difference 8–13 C [73] P Mean annual precipitation 400–1200 mm/yr [73] α Reforestation rate 0.001–0.006 1/yr [67] β Natural regeneration rate 0.005–0.03 1/yr [67] h Harvesting rate 0.01 1/yr [61] a Adult mortality coefficient 0–0.06 1/yr Calculated from [15,25,26,31] b Drought-induced mortality coefficient 0–0.001 1/cmyr Calculated from [15,25,26,31] pI Proportion of drought intolerant species 0–0.18 [61,62,77] Proportion of moderately

65 pM drought tolerant species 0.25–0.55 [61,62,77] pD Proportion of drought tolerant species 0.32–0.6 [61,62,77] Climate moisture index threshold CMII for drought intolerant species 21.7 cm Calculated from [70] Climate moisture index threshold CMIM for moderately drought tolerant species 12.2 cm Calculated from [70] Climate moisture index threshold CMID for drought tolerant species -34.9 cm Calculated from [70] Temperature modifying coefficient ◦ mI for drought intolerant species 2.8 cm/ C Calculated from [70] Temperature modifying coefficient ◦ mM for moderately drought tolerant species 0 cm/ C Calculated from [70] Temperature modifying coefficient ◦ mD for drought tolerant species 3.1 cm/ C Calculated from [70] Rate of threshold change ηI for drought intolerant species 3.5 cm Calculated from [70] Rate of threshold change for ηM moderately drought tolerant species 6.4 cm Calculated from [70] Rate of threshold change ηD for drought intolerant species 19.3 cm Calculated from [70] γ Non-linear positive feedback coefficient 0.5 Calibrated (α + β)p (C)F ∗ (α + β)p (C)(1 − F ∗)γ − γ e − ν − h < 0 (7) e (1 − F ∗)γ

∗ In the trivial case, F = 0 is stable when (α+β)pe(C) < ν +h (C < 11), similarly the non-trivial equilibrium stability depends on seedling establishment probability (pe(F,C)) and adult mortality (ν) at C (eq.(6)). The unstable equilibrium in the system corresponds to the steep incline on the equilibrium curve, for 11 < C < 17 (Fig. 3.4). Therefore, the forest cover is unstable when 0 < F < 0.6. Forest cover between 60 and 90% is stable, however from time-series analysis we determine that it takes millennia to occur. The unstable state represents a transient state between equilibrium states, that is either decreasing towards F = 0 or increasing towards F > 0.6.

1 Full Forest Cover

0.8 Open Forest Cover 0.6 * F 0.4 Aspen Parkland/ Woodland 0.2

Grass/Shrubland 0 -40 -20 0 20 40 60 80 Climate Moisture Index (C)

Figure 3.4: The black line represents the forest equilibrium for a range of climate moisture indices. The aspen parkland/woodland represents a transient unstable state, whereas grassland/shrubland (F = 0) is a stable state for C < 11, full forest cover (F > 0.7) is maintained by C > 23 and maximum forest cover (F = 0.91) is stable for C > 50. Open forest cover can be stable (0.6 < F < 0.7) or unstable (0.4 < F < 0.6).

All parameters modelled have an important role in determining forest cover, α and β (regeneration rates) generate horizontal shifts in the threshold response of forest cover to climate moisture index (Fig. 3.S2). Based on the stability conditions from equation (6), harvesting (h) has the potential to collapse the system, if faster than regeneration. The relationship between seedling establishment (pe(F,C)) and mortality (ν(C)) creates the threshold response shown in Fig. 3.4, the transition begins when ν(C) = 0.015pe(C). The positive feedback (γ) controls the steepness of the threshold. Not surprisingly, the stronger the feedback (γ → 0), the more rapid the transition from non-forested land to full forest cover.

3.1.1 Current Forest Composition in the Face of Climate Change Contrary to our predictions, the region does not show coexisting alternative stable states, except for very small pockets (Fig. 3.5, white area). Rather the system appears to be driven by thresholds to temperature (T ) and precipitation (P ), as there exists a distinct transition from non-forested land (1 − F ) to forested land (F )

66 Figure 3.5: Parameter plane for changing climatic conditions. We represent the proportion of forest cover over a range of potential precipitation and temperature regimes at low latitudes and low elevations (a), low latitudes and high elevations (b), mid latitudes and mid elevation (c), high latitudes and low elevations (d), high latitudes and high elevations (e). The yellow x represents normal (1961-1990) climate conditions from ClimateNA and red box represents predicted temperature and precipitation conditions.

67 for P=500–650 mm/yr depending on the temperature (T ). The transition area (Fig. 3.5, light grey area) represents a stable equilibrium with an alternative transient state. The transient state represents declining or expanding forest cover that has not yet reached a stable equilibrium. At the lowest simulated latitude (54.798◦N) and the lowest simulated elevation (600m) (Fig. 3.5a), full forest cover currently dominates, albeit on the cusp of unstable open forest or aspen parkland. However at the turn of the century (end of 21st century) the full forest cover is likely to be dominated by non-forested land or an unstable transient state. According to climate prediction models, this region will experience increases in temperatures with disproportionate increases in precipitation. This region maintains the greatest diversity of potential future landscape compositions, including stable open forest (Fig. 3.5a, grey/black area) and alternative stable open forest/non-forested states (Fig. 3.5a, white area). Regions at low elevations (Fig. 3.5a), particularly at the southern extent of Tree Farm Licence 48, are vulnerable to drought-induced mortality or vegetation transitions from F to 1 − F . The regions that currently maintain grass/shrubland are likely to remain in a non-forested state (Fig. 3.5d). The mid-range latitude (55.832◦N) and higher elevations (900-1200 m) currently represent SBS forest, which is a moist and resilient forest at present and will continue to be in the future (Fig. 3.6b). Higher elevations across all latitudes in TFL 48 provide favourable conditions for forest development; future climatic conditions are predicted to maintain C > 20, which results in infrequent disturbance (ν = 0.001) and seedling establishment probability of at least 70% (pe(C) ≥ 0.7). The highest latitude simulated (56.130◦N) is currently the only region in TFL 48 with grassland or aspen parkland. The grassland/parkland landscape occurs in the valleys and transition to boreal and sub-boreal forests at higher elevations (900-1200 m). However, for the predicted change in T and P , the region shifts into an unstable transient alternative state (Fig. 3.5e). Therefore, the area of grassland/parkland is predicted to expand from the valleys to the nearby mountains, as increases in P are minimal compared to the change in T .

3.1.2 Alternative Stable States The regions of supposed bistability between aspen parkland and plains grassland, fall within one of the few instances of climatic conditions that support bistability (yellow box, Fig. 3.6a). Therefore, the observed vegetation patterns may correspond to a fragile region of bistability that is vulnerable to small changes in P and T . If the increase in P is not proportional to the increase in T , the region will tend to either full forest cover or grassland. Interestingly, the predicted change in T and P also have the potential to maintain bistability between grassland and open forest (red box, Fig. 3.6). If we ignore climatic conditions and model seedling establishment as a function of forest cover (F ) only and mortality as a constant (within the range of mortality obtained from ν(C) = a − bC and seedling establishment pe(F,C)), as depicted in Fig. 3.1, model 1, the region of bistability increases (Fig. 3.6b). However, unprecedented warming and minimal increases in precipitation will likely alter climate moisture indices and force the system to an alternative state (Fig. 3.1, model 2). This region clearly experiences a threshold response to climate variables, however the parameter planes (Fig. 3.5) and equilibrium curve (Fig. 3.4) do not provide support

68 Figure 3.6: The region of bistability (white region on plot) in a model of vegetation dynamics with changing climatic conditions, as presented here, (a) is much smaller than the region of bistabililty in the same model of vegetation without varying climatic conditions (b). Bistability between non- forest and open forest is present under the current range of climatic conditions (yellow box, a) and future conditions (red box, a). In the absence of climatic conditions, bistability also depends on the ratio of seedling survival to adult mortality, but the parameters are not constrained by climate, there is a greater range of possibilities. for the alternative stable states paradigm, in which multiple states are stable under the same conditions.

3.1.3 Alternative Reforestation Strategies Reforestation guidelines suggest altering the species planted in each biogeoclimatic zone in an attempt to moderate the impact of climate change on forest health. We test two alternative reforestation strategies: removing drought intolerant species from reforestation eﬀorts and planting the maximal proportion of drought tolerant species. We generate equilibrium curves similar to Fig. 3.4 (the current reforestation strategy equilibrium curve) for reforestation in the absence of drought intolerant species (Fig. 3.7a) and reforestation with maximal drought tolerant species (Fig. 3.7b). The equilibrium stability conditions for the alternative reforestation strategies are the same from equation (6). Both curves shift the threshold response of forest cover to climate moisture index to the left, which increases the range of stable forest cover. The current reforestation strategy results in grassland/shrubland at C < 11, whereas the alternative strategies yield grassland/shrubland for C < −1 and C < 2, for reforestation in the absence of drought intolerant species and maximal drought tolerant species, respectively. Forest cover between 0% and 55% is unstable, corresponding to −1 < C < 5 under reforestation in the absence of drought intolerant species. Refor- estation with maximal drought tolerant species yield unstable forests for 2 < C < 11. The unstable regions correspond with the steepest portion of the equilibrium curve and although equilibrium points between 0.55 < F < 0.9 are stable, the timescale is ecologically signiﬁcant, but not from a management perspective. The shift in threshold response increases the forest’s resilience to gradual changes in climate and could maintain forest cover at lower elevations, based on predicted climate moisture index (Table 3.S1). The shift in F in relation to C, under the

69 Figure 3.7: Alternative reforestation threshold response to climatic conditions. Subpanel (a) represents the forest equilibrium for a range of climate moisture indices under reforestation guidelines that remove drought intolerant species from stocking guidelines. The aspen parkland/woodland represents a transient state, whereas grass/shrubland is (F = 0) is stable for C < −1, full forest cover (F > 0.7) is maintained for C > 8 and maximum forest cover (F = 0.91) is stable for C > 31. Subpanel (b) represents the F ∗ under reforestation with maximal drought tolerant species, where F = 0 is stable for C < 2 and F > 0.7 is maintained by C > 17. The maximum forest cover (F = 0.91) is the stable for C > 48. reforestation in the absence of drought tolerant species, is primarily the result of decreased mortality. Meanwhile, the shift in threshold response under reforestation with maximal drought tolerant species is caused by up to three-fold increases in seedling establishment probability.

4 Discussion

The model presented here takes a closer look at the threshold response of boreal forest to climatic conditions, outlined by Scheffer et al. [34]. We reiterate the importance of a non-linear response of forest cover to precipitation and temperature, while providing mechanisms for vegetation transitions. In fact, the threshold response to temperature and precipitation dominates in our simulations, showing very little coexistence between alternative stable states under the same climatic conditions. Instead, we find that both seedling establishment probability and adult tree mortality are driven by changes in temperature and precipitation. As such, the threshold response can be quantified with empirical data and calculated probabilities for seedling establishment and drought-induced mortality over a range of climate moisture indices. The model is novel in its ability to estimate how much moisture stress a forest can tolerate before collapsing, which is useful for forest management. The uncertainties surrounding the mechanisms responsible for positive feedbacks in the system remain, however it appears that the threshold response to climatic conditions has an overwhelming force on system dynamics. If the positive feedback occurs between seedling establishment and forest cover, as we model here, then the positive feedback accelerates the shift towards full forest cover. There is strong evidence, both observational and theoretical, for threshold responses in forest cover to precipitation regimes and temperature in our study region, but there is little reason to suspect alternative states that can exist under the same climatic conditions.

70 Given that the study region is topographically and climatically diverse, the climatic conditions of a site provide the most plausible explanation for the transition between full forest cover, open forest, woodland and grassland. The small region of bistability reflects a very specific climate region that exhibits coexistence between open forest and non-forested land. Over the past 3000 years the vegetation and climate dynamics of the region have remained relatively constant [52], which may explain our understanding of alternative states in the region. However, this region of bistability is extremely vulnerable to changes in precipitation and temperature, similar to many forest systems which operate on the fringe of hydraulic failure boundaries [18]. An increase in precipitation will likely yield a transient woodland state or full cover, whereas an increase in temperature will shift the system into a non-forested state. The alternative stable states paradigm is well-studied and has many applications in biological and ecological systems. The dominant theory of alternative stable states suggests that multiple equilibria states exist simultaneously under the same set of conditions, but require large perturbations to shift the system from one state to another [39]. However, there is an alternative way of conceptualizing alternative stable states, such that parameters regulate state variables and their interactions (Fig. 3.1, model 2). The work shown here is clearly a case of communities shaped by parameter changes. Very few models focus on the latter theory, which raises questions about bistability and the impact of climate change in other regions (e.g. savanna systems, tropical tree-grass systems). Will alternative stable states be conveyed through parameter shifts, as climate is predicted to experience unprecedented changes? Do we only recognize bistability under very specific conditions? Our study area does not demonstrate widespread climate-induced mortality within the 100 years. Forest cover at lower elevations and adjacent to parklands and grasslands are the only regions vulnerable to abrupt changes, as a result of the threshold response. This is consistent with increased mortality among dry forests, but not forests across a spectrum of environmental conditions [78]. The BWBS component of the Tree Farm Licence 48 is likely to experience the greatest shift in vegetation, as it has a sub-mesic moisture regime at present. The already fragile ecosystem is predicted to experience increases in potential evapotranspiration greater than the increase in precipitation, resulting in decreased moisture availability and a shift to aspen parkland/woodland. The temperate forests are likely to be maintained at higher elevations, although the model is non-spatial, thus we are not certain whether temperate forests or boreal forests will expand or contract, rather we are more in- terested in the particular threshold and range of temperature and precipitation that shifts occur. Future work could benefit from the addition of a spatial component and more specific vegetation distribution patterns. Even though widespread forest die-off is not likely in our study region, forest managers recognize the need to alter reforestation stocking guidelines to maintain full forest cover [77]. Incorporating mechanisms responsible for driving shifts in vegetation allows us to explore potential adaptive forest management strategies. We explore two potential reforestation strategies that fall within current stocking guidelines for preferred and acceptable species: reforestation in the absence of drought intolerant species and reforestation with the maximal proportion of drought tolerant species. Although the use of species drought tolerance characteristics and average

71 percentage of each drought class in the region is a crude measure of vegetation composition, it provides an initial attempt at comparing adaptive forest management strategies and potential shifts in threshold. Both alternative reforestation strategies shift the threshold response of forest cover with respect to climate moisture index to withstand much drier conditions for at least a century. Reforestation in the absence of drought tolerant species decreases the mortality of adult trees, whereas reforestation with maximal proportions of drought tolerant species increases the rate of seedling establishment. It appears that adult mortality is the limiting process in this system, as the threshold shifts further through reforestation in the absence of drought intolerant species and the transition to maximal forest cover experience positive changes when adult mortality is minimal. Both alternative stable states and drought-induced mortality are widely studied areas of forest ecology, yet they are rarely discussed in tandem, beyond theoretical assumptions or observational patterns. Incorporating climate change and empirical data allows us to predict changes in vegetation, but more importantly gain a better understanding of the dynamical processes and driving factors. Sustainable management of forests requires an understanding of the underlying processes, which cannot be obtained from modelling transitions in vegetation or climate change alone.

Acknowledgements

The research was supported by a James S. McDonnell Foundation Complex Systems Award to MA, NSERC Discovery grants to MA and CTB, and NSERC CREATE and RAP NRCan scholarships to KAH. We thank C. Nitschke for TACA model assistance and discussions.

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S1 Supplementary Information Text

S1.1 TACA seedling survival

We use regression analysis to determine seedling establishment probability. TACA provides data on seedling survival probability for sites under a range of potential covariates (i.e. minimum temperature, maximum temperature, average temperature, maximum, daily temperature difference, precipitation, frost, growing degree days, latitude, climate moisture index, elevation, bud break, chilling requirement). Of the 12 covariates tested, climate moisture index has the greatest impact on seedling survival rates for all species drought class (p < 0.005). However, using the Wald test we determine that using average temperature and climate moisture index results in a statistically significant improvement in the fit of the model. The logistic equations for each drought-class (intolerant I, moderately tolerant M, tolerant D) are given by:

 1 (I)  1+exp(6.2046−0.2843C+0.8099T )    1 pe(C) = 1+exp(4.41686−1.9664C−0.83017T ) (M) (S1)    1  1+exp(−1.80815−0.505186C+0.15910T ) (D)

The relationship between seedling survival/establishment and CMI from TACA data is shown in Fig. 3.S1a. The logistic regression curves for the tree species in drought-class I, M and D are given in Fig. 3.S1b. We simpliﬁed these equations

79 Figure 3.S1: Logistic regression curves for each drought class species. Subalpine ﬁr (Bl) is an example drought intolerant species (a), the curve is extrapolated for pI (d) for a wider range of climate moisture indices (CMI). Black spruce (Sb) data (b) is used to generate moderately drought tolerant species seedling establishment (subpanel e, pM ) and lodgepole pine (Pl) data (c) represents seedling establishment probability for drought tolerant species (f, pD). to represent a threshold in seedling establishment with respect to CMI (C) and temperature (T ).

 1 (I)  1+exp 21.7−C+2.8T  3.5    1 (M) pe(C) = 12.2−C+0T (S2) 1+exp 6.4    1 (D)  −34.9−C+3.1T 1+exp 19.3

S1.2 Mortality function

Drought-induced mortality has been observed in many regions across western North America [15, 24, 26, 27, 31, 33]. The relationship between C and the probability of adult tree mortality is derived from field observations of tree die-off following severe drought years. Hogg and colleagues [26] calculated aspen die-off following severe drought during 2001-2002 at studies sites in Alberta and Saskatchewan. The resulting linear regression equation for percent die-off serves as a template for percent of drought-induced mortality, following the form mortality = a − bC. We use mortality observations and historical climate data from the study and ClimateNA to generate equations for drought-induced mortality for drought intolerant [15], moderately

80 drought tolerant [27] and drought tolerant species [31]. The linear regression gives the following equations:   0.0516 − 0.00087C (I) ν(C) = 0.008664 − 0.000596C (M) (S3)  0.001816 − 0.000228C (D)

When C is large there the above equation assumes negative mortality, however this is biologically not possible, therefore we set ν = 0.001 to account for average mortality in a region without drought stress from permanent sample plot data.

S1.3 Converting evapotranspiration to temperature

ClimateNA along with many other studies, calculate reference evapotranspiration using Hargreaves’ method [72]:

0.5 Eref = 0.0023RTad (Ta + 17.8), (S4)

−2 where R is the extraterrestrial radiation, measured in MJm d−1. Ta is the daily average temperature and Tad is the difference between maximum and minimum daily temperature, both in ◦C. The literature uses reference evapotranspiration and potential evapotranspiration interchangeably, although erroneous, for simplicity and for consistency we will refer to reference evapotranspiration (Eref) as potential evapotranspiration (PET ) for the remainder of the text. Equation (S4) is on a daily timescale and R is not widely available, thus eq. (S4) is difficult to incorporate into an ordinary differential equation, where time is continuous and the variables are determined by rates of change. To simplify the equation for PET , we applied linear regression analysis to climate data from ClimateNA (Table3.S1). We use our climate data from across our 9 sites to determine which covariates have the greatest impact on potential evapotranspiration. Climate covariates include mean annual temperature (T ), mean temperature difference between mean seasonal maximum and minimum temperatures (Td). Radiation is dependent on latitude, therefore we also included topographic covariates: elevation (Elev) and latitude (L). ClimateNA data from 1961-1990 (Normal) and predictions from sev- eral models (CanESM2, CNRM CM5, HadGEM2-ES) for 2085, at the nine locations, show that evapotranspiration is most strongly correlated with average annual temperature (r = 0.8835) and less so with elevation (r = −0.5575), temperature difference (r = 0.4800) and latitude (r = −0.1279). The linear regression equation that has the strongest correlation with climate data PET (r = 0.9429) is given by

81 PET = 872.40255 + 30.53065T + 21.32348Td − 0.02135Elev − 11.78707L. (S5)

82 Table 3.S1: Climate variables from ClimateNA for three regions in TFL 48.

◦ ◦ P (mm/yr) Eref (mm/yr) CMI (cm/yr) T ( C) Td ( C ) Lat. Long. Elev. (m) Normal 2085 Normal 2085 Normal 2085 Normal 2085 Normal 2085 610 670 542 649 6.8 1.5 2.7 6.3 12.1 11.8 54.798 -120.894 600 750 829 501 594 24.9 23.5 1.9 5.7 11.1 10.7 900 83 890 985 460 549 43.0 43.8 1.2 4.9 10.1 9.5 1200 571 640 525 615 4.6 2.5 1.9 5.7 11.6 11.6 55.832 -122.151 600 696 786 482 568 21.4 21.7 1.1 4.9 10.7 10.3 900 820 931 440 522 38.0 44.2 0.3 4.1 9.7 9.1 1200 461 515 530 580 6.9 -10.3 1.5 5.4 11.8 10.8 56.130 -121.517 600 507 565 481 565 2.6 0.07 1.1 4.9 11.0 10.6 900 553 616 433 511 12 10.6 0.6 4.4 10.3 10.5 1200 S2 Supplementary Figure

1 α=0.0001, β=0.03 α=0.0075, β=0.03 0.8 α=0.001, β=0.03 α=0.0075, β=0.02 α=0.0075, β=0.04 0.6

0.4 F Equilibrium

0.2

0 -40 -20 0 20 40 60 80 CMI

Figure 3.S2: The rate at which forest is replaced with planted (α) or natural (β) forest shifts the threshold response of forest cover (F) to climate moisture index (CMI). Greater investment in reforestation can maintain forest cover over a wider range of climatic conditions.

84 Chapter 4

Landowner perceptions of the value of natural forest and natural grassland in a mosaic ecosystem in southern Brazil

Kirsten A Henderson, Mateus Reis, Carolina C Blanco, Valrio D Pillar, Rodrigo C Printes, Chris T Bauch, Madhur Anand

Published in Sustainability Science 11(1): 321-330 (2016)

Key Words: Restoration, Perception, Land use change, Forest-grassland mosaic, Policy

85 Abstract

The forest/grassland mosaics of southern Brazil have been subject to many land use and policy changes over the decades. Like many grasslands around the world, the Campos grasslands are declining with few conservation efforts underway. In contrast, forests receive much attention and many incentives. It is hypothesized that perception of land cover has the potential to shape ecosystems. Here we conduct a questionnaire to further our understanding of decision-making practices that alter landscapes (Campos grassland, Araucaria forest, agriculture and plantation) and direct land policies in the region. Our analysis reveals that plantations are significantly less desirable than the other landscape types. However, plantation land use has increased by 87% over the past few decades, as a result of industry and government incentives. The proportions of other landscape types have remained consistent over the past two decades. Restoration of native vegetation is not a priority of landowners and restoration would require a financial incentive.

1 Introduction

Deforestation has become notorious in tropical and subtropical South America due to the impact on biodiversity and the rapid rate of clearance [1–3]. As a result, government and private programs have established numerous conservation initiatives. Pristine grasslands are also declining, yet with little in the way of conservation efforts [4, 5]. These grasslands are sometimes erroneously considered to be degraded lands, a result of anthropogenic activities or the early successional stages of forests, while forests are perceived as more productive, pristine landscapes full of diversity [6]. Likewise, land conservation in Brazil reflects a high forest bias [7]. The Campos grasslands form a mosaic with mixed forests on slopes and valleys in the east of the South Brazilian Plateau and Araucaria forest in the highlands of southern Brazil [8]. The grasslands are considered the older vegetation type; however, recent wet climatic conditions have provided a favourable environment for forest development [9]. Fire and grazing are the main disturbances that impede forest expansion [5,8]. Other anthropogenic influences such as afforestation of grasslands with pine plantations, logging of Araucaria angustifolia forests and large-scale conversion of native vegetation for agricultural purposes have altered the landscape [9]. It is estimated that 50% of the Brazilian Campos is still natural grassland in Rio Grande do Sul [10] and only 12-16% of the original landscape cover remains in the Atlantic Forest [11].

86 Forest conservation takes precedence, following a history of forest degradation in the Atlantic Forest. The Araucaria forests have been extensively logged or cleared for agriculture, yielding a critical conservation status [12]. A. angustifolia is one of few indigenous gymnosperm tree species remaining in Brazil [13], with important socioeconomic and ecological benefits [14]. The number of non-native species plantations (pine and eucalypts) increased by 23% across Brazil from 2005 to 2010 [15]. In terms of overall planted forest area, native forest species formed less than 5% of planted areas, while pine and eucalypt species comprised 93% of planted forests [16]. The state of Rio Grande do Sul recorded 14.4% increase in non-native planted forests from 2005 to 2006 [17]. Government and social movements that promote regional development through agroforestry and, more likely, development of the forestry sector are thought to be responsible for the increase in planted area [18]. Policy-makers often promote afforestation of grassland to increase productivity and mitigate elevated atmospheric carbon dioxide [4]. Meanwhile, the native Campos grasslands of Brazil have undergone extensive land transformation. In the past three decades, approximately 25% of the Brazilian Campos have been converted to agriculture or plantation forestry [5]. In the 1990s, agricultural practices gained popularity with rice and soya crops occupying fertile soil and forest plantations composed of eucalypts and pine on poorer growing soils [10, 19]. These grasslands represent important biodiversity sites and provide numerous ecosystem functions, in addition to supporting livestock production and the Gaucho culture [20,21]; however, only 0.15% is formally protected as conservation units [22]. The Brazilian Forest Code (BFC) is responsible for the conservation of native vegetation on private lands [23, 24]. The BFC was created in 1965 and enforced by the ‘environmental crimes law’ established in the late 1990s [25], promoting the restoration and conservation of native vegetation [7, 26]. In 1965, the BFC imposed regulations and penalties, in effort to regulate land use on private properties, under the notion that forest is a common good [27]. In 1981, the Brazilian National Envi- ronmental Policy Law addressed the need to restore all degraded lands [28]. It follows that the requirements for conservation of native vegetation should constitute 80% of property in the Legal Amazon [29], 35% in the Cerrado biome (savannas) and 20% in other biomes [30]. However, agribusiness has persistently lobbied against the BFC, claiming the provisions of the bill directly impede agricultural production [7,26]. Af- ter record high deforestation rates in 1995, predominantly as a result of agricultural sprawl, regulation changes were prompted, enforcing stricter laws on rural property land use. Revisions of the BFC in 2012 were elicited by agribusiness’ condemnation of the strict conservation laws. The most significant changes to the law involve amendments to lessen the regulations on watershed protection and riparian vegetation, as

87 well as the elimination of hilltop native vegetation protection [24, 31]. Furthermore, under the new regulations, land that was illegally altered prior to 2008 is exonerated from restoration requirements and property size-specific regulations were included, relaxing requirements on small properties. On the state level, the government has been promoting alternative land use practices, primarily through increased tree cover. Silvicultural activities started in the late 1980s in Uruguay, Argentina and Rio Grande do Sul in Brazil, initiating competition among the countries to attract world corporate leaders from the cellulose industry [26]. As a result, landowners received massive public subsidies. The 1992 State Forest Code forbid the use of fire to maintain grasslands [32], contributing to increased silvicultural activities [33, 34]. In 2004, state environmental administra- tion implemented Environmental Zoning for Silviculture Activity (ZAS) to regulate tree farms in Campos grasslands, according to ecological vulnerabilities defined at different spatial unit scales [26]. The original ZAS regulations (2006) permitted 25- 50% of property to be planted with tree farms; larger properties were permitted to convert lower percentages of land to plantation. The latest version of ZAS regulations establishes a maximum percentage of plantation per mixed spatial unit (wa- tersheds divided by landscape unit), a minimum distance between plantations and offers watershed protection. Moreover, Brazil’s environmental legislation requires each plantation of exotic trees to have an environmental permit. In addition, the Low-Carbon Agriculture program provides loans to increase agriculture productivity while reducing associated carbon emissions and supporting forest restoration [7]. The native Araucaria forests in Brazil have further regulations prohibiting deforestation and promoting conservation. In 1965, the Brazilian Government banned the harvest of native vegetation in permanent preservation areas, which includes A. angustifolia [30]. As of 2001, the tree has been listed as critically endangered and export of the species has been prohibited [35]. Although the law requires all types of native vegetation to be protected, landowners are often unaware or do not acknowledge this [21]. Throughout the years, the BFC and other state initiatives have experienced many changes to the legal requirements for preservation of native vegetation, known as Legal Reserves (LR), in addition there have been various incentive programs and conservation initiatives, resulting in non-conformity among landowners, while making it difficult to monitor the land use transitions [27]. Non-compliance has been an issue for policy-makers, particularly in the Amazon and Atlantic Forest biomes, over the past decades [7]. A significant reason for non-compliance with LR standards is the substantial cost to landowners, not only from restoration efforts, but also through foregone income from crops and cattle ranching [23,27].

88 Human behaviour has a signiﬁcant inﬂuence on land use and ecosystem stability [36]. Many studies have looked at the decision-making behind conservation ecology. The scarcity hypothesis refers to conservation based on economic returns from ecosystem resources, such as timber. When a resource becomes scarce, the market value increases, providing an incentive for individuals to protect the resource [37–39]. Alternatively, the ecosystem service hypothesis states that environmental degradation associated with native vegetation loss increases the vulnerability of the system to further degradation, which reduces the incentive to restore ecosystem structure [37]. Moreover, individuals frequently demonstrate imitation behaviour, following the decisions of media or respected individuals in a community [40,41]. Moser [40] underlines the importance of social norms when communicating about climate change; climate change initiatives are more likely to be accepted when the views conform to those of the social group and therefore, individuals who engage in conservation initiatives are unlikely to be ostracized. Most land use research in Brazil has focused on the rates of decline and forest area lost, particularly in the Legal Amazon, and the role of policy-makers. Few studies have been conducted in the southern region of Brazil and even less is known about the forces driving land use transformation. The South and Southeast regions of Brazil are more heavily occupied and the majority of native vegetation is on private land [42]. Approximately, 80% of the Atlantic Forest biome is on private property [43]; hence the importance of enhancing our knowledge of the decision-making practices of landowners. The decisions landowners make and the resulting land changes form complex patterns in ecosystem landscapes. The main objective of our study is to gain knowledge on individuals’ preference and perception of conservation values (including sustainable use) of natural ecosystems, relative to their abundance in the region, and how this perception changes considering past and possible future landscape compositions in the forest/grassland mosaics of southern Brazil. It is hypothesized that individuals show no preference for one or the other native landscape type (Araucaria forest or Campos grassland), compared to non-native ones (agricultural land and non-native plantation). In addition, we hypothesize that decisions regarding land use and conservation are consistent with imitation and rarity-based behaviour.

2 Methods

2.1 Study area

The study area is located in the region of S˜aoFrancisco de Paula (town: 29◦27’03’S, 50◦35’41’W at an altitude of 912 m), in the South Brazilian plateau, northeastern

89 Figure 4.1: Location of the study site. a Map showing the 30 properties surveyed in the S˜ao Francisco de Paula region taken from Google Earth. b Inset of South America using ArcMap (ESRI 2012)

Rio Grande do Sul (RS), Brazil (Planalto das Araucrias). The regional climate is described as subtropical, with moderate temperatures (annual mean 14.5◦C) and high annual precipitation (mean 2252 mm) without a marked dry season [44]. The northeastern region of RS represents the southern limit of the Atlantic Forest distribution [45] and is characterized by forest/grassland mosaics composed of native Campos grassland and native A. angustifolia. The soil characteristics (Andosols or Umbrisols) are uniform through the forest and grassland landscape types [44]. The primary anthropogenic land uses are cattle grazing, logging practices, agriculture and tree plantations. The 300 km2 region around S˜aoFrancisco de Paula is composed of 30% native Campos grassland, 25% native Araucaria forest and 45% other human land use (agriculture and/or tree plantation) [20].

2.2 Sampling and analysis of land use

Data regarding the perception of changes and individual interactions with the natural environment were collected using a questionnaire. Thirty properties were selected using a stratiﬁed sampling technique, in which we chose to interview cattle ranch- ers with signiﬁcant proportions of native vegetation on their land as our reference group. There was also an element of ‘snowball’ sampling, where each farmer suggested the next person to survey. Figure 4.1 represents a site map of the properties surveyed. Each property was given a questionnaire (see Supplementary Information

90 for full questionnaire) with ten questions concerning the past/present composition and preference for four landscape types (native Campos grassland, native Araucaria forest, agricultural land and non-native plantation), how experiences are shared with other people about land use and opinions about the importance of the conservation of native (i.e. unplanted) ecosystems. All composition values were gathered as a percentage of the landowner’s property. To assure landowners understood the clas- sification of landscapes, landowners were shown images of native Araucaria, forest/ grassland mosaic and native grassland prior to answering survey questions. Questions 1 and 2 of the questionnaire relate to the composition of each landscape type on each landowner’s property and their preferred composition. Both current land composition/preference and land composition/preference from more than 10 years ago were considered to ascertain land use and perception changes in recent years. The next set of questions aims to determine landowner decision-making practices and primary influences. With this we include changes in the landscape in a 5 km radius from the landowner’s property to explore whether imitation behaviour is present or if the scarcity hypothesis applies. Questions 6 and 7 relate to the land composition in the SãoFrancisco de Paula region. The purpose of these questions is to note the feedbacks between landowners’ preference and the composition of the region. The final set of questions was devoted to gauging the interest of landowners to restore native Araucaria forest or native Campos grassland. Question 9 presents a hypothetical scenario in which landowners’ properties are composed entirely of Araucaria forest or Campos grassland; landowners were then asked how much of each native vegetation they would replace with the other. In addition, the questions explore the preference of restoring one native ecosystem over the other and the financial incentive required to convert anthropogenic land uses on their property to native vegetation. Statistical analyses were performed using descriptive statistics and non-parametric tests (Wilcoxon signed rank test, Spearman correlation) in R [46]. Differences were considered statistically significant when P < 0.05.

3 Results

3.1 Composition and Preference

Relating to Q1, the native Araucaria forest comprises the greatest percentage of land use on surveyed properties, with an average of 35%. Native Campos grassland makes

91 up 30% of the surveyed area, giving a combined native vegetation composition of 65% with no significant difference between the amount of the two landscape types (P = 0.8642). The mean compositions of agriculture and non-native plantation land use are 20% and 15%, respectively. There is significantly less plantation land use (P = 0.01401) and agriculture land (P = 0.04075) compared to native Araucaria forest. The preference for each landscape type (Q2 from questionnaire) does not vary significantly compared to the current composition landscape, with the exception of preference for more agricultural land use (P = 0.01417). On average, the mean preference for agriculture is 35%, which is 15% more agricultural land use than the current composition. The main reason landowners state for preferring agricultural land use is that agricultural practices are more profitable. The landscape composition preference for tree plantation is significantly less than the preference for both native ecosystems and agricultural land (P < 0.005). The landscape composition preferences for Araucaria forest, Campos grassland and agriculture do not vary significant from one another (P > 0.05).

3.2 Composition and preference change

In general, composition on landowner properties has not changed signiﬁcantly over the past three decades (Q3a from questionnaire). There has been a greater shift towards forested land, the mean tree plantation composition increased 87%, the percent composition of plantation land use on properties increased from 8 to 15% (P = 0.01418), while the mean percent composition of native Araucaria forest increased from 30 to 35%, a 16% increase in A. angustifolia composition over the years (P = 0.3244). The composition of Campos grassland decreased by 17%, past mean compositions on individual properties decreased from 36 to 30% (P = 0.05130). Likewise, the percentage of agriculture land use on individual properties decreased on average by 20% from 25 to 20%, (P = 0.8077). This decrease in grassland was perceived by 83% of landowners within a 5 km radius of their property (Q5 from questionnaire). Within the 5 km radius surrounding their property, 52% of landowners stated they observed a shift towards increasing Araucaria forest, while 34% of landowners claim to have observed no landscape transitioning and 14% of landowners stated they observed a shift towards decreasing forest. The correlation between the composition change of both native vegetation and the observed/perceived change in the 5 km radius is not signiﬁcant for Araucaria forest (ρ = −0.001880,P = 0.9923), nor for Campos grassland (ρ = 0.1805,P = 0.3487). The majority of landscape changes occurred between 10 and 15 years ago.

92 Table 4.1: Correlation between past landscape composition preference and current composition using the Spearman correlation test.

Landscape type ρ P value Strength Native Campos grassland 0.7454 0.000002289 Strong Native Araucaria forest 0.6159 0.0002908 Strong Plantation 0.3618 0.0248944 Moderate Agriculture 0.3245 0.08024 Moderate

Corresponding to Q3b, landscape composition preference has not changed significantly over the years. All P values for the change in composition preference are greater than 0.5. Few individuals changed their preference for Araucaria forest composition (n = 5) over the past decades; however, there exists a weak negative correlation between the slight increase in preferred composition and the perceived change in forest cover within the surrounding 5 km radius (ρ = −0.2602,P = 0.1729). Three landowners changed their preferred composition of Campos grassland; the minimal decrease in individual preference change for Campos grassland shows a weak positive correlation with the perceived decrease of grassland in the surrounding area (ρ = 0.2166,P = 0.2592). The negative correlation between the change in preferred forest composition and perceived forest cover change demonstrates rarity-based decision-making practices, inconsistent with the high discount rates on timber in Brazil [47]. The past landscape composition preference appears to be reﬂected in the current composition of land, which is positively correlated with the past preference for each landscape composition (Table 4.1).

3.3 Land use inﬂuence

The results from Q4 show that landowners are much more likely to gather information from someone they know with the same vocation (70% of landowners, P = 0.02932), such as parents, neighbours or cooperatives. The other 30% of landowners receive information from television, the newspaper or the internet. On a scale of 1-5, the average self-reported inﬂuences from both personal contacts and media are 3.3 and 3.4, respectively.

3.4 Regional composition

Relating to Q6, landowners are unlikely to change their preference for Araucaria forest (P = 0.3938) or Campos grassland (P = 0.4313) after being informed of the current composition of land in the region. On average, the landowners would prefer to see the region of S˜aoFrancisco de Paula composed of 39% native Campos grassland,

93 29% native Araucaria forest, 26% agriculture and 2% plantation (Q7 from questionnaire). The majority of landowners would prefer that non-native tree plantations be replaced by one of the three other landscape types (P < 0.00005) and would like to increase the income generated, in addition to the productivity of properties. Seventy- three percent (n = 22) of landowners stated a preference for agriculture and ranching in the region for ﬁnancial reasons or food productivity. However, 17% of landowners (n = 5) stated the importance of landscape services provided by Araucaria forests. The preferences for Araucaria forest and tree plantation on individual properties show weak negative correlation with the preferences in the region (ρ = −0.04, P = 0.8335 and ρ = −0.3187, P = 0.08609, respectively). The preference for agriculture shows a moderate positive correlation with regional preference (ρ = 0.5088, P < 0.005) and grassland is strongly positively correlated to the regional preference (ρ = 0.6444, P < 0.0005).

3.5 Restoration

Ninety-three percent of landowners (n = 28) are willing to restore Araucaria forest at the expense of Campos grassland (Q9 from questionnaire), versus an almost equal 90% (n = 27) willing to restore grassland at the expense of forest (P = 1). Landowners consider on average transitioning 36% of hypothetical full forest cover on their property to Campos grassland, while landowners consider converting 32% of hypothetical full Campos cover to Araucaria forest (P = 0.5451). However, given the choice of restoring either Campos grassland or Araucaria forest on their current property (Q8 from questionnaire), the majority of landowners (67%, P = 0.02415) would rather restore Campos grassland than Araucaria forest. There is no strong negative correlation between the desire to restore the native grassland vegetation and the observed/perceived decrease in Campos grassland (ρ = −0.09485, P = 0.6245). Two out of 30 landowners did not select either native landscape types for restoration. The results from Q10 show that compensation for converted croplands does not vary signiﬁcantly between Araucaria forest and Campos grassland (Fig. 4.2).

4 Discussion

In past decades, restoration ecology has gained popularity in Brazil [48]. Restoration ecology presents many challenges from environmental, social and economic perspectives. Our study oﬀers insight into managing land use and behaviour that contribute to ecosystem transformations.

94 Figure 4.2: Required incentive to convert cropland to native vegetation. Q10 asks landowners how many Reals (R$) per hectare are required to consider converting cropland to native vegetation on their property. No landowners would restore native vegetation on their property without an incentive. Forty percent of landowners would restore both native vegetation landscapes for R$2000 (approx. US$765) to R$10000 (approx. US$3825) per hectare converted. The greatest proportion of landowners require more than R$10000 (approx. US$3825) per hectare converted to establish native vegetation (46% for grassland, 43% for forest). Some landowners would not restore native vegetation on their property for any amount of money (13% for grassland, 17% for forest)

95 The literature indicates that landowners tend to prefer agricultural land use [5] and grasslands for their ability to support livestock production [21]. Furthermore, the current value of one hectare of grassland is approximately five times greater than the same area of forest (R. Printes, personal communication). Despite the vast majority of the written comments stating a preference for native Campos grassland and agriculture for their ability to generate greater profits and productivity, Araucaria forest comprises the highest average composition in the region and there has been a decrease in Campos grassland over the past decades. This could be a result of the perceived benefit from forest ecosystem services or the laws that promote forest conservation and prohibit logging of the native Araucaria forest. Seventeen percent of landowners stated ecological services as a reason for maintaining forest, as well as the attraction of tourists. From landowner responses, we deduce that ecosystem services influence land management practices, in agreement with the ecosystem service hypothesis. Forest transition in Brazil generally results from urbanization, industrialization, conservation, agricultural demand, rural exodus or land value changes [49]. Many studies have described forest encroachment into adjacent grasslands [8,9,44,50]. For- est encroachment provides a well-founded explanation for the decrease in grassland and the increase in both native and exotic tree species in the region. Seed dispersal and germination are very effective at expanding over nearby grasslands [51], especially as the climate becomes warmer and moister with increased carbon dioxide in the atmosphere. The change in legislation that prohibits the logging and export of A. angustifolia and encourages conservation appears to have slightly increased the native forest cover in the region. Furthermore, it has been suggested that fire suppression in the region is an important contributor to the expansion of forest cover [9]. Plantations were the only landscape type to experience a significant increase in the last 30 years. Lang [20] noted an increase of 92.4% in plantation area, consisting mostly of Pinus sp. in the Campos de Cima da Serra region (subtropical highland grasslands, northeastern Rio Grande do Sul). We suggest that the government and private industry incentives for the cultivation of exotic species prompted an increase of silvicultural activities in the area. In addition, the forestry industry strongly influences the bans placed on fire (R. Printes, personal communication), favouring the development of plantation trees. There has been a marked increase in recent years of plantation land use, contrary to the average landowner‘s preference to reduce the composition of tree plantation on their property. Plantation land use is significantly less preferred than any other landscape type, possibly as a result of the high discount rates on timber in Brazil, which can make monoculture plantations economically unviable when considering production costs and profits [52,53].

96 The decrease in agricultural land use could be evidence of intensified law enforcement over the years noted by Soares-Filho et al. [7] or marginal growing conditions on the slopes south of SãoFrancisco de Paula, causing landowners to abandon agriculture practices. Historically, agribusiness has taken advantage of weak enforcement and ineffective monitoring [54]. When discussing the reasons for changing their land use, most of the landowners made changes that generated greater profits, while some landowners remarked a change in legislation that prohibited logging and certain management strategies. Grazing and fire as maintenance strategies for grasslands are not approved by the Brazilian conservation policy in protected areas [21], though fire use for land management is allowed on the majority of grasslands with permission from the municipal government [55]. For the small percentage of grassland in protected areas, the ban on grazing and fire could contribute to the observed decrease in Campos grasslands [56]. Numerous studies have demonstrated the impact of human behaviour on landscape transitions either directly through preference for a given vegetation type and management strategies or indirectly through climate change [36, 50, 57, 58]. The amendments to the BFC and other conservation initiatives at the state level for Rio Grande do Sul provide some insight into the shifts in resource and ecological services perceptions over the decades. This study aims to determine what drives decision-making. The questionnaire shows that landowners are much more likely to seek information from individuals with similar experiences. The perceived change in composition within a 5 km radius surrounding the properties slightly influences the preference for the landscape type; however, the change in native vegetation composition on individual properties does not appear to be affected by the changes in the region. Human decision-making follows a set of valuation processes, in which individuals often select the outcome with the greatest perceived utility, the most immediate return and the greatest degree of certainty [40, 59]. Our results are consistent with decision-making practices described by Rangel et al. [59] and Moser [40]. From our results, it is not possible to make any conclusive remarks on the use of rarity-based decision-making practices in the region; we argue that the region has not experienced significant enough declines in native vegetation cover to generate concern that would be reflected in the questionnaire. The high discount rates in Brazil decrease gains from timber and often preclude scarcity conservation [47, 52]. There is a significant difference in composition and preference for Araucaria forest compared with plantations (P = 0.001261), despite the greater profits from non- native plantations [60], which reflects landowner conservation values for native forests. The Campos grasslands are important to the gaucho culture and provide significant income to the region [20, 21], which is consistent with landowner comments. From

97 landowner responses, we infer that landowners maintain land that generates the most profit while adhering to laws and regulations. From the collected data, we gather that the preferred landscape on an individual property reflects the desired composition in the region and the information given about the region does not change the preference of landowner’s composition. We argue that landowners in the region have a good understanding of the land composition in their region and thus the information given about the area had no impact on their preference because they were already aware of the regional ecosystem composition. The landscape composition of the region is similar to the average and mode compositions on individual property, which may suggest imitation behaviour. Rates of transformation and degradation are not uniform throughout Rio Grande do Sul [10]. The majority of southern Rio Grande do Sul falls within 80-100% compliance with the 2012 BFC [7]. The region of our study showed an over 80% compliance with the 2012 BFC and within this region landowners were shown to maintain between 0.8 and 3 times the required native vegetation. Similarly, our results indicate that the composition on each individual property varies widely, while 93% of landowners maintained at least 20% combined native vegetation. Considering the state of RS has a surplus of 664,000 ha of land in the Atlantic Forest biome, with the potential to be converted from native vegetation to other land uses and 3 million surplus ha of land in the Pampa biome [7], we reason that the 7% of landowners with less than 20% LR may legally be permitted to maintain a lower composition of native vegetation through the Environmental Reserve Quota; whereby, landowners can trade their excess required native vegetation quota with others, in the same biome, that failed to meet the LR [7]. One very clear pattern that emerged from the respondents is that restoration can be costly and large incentives are required by landowners to restore native vegetation at the expense of croplands. Strict regulations can result in compliance issues, as seen by increasing the LR requirement [27]. From the comments on the question- naires it is evident that land productivity and profit are important to landowners, we argue more important than restoring native vegetation. Landowner responses concerning the amount required for restoration indicate that restoration is viewed as selling land to conservation authorities. The average cropland is valued at approximately R$ 9500 (approx. US$ 3625) [61](, whereas forested land is valued at R$ 1000 (approx. US$ 380) and grassland at R$ 5000 (approx. US$ 1910) (R. Printes, personal communication). Our work suggests that landowners wish to profit from restoration initiatives or reclaim lost revenue from cropland conversion. The majority of landowners would rather restore native Campos grassland on their property at the expense of croplands since grasslands inherently support ranching practices,

98 the sole income for many of the landowners. Conversely, landowners demonstrate equal willingness to restore both native ecosystems at the expense of the other in the hypothetical situation.

5 Conclusion

This analysis provides useful information for policy-makers by quantifying changes in land management and preference of land use in SãoFrancisco de Paula over the past decades. We must take into consideration that surveyed landowners maintain properties in the region with the highest composition of native vegetation and thus are likely to be in compliance with land management regulations. While the collection of landowner knowledge has some inherent bias it does not appear to include deliberate misinformation, the results are consistent with landscape changes noted in other studies of the region, as well as changes in policy [7, 21, 56]. The major study results indicate that there is no preference for either of the native vegetation types, in agreement with our null hypothesis. In addition, we find that landowners have no significant preference for the proportion of landscape composed of agriculture over native vegetation, while plantations are clearly less desirable than any other landscape. From landowner written responses, we conclude that land productivity and profit are priorities for the majority of landowners. However, maintenance of ecosystem services also influences the decision-making of many landowners. Sampling of other landowners’ preferences further influences individuals, while the proportion of native vegetation does not seem to be low enough to test the scarcity hypothesis. Restoration of native vegetation is not a priority of landowners and any form of restoration would require a financial incentive. Our results suggest that the economics of restoration and conservation are crucial to the success of policies and the maintenance of native ecosystems. The responses of landowners to the questionnaire give an indication of when changes in legislation have occurred and whether or not they were successful. Landown- ers in the region of SãoFrancisco de Paula show a high compliance with regulations and this in turn appears to maintain some level of conservation of the native vegetation. Reflecting on past land management strategies and adapting future policies to include information on landowner preferences can circumvent unsuccessful strategies and promote positive changes [62]. The data collected on land composition in the region enhance our understanding of land management strategies and vegetation composition for future fire regulation policies. The results will be used in future analysis to parameterize land use behavioural models.

99 Acknowledgements

This project was funded by the Natural Sciences and Engineering Research Council of Canada and the James S. McDonnell Complex Systems Scholar Award.

100 References

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106

SCHOOL OF ENVIRONMENTAL SCIENCES UNIVERSITY OF GUELPH GUELPH, ON, CANADA

- QUESTIONNAIRE FOR SOCIOLOGICAL SURVEY -

Project title: Coupled human-environment system dynamics and alternative stable states in complex mosaic ecosystems

107

Guide to the interviewer:

This questionnaire is part of a research project under the coordination of the University of Guelph, Canadá, and in collaboration with the Universidade Estadual do Rio Grande do Sul, Brazil (UERGS). The cover letter attached to this questionnaire presents a more formal introduction and detailed information of the research project. The cover letter must be read to and discussed with each participant. A copy should be left with each participant, and proper explanations and clarifications should be given if required. If employees are being approached, care must be taken that there is no pressure to take part on part of the employer – nor should the employer receive any identified data. Bellow is some general information to guide you for the application of this questionnaire.

Main objectives: The main objective of this questionnaire is to know what is the people’s perception about conservation values (including sustainable use) of natural ecosystems, relative to their abundance in the region, and how this perception change considering possible past and future landscape compositions.

Where to apply the questionnaire: South Brazilian plateau in northeastern RS, Brazil (Planalto das Araucárias). 30 properties should be selected among those with higher proportions of remaining areas of natural mosaics between Campos and Araucaria forest in the region of São Francisco de Paula.

Target: Interviews should be applied preferably to the landowner of the properties.

108 Introduction:

(To be read/explained to the respondents, before starting the questionnaire)

Araucaria forest (i.e., not planted) and Campos grasslands (not planted, but could still have grazing by cattle which we consider to be “natural”) are the two original native vegetation types in the region, and in some areas they have been coexisting side by side for centuries, forming mosaics in the landscape (show Figure 1).

However, the occurrence of both ecosystems in the region has been reduced very fast over the last centuries, to account for the necessity of using the land for other purposes (e.g. agriculture, forestry, planted pastures, etc.). Therefore, we would like to know how you perceive these changes and interact with the natural environment, how you share your experiences with other people about land use, and what your opinion is about the importance of the conservation of native (i.e. unplanted) ecosystems. Ten questions will be asked in the following questionnaire. There are no right or wrong answers. We only want to know your opinions.

109

Figure 1: Native vegetation types and their occurrence in the region (area of São Francisco de Paula).

A. Native forest (Araucaria forest) B. Forest-grassland mosaic C. Native grassland (Campos)

110 Q1. What is the current landscape composition your property?

[Interviewer should make sure these add up to 100%]

% native Campos grassland: ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Please explain the land-use if there is agriculture or tree plantation (e.g., type of crops or tree species planted):

Q2. Which landscape composition do you prefer on your property (if different from Q1) and why?

[Interviewer should make sure these add up to 100%]

% native Campos grassland : ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Why do you prefer this composition?

______

111 Q3. Have you been on your property for more than 10 years? If yes, was there a time in the past 10 years when you….

A) preferred a different landscape composition? If so, what was it?

[Interviewer should make sure these add up to 100%]

% native Campos grassland : ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Why do you prefer this composition?

______

How many years ago did you change your mind?

______

B) actually had a different landscape composition? If so, what was it?

% native Campos grassland : ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Why do you have this different composition?

______

How many years ago did you change your landscape composition?

______

112 Q4. When deciding about land use on your property (e.g. change management or change land use activity), do you ask someone for advice (e.g., neighbor, parents, cooperative members, etc)?

Yes -> With whom do you usually talk about it?

What is his/her profession? ______

In a scale of 1 to 5 (1 = not at all influential; 5 = very influential), what is the influence of this opinion in your decisions? ______

No -> What kind of other sources of shared information available most influence you on this decision (e.g. TV, radio, newspaper, internet, etc):______

In a scale of 1 to 5 (1 = not at all influential; 5 = very influential), what is the influence of this information in your decisions? ______

Q5. What change have you been noticing or heard about in the 5km radius of your property?

[interviewer should circle their responses below].

Land cover of native Campos grasslands increased/decreased/stayed the same. Land cover of native Araucaria forests increased/decreased/stayed the same.

113 Q6. According to recent studies, in this region (300 km2 around São Francisco de Paula) the landscape composition is:

% native Campos grassland (including areas grazed by cattle): 30% % native Araucaria forest: 25% % other human land use (agriculture and/or plantation) : 45%

Considering this information, does your preference indicated in Q2 change? If so, which landscape composition would you now prefer?

[Interviewer should make sure these add up to 100%]

% native Campos grassland : ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Why do you prefer this composition?

______

114

Q7. What is your preferred landscape composition in the region (area of São Francisco de Paula)?

[Interviewer should make sure these add up to 100%]

% native Campos grassland : ______%

% native Araucaria forest: ______%

% agriculture: ______%

% non-native tree plantation: ______%

Why do you prefer this composition?

______

115

Q8. Suppose you wanted to restore natural vegetation on your land, which would you prefer to restore?

Native Araucaria forest Native Campos grasslands

Q9. Suppose on your property the only natural vegetation is native Araucaria forest. If this were the case, do you think Campos grasslands should be restored on your property at the expense of native Araucaria forest? If yes, how much (in % relative cover)?

______

Suppose on your property the only natural vegetation is native Campos grassland. If this were the case, do you think Araucaria forest should be restored on your property at the expense of native Campos grassland? If yes, how much (in % relative cover)?

______

[interviewer, please make sure they answer both of the questions above]

Q10. If you have/had a crop on your land (agricultural or tree plantation), how much would money per hectare would you accept to convert your cropland into

A. native Araucaria forest? ______

If you don’t have a specific value in mind, please answer one of these:

a) < R$2000 b) R$2000-5000 c) R$5000-10.000 d) >R$ 10.000

B. native Campos grassland (could be with cattle)? ______

If you don’t have a specific value in mind, please answer one of these:

a) < R$2000 b) R$2000-5000 c) R$5000-10.000 d) >R$ 10.000

116 Cover Letter

We thank you for agreeing to participate in this research. This research is being coordinated by the University of Guelph (School of Environmental

Sciences), Canadá, and in collaboration with the Universidade Estadual do Rio

Grande do Sul, Brazil.

The main objective of this research is to predict how the landscape in this region will be in the future, by the analysis of the interactions between the natural environment and human’s decisions about land use. For this, we would like to know how you perceive and interact with the natural environment, how you share your doubts, knowledge and experiences with other people about land use, and what is your opinion about the importance of the conservation of native (i.e. unplanted) ecosystems.

All these questions will be asked in the following questionnaire, and would take approximately 30 minutes. There are no right or wrong answers, we only want to know your opinions, and you can decline to answer any question(s). There will be no risks, discomforts and/or inconveniences to you

(including physical, psychological, emotional, financial and social) on participating in this survey.

Your participation in this research is very important and the results can help you and the local community to plan long-term sustainable managements that guarantee community benefits by land use, in a way that preserves its natural state for future generations. Research findings will be available in the public library or local partner institution (UERGS library) closest to you.

All the information obtained with this questionnaire will be used only for research and teaching purposes, and we ensure the confidentiality of all your personal information to the best of our ability.

117 The project has been reviewed and received ethics clearance through the University of Guelph Research Ethics Board. If you have any questions regarding the use and safety of human subjects in this research project you may contact S. Auld, Director, Research Ethics, 519-824-4120, ext. 56606, [email protected].

Sincerely,

______Prof. Madhur Anand, project coordinator School of Environmental Sciences University of Guelph

Contact information:

Madhur Anand (principal investigator) School of Environmental Sciences, University of Guelph. 50 Stone Road East. Edmund C. Bovey Building, Room 2241. Guelph, ON, Canada. N1G 2W1. Phone: 519-824-4120 x56254 e-mail: [email protected]

Chris Bauch (co-investigator) Department of Applied Mathematics, University of Waterloo. 200 University Avenue West Waterloo, ON, Canada. N2L 3G1. Phone: 519-888-4567 ext. 32250 e-mail: [email protected]

Rodrigo Cambará Printes (co-investigator) Laboratory of Environmental Management and Negotiation of Conflicts. Universidade Estadual do Rio Grande do Sul. Rua Assis Brasil, 842. São Francisco de Paula, Rio Grande do Sul, Brazil. CEP: 95400-970. Phone: +55 54 99260351 e-mail: [email protected]

118 Chapter 5

Seeing the Forest for the Grasslands and the People: Sustainability of Coupled Human-Environment Mosaic Ecosystems

Kirsten A Henderson, Madhur Anand, Chris T Bauch

Review process in Proceedings of the National Academy of Sciences

Key Words: human-environment coupling, forest-grassland mosaic, ecosystem services valuation, rarity-based and proﬁt-based decision-making

119 Abstract

We model the influence of human behaviour, through the valuation process of natural ecosystems and land conversion, on natural forest-grassland mosaics interspersed with agriculture and silviculture in southern Brazil. These natural forest-grassland mosaic ecosystems have previously been explored with respect to the existence of alternative stable states, driven by recruitment threshold responses to fire and moisture regimes. However, the pervasive expansion of human dominance means that the relatively few natural ecosystems that remain (both the forests and the grasslands) are being extremely threatened, thus models should couple human-environment interactions to gain an understanding of the processes driving change in these systems. The addition of human influence into a system driven by threshold responses, such as forest-grassland mosaics, could lead to unforeseen outcomes or even catastrophic changes. We use empirical data on profits and discounting processes, in addition to questionnaire results related to landowner preferences and conservation values, to parameterize our non-linear dynamical model. We find that, in addition to recruitment thresholds, rarity-based valuation can lead to bistability in the forest-grassland mosaics of southern Brazil. The use of decision-making factors, such as conservation values, discount rates and discount time horizons, allow us to show that in the current state, we are at a critical point, where the valuation of natural ecosystems has an important role in determining whether the natural ecosystems will be maintained or if converted land will dominate in the future.

1 Introduction

Historically, humans have often manipulated their environment beyond sustainable levels, leading to local or regional collapses in resources or even civilizations [1–3]. The current paradigm of the human-environment relationship is a dominant one- way deleterious impact of humans on natural ecosystems (Fig. 5.1a) [4]. Human activities, including agriculture, forestry and livestock management, contribute to widespread conversion of natural ecosystems to cultivated areas at the expense of ecosystem services [5, 6], and as human populations continue to expand, the scope and magnitude of human inﬂuence on natural ecosystems also grows [7]. While it is clear that this negative paradigm needs to be superceded [4,8], it has been argued that this can only happen through understanding the coupled nature of human behaviour and ecosystem dynamics [9–13]. As much previous research on human-environment systems has found, the importance of human behaviour in conservation biology is undeniable, suggesting that an integrated human-environment

120 Figure 5.1: Human-environment coupling. The negative relationship between humans and natural ecosystems is driven primarily by competition with agricultural land (a). Alternatively, sustainable human behaviour (i.e., valuation of natural ecosystem services) leads to positive changes in natural ecosystems when natural ecosystems are rare (b), whereas the perception of abundant natural ecosystems results in a decreased desire to conserve natural ecosystems. approach is necessary for successful conservation [14–17]. Human-environment interactions can occur when humans are motivated not only by consumption, but also by endangerment of species and ecosystems, and ecosystem services valuation and their related policies and subsidies [18]. This can in turn have a positive impact on natural systems. For example, when natural land becomes rare, individuals and institutions (i.e., policies and subsidies) support conservation (positive feedback) (Fig. 5.1b). Once the natural system is restored to a certain level, it may no longer remain a conservation priority, allowing for greater resource extraction (negative feedback). This negative feedback loop is exemplified by the process of sustainable forest management (e.g., protected areas, harvesting limits, reforestation projects, import regulations), but can also occur in other human-environment systems (e.g., fisheries, hunting quotas, endangered species recovery) [19]. One well-known case is the recovery of the dry tropical forests of Costa Rica. Similar to many tropical countries, Costa Rica experienced rapid deforestation for agricultural development and cattle ranching. However, Costa Rica is notable in its vigorous implementation of national conservation policies to restore forests, including payments for environmental services, protected areas and restrictions on timber extraction [20, 21]. While regional and national successes are evident, many other natural areas of the tropics and subtropics remain a conservation priority because of overwhelming endangerment and a poor understanding of coupled human-environment systems [22,23]. When natural ecosystems occur as alternative stable states, an understanding of human-environment relationships can become even more complicated [24]. One such example is forest-grassland mosaics (Fig. 5.2), where natural grassland and natural forest coexist, and can alternate in dominance over time based on positive feedbacks in threshold responses to disturbance regimes [12,25–28]. Pollen and charcoal records reveal vegetation changes following climate shifts and environmental condition shifts on a millennial time scale, while human activities can cause dramatically different

121 Figure 5.2: Bistability in forest-grassland-silviculture system. The above image (a) depicts a natural mosaic in southern Brazil without human influence, where dominant Araucaria forest (F ) or dominant Campos grassland (G) are alternative stable states. The image below (b), is an example of bistability in a mosaic of natural forest (F ) and natural grassland (G) with converted land (agriculture, A). The alternative stable states are dominant converted land (agriculture and/or silviculture, F GA) and dominant forest (FG). states within centuries [29–31]. The expansion of human influence (both positive and negative) has the potential to catastrophically impact the stability dynamics of mosaic ecosystems [12,32,33]. In southern Brazil, as in many other parts of the world (e.g., Southwestern Ghats Montane Forests in India, Jos Plateau Forest-Grassland Mosaic in Nigeria), these forest-grassland ecosystems are doubly endangered in the sense that both the natural grasslands and the natural forests are extremely rare [34, 35]. Grassland conservation is often overshadowed by forest conservation, as individuals perceive forest as having higher aesthetic value [22, 36]. Brazil’s Forest Code–the law that protects all natural vegetation in Brazil–reflects this perceived bias in the valuation of forest [36], such that individuals are often unaware or unwilling to protect grassland. In earlier work using a relatively simple model, we suggested that introducing strong human coupling (through harvesting and other human impacts) removes bistability in these mosaics [12]. Other researchers have also pointed out that attempting to manage natural ecosystems without appreciating the potentially large role played

122 by alternative stable states may lead to unforeseen collapses in ecosystems because of the presence of tipping points [29]. Therefore, in systems where both bistability and strong human influence are present, there is value in developed coupled human- environment system models. With increased awareness of the possible effects of human interventions, we can examine sustainability in the context of both naturally- occurring and human-influenced catastrophic regime shifts. Here we couple human social dynamics, in terms of imitation, conservation values and economic gains, with an ecological model of a forest-grassland mosaic. The objective of this work is to understand the dynamics arising from coupling between decision-making about land conversion (a complex process which considers both human values and economic gains) and bistable mosaic ecosystems, and draw conclusions about potential land use policy implications. We investigate how this coupling might lead to outcomes that cannot be understood when these systems are considered in isolation. We evaluate the effectiveness of conservation values, discount rates and discount time horizons at maintaining natural mosaics. We use empirical data and questionnaire results from a human-dominated forest-grassland mosaic system in southern Brazil as a case study to parameterize our model. Modelling approaches for nonlinear dynamical systems vary across a spectrum from simple dynamical models that can be analyzed by pencil and paper (or chalk and chalkboard) to detailed statistical models and spatially explicit, stochastic, agent-based models. Simple dynamical models allow us to explicitly describe underlying mechanisms in complex biological systems, thereby ”enabling meaningful comparison between the consequences of basic assumptions and empirical facts” and allowing space for a par- simonious description to emerge, although oversimplification may prevent researchers from answering ecological questions [37]. Most coupled human-environment systems models are relatively detailed agent-based models, whereas differential equation models of intermediate complexity are seldom used. Because of this gap in the ”ecology” of human-environment system models, and according to the data that were available to us, we opted to develop a differential equation model of intermediate complexity. The model is described in the following section.

2 Materials and Methods

2.1 Study System

The dominant land cover of the southeastern Brazilian highland region has historically alternated between forest and grassland with changes in climate and greater human inhabitance (i.e., ﬁre and grazing) [25,38]. Paleoecological records provide an

123 historical range of vegetation patterns and natural disturbance regimes, which are used to infer potential multiple stable states. The forest-grassland mosaics of southern Brazil (23◦ to 30◦ S and 55◦ to 48◦ W) are among the most diverse in the world [25]. The Campos grasslands and the Atlantic forest are rich in species diversity [39, 40]. In addition the Atlantic forest is host to many endemic species including the endangered Araucaria angustofolia tree species. Over the past 30-60 years, converted (agriculture and/or silviculture) land use has expanded into these ecological hotspots of southern Brazil [25,39]. This provides an opportunity to study a natural mosaic ecosystem under rapidly evolving (and growing) human inﬂuence. Thus the Campos-Araucaria mosaic constitutes an important case study for anthropogenically disturbed mosaic ecosystems.

Figure 5.3: Conceptual diagram of model. Land states in our study region include: forest (F ), grassland (G), or converted land (agriculture and/or silviculture, A). Green arrows represent environmental drivers (natural disturbance (ν), recruitment (r(F,G)) (eq.(4)) and abandonment (aF , aG) in eqns.(1,2,3) and black arrows represent human drivers (penalties (pB, eq.(8)), proﬁts (pF ,pG,pA, eqns.(7,8)) and conservation values (qF , qG, eq.(7)).

2.2 Environment (Land-Use & Natural Dynamics) Model

We build on previous models of forest-grassland dynamics [12,41,42], where biophysical processes regulate changes between grassland and forest. We model transitions between forest (F ), grassland (G) and converted land (agriculture and/or silviculture, A), based on landowner preference for each F , G, or A. A conceptual diagram of the model is presented in Fig. 5.3 and the equations for land cover dynamics are: dF = r(F,G)FG − vF + J(x )F (1 − F ) − J(x )FG − J(x )FA + a A, (1) dt F G A F

dG = vF − r(F,G)FG + J(x )G(1 − G) − J(x )GF − J(x )GA + a A, (2) dt G F A G

dA = J(x )A(1 − A) − J(x )AF − J(x )AG − a A. (3) dt A F G G 124 Parameter definitions and baseline values are provided in Table S1. Landowner preferences are reflected by the quantities xF , xG, and xA, representing the proportion of the landowner population preferring more forest (forest-preferrers), grassland (grass- preferrers), and converted land (convert-preferrers) on their property, respectively, compared to current land composition. In the fully coupled human-environment system, these quantities become model variables (see next section). Natural processes governing change in natural land cover are the recruitment rate (r(F,G)) and natural disturbance rate (ν). Abandonment and reversion of plantation to forest cover (aF ) and crops to grassland (aG) occur at a constant rate. J(xi) is the land conversion rate as a function of landowner preferences xi for land cover i, where i = F, G, A. All land cover is assumed to be composed of either forest, grassland or converted land (agriculture and/or silviculture), such that A + F + G = 1. We can therefore always obtain A from the relation A = 1 − F − G, and only need to solve equations 1 and 2. We use a sigmoidal function to represent the recruitment rate, whereby recruitment of forest is high when F > 0.4 and low when F < 0.4, reflective of the fire threshold limiting recruitment [12, 43]. The recruitment function is parameterized using data on soil moisture content (S) and forest cover (F ) (see SI: Materials and Methods for details): α r(F,G) = . (4) 1 G − ψ 1 + e ω ( F +G β(0.5−S) ) The maximum potential recruitment rate, α, is limited by environmental conditions and herbivory [44, 45]. S represents the soil moisture content of the region or land patch [46]. ψ is the grassland proportion, which yields 50% maximum potential recruitment, in the absence of moisture influence. ω controls the overall steepness of the recruitment curve and β is a conversion factor for fuel moisture.

2.3 Human Behaviour Model

Conversion of rural land is greatly influenced by values associated with the landscape [47]. Human influence on land cover dynamics (see below, eq. 9) is modelled as a function of landowner preferences for land cover i (i = F, G, A), xF , xG, and xA (see previous subsection for definition). Landowner preferences and parameterization of the human behavioural model are gleaned from questionnaire responses [48]; details are provided in SI: Materials and Methods. The behavioural model equations are given by dx F = sx x u (F ) − u (G) + sx (1 − x − x )u (F ) − u (1 − F − G), (5) dt F G F G F F G F A

dx G = sx x u (G) − u (F ) + sx (1 − x − x )u (G) − u (1 − F − G). (6) dt G F G F G F G G A 125 We note that xA = 1 − xF − xG, hence an equation for xA is not needed. Also, we have used A = 1 − F − G. s is the rate at which landowners sample others and adopt their preference, if the utility for changing preferences is higher. The value of F and

G are described as utilities via the term uj(j), where j = F,G. uj(j) reﬂects both economic (pj) and non-monetary gains (qj) according to

n m X 1 k X 1 k uj(j) = qj(1 − j) + pj . (7) 1 + dc 1 + de k=1 k=1 Human behaviour is in part driven by the perceived future gains for their present actions [42,48,49], prompting the use of a discount factor. de is the economic discount rate [50, 51] and dc is the conservation discount rate. We assume dc < de (see SI: Materials and Methods for discussion and justiﬁcation) [52,53]. The discounting time horizon m and n are the amount of foresight applied to decisions for economic and conservation utilities, respectively [15,54]. The decision to convert natural land into agriculture and/or silviculture is determined by economic gains and compliance with minimum natural vegetation requirements. The function was parameterized using data on proﬁts from crops (pcr) and plantations (ppl) and penalties (pB) for not adhering to Brazil’s Forest Code. The converted land utility is given by

m X 1 k uA(1 − F − G) = pcr + ppl − pB(0.2 − F − G). (8) 1 + de k=1 pB = pB(F,G) is a piece-wise function, such that when the legal reserve requirements are met by landowners (F + G ≥ 0.2), pB(F,G) = 0. Annual profits from plantation (ppl) depend on the stage in the harvest rotation cycle. Parameterization and plantation profit details are given in SI: Materials and Methods. Landowner behaviour rationale is described in terms of innovation and imitation [55, 56]. The diffusion of practices among individuals follows a sigmoidal curve as the initial proportion of adopters is minimal, but gradually gathers momentum as individuals imitate others [55] (see SI: Materials and Methods). J(xi) represents land conversion of land state i: ρ J(xi) = . (9) 1 + e(X−xi)/τ ρ is the maximum potential influence of landowners, X is the threshold proportion of landowners preferring land cover i for which land conversion J(xi) is 0.5ρ, and τ controls the steepness of the curve.

126 2.4 Analysis

We construct parameter planes for conservation values (qF , qG), discount rates (de, dc) and discount time horizons (m, n) to determine the land state dynamical regimes for a range of initial conditions after 1000 years. Each simulation is run under weak, moderate and strong human influence, to show varying degrees of human-environment interactions. For details on parameter ranges for our base case (SãoFrancisco de Paula) see SI: Materials and Methods. Model simulations use ode45 in MATLAB (ode15s was used to check for consistency) (details in SI: Appendix). We use a burn-in time of 5000 years to allow sufficient time for damped oscillations to settle down to an equilibrium state. After 5000 years, model simulations indicate either an equilibrium point or stable limit cycles. After burn-in, the time series were used to confirm land cover dynamics at various points in the parameter planes and at the edges between land states.

3 Results

3.1 Base Case

At the base case parameter values, in the short term (100 years), the model predicts that land conversion will continue to grow over the next 40 years at the expense of forest (F ) and grassland (G) (Fig. 5.4). Converted land (A) increases to just above A = 0.8, after which the compliance penalty and the rarity of natural landscapes motivates an increase in conservationist behaviour and therefore a decrease in the value of A below that of F and G. Interestingly, the prevalence of landowners preferring forest (xF ) increases more strongly than the prevalence of landowners preferring grassland (xG) over this period, despite the proportion of F and G not being different and despite F being the least profitable land state. As a result, F and G eventually return to approximately 40% cover, at which point they are no longer perceived as rare or endangered and the cycle continues. The large fluctuations in xF are due to the negative feedback loop, which increases xF when F becomes rare and forest conservation values (qF ) are high (Fig. 5.1b). The preference for grassland (xG) and converted land (xA) are moderated by constant profits, so that their oscillations are less dramatic than the oscillations for xF . Also, the amplitude of oscillations in xF and xG exceeds that of the landscape cover (F,G). This is a reflection of social dynamics occurring at more rapid timescales than forest dynamics. In our questionnaire responses [48], we observe that landowner preference is not always reflected in actual land-use, but there is a correlation between preferred and actual land composition.

127 Figure 5.4: Base case landscape. In the short-term, our study region continues to exist in an unstable forest-grassland-converted land (F GA) state. The proportion of forest (F ), grassland (G) and and converted land (A) are determined by landowner preference for forest (xF ), grassland (xG) and converted land (xA). The preference is driven by utility (i.e. conservation values and proﬁts). Table S1 gives parameter values for the time series simulation.

Consistently, the oscillations in F ,G and A shadow oscillations in xF , xG and xA, following a lag of 15-20 years Fig. 5.4.

3.2 Changing Conservation Values

Increasing the conservation value of forest (qF ) has less predictable consequences on forest cover (F ) and a larger increase is required to conserve F than attempting to conserve grassland (G) by increasing its conservation value (qG) (Fig. 5.5). Under moderate and strong human influence, increasing the conservation value of grassland beyond qG = 0.03 causes a change from converted land (A) to a state where G can coexist with A (and, in the case of weak human influence, with F as well). In the case of increasing qF , there exists a critical threshold at qF = 0.09, below which F is non-existent (Fig. 5.5b,c). Additional increases in qF can actually result in the exclusion of F (for moderate and strong human influence). This occurs because extreme oscillations can put the proportion of humans preferring forest (xF ) close to zero, risking the extinction of this sub-population. These dynamics exemplify the law of unintended consequences.

Moreover, increases qF can result in an increase in both natural states (F and G) as increased utility for natural vegetation outweighs the utility from A. G is both profitable and culturally significant, which increases the likelihood of being in a G state for all scenarios (Fig. 5.5). In contrast, F relies upon rarity-based conservation feedbacks due to lack of profitability and therefore, F is more susceptible

128 Figure 5.5: Increasing the grassland conservation value (qG) leads to landscape compositions with grassland (G), for all conservation values, except qG < 0.03 and qF < 0.09, for all human inﬂuence scenarios (a) weak, b) moderate, c) weak). Natural forests (F ) rely on forest conservation values (qF ) to increase the utility of F , therefore qF must be large enough to counterbalance the utility of (G) and converted land (A). The small white x (subpanel b) marks current conditions in our study region of S˜aoFrancisco de Paula.

129 to temporal variability and the types of dynamics observed in the parameter plane as qF increases. Conservation values are not the sole factor maintaining natural forest- grassland mosaic systems. Since utility is the dominant force in the system, discount rates and discount time horizons have an important role in determining vegetation cover, which we will see in the next sections.

3.3 Changing Economic and Conservation Discount Rates

We find that increasing economic discount rates (de) can dampen oscillations and regenerate natural landscapes, because future profits from land conversion are not strongly influential. In contrast, low de and very high conservation discount rates (dc) increase the tendency of land cover towards converted land (A), because long-term value from conservation efforts is not strongly influential (Fig. 5.6). Both de and dc are equally important in determining the landscape dynamics. The landscape cover depends on the ratio between d and d . When de 6, A dominates, otherwise the e c dc . de natural ecosystem mosaic (FG) dominates. When dc ≈ 5, the landscape tends to a combination of FG and A, either as bistable states, in the case of weak human influence (Fig. 5.6a), or F GA limit cycles, for strong and moderate human influence scenarios (Fig. 5.6b,c). Although dc is probably less than de, it is not clear on which side of the threshold human populations fall. Moreover, the discount time horizons (m, n) alter the threshold ratio for discount rates.

3.4 Changing Economic and Conservation Discounting Time Horizons

Similar to discount rates, the inclusion of a long conservation discount time horizon (n) can maintain and improve natural landscapes (Fig. 5.7). In addition, long n reintroduces bistability for the strong human influence scenario (Fig. 5.7c). Instead of being driven by recruitment, as in the natural mosaic without converted land, long n drives changes in natural landscapes through rarity-based decision-making. When F or G is rare, n increases the utility of natural states above that of converted land, which in turn increases the preference for natural landscapes (xF , xG) and at strong human influence landowner preference is reflected in landscape composition. The discount time horizon for conservation (n) has a much greater influence on landscape dynamics than the economic discount time horizon (m). More specifically, a conservation discount time horizon of at least 45 years is required to maintain natural states and n > 70 results in a system dominated natural mosaics (Fig. 5.7a,c). Economic discount time horizons are comparatively less important since here we assume profits to be constant over time, except for plantation forest (which is on a 7

130 Figure 5.6: Economic discount rates (de) six times greater than conservation discount rates (dc) promote a landscape with forest and grassland (FG) and de/dc ¡6 results in a landscape dominated by converted land (A or F GA), for all human influence scenarios (a,b,c). Moderate human influence (b) has an additional region of GA limit cycles when G has the highest utility. Weak human influence (a) results in equilibria states and FG for all possible discount rates, whereas moderate (b) and strong (c) human influence scenarios result limit cycles and A only stable state. The small white x (subpanel b) marks current conditions in our study region of SãoFrancisco de Paula.

131 Figure 5.7: A conservation discount time horizon (n) less than 45 years promotes a landscape dominated by converted land (A or F GA), for all human influence scenarios (a,b,c). Longer conservation time horizons promote natural landscapes. Weak human influence (a) results in equilibria states and FG for all possible discount rates, whereas moderate (b) and strong (c) human influence scenarios result limit cycles and a converted land only stable state. Strong human influence has an additional region of FG bistability, driven by rarity. The small white x (subpanel b) marks current conditions in our study region of SãoFrancisco de Paula.

132 year rotation cycle). The moderate human influence scenario is an exception, where high m and n values lead to a proliferation in outcomes in the system (Fig. 5.7b; see also next section). The initial conditions strongly influence the landscape composition for the moderate scenario. The system can be driven by rarity, when F is rare the landscape tends to FG and when G is rare the landscape tends to G. Alternatively, when rarity is not a concern for landowners (F > 0.3, G > 0.3), the system can be driven by profits (tends to GA), or recruitment (tends to FG or G).

3.5 Extent of Human Inﬂuence

As mentioned previously, incorporating anthropogenic activity into a natural mosaic ecosystem increases the long-term instability in the system by introducing prolonged oscillatory cycles (Fig. 5.4). In the weak human influence scenario, natural processes counterbalance anthropogenic activities, resulting in dominant natural landscapes and the characteristic bistable dynamics of natural forest-grassland mosaic systems (FG), with the additional outcome of bistability with converted land (F GA, (Fig. 5.5a, Fig. 5.6a, Fig. 5.7a). The most complex interactions occur in the moderate human influence scenario, which allows feedbacks from both natural processes (recruitment) and human values (land rarity, profits, environmental services) (Fig. 5.5b, Fig. 5.6b, Fig. 5.7b), whereas, the strong human influence scenario is primarily driven by the costs and benefits of human values, promoting the expansion of converted land (A) and grassland (G) (Fig. 5.5c, Fig. 5.6c, Fig. 5.7c). Near base case parameter values (for slightly smaller conservation values, lower economic discount rates/higher conservation discount rates, and a longer conservation time horizon than the base case), there exists a stable (A) state with minimal forest (F ) or G (Fig. 5.6b,c, 5.7b,c). In such a state, abandonment (aF and aG) prevents either natural ecosystem state (F or G) from complete extinction, however we interpret this dependence on transient abandonment processes to signify that the natural land cover is relatively degraded. Under moderate and strong human influence, the stable state is converted land, and forests occurs in less than 50% of parameter space (Fig. 5.5b,c, Fig. 5.6b,c, Fig. 5.7b,c). Moderate and strong human influence removes bistability from the forest-grassland mosaic system [12], except for long conservation discount time horizons (n) and short economic discount time horizons (m). Instead, we find that human influence replaces bistability, the existence of alternative stable states, with a stable state and an alternative limit cycle or multiple alternative limit cycles. In the strong human influence case we also exist near a threshold where a slight change in param-

133 eter values can cause a slip into dominance of converted land at the expense of F and G.

4 Discussion

Coupling human and environment models allows us to examine feedbacks between the two subsystems, resulting in dynamics that cannot and should not be studied in isolation, especially for systems under threat by human activities such as mosaic ecosystems. The overarching findings from our simulations show how tightly these systems are coupled and how important feedbacks can be. As Stern [16] states, ‘Environmentally significant behaviour is dauntingly complex, both in its variety and in the causal influences on it’. Dynamical systems approaches using relatively simple models such as the one we explored in this paper can provide a level of clarity regarding feedbacks and complex nonlinear processes that is often harder to capture using agent-based models or econometric models. When data is available to meaningfully parameterize such models, as in the case study presented here, models can provide insight, potentially leading to policy changes. Our analysis finds the southern Brazilian forest-grassland mosaic is in a place where many possibilities may unfold in the future. For instance, a relatively small drop in forest conservation values could easily push the system into a region where forest and possibly also grassland are lost. Similarly, an increase in forest and/or grassland conservation values will support a higher average level of natural land cover, but in the case of forest conservation values, it may also increase the tendency toward unstable dynamics due to the rarity-based feedbacks. Rarity-based feedbacks also contribute to unstable dynamics for small increases in the conservation discount time horizon, while a decrease in conservation discount time horizon could remove forest and grassland from the system. The model predicts that current trends toward more land conversion to agriculture and silviculture is likely to continue, thereby further threatening the natural forest-grassland mosaics. However, we also find that this process can be mitigated through changes in attitude (valuation of ecosystem services) and discounting conservation utilities less than economic gains from converted lands. Our results indicate that cultivating a conservation mindset in the population requires moderate to strong conservation values and foresight (conservation discount time horizon) greater than 60 years. Our results also indicate that the effects of increasing grassland conservation values are more straightforward than the effects of increasing forest conservation values, due to rarity-based feedbacks being necessary to sustaining forests. Increas- ing forest conservation values can remove converted land from the forest-grassland

134 mosaic, promoting either forest or grassland states. Unlike grassland conservation, forest conservation maintains alternative natural states (e.g. grassland), by reducing the relative utility of converted land. We can relate this finding back to Brazil’s Forest Code (BFC), the implied bias in BFC towards forest valuation may in fact be not as detrimental to other natural vegetation types (grassland) as first thought, because, as we show, the conservation of forests alone can promote alternative natural landscapes (e.g. grassland). A novel component of our model is the distinction between conservation and economic discount rates. This allows us to ask different questions about the influence of discounting on decision-making. When discount rates are taken to be the same in our model, heavy future discounting would remove natural ecological states, as has been found in previous works [42,57]. However, if they are allowed to differ, the outcomes may correspondingly range from high rates of natural mosaic conservation to high rates of land conversion, and various combinations thereof. Given the different predictions when economic and conservation discount rates are allowed to vary, as may apply in real populations, it is desirable for future behavioural models to allow the two discount rates to differ. Strong human influence has also been shown to preclude bistability in previous theoretical models of forest-grassland mosaic systems, and that weak human influence has the greatest potential to maintain forest-grassland mosaics in a natural state [12]. We expanded on this previous work by including agricultural land states and other realistic characteristics of human decision-making such as discounting. An unexpected result of including discount time horizon (foresight) is the surprising reintroduction of forest-grassland bistability under strong human influence. In our model, bistability is restored when individuals make decisions with long-term conservation goals, but instead of being driven by natural recruitment, the bistability is human-originated, according to rarity of natural landscapes. We note the consistency of this finding with our questionnaire results [48], which found that when natural states were conserved on a property, the natural land cover was usually strongly dominated by either grassland or forest. The utilities for the three land states in the base case were very similar to one another. This leads to very long-term oscillations, suggesting that it might be as important to study transient states, as it is to study equilibrium states [58]. Moreover, increasing conservation values would have a double benefit: this would not only improve the utilities for future land states and thus increase their average cover, it would also stabilize overall dynamics by increasing the incremental difference between utilities. Improving parameter estimates is therefore a suitable avenue for future work.

135 The dominant paradigm of human-environment interactions has been negative for most of human history, as we have already noted in the introduction. However, human-environment relationships are not unidirectional and our ability to adapt also applies to our relationship with the environment. Assuming the complete extinction of endangered ecosystems such as forest-grassland mosaics based on past trends therefore neglects an important aspect of human-environment interactions and assumes that humans are not able to adapt. Our research demonstrates how nonlinear, coupled human-environment systems can exhibit complex dynamics due to multiple interacting social and natural feedbacks. The endpoints of such systems are not known, but modelling can help us see what the outlines of such endpoints might be. Empirically grounded simulation models such as we have developed here may be useful for guiding future land use and conservation policies.

Acknowledgements

The research was supported by a James S. McDonnell Foundation Complex Systems Award to MA, NSERC Discovery grants to MA and CTB, and NSERC CREATE scholarships to KAH. We thank G. Hailu, S.A. Levin and V. de Patta Pillar for discussions.

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S1 Supporting Information: Materials and Meth- ods

S1.1 Environment (Land-Use & Natural Dynamics) Model

In the first set of equations (1-3), the terms and parameters are based on Innes and colleagues earlier work [12], although the functional form of recruitment (r(F,G), explained in next paragraph) and the functional form of human influence (J(xi), explained below) are markedly different. We have also include a third land cover state, converted land (A), since in recent years the forest-grassland mosaic landscape, characteristic of southern Brazil, has experienced gains in converted land (i.e. plantations and crops) [39, 48]. Shifts in land use between converted land and natural land are

143 often motivated by economic gains and demand for food. Any non-pecuniary transitions from converted land to natural land are defined as abandonment, for reasons such as poor soil fertility, climate shifts and modernization. The natural mosaic exists as alternative stable states, dominant grassland and dominant forest, driven by recruitment (Fig. 2a). The positive feedback loop between recruitment and the proportion of grass cover/tree cover is governed by a fire threshold response. Once tree cover exceeds 40% cover, the frequency and severity of fire are diminished, thus allowing seedlings to develop [43]. The dynamic vegetation model presented by Higgins et al. [41] describes tree recruitment rates in terms of grass cover, with an implicit fire-driven threshold. We use Higgins and colleagues’ model and model assumptions as a framework for the rate of change from G to F , by combining multiple equations, using the general threshold function from equation 16.2 and incorporating the assumption that moisture availability alters fire intensity and ultimately probability of topkill (eqns. 7-9) to generate equation 4 in our model. As described in the main text, ψ is the grass cover that yields 50% chance of obtaining maximum recruitment rates (G0.5, in Higgins et al. [41]), without considering moisture availability. However, in the original dynamic vegetation model, grass biomass is dependent on moisture availability. To reconcile the impact of moisture availability on fire and tree recruitment probabilities, as described by Higgins et al. [41] and Archibald et al. [43], we incorporate a moisture-limited threshold response to forest ψ recruitment. Hence, the term β(0.5−S) , where β is calibrated to yield nominal forest recruitment for F < 40% and maximal recruitment for F > 40%, as described in earlier work [12, 43]. Furthermore, the forest recruitment threshold is related to the G proportion of grasses in natural ecosystems, hence the term F +G . We assume that forest is incapable of natural expansion into converted land, as farming practices suppress forest succession; therefore when F and G are small, recruitment is limited.

S1.2 Human Behaviour Model

The expansion of converted lands introduces an additional alternative stable state (dominant converted land) that is driven primarily by proﬁts (Fig. 2b). Converted land is primarily driven by economic gains [48], whereas natural land cover states ap- peal to cultural and ecological interests, in addition to monetary gains. In equations (5,6), landowners are assumed to share information among each other, as indicated in questionnaire responses [48]. Imitation is a common behaviour among individuals, particularly within groups that share interests [14, 59, 60]. Finally, landowners consider the value of each state and select the most proﬁtable state or the natural state with the highest likelihood of extinction.

144 In equation (7), the utility functions for natural forest (uF (F )) and natural grassland (uG(G)) capture economic gains (pj,j = F,G) and conservation values (qj, j = F,G). The term qj(1 − j), j = F,G reflects the conservation value of F and G, which are determined by the relative abundance of either natural state. Hu- man behaviour is in part driven by the perceived future gains for their present actions [42, 61–63], which requires the use of a discount factor. A discount factor is applied in economics (including behavioural economics) to align future profits with present values, in an effort to explain preferences in consumption, monetary inflation and uncertainties in the future. From Satake and Rudel [42] we set the discount factor at 1 and 1 for mone- 1+de 1+dc tary gains and conservation values, respectively. A significant body of environmental economic literature prescribes a small discount rate for conservation projects or values [15, 53, 61–63], as a means to minimize land conversion. However, there are also empirical and theoretical reasons to think that individuals use lower discount rates in their decision-making for conservation projects than they do for strictly economic activities. For instance, Broome et al. [52] aptly summarize the Hotelling Rule, whereby it is argued that interest rates for scarce, non-reproducible resources (e.g., rare ecosystems) are lower than for conventional commodities produced within an economic system, because non-reproducible resources–unlike many commodities– cannot be converted into a greater quantity of future non-reproducible resources, by definition. Therefore the discount rate for non-reproducible resources should be lower (or even zero) than for conventional commodities [52]. In the context of the southern Brazilian forest-grassland mosaic, it has also been noted that Gaucho culture favours grassland [25] and natural ecosystems (F and G) not only because they provide valuable environmental services, but also because they are important to Gaucho heritage. Therefore, for our study system we expect that individuals will use a lower discounting rate for the value of future grassland-forest mosaics than for economic gains. Nonetheless, individuals are generally shortsighted and impatient, making decisions with respect to financial returns based on harvest rotations and the perceived risk of ecological crises impacting the next generation [63].

In equation (8), annual proﬁts from crops (pcr) are estimated from the 2006 IBGE

Agricultural Census [64]. The profit from crops (pcr) and the profit from plantation management (ppl) are greater than either natural land state (pF , pG), we estimate pA = 2.5pG = 20pF [64, 65]. An economic discount rate is applied to annual profits from crops analogous to natural forest and grassland utilities (eq. (7)). The penalty for non-compliance with the legal reserve requirements is reflected by pB [66, 67]. Brazil’s Forest Code requires 20% of land in Pampa and Atlantic Forest biomes to

145 be conserved in a natural state [67]. When natural land exceeds the legal reserve quotas, landowners are not penalized and pBis zero. Plantation forestry requires a greater initial investment and generates delayed returns. The harvest rotation cycle leads to net losses when establishing (ppl1, at time int) and maintaining (ppl2, at time mt) the plantation [64, 68]. Trees generate revenue in later years through thinning for charcoal (ppl3, at time δ), while the greatest gains occur at the time of ﬁnal harvest (ppl4, at time h).

i m δ h X 1 k X 1 k X 1 k X 1 k ppl = ppl1 nt +ppl2 t +ppl3 +ppl4 1 + de 1 + de 1 + de 1 + de k=1 k=1 k=1 k=1 (S1)

The sigmoidal function used to describe the relationship between landowner decision- making processes and land-use change (eq. (9)) is seen in the adoption practices of a broad range of innovations from the agriculture industry to technology launches [69, 70]. The parameter values for X and τ are estimated from Rogers [55]. The sharpest increase in land use change occurs between 16-84% of the landowner population preferring land cover i (i = F, G, A), in such cases changes in land composition increase rapidly as preference for a given land state increases. When preference for a land cover i is below < 16%, landowners are not motivated to make changes to their land composition. Contrarily, above 84% of the landowner population preferring land cover i, most landowners have already altered their land composition.

S1.3 Parameter Selection S1.3.1 Base Case Study

The SãoFrancisco de Paula region contains natural forest-grassland mosaic interspersed with lands converted to agriculture and silviculture (F GA). We parameterize the model with data (Table S1) on profit and conservation values obtained from the literature and a detailed questionnaire about landowner behaviour from the São Francisco de Paula region [48]. We set the base case parameters using landowner preferred composition for each land cover type (F , G, or A) and the current land composition. For each parameter there is a range of empirically plausible values that can be obtained from the literature. The model-simulated composition should reflect what we see in our study region, if our assumptions are correct. Therefore, we calibrated all model parameters except the economic discount rate to fit the regional land composition, 0.25 ≤ F ≤ 0.35, 0.25 ≤ G ≤ 0.35, 0.2 ≤ A ≤ 0.45, while ensuring the calibrated parameter value remained within the empirically plausible values [48]. The base case economic discount rate was set at 10% [51] and the conservation discount

146 rate, referred to as discounting well-being in the literature, is set at 0.1% [53]. The majority of the farms (crops or livestock) in southern Brazil, where forest-grassland mosaics occur, are small family farms (¡ 40 ha) and the revenue generated from farm activities accounts for the majority of the landowner’s income [64]. There has been significant expansion of converted land in the past few decades [36, 39, 48], suggesting that human influence dominates over ecological processes. Therefore, we choose a value of ρ = 0.15 (i.e. moderate) to represent the base case assumption for the strength of human influence. At this value for human influence, human behaviour and natural forest recruitment both impact the land composition. We explore the effectiveness of variations in conservation values, discount rates and discounting time horizons at maintaining natural land cover across a spectrum of human influence scenarios to increase the scope of our model. In the following subsections we describe how we choose the parameter ranges for constructing parameter planes that allow us to understand how model dynamics vary as parameters are increased or decreased.

S1.3.2 Changing Conservation Values

We simulate the influence of conservation values (qF ,qG) as a function of rarity, as a way of evaluating sustainable decision-making practices. The range of values for qF and qG are estimates based on questionnaire results describing landowner preferences [48] and data on profits from natural lands [64]. In our study region (SãoFrancisco de Paula), the percentage of landowners preferring forest, grassland and converted land are 30%, 28% and 42%, respectively. Furthermore, 79% of landowners would rather restore Campos grassland than Araucaria forest, as G produces greater profits.

Therefore, we assume uA(A) > uG(G) ≥ uF (F ). Utilities represent the combined value of each land state from financial gains and conservation values, therefore we use the landowner preference and profit to estimate conservation ranges for qF and qG. Profits generated from natural forest are considerably lower than profits from natural grassland and converted land, yet the proportion of natural forest is the largest in our study area. We observe from questionnaire results that individuals cite conservation as a motivation for preserving forest on their lands, and moreover, legal restrictions on Araucaria angustifolia harvesting (which in turn reflect conservation values of the voting public) limit how many trees landowners can fell. Therefore, we set qF greater than the profit (pF ), qF ∈ [0, 0.15]. Grasslands hold conservation value, in addition to being profitable, therefore we set qG ∈ [0, 0.75]. The range for qG exceeds estimates from the questionnaire data, however it is to explore potential interesting changes in land cover for grassland conservation values that exceed pG.

147 We expect that increasing conservation values will increase the proportion of natural land cover.

S1.3.3 Changing Economic and Conservation Discount Rates

We simulate land cover dynamics over a range of economic discount rates (de) and conservation discount rates (dc) to explore possible mechanisms that drive landowner preference. There is a wealth of literature suggesting that dc should be as close to zero as possible to accommodate the uncertainty associated with environmental time scales [15, 53, 62, 63], while experimental studies suggest that de can be as high as 43% [50]. Theoretically, scarce commodities, such as endangered species, should not be discounted since future quantities will not exceed those of the present [52].

Land cover dynamics for de ∈ [0.001, 0.99] and dc ∈ [0.001, 0.2] are represented in a parameter plane. High discount rates typically lead to land exploitation, as the present holds more value than the future [42, 57]. Thus we expect that increases in de and dc will decrease the proportion natural states.

S1.3.4 Discounting Economic and Conservation Time Horizons

Discount time horizons (i.e. foresight) can contribute to sustainable land management practices [15, 62]. We use a parameter plane to explore the eﬀectiveness of discount time horizons at maintaining natural land cover. Natural systems are eval- uated over a much greater time scale compared to industrial or anthropogenic activities, therefore we simulate conservation discount time horizons (n) from 1 to 100 and economic discount time horizons (m) from 1 to 50 [54]. The impact of increasing discount time horizons on land cover dynamics is highly dependent on the assumptions made by landowners. Therefore, assuming constant values over the discount time period, increasing discount time horizons (m, n) should maintain the current land composition.

S1.3.5 Weak, Moderate and Strong Human Inﬂuence

Aside from the moderate human influence scenario, we evaluate two alternative scenarios: weak and strong. Weak human influence is set at ρ = 0.05, such that maximum potential human influence is less than maximum potential recruitment. Strong human influence (ρ = 0.25) represents intense management system, where human values outweigh the feedbacks from natural processes. Thus, strong human influence should shift the system towards the land composition with the greatest utility and weak human influence should converge to a natural forest-grassland mosaic. From

148 previous work [12], we expect that increasing human influence will preclude bistability. We also run simulations under no human influence (ρ = 0) to confirm natural mosaic bistability. In the absence of human influence, conservation values, discount rates and discount time horizons have no impact on land cover changes. Instead, the positive feedback between recruitment and fire is the major determining factor in land cover changes, and as such the system is bistable for all possible human-based parameters.

149 Table 5.S1: Model parameters from empirical data and questionnaire results. Parameter selection and calibration is described in the the supplementary text (SI1).

Parameter Description Range Value Simulated Source ν Natural disturbance rate 0 − 1 0.02 [44] aj,j = F,G Converted land abandonment to F and G 0 − 1 aF = 0.0043, aG = 0.0057 [42] S Soil moisture content 0 − 0.5 0.2 [46] β Fuel moisture converter 2.8 Calibrated α Maximum recruitment rate 0 − 1 0.2 [45] ψ Non-forest recruitment threshold 0 − 1 0.417 [41] ω Rate of transition 0 − 1 0.0667 [41]

150 pjj = F,G Annual profit from natural land F and G 0 − 1 pF = 0.05, pG = 0.35 [48,64,65] pAa Annual profit from agricultural land 0 − 3 1 [48,64] pAf Annual profit from plantation on 7 year rotation −1.3 − 15 pAin = −0.4, pAmt = −1.2, pAδ = −0.4, pAh = 12 [68] pB Penalty for non-compliance with BFC 0 − 1 0.01 [66,67] s Social learning constant 0 − 1 0.42 [12,48] qj, j = F,G Conservation value of natural land (F,G) 0 − 1 qF = 0.1, qG = 0.03 [12,48] de Economic discount rate 0.001 − 1 0.1 [50,51,57] dc Conservation discount rate 0.001 − 0.2 0.001 [15,62] m Discount time horizon for economic gains 1 − 50 7 [68] n Discount time horizon for conservation values 1 − 100 28 [15] X Diffusion of practices threshold 0 − 1 0.5 [55,69,70] τ Diffusion of practices rate 0 − 1 0.075 [55,69,70] ρ Maximum potential human influence 0 − 0.25 0-0.25 [55,69,70] Chapter 6

General Conclusions

151 Alternative stable states may be difficult to observe in real world ecological systems [1,2], especially when there are overwhelming environmental and social drivers, such as temperature and economic valuation. The models in this thesis highlight the fragility of bistable forest/non-forest systems to exogenous stresses and demographic characteristics (Chapter 2), climatic conditions (Chapter 3), and human behaviour (Chapters 4 and 5). Despite the breadth of research related to alternative stable states there is still a gap in our understanding as to when and what causes such shifts to happen [3]. The work presented here uses empirical data along with dominant theories on alternative stable states (e.g. positive feedbacks) [4–6], human behaviour (e.g. economic valuation,rarity-based conservation) [7–10] and biophysical processes (e.g. recruitment) [11, 12] to parameterize models and gain a better understanding of mechanisms responsible for regime shifts. There is a wealth of literature describing vegetation shifts in tree-grass systems, few models describe these transitions using simple, mechanistic processes. Chapter 2 addresses this gap, offering insight into the mechanisms responsible for abrupt shifts between trees and grasses. Following a thorough review of models describing tropical and subtropical tree-grass systems, soil moisture content is shown to be a proxy for limitations in tree recruitment imposed by fire and seedling desiccation. This is consistent with earlier models [13,14] and empirical studies [15]. Unlike many existing dynamical models [16, 17], the work presented here provides a quantifiable approach to modelling recruitment in tree-grass, and has the advantage of being relatively simple compared to statistical or dynamic vegetation models [12, 18, 19]. Additionally, incorporating measurable parameters and underlying mechanisms into phenomenological models of fire-disturbance [16,17,19,20] has potential applications across a wide range of systems, providing an avenue for research. In a similar process to the model calibration in Chapter 2, Chapter 3 explores the influence of temperature and precipitation on seedling establishment and adult tree mortality in boreal/temperate biomes. Continuing with the notion that hydrologic conditions have an important role in determining forest expansion [21–23], this model uses climate moisture index to indicate regions of boreal and temperate forests vulnerable to regime shifts, as climate changes. The ability to predict the resilience of forest to future disturbance regimes and environmental stresses is a priority for forest managers and ecologists, alike [24–27]. Therefore, the ability to quantitatively identify critical thresholds in climatic conditions and compare the effectiveness of adaptive management strategies contributes to both scientific literature and sustainable forest management practices. Model simulations indicate that the threshold response to temperature and precipitation dominates over the positive feedback that maintains the coexistence of distinct alternative stable states. As a result, the region

152 of bistability is minimal and will likely be eclipsed, as temperature and precipitation change in the future; suggesting that bistability may be limited to small ranges of climatic conditions. This claim is substantiated by modelling the same system in the absence of climatic condition, for which a larger region of bistability is maintained. The dominant framework of alternative stable states describes coexisting states that rapidly transition from one stable state to another following direct perturbations to the state variable (i.e. initial conditions shape the community structure) [4, 28, 29]. However, this work supports an alternative framework to the dominant alternative stable state paradigm, whereby changes in parameters force a shift in state from one dominant state to an alternative [4]. It is also important to note that bistability and threshold responses are not synonymous, a common misconception when describing alternative stable states in ecosystems [30]. This work emphasizes the importance of incorporating climatic variation in models, management practices and policies, as changes in climatic conditions are expected to be unprecedented and past practices are unlikely to be effective in the future [24,31]. The work presented here raises questions about bistability in other regions (e.g. subtropical tree-grass systems), in the face of climate change. Future work should expand on this idea of fragile bistability. Human land-use and management practices threaten the existence of bistable systems [16, 32], particularly in tropical and subtropical systems [33, 34]. To gain a better understanding of landowner behaviour and the resulting influence on forest- grassland mosaics, Chapter 4 presents a questionnaire detailing landowner perception, land composition, the valuation process and conservation priorities. Consistent with earlier studies, the forest-grassland mosaics of Brazil have experienced a significant gain in plantation forestry [35, 36], despite being considered less desirable by landowners. The inconsistency between landowner preferences and land composition, highlighted in Chapter 4, reflect the influence of government incentives and policies. Not surprisingly, agriculture expansion occurs at the expense of grassland [37, 38], with profits motivating the conversion. In terms of natural landscapes, individual landowners show distinct preference for either natural grassland or forest, although the averaged preference is equivalent. The questionnaire responses contributes to literature on decision-making practices and has practical applications in policy-making. The results from Chapter 4 are used to parameterize the coupled human-environment interaction model in Chapter 5. In addition to disturbance (Chapter 2) and climate (Chapter 3), bistability of forest-grassland mosaics is altered by introducing a converted land state into the system and the accompanying human behaviour – economic valuation (Chapter 5). As expected, strong human influence precludes bistability [16]. When strong human influence is combined with short-sighted behaviour and economic gains, converted

153 land becomes the dominant state in the system. However, strong human inﬂuence combined with foresight and strong conservation values reintroduces bistability, as a result of rarity-based conservation. Rarity-based conservation creates an additional threshold response in the forest-grassland system, which counteracts the natural ﬁre- response threshold. Alternative stable states and land-use change receive considerable attention, although coupled human-environment interaction models are rare. Incorporating empirical data and well-formed theories about alternative stable states provides realistic predictions in vegetation change, but more importantly enhances our understanding of the dynamical processes and driving factors within a system. Forests and grasslands provide many valuable ecosystem services and the sustainability of both states requires an understanding of the underlying processes, which cannot be obtained by applying observational studies of vegetation change or theories of alternative stable states separately.

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158 A1 MATLAB Code

A1.1 Forest cover: climate moisture index

%% Forest cover in relation to climate moisture index MATLAB code

function dFdt =forest_CMI(t,F,P,T,CMI_I,CMI_M,CMI_D,etaI,etaM,etaD,mI,mM,mD,aI,bI,aM,bM,aD, bD,h,alpha,beta,pI,pM,pD,L,Elev,Td)

C=P-872.40255-30.53065*T-21.32348*Td+0.02135*Elev+11.78707*L;

survival=(pI./(1+exp((-CMI+CMI_I+mI*T)./etaI))+pM./(1+exp((-CMI+CMI_M-mM*T)./ etaM))+pD./(1+exp((-CMI+CMI_D+mD*T)./etaD)))/(1-F(1))^0.5;

mortality=pI*(aI-bI*(CMI))+pM*(aM-bM*(CMI))+pD*(aD-bD*(CMI)); if mortality<0.001 mortality=0.001; end

dFdt = [survival*alpha*F(1)*(1-F(1))+survival*beta*F(1)*(1-F(1))- mortality*F(1)-h*F(1)];

%% Parameter planes single variable ode tspan=0:250; epsilon=0.01;

p=1804; A1=ones(p,1); B1=ones(p,1); C1=ones(p,1); D1=ones(p,1); H1=ones(p,1); I1=ones(p,1); J1=ones(p,1); K1=ones(p,1); L1=ones(p,1); M1=ones(p,1);

for e=0.05:0.1:0.95 % loop through initial conditions

F0=[e];

for i=1:1 for j=1:1 E=zeros(i,1);

for T=0:0.16:7 %range of temperature for P=400:20:1200 % range of precipitation

%simulate ode

[t,F]=ode45(@(t,F)forest_CMIn(t,F,P,T, 21.9,12.2,-34.9,3.5,6.4,19.3,2.8,0,3.1,0.0516,0.00087,0.008664,0.000596,0.001

159 816,0.000228,0.01,0.0075,0.03,0.18,0.5,0.32,56.01,600,11),tspan,F0); max_pt(j)=0; min_pt(j)=200;

for t=235:250 % loop through the last 15 years to find oscillations

if F(t)>max_pt(j) max_pt(j)=F(t); %find greatest proportion of forest cover in over the last 15 years t=t+1; end if F(t)

t=t+1;

end end

if abs(max_pt(j)-min_pt(j))>epsilon %see if oscillations or changes in forest cover occur E(i)=10; %assign value of 10 to with oscillations for pcolor plot

else E(i)=F(250);% otherwise equilibrium is the last result from the ode simulation

end j=j+1; i=i+1; end end

% assign value to range of forest cover, F<=0.05 gives grassland/shrubland, 0.05=0.7 full forest cover if 0<=e && e<0.1 A1(E<=0.05)=0; A1(E==10)=10; A1(E>0.05 & E<=0.4)=3; A1(E>0.4 & E<0.7)=5; A1(E>=0.7 & E<=1)=7; elseif 0.1<=e && e<0.2

160 B1(E<=0.05)=0; B1(E==10)=10; B1(E>0.05 & E<=0.4)=3; B1(E>0.4 & E<0.7)=5; B1(E>=0.7 & E<=1)=7; elseif 0.2<=e && e<0.3 C1(E<=0.05)=0; C1(E==10)=10; C1(E>0.05 & E<=0.4)=3; C1(E>0.4 & E<0.7)=5; C1(E>=0.7 & E<=1)=7; elseif 0.3<=e && e<0.4 D1(E<=0.05)=0; D1(E==10)=10; D1(E>0.05 & E<=0.4)=3; D1(E>0.4 & E<0.7)=5; D1(E>=0.7 & E<=1)=7; elseif e>=0.4 && e<0.5 H1(E<=0.05)=0; H1(E==10)=10; H1(E>0.05 & E<0.4)=3; H1(E>=0.4 & E<0.7)=5; H1(E>=0.7 & E<=1)=7; elseif e>=0.5 && e<0.6 I1(E<=0.05)=0; I1(E==10)=10; I1(E>0.05 & E<=0.4)=3; I1(E>0.4 & E<0.7)=5; I1(E>=0.7 & E<=1)=7; elseif e>=0.6 && e<0.7 J1(E<=0.05)=0; J1(E==10)=10; J1(E>0.05 & E<=0.4)=3; J1(E>0.4 & E<0.7)=5; J1(E>=0.7 & E<=1)=7; elseif e>=0.7 && e<0.8 K1(E<=0.05)=0; K1(E==10)=10; K1(E>0.05 & E<=0.4)=3; K1(E>0.4 & E<0.7)=5; K1(E>=0.7 & E<=1)=7; elseif e>=0.8 && e<0.9 L1(E<=0.05)=0; L1(E==10)=10; L1(E>0.05 & E<=0.4)=3; L1(E>0.4 & E<0.7)=5; L1(E>=0.7 & E<=1)=7;

161 elseif e>=0.9 && e<1 M1(E<=0.05)=0; M1(E==10)=10; M1(E>0.05 & E<=0.4)=3; M1(E>0.4 & E<0.7)=5; M1(E>=0.7 & E<=1)=7; end

end end end

% determine if multiple stable states exist under same conditions for id=1:length(A1) if A1(id)==10 && B1(id)==10 && C1(id)==10 && D1(id)==10 && H1(id)==10 && I1(id)==10 && J1(id)==10 && K1(id)==10 && L1(id)==10 && M1(id)==10; O(id)=10; % all initial conditions yield oscillations or changing dynamics elseif A1(id)==10 || B1(id)==10 || C1(id)== 10 || D1(id)==10 || H1(id)==10 || I1(id)==10 || J1(id)==10 || K1(id)==10 || L1(id)==10 || M1(id)==10; O(id)=12; % some initial conditions yield oscillations or changing dynamics and some yield stable equilibrium elseif A1(id)==12 || B1(id)==12 || C1(id)== 12 || D1(id)==12 || H1(id)==12 || I1(id)==12 || J1(id)==12 || K1(id)==12 || L1(id)==12 || M1(id)==12 ; O(id)=12; % some initial conditions yield oscillations or changing dynamics and some yield stable equilibrium elseif A1(id)==B1(id) && B1(id)==C1(id) && C1(id)==D1(id) && D1(id)==H1(id) && H1(id)==I1(id) && I1(id)==J1(id) && J1(id)==K1(id) && K1(id)==L1(id) && L1(id)==M1(id); O(id)= C1(id); % all initial conditions yield same equilibrium point else O(id)=15; % bistable equilibrium, some initial conditions yield no forest cover others yield forest cover end end

% save O mat file with state dynamics

%% plot parameter planes function mat= vec2mat(vec,x) load('O.mat') %% open saved mat file with state dynamics x=41; % m is the first set of parameters that you loop through vec=O;

162 y=(length(vec))/x; % n is the second set of parameters that you loop through mat=(reshape(vec,x,y));

T=0:0.16:7; P=400:20:1200; pcolor(T,P,mat) % pcolor(x,y,c) x=m, y=n and c=mat colormap(gray) plotbrowser % end

%% similar code is used to generate parameter planes for recruitment in terms of soil moisture content using the model equations function dTdt =forest_soil(t,T,S,v,beta,alpha,omega,phi,S_avg) recruitment=alpha/(1+exp((1-T(1)-phi/(beta*(0.5-S)))/omega));

% T(1) represents the proportion of forest cover dTdt = [recruitment*T(1)*(1-T(1))*S/S_avg - v*T(1)];

163 A1.2 Forest cover: human inﬂuence

%% human-environment model function dGdt =forest_human(t,G,S,v,rho,beta,alpha,omega,psi,x,s,a_G,a_F,n,m,pF,qF,pG,qG,pA f_ini,pAf_mt,pAf_delta,pAf_h,pAa,pB,dc,de)

% recruitment function

recruitment=alpha/(1+exp((G(2)/(G(1)+G(2))-psi/(beta*(0.5-S)))/omega)); % J(x_F) human influence on forest term in model, conditional on the preference for forest

human_influenceF = rho/(1+exp((x-G(3))/0.075));

% J(x_G) human influence on grassland term in model, conditional on the preference for forest

human_influenceG = rho/(1+exp((x-G(4))/0.075));

% J(x_A) human influence on agriculture term in model, conditional on the preference for forest

human_influenceA = rho/(1+exp((x-(1-G(3)-G(4)))/0.075)); % x represents value for which others get on board

% piecewise penalty function if G(1)+G(2)>0.2 pB=0; else pB=pB;

end

% harvesting cycle profits for int=1:m if int==1 || rem(int,7)==1 ini=int; pAf_ini=pAf_ini; else pAf_ini=0; ini=0; end

if int==2 || int==4 || int==6 || rem(int,7)==2 || rem(int,7)==4 || rem(int, 7)==6 mt=int; pAf_mt=pAf_mt; else pAf_mt=0; mt=0; end

if int==3 || int==5 || rem(int,7)==3 || rem(int,7)==5 delta=int; pAf_delta=pAf_delta;

164 else pAf_delta=0; delta=0; end if rem(int,7)==0 h=int; pAf_h=pAf_h; else pAf_h=0; h=0; end pAf_ini = pAf_ini*(((1/(1+de))^ini)-((1/(1+de))^(ini+1)))/(1-(1/(1+de))); pAf_mt = pAf_mt*(((1/(1+de))^mt)-((1/(1+de))^(mt+1)))/(1-(1/(1+de))); pAf_delta = pAf_delta*(((1/(1+de))^delta)-((1/(1+de))^(delta+1)))/(1-(1/ (1+de))); pAf_h = pAf_h*(((1/(1+de))^h)-((1/(1+de))^(h+1)))/(1-(1/(1+de))); a(int)=sum(pAf_ini); b(int)=sum(pAf_mt); c(int)=sum(pAf_delta); d(int)=sum(pAf_h); int=int+1; end pAf=sum(a)+sum(b)+sum(c)+sum(d);

% utility of forest cover (u_F), grassland cover (u_G) and converted land cover (u_A) u_F = qF*(1/(1+dc))*(1-(1/(1+dc))^n)/(1-(1/(1+dc)))*(1-G(1)) + pF*(1/ (1+de))*(1-(1/(1+de))^m)/(1-(1/(1+de))); u_G = qG*(1/(1+dc))*(1-(1/(1+dc))^n)/(1-(1/(1+dc)))*(1-G(2)) + pG*(1/ (1+de))*(1-(1/(1+de))^m)/(1-(1/(1+de))); u_A = 0.57*pAa*(1/(1+de))*(1-(1/(1+de))^m)/(1-(1/(1+de))) + 0.43*pAf - pB*(0.2-G(1)-G(2));

% G(1) represents proportion of forest cover, % G(2) represents proportion of grassland cover, % G(3) represents preference for forest, % G(4) represents preference for grassland

dGdt = [ recruitment*G(1)*G(2)*S/0.2 - v*G(1) + human_influenceF*G(1)*(1-G(1)) - human_influenceG*G(1)*G(2) - human_influenceA*G(1)*(1-G(1)-G(2)) + a_F*(1- G(1)-G(2));...

v*G(1) - recruitment*G(1)*G(2)*S/0.2 + human_influenceG*G(2)*(1-G(2)) - human_influenceF*G(2)*G(1) - human_influenceA*G(2)*(1-G(1)-G(2)) + a_G*(1- G(1)-G(2));...

165

s*((u_F-u_A)*G(3)*(1-G(3)-G(4)) + (u_F-u_G)*G(3)*G(4));...

s*((u_G-u_F)*G(4)*G(3) + (u_G-u_A)*G(4)*(1-G(3)-G(4)))];

%% to reconcile numerical errors in simulations if (G(3)>=1 && dGdt(3)>0) dGdt(3)=0; dGdt(4)=dGdt(3)+dGdt(4); end if (G(4)>=1 && dGdt(4)>0) dGdt(4)=0; dGdt(3)=dGdt(3)+dGdt(4); end if (G(1)>=1 && dGdt(1)>0) dGdt(1)=0; dGdt(2)=dGdt(1)+dGdt(2); end if (G(2)>=1 && dGdt(2)>0) dGdt(2)=0; dGdt(1)=dGdt(1)+dGdt(2); end

%% Parameter planes human-environment model tspan=0:1000; options=odeset('NonNegative',1:4); epsilon=0.02; p=2601; A=ones(p,10); B=ones(p,10); C=ones(p,10); D=ones(p,10); H=ones(p,10); I=ones(p,10); J=ones(p,10); K=ones(p,10); L=ones(p,10); M=ones(p,10);

A1=zeros(p,1); B1=zeros(p,1); C1=zeros(p,1); D1=zeros(p,1); H1=zeros(p,1); I1=zeros(p,1);

166 J1=zeros(p,1); K1=zeros(p,1); L1=zeros(p,1); M1=zeros(p,1); O=zeros(p,1);

for e=0.05:0.1:0.95 for b=0.05:0.1:0.95

G0=[e;(1-e)*b;0.2;0.3]; for i=1:1 for j=1:1

E=zeros(i,1);

for qF=0:0.003:0.15 %loop through seedling survival

for qG=0:0.015:0.75 %loop through natural disturbance %simulate ode

[t,G]=ode45(@(t,G)forest_humanS2A(t,G, 0.2,0.02,0.25,2.8,0.2,0.0667,0.417,0.5,0.42,0.0057,0.0043,28,7,0.05,qF, 0.35,qG,-0.4,-1.2,-0.4,12,1,0.01,0.001,0.1),tspan,G0,options); max_pt(j)=0; min_pt(j)=500;

for t=970:1000 % loop through the last 30 years to find oscillations

if G(t)>max_pt(j) max_pt(j)=G(t); %find greatest proportion of forest cover in over the last 15 years

end

if G(t)

t=t+1; end

if abs(max_pt(j)-min_pt(j))>epsilon %see if oscillations occur E(i)=10; %set point equal to 0.2 for cycle in future use of pcolor plot

else

167 E(i)=G(1000);% otherwise equilibrium is the last result from the ode simulation

end

j=j+1; i=i+1;

end

for c=1:10 if 0<=e && e<0.1 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 A(E<=0.05,c)=0; A(E>0.05 & E<0.5,c)=3; A(E==10,c)=10; A(E>=0.5 & E<0.9,c)=5; A(E>=0.9 & E<=1.1,c)=7; elseif 0.1<=e && e<0.2 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 B(E<=0.05,c)=0; B(E>0.05 & E<0.5,c)=3; B(E==10,c)=10; B(E>=0.5 & E<0.9,c)=5; B(E>=0.9 & E<=1.1,c)=7; elseif 0.2<=e && e<0.3 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 C(E<=0.05,c)=0; C(E==10,c)=10; C(E>=0.05 & E<0.5,c)=3; C(E>=0.5 & E<0.9)=5; C(E>=0.9 & E<=1.1,c)=7; elseif 0.3<=e && e<0.4 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 D(E<=0.05,c)=0; D(E==10,c)=10; D(E>0.05 & E<0.5,c)=3; D(E>=0.5 & E<0.9,c)=5; D(E>=0.9 & E<=1.1,c)=7; elseif e>=0.4 && e<0.5 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 H(E<=0.05,c)=0; H(E==10,c)=10; H(E>0.05 & E<0.5,c)=3; H(E>=0.5 & E<0.9,c)=5; H(E>=0.9 & E<=1.1,c)=7; elseif e>=0.5 && e<0.6 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 I(E<=0.05,c)=0; I(E==10,c)=10; I(E>=0.05 & E<0.5,c)=3; I(E>=0.5 & E<0.9,c)=5;

168 I(E>=0.9 & E<=1.1,c)=7; elseif e>=0.6 && e<0.7 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 J(E<=0.05,c)=0; J(E==10,c)=10; J(E>0.05 & E<0.5,c)=3; J(E>=0.5 & E<0.9,c)=5; J(E>=0.9 & E<=1.1,c)=7; elseif e>=0.7 && e<0.8 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 K(E<=0.05,c)=0; K(E==10,c)=10; K(E>0.05 & E<0.5,c)=3; K(E>=0.5 & E<0.9,c)=5; K(E>=0.9 & E<=1.1,c)=7; elseif e>=0.8 && e<0.9 && b>=0.1*(c)-0.06 && b<0.1*(c)+0.03 L(E<0.05,c)=0; L(E==10,c)=10; L(E>0.05 & E<0.5,c)=3; L(E>=0.5 & E<0.9,c)=5; L(E>=0.9 & E<=1.1,c)=7; elseif e>=0.9 && e<1 && b>=0.1*(c)-0.05 && b<0.6*(c)+0.03 M(E<=0.05,c)=0; M(E==10,c)=10; M(E>0.05 & E<0.5,c)=3; M(E>=0.5 & E<0.9,c)=5; M(E>=0.9 & E<=1.1,c)=7; % end end end

end end

end

for id=1:length(A) if A(id,1)==10 && A(id,2)==10 && A(id,3)==10 && A(id,4)==10 && A(id,5)==10 && A(id,6)==10 && A(id,7)==10 && A(id,8)==10 && A(id,9)==10 && A(id,10)==10; A1(id)=10; elseif A(id,1)==10 || A(id,2)==10 || A(id,3)== 10 || A(id,4)==10 || A(id, 5)==10 || A(id,6)==10 || A(id,7)==10 || A(id,8)==10 || A(id,9)==10 || A(id, 10)==10 ; A1(id)=12; elseif A(id,1)==A(id,2) && A(id,2)==A(id,3) && A(id,3)==A(id,4) && A(id, 4)==A(id,5) && A(id,5)==A(id,6) && A(id,6)==A(id,7) && A(id,7)==A(id,8) &&

169 A(id,8)==A(id,9) && A(id,9)==A(id,10); A1(id)= A(id,3); else A1(id)=15; end

end for id=1:length(B) if B(id,1)==10 && B(id,2)==10 && B(id,3)==10 && B(id,4)==10 && B(id,5)==10 && B(id,6)==10 && B(id,7)==10 && B(id,8)==10 && B(id,9)==10 && B(id,10)==10; B1(id)=10; elseif B(id,1)==10 || B(id,2)==10 || B(id,3)== 10 || B(id,4)==10 || B(id, 5)==10 || B(id,6)==10 || B(id,7)==10 || B(id,8)==10 || B(id,9)==10 || B(id, 10)==10; B1(id)=12; elseif B(id,1)==B(id,2) && B(id,2)==B(id,3) && B(id,3)==B(id,4) && B(id, 4)==B(id,5) && B(id,5)==B(id,6) && B(id,6)==B(id,7) && B(id,7)==B(id,8) && B(id,8)==B(id,9) && B(id,9)==B(id,10); B1(id)= B(id,3); else B1(id)=15; end end for id=1:length(C) if C(id,1)==10 && C(id,2)==10 && C(id,3)==10 && C(id,4)==10 && C(id,5)==10 && C(id,6)==10 && C(id,7)==10 && C(id,8)==10 && C(id,9)==10 && C(id,10)==10; C1(id)=10; elseif C(id,1)==10 || C(id,2)==10 || C(id,3)== 10 || C(id,4)==10 || C(id, 5)==10 || C(id,6)==10 || C(id,7)==10 || C(id,8)==10 || C(id,9)==10 || C(id, 10)==10; C1(id)=12; elseif C(id,1)==C(id,2) && C(id,2)==C(id,3) && C(id,3)==C(id,4) && C(id, 4)==C(id,5) && C(id,5)==C(id,6) && C(id,6)==C(id,7) && C(id,7)==C(id,8) && C(id,8)==C(id,9) && C(id,9)==C(id,10); C1(id)= C(id,3); else C1(id)=15; end end

170 for id=1:length(D) if D(id,1)==10 && D(id,2)==10 && D(id,3)==10 && D(id,4)==10 && D(id,5)==10 && D(id,6)==10 && D(id,7)==10 && D(id,8)==10 && D(id,9)==10 && D(id,10)==10; D1(id)=10; elseif D(id,1)==10 || D(id,2)==10 || D(id,3)== 10 || D(id,4)==10 || D(id, 5)==10 || D(id,6)==10 || D(id,7)==10 || D(id,8)==10 || D(id,9)==10 || D(id, 10)==10; D1(id)=12; elseif D(id,1)==D(id,2) && D(id,2)==D(id,3) && D(id,3)==D(id,4) && D(id, 4)==D(id,5) && D(id,5)==D(id,6) && D(id,6)==D(id,7) && D(id,7)==D(id,8) && D(id,8)==D(id,9) && D(id,9)==D(id,10); D1(id)= D(id,3); else D1(id)=15; end end for id=1:length(H) if H(id,1)==10 && H(id,2)==10 && H(id,3)==10 && H(id,4)==10 && H(id,5)==10 && H(id,6)==10 && H(id,7)==10 && H(id,8)==10 && H(id,9)==10 && H(id,10)==10; H1(id)=10; elseif H(id,1)==10 || H(id,2)==10 || H(id,3)== 10 || H(id,4)==10 || H(id, 5)==10 || H(id,6)==10 || H(id,7)==10 || H(id,8)==10 || H(id,9)==10 || H(id, 10)==10; H1(id)=12; elseif H(id,1)==H(id,2) && H(id,2)==H(id,3) && H(id,3)==H(id,4) && H(id, 4)==H(id,5) && H(id,5)==H(id,6) && H(id,6)==H(id,7) && H(id,7)==H(id,8) && H(id,8)==H(id,9) && H(id,9)==H(id,10); H1(id)= H(id,3); else H1(id)=15; end end for id=1:length(I) if I(id,1)==10 && I(id,2)==10 && I(id,3)==10 && I(id,4)==10 && I(id,5)==10 && I(id,6)==10 && I(id,7)==10 && I(id,8)==10 && I(id,9)==10 && I(id,10)==10; I1(id)=10; elseif I(id,1)==10 || I(id,2)==10 || I(id,3)== 10 || I(id,4)==10 || I(id, 5)==10 || I(id,6)==10 || I(id,7)==10 || I(id,8)==10 || I(id,9)==10 || I(id,

171 10)==10; I1(id)=12; elseif I(id,1)==I(id,2) && I(id,2)==I(id,3) && I(id,3)==I(id,4) && I(id, 4)==I(id,5) && I(id,5)==I(id,6) && I(id,6)==I(id,7) && I(id,7)==I(id,8) && I(id,8)==I(id,9) && I(id,9)==I(id,10); I1(id)= I(id,3); else I1(id)=15; end end for id=1:length(J) if J(id,1)==10 && J(id,2)==10 && J(id,3)==10 && J(id,4)==10 && J(id,5)==10 && J(id,6)==10 && J(id,7)==10 && J(id,8)==10 && J(id,9)==10 && J(id,10)==10; J1(id)=10; elseif J(id,1)==10 || J(id,2)==10 || J(id,3)== 10 || J(id,4)==10 || J(id, 5)==10 || J(id,6)==10 || J(id,7)==10 || J(id,8)==10 || J(id,9)==10 || J(id, 10)==10; J1(id)=12; elseif J(id,1)==J(id,2) && J(id,2)==J(id,3) && J(id,3)==J(id,4) && J(id, 4)==J(id,5) && J(id,5)==J(id,6) && J(id,6)==J(id,7) && J(id,7)==J(id,8) && J(id,8)==J(id,9) && J(id,9)==J(id,10); J1(id)= J(id,3); else J1(id)=15; end end for id=1:length(K) if K(id,1)==10 && K(id,2)==10 && K(id,3)==10 && K(id,4)==10 && K(id,5)==10 && K(id,6)==10 && K(id,7)==10 && K(id,8)==10 && K(id,9)==10 && K(id,10)==10; K1(id)=10; elseif K(id,1)==10 || K(id,2)==10 || K(id,3)== 10 || K(id,4)==10 || K(id, 5)==10 || K(id,6)==10 || K(id,7)==10 || K(id,8)==10 || K(id,9)==10 || K(id, 10)==10; K1(id)=12; elseif K(id,1)==K(id,2) && K(id,2)==K(id,3) && K(id,3)==K(id,4) && K(id, 4)==K(id,5) && K(id,5)==K(id,6) && K(id,6)==K(id,7) && K(id,7)==K(id,8) && K(id,8)==K(id,9) && K(id,9)==K(id,10); K1(id)= K(id,3); else

172 K1(id)=15; end end for id=1:length(L) if L(id,1)==10 && L(id,2)==10 && L(id,3)==10 && L(id,4)==10 && L(id,5)==10 && L(id,6)==10 && L(id,7)==10 && L(id,8)==10 && L(id,9)==10 && L(id,10)==10; L1(id)=10; elseif L(id,1)==10 || L(id,2)==10 || L(id,3)== 10 || L(id,4)==10 || L(id, 5)==10 || L(id,6)==10 || L(id,7)==10 || L(id,8)==10 || L(id,9)==10 || L(id, 10)==10; L1(id)=12; elseif L(id,1)==L(id,2) && L(id,2)==L(id,3) && L(id,3)==L(id,4) && L(id, 4)==L(id,5) && L(id,5)==L(id,6) && L(id,6)==L(id,7) && L(id,7)==L(id,8) && L(id,8)==L(id,9) && L(id,9)==L(id,10); L1(id)= L(id,3); else L1(id)=15; end end for id=1:length(M) if M(id,1)==10 && M(id,2)==10 && M(id,3)==10 && M(id,4)==10 && M(id,5)==10 && M(id,6)==10 && M(id,7)==10 && M(id,8)==10 && M(id,9)==10 && M(id,10)==10 ; M1(id)=10; elseif M(id,1)==10 || M(id,2)==10 || M(id,3)== 10 || M(id,4)==10 || M(id, 5)==10 || M(id,6)==10 || M(id,7)==10 || M(id,8)==10 || M(id,9)==10 || M(id, 10)==10 ; M1(id)=12; elseif M(id,1)==M(id,2) && M(id,2)==M(id,3) && M(id,3)==M(id,4) && M(id, 4)==M(id,5) && M(id,5)==M(id,6) && M(id,6)==M(id,7) && M(id,7)==M(id,8) && M(id,8)==M(id,9) && M(id,9)==M(id,10) ; M1(id)= M(id,3); else M1(id)=15; end end for id=1:length(A1)

173 if A1(id)==10 && B1(id)==10 && C1(id)==10 && D1(id)==10 && H1(id)==10 && I1(id)==10 && J1(id)==10 && K1(id)==10 && L1(id)==10 && M1(id)==10; O(id)=10; elseif A1(id)==10 || B1(id)==10 || C1(id)== 10 || D1(id)==10 || H1(id)==10 || I1(id)==10 || J1(id)==10 || K1(id)==10 || L1(id)==10 || M1(id)==10; O(id)=12; elseif A1(id)==12 || B1(id)==12 || C1(id)== 12 || D1(id)==12 || H1(id)==12 || I1(id)==12 || J1(id)==12 || K1(id)==12 || L1(id)==12 || M1(id)==12 ; O(id)=12; elseif A1(id)==B1(id) && B1(id)==C1(id) && C1(id)==D1(id) && D1(id)==H1(id) && H1(id)==I1(id) && I1(id)==J1(id) && J1(id)==K1(id) && K1(id)==L1(id) && L1(id)==M1(id); O(id)= C1(id); else O(id)=15; end end

174