Population-Based Threshold Models for Predicting Weed Emergence: A Synthesis as a Conceptual Framework for the Development of Tools for Site-Specific Management

Abstract

Effective weed management is crucial for optimizing agricultural productivity and minimizing environmental impacts. Weeds are most effectively managed during their seedling or early growth stages, which can be achieved with the aid of tools for predicting seedling emergence. However, many persistent weed species exhibit dormant seedbanks, thus complicating prediction attempts. The number of seedlings emerging in these species is closely tied to seedbank dormancy levels, which are influenced by seasonal variations. Thus, predictive population-based threshold models incorporate seedbank dormancy regulation to accurately forecast seedling “window” emergence. These models use the functional relationship between environmental cues (i.e., temperature, light, alternating temperatures, and soil water content) and seed dormancy behavior. Considering that these environmental signals vary among microsites in the field, these tools can be adapted to predict weed emergence in both temporal and spatial dimensions, thus making them suitable for site-specific weed management. The aim of this review is to synthesize existing modeling approaches and present a conceptual framework for dynamic, site-specific weed emergence predictions, supported by case-study-based applications. The illustrative application shows that incorporating soil water content into dormancy dynamics modifies emergence timing and magnitude, restricting emergence to specific topographic zones and potentially reducing herbicide use by up to 60–70%. This approach can improve the efficiency of herbicide applications and other control measures, reducing costs and environmental impact while enhancing crop yields. This work underscores the potential of integrating environmental cues into sophisticated modeling approaches to address the complexities of weed emergence in diverse agricultural landscapes.

1. Introduction

The incidence of weeds in agronomic crops causes significant reductions in the profitability of agricultural production systems [1]. On the one hand, weeds compete with arable plants for soil nutrients, water, light and space [2,3,4,5]. On the other hand, they can affect harvesting operations, the quality of harvested grain, and serve as a source of insects and diseases harmful to crops [6,7]. Understanding these negative aspects is essential because it allows for the development of targeted and efficient weed control strategies, reducing the negative impacts on crop yields and quality. Furthermore, it aids in the optimization of resource use, minimizing the environmental footprint of agricultural practices.

In recent decades, control strategies were mainly based on the use of herbicides, particularly glyphosate [8,9,10]. However, the reduced availability of products to selectively control weeds, the increase in the frequency of individuals resistant and tolerant to the application of certain herbicides, as well as the growing pressure to reduce the use of agrochemicals due to their harmful effects on the environment, make it necessary to optimize the application of control measures within a framework of more rational control strategies [11,12]. Despite the progress made in understanding the key processes of weeding (such as dispersal, competition, and establishment of weeds) in recent decades, the persistence of the problem in current agricultural systems highlights our inability to predict and control this phenomenon with sufficient precision [13,14]. This is partly due to our lack of knowledge regarding various aspects related to the regulation of weeding processes [3,12]. However, the possibility of designing more effective integrated weed management systems depends not only on gathering this knowledge, but also on the ability to predict in time and space, and under different environmental and management practice scenarios, the intensity with which the weeding processes occur [13,15,16]. In this sense, predicting weed emergence is of vital importance, as the seedling stage is the most vulnerable to control practices [17,18,19]. To achieve this, it is necessary to understand different aspects of weed biology underlying the emergence process, such as dormancy and germination, as a preliminary step to develop tools to guide decision-making [4,15,20,21]. Although there is a wealth of published information related to the study of these biological aspects in many weedy species of agricultural importance, this knowledge is scattered and not enough efforts have been made to integrate this information within a conceptual framework that would allow the development of transfer tools to assist farmers and technicians in decision-making for the management of weeds under both productive and environmental rationales.

Weed management is a key component of agricultural systems, with major implications for both crop yields and environmental sustainability. Predicting weed emergence, however, remains difficult due to the influence of seed dormancy and the persistence of soil seedbanks. Integrating germination and dormancy models with site-specific management allows controls strategies to be adjusted to local conditions, improving the time and precision of interventions. This approach increases control efficiency by accounting for the spatial and temporal variability of seedbanks dynamics. In this context, the present review aims to synthesize concepts, models, and applications for predicting weed emergence using population-based threshold models (PBTMs) which link environmental drivers, particularly temperature and soil water content, with dormancy dynamics. Rather than introducing a new modeling framework, this work consolidates existing knowledge into a conceptual structure supported by case-based applications, providing a basis for dynamic, site-specific predictions that enhance targeted weed management while reducing inputs and environmental impacts.

Over recent decades, research on weed emergence and dormancy modeling has expanded substantially, reflecting a shift toward predictive, process-based approaches with increasing relevance for applied management.

2. Literature Search and Selection

This section defines the scope and selection framework used to structure this narrative review. A structured literature search was performed using the following databases: Scopus, Web of Science Core Collection, CAB Abstracts, and Google Scholar (coverage 1980–2026; final search January 2026). We complemented results with targeted queries on publisher platforms (ScienceDirect, SpringerLink, MDPI). Search strings combined terms on emergence prediction, dormancy dynamics, and site-specific management (i.e., weed AND (emerg* OR germinat*) AND (model* OR “population-based threshold*” OR “thermal time” OR hydrotime OR hydrothermal); “dormancy cycling” OR stratification OR “after-ripening”. Inclusion criteria were (1) peer-reviewed journal articles and scholarly books/chapters. (2) Quantitative models predicting germination/emergence timing and/or dormancy changes, including thermal-time threshold-based families [Thermal-time (TT), Hydro-time (HT), Hydrothermal-time (HTT), Stratification thermal-time (Stt), Dormancy Induction thermal-time (DItt), After-ripening (AR)] and density-dependent, spatial, or hybrid approaches. (3) Focus on agricultural weed species (annuals prioritized, i.e., Echinochloa, Amaranthus, Lolium, Polygonum), these species were selected for their agronomic relevance, herbicide resistance and data availability for modeling [22,23,24,25,26]. (4) At least one environmental driver (temperature, soil water potential/moisture, or light/alternating temperatures; seed-depth measurements preferred). (5) Outputs including emergence date/curve, emergence window, fraction emerged, and/or dormancy level dynamics and (6) sufficient methodological detail (equations/parameters, drivers, species) for interpretation or replication. Exclusion criteria were (1) purely descriptive ecology without quantitative modeling; (2) non-agricultural contexts not transferable to field weed management; (3) models not addressing emergence timing, dormancy dynamics, or usable risk/prescription outputs and (4) pure lab physiology lacking any modeling component or operational link to field emergence/dormancy prediction.

3. Seed Dormancy in Weed Species

Seed dormancy is a key determinant of weed seedbank persistence and regulates the timing of weed emergence [27,28]. It enables seeds to survive in the soil for extended periods and synchronizes germination with favorable environmental conditions [29,30]. It is important to distinguish dormancy from the failure to germinate caused by unfavorable environmental conditions. Seeds that do not germinate because temperature, water availability, oxygen, or light fall outside the range of environmental conditions that permit germination are considered quiescent, whereas dormancy refers to an intrinsic physiological state that prevents germination even when environmental conditions are otherwise adequate [31,32,33]. Dormancy regulation is influenced by environmental factors such as temperature and seed water content which drive dormancy release and induction processes. In contrast, cues such as light and alternating temperatures remove the final constraints to germinate in non-dormant seeds and provide signals related to soil disturbance, burial depth and canopy cover [22,31,32]. Understanding these cues and their interactions is essential for developing models capable of accurately predicting weed emergence. Seed dormancy is likely the dominant process shaping seedbank emergence dynamics in agricultural fields [4,15], as it regulates the temporal window during which seeds can respond to environmental signals [3,33,34,35,36].

Seed dormancy has been defined from complementary perspectives. Bewley and Black [37] define dormancy as an internal characteristic of the seed that prevents germination under environmental conditions that would otherwise have been suitable for germination. On the other hand, Vleeshouwers et al. [38], stated that dormancy is “a characteristic of the seed, the level of which will define what conditions must be met for the seed to germinate”. Later, Benech-Arnold et al. [3] proposed a definition of dormancy that reinforces the intrinsic character of the phenomenon, defining it as “an internal seed condition that prevents seed germination under water, thermal and gaseous conditions that would otherwise have been suitable for germination to take place”. All these definitions denote that once the impedances have been removed, germination will occur under a wide range of environmental conditions. Depending on the timing of dormancy, dormancy can be classified into primary and secondary dormancy [36,39]. Primary dormancy refers to the dormancy of seeds dispersed from the mother plant, while secondary dormancy results from the reinduction of dormancy in seeds that had been previously released from primary dormancy [39,40,41,42,43].

In many cases, release from primary dormancy is followed by subsequent reinductions into secondary dormancy, determining the existence of cyclical patterns in the dormancy level (Figure 1) [44]. Many problematic weeds, particularly those capable of forming persistent seedbanks, often exhibit cyclical changes in dormancy [45,46]. For example, many spring annuals have a high dormancy level in autumn after dispersal, which decreases during the cold winter months and then increases again in the summer months. In contrast, winter annual species generally show an inverse temporal pattern in their dormancy level changes [47,48]. This behavior highlights the adaptive value of dormancy, allowing seeds to synchronize germination with favorable environmental conditions and avoid establishment under unfavorable conditions such as dense canopy cover or excessive burial depths [36,49,50].

4. Environmental Factors Regulating Changes in Seed Dormancy

The main environmental factors regulating weed emergence patterns are temperature and water availability [51,52]. These factors alter the dormancy level of seedbanks, determining seasonal patterns of weed emergence in the field [13,22,32,46]. In winter annual species (temperate climates), high summer temperatures promote dormancy release, while low winter temperatures induce secondary dormancy of seeds [52]. This is the case for Capsella bursa-pastoris [53], Avena fatua [54], Lolium rigidum [35], Bromus tectorum [55] and Lithospermum arvense [56] and among others. In contrast, in summer annuals (temperate climates), low winter temperatures act as dormancy relivers, leading to a minimum dormancy level in early spring. This pattern is well-documented among several weed species. For example, in Polygonum aviculare, cold temperatures (0–10 °C) significantly reduces dormancy, and the rate of this release is inversely related to temperature within this range [18,24,57]. Similarly, a period of 4–8 weeks at 0–5 °C effectively releases dormancy in Chenopodium album [58], and dormancy release in Ambrosia artemisiifolia is maximized after 6–12 weeks at approximately 5 °C [58,59]. Furthermore, the dormancy release rate in Echinochloa crus-galli is highest when seeds are exposed at 10 °C [25]. Conversely, the high temperatures that prevail in late spring and summer (>20 °C) promote the induction of secondary dormancy in this species, effectively closing the temporal window for germination.

The process by which summer annual species are released from dormancy during winter is known as ‘stratification’ or ‘chilling’ and is equivalent to expose the seeds to low temperatures under humid conditions. In the case of winter annuals, high summer temperatures acting on seeds with a low moisture content, alleviate dormancy; this process is called ‘after-ripening’ [60,61]. The moisture content of the seeds determines whether or not the above-mentioned processes (i.e., stratification or after-ripening) take place, as the moisture content of the seeds acts as a modulator of the effect of temperature on the dormancy level [22,50,62]. For example, Wang et al. [63] observed that dormancy release at low temperatures in Vitis vinifera was zero below 20% seed moisture content and then increased to a maximum at 40% seed moisture content. In turn, Bair et al. [52] quantified the effect of soil water status on the dormancy release in seeds of B. tectorum, observing that the inclusion of this factor in the model developed improved the prediction made. More recently, Malavert et al. [22] quantitatively characterized the interaction between seed water content (SWC) and stratification temperature. The authors observed that in P. aviculare seeds, the dormancy release rate was zero below 15% SWC and above that value, the release rate increased until it became maximal at 31% SWC. These results made it possible to describe the modulating effect of SWC on changes in dormancy level and to test a model that predicts adequately changes in P. aviculare dormancy level as a function of the variation in SWC experienced by the seeds in the soil. Beyond this evidence, very few studies have attempted to quantify the effect of soil water content on seed moisture content and how this affects the cyclical changes in the dormancy level of seed populations.

Seed dormancy is a relative rather than an absolute phenomenon. The concept of relative dormancy levels was introduced by Vegis [64] from observations obtained during the dormancy release process: the range of temperatures permissive for germination widens to a maximum as seeds are released from dormancy. In contrast, as dormancy is induced, the range of temperatures within which germination can proceed narrows until germination is no longer possible at any temperature. On this basis, Karssen [36] proposed that seasonal patterns of emergence of annual species are the combined result of seasonal cycles in soil temperatures and physiological changes within seeds that alter the permissive temperature range for germination. Therefore, germination in the field is restricted to periods when soil temperature and the temperature range within which germination can proceed overlap (Figure 2).

Thus, an increase or decrease in the dormancy level could be expressed as a widening or narrowing of the permissive temperature range for germination. These variations in the range of permissive temperatures for germination can be quantified from two threshold limit temperatures: lower limit temperature (T_l) and higher limit temperature (T_h) [18,57,65]. These threshold temperatures (T_l and T_h) vary among seeds within the same population [47,57,65]. For example, T_l(50) and T_h(50) represent the temperatures below and above which dormancy is expressed for 50% of the population. In summer annuals, changes in the dormancy level are due to increases or decreases in T_l, while in winter species are due to fluctuations in T_h. For summer annual species, such as P. aviculare, germination of a fraction of the seedbank population occurs when the increase in soil temperature (in spring) exceeds the T_l for that fraction [24,38,66,67]. This proportion of the seedbank able to emerge at a given time, can be predicted if the distribution of T_l within the seed population and its associated changes with the level of seed dormancy, are known [24,47,57], see Figure 2.

5. Seed Dormancy Terminating Factors

As previously mentioned in Section 4, the dormancy level is constantly changing in the seedbank. Often, when the dormancy level of a seed population is sufficiently low, certain species require exposure to specific environmental signals that act as dormancy terminators [68,69,70]. These signals remove the final barriers and initiate the germination process [3,67,71]. Among the most studied dormancy-terminating factors are light and alternating temperatures, as these typically have the greatest effect under field conditions [72,73,74,75]. The requirement for light is associated with the possibility of detecting gaps in the canopy or the depth to which the seeds are buried and is also regarded as an adaptation to recurrent tillage operations in agricultural systems [3,53,76]. Conversely, alternating temperatures constitute an important environmental signal for dormancy termination, since below the first millimeters of depth in the soil, the influence of the light environment is null and, therefore, alternating temperatures are the only way of detecting burial depth [77,78,79].

The changes in dormancy level not only comprise changes in the range of temperatures permissive for germination, but also changes in the sensitivity of the seed population to the effects of these dormancy-terminating factors [3]. For example, in the case of seeds that require light stimulus to terminate dormancy, Batlla and Benech-Arnold [73] and Malavert et al. [74] observed that the dynamics of changes in the dormancy level in P. aviculare seeds during stratification were associated with changes in the light sensitivity of the seed population: the fraction of the seed population responsive to light increased as dormancy decreased and vice versa. Similarly, for seeds requiring temperature fluctuations to terminate dormancy, Benech-Arnold et al. [80] showed that the fraction of the Sorghum halepense L. seed population responding to the temperature fluctuations increased as a consequence of a burial period under winter temperatures. The authors observed that this increase was also accompanied by changes in the number and amplitude of fluctuating temperature cycles required to complete exit from dormancy. S. halepense seeds that had spent one winter buried in the soil required exposure to fewer cycles of alternating temperatures to exit from dormancy and acquired the ability to respond to cycles of lower thermal amplitude.

6. Population-Based Threshold Models Framework

The use of predictive models in weed control strategies is becoming increasingly relevant due to current pressures to reduce the excessive use of chemical controls in agricultural production [25,81]. These models rely on biological timing, where germination occurs at different rates depending on environmental conditions [82,83]. These rates are determined by the progress towards germination as a function of the difference between environmental conditions and a minimum threshold value, below which germination does not occur, or a maximum threshold value, above which there is also no response [31,84]. For example, the timing and likelihood of seed germination are determined by the seed’s threshold sensitivity to environmental signals, the greater the signal above the threshold, the faster the response.

From a broader modeling perspective, threshold-based approaches used to predict weed emergence can be systematized according to their primary drivers and scale of application. The first category comprises phenological or thermal models, which relate emergence timing to accumulated degree-days or growth stages under the assumption that temperature governs developmental rates [85]. Classical Thermal-time (TT), Hydro-time (HT) and Hydrothermal-time models (HTT) widely applied in weed science fall within this group [15,26,81,84]. A second category includes density-dependent threshold models, in which intervention thresholds are defined based on weed density or seedling counts, often linked to economic injury levels and management decision criteria [86,87,88]. These models emphasize the relationship between population size and crop yield loss rather than physiological drivers.

A third category encompasses spatially explicit models, which incorporate geographic variability through GIS tools, interpolation techniques, and risk mapping to predict heterogeneous weed emergence across agricultural landscapes [89,90,91]. Such approaches are central to precision agriculture and variable-rate management strategies. Finally, hybrid models integrate environmental drivers (i.e., temperature and soil moisture) with population density dynamics and spatial variability, providing multidimensional predictions that are particularly relevant for site-specific weed management [91,92,93,94]. Within this broader framework, population-based threshold models (PBTMs) belong primarily to the phenological–physiological domain, but they can also function as the mechanistic core of hybrid and spatially explicit predictive systems.

In contrast to other modeling approaches, PBTMs provide a mechanistic framework grounded in seed ecophysiology. While spatially explicit models focus on predicting the geographic distribution of weed emergence through environmental heterogeneity and density-dependent threshold models define management actions based on weed abundance and economic injury levels. PBTMs explicitly link environmental drivers with variability in physiological thresholds within seed populations. This distinction allows PBTMs to predict not only where weeds may occur, but also when and what proportion emergence will take place, thereby complementing spatial and decision-based modeling approaches.

Population-based threshold models (PBTMs) describe how individual seeds within a population respond to environmental factors based on varying physiological thresholds. In these models, each seed is characterized by its own base threshold (i.e., base temperature or base water potential), and the population is represented as a distribution of these thresholds [84]. As environmental conditions change, an increasing fraction of seeds surpasses their individual thresholds, resulting in cumulative population-level responses, typically expressed as quantal outcomes (i.e., germinated or not) [95,96]. PBTMs are useful for predicting collective behaviors such as seed germination patterns or emergence timing by explicitly accounting for inter-individual variability within the population. This approach provides a robust framework for predicting how weed populations respond to environmental shifts, making it increasingly relevant for adapting weed control strategies under climate variability. While many PBTMs focus on germination processes, comparatively few incorporate dynamic changes in dormancy level.

As a unifying baseline formulation, PBTMs can be expressed as threshold distribution models in which each seed is characterized by an individual physiological threshold (i.e., base temperature (T_b) or base water potential (Ψ_b)) drawn from a population distribution, commonly approximated as normal with parameters mean (μ) and standard deviation (σ) [84,95]. Germination emerges as the cumulative fraction of individuals whose thresholds are exceeded by the prevailing environmental driver, E(t), and progress toward germination can be represented as the accumulation of effective driving units above the individual threshold until a physiological requirement (θ) is met. This generic formulation provides a common theoretical structure for TT, HT and HTT families (as described below), differing primarily in the definition of the environmental driver and the corresponding time constant [84,92,95,96].

To facilitate practical application, a structured synthesis of model families, key drivers, required inputs and outputs is provided in

Table 1. Structured synthesis of weed emergence modeling approaches, summarizing model families, key environmental drivers, required inputs, main outputs, spatial and temporal scales and their typical applications in weed science and management. Thermal-time models (TT), Hydro-time models (HT) and Hydrothermal-time models (HTT) describe germination and emergence responses to temperature (T) and water availability (Ψ). Stratification, dormancy induction models (Stt/DItt) and after-ripening models (AR) captures seasonal dormancy cycling dynamics. Spatial and density-dependent models address variability across landscapes and economic decision-making thresholds, respectively. Hybrid approaches integrate environmental, spatial and population components to support site-specific weed management (SSWM).

Model Family	Key Drivers	Required Inputs	Outputs	Spatial/Temporal Scale	Typical Application
TT	Temperature	Daily T	Emergence timing	Temporal	Phenology
HT	Water potential	Ψ	Germination fraction	Temporal	Drought
HTT	T + Ψ	T + SWC	Emergence curves	Temporal	Field prediction
Stt/DItt	T + time	Soil T	Dormancy cycling	Seasonal	Seedbank
AR	Dry storage T	Soil T	Dormancy release	Seasonal	Winter annuals
Spatial models	Variable	GIS layers	Risk maps	Spatial	Precision agriculture
Density models	Population size	Counts	Thresholds	Field	Economic decisions
Hybrid	T + Ψ + space	Multi-source	Emergence maps	Spatio-temporal	SSWM

. The most used germination models are then described in the following section.

7. Models to Predict Germination

Thermal-time model (TT): This model predicts germination in non-dormant seeds as a function of soil temperature. This type of model consists of certain variables that need to be characterized to estimate the percentage of seed population germination at a given time: base temperature (T_b), optimum temperature (T_o), maximum temperature (T_m), and thermal-time (θ, expressed as °Cd) required for a specific fraction of the population to germinate (i.e., 25% (TT₂₅), 50% (TT₅₀), and 75% (TT₇₅) of the population). The thermal-time concept can be expressed as:

θ_T = (T_s − T_b)·t_g

or equivalent GR = 1/t_g = (T_s − T_b)/θ_T

(1)

where T_s is the soil temperature, T_b is the baste temperature below which germination does not occur, t_g is the time to germination for a given population fraction. GR is the germination rate and θ_T is the thermal-time constant (°Cd).

The model accumulates degree days (°Cd) per day from a T_b in a sub-optimal (i.e., T_b < T < T_o) and supra-optimal (T_o < T < T_m) temperature range (Figure 3A). It is useful for studying germination at different temperatures (a wide range of temperatures). This approach has been applied to species such as Setaria (i.e., S. viridis, S. verticillata, and S. glauca; [97], and the work demonstrates that S. glauca has lower cardinal temperatures compared to other Setaria species. Using this model, the germination requirements and time of emergence can be predicted to optimize weed management for these species. In Amaranthus retroflexus, Chenopodium album, Digitaria sanguinalis and Abutilon theophrasti a similar approach was used to identify the T_b and TT to predict the cumulative emergence in the field [26]. This type of approach has been widely used to determine T_b and TT of many weeds which is critical for optimizing weed control timing, since knowing when a certain proportion of weed seeds will likely emerge enables precise application of herbicides or cultivation practices.

Hydro-time model (HT): This model focuses exclusively on the effect of water potential (Ψ) on seed germination. It assumes that each seed within a population has a specific base water potential threshold for germination, which enables the modeling of population-level responses under varying levels of water availability (Figure 3B) [98]. The hydro-time concept can be expressed as:

θ_H = (Ψ_s − Ψ_b)·t_g

or equivalent GR = 1/t_g = (Ψ_s − Ψ_b)/θ_H

(2)

where θ_H is the hydro-time constant (MPa), representing the amount of hydro-time required for a given population fraction to germinate; Ψ_s is the soil water potential, Ψ_b is the base water potential threshold for the fraction (g) of the population, below which sees cannot germinate; t_g is the time to germination for that fraction; and GR is the germination rate.

The model has been successfully applied to quantify the effects of water potential on germination and to describe the variability in germination timing among individual seeds. For example, Huarte [99] applied the hydro-time model to estimating key parameters such as the hydro-time constant (θ_H), the median base water potential (Ψ_b(50)), and its standard deviation (σ_Ψb). This approach demonstrated that individual seeds differ in their base water potential thresholds, resulting in heterogeneous germination patterns across environmental conditions. Similarly, Tao et al. [100] applied the model to Astragalus sinicus, a forage legume, and demonstrated that hydro-time parameters not only vary between seed lots but also correlate with seed vigor and seedling emergence performance. In another example, Boddy et al. [96] used the hydro-time approach with Echinochloa phyllopogon, showing how environmental data combined with HT modeling can accurately describe temperature and moisture effects on germination and emergence, supporting improved weed control strategies. Collectively, these studies highlight the versatility and predictive value of the hydro-time model for understanding and managing seed germination under water-limited and fluctuating environmental conditions.

Hydrothermal-time model (HTT): This model extends the basic thermal-time model by including both temperature and water potential [95]. It calculates the accumulation of HTT required for germination fraction (i.e., HTT₂₅, HTT₅₀, HTT₇₅) to occur and is widely used to simulate germination under water stress conditions. The HTT concept can be expressed as:

θ_TT = (Ts − T_b)·(Ψ_s − Ψ_b)·t_g

or equivalent GR = 1/t_g = [(Ts − T_b)·(Ψ_s − Ψ_b)]/θ_TT

(3)

This approach was used to study the germination and emergence of Amaranthus retroflexus in response to water and temperature stress [101]. The HTT model has been used to assess the combined effects of temperature and water potential on the germination of A. retroflexus, a problematic weed in agriculture. The authors modeled the HTT required for germination under various environmental conditions, demonstrating that water stress alters the optimal temperature for germination. The HTT model provided a robust framework for predicting weed emergence in varying field environmental conditions, contributing to improved timing of weed control measures.

8. Models to Predict Seed Dormancy and Germination

8.1. Stratification Thermal-Time and Dormancy Induction Thermal-Time

The germination models (i.e., TT, HT and HTT) explained above work well for non-dormant seeds. However, when a seedbank contains seeds with dormancy, it is essential to establish functional relationships between the environmental factors that regulate variations in the dormancy level and the rate change at which seeds decrease or increase dormancy. Since temperature and water availability are the main factors that regulate these cyclical changes in dormancy level, we must define parameters that accurately characterize these changes. As mentioned above, the changes in seed dormancy can be characterized through the range of temperatures within which seeds can germinate. This range can be characterized by changes in the limit temperatures that allow germination: T_l and T_h and their deviations (Figure 2). To establish functional relationships between time, temperature and dormancy level, Batlla and Benech-Arnold [57] developed a Stratification thermal-time model (S_tt; Figure 4A,B) and Malavert et al. [24], Dormancy induction thermal-time (DI_tt; Figure 4C,D) for Polygonum aviculare. These models quantify seed dormancy release and induction for seeds stratified at different temperatures through changes in the range of temperatures permissive for germination as a consequence of changes in the mean lower limit temperature of the range (T_l(50); see Figure 2). These thermal-time approaches are similar to that usual in other weed species to relate germination or emergence processes as a function of time and temperature. However, in contrast to common thermal-time models in which °Cd are accumulated over a T_b, S_tt and DI_tt accumulate °Cd below or above a ceiling threshold temperature below which dormancy release or above dormancy induction occurs [92]. The accumulation of thermal-time for dormancy release and induction can be expressed as:

S_tt = ∑(T_c − T_s)

DI_tt = ∑(T_s − T_uDI)

(4)

where S_tt is stratification thermal-time units (°Cd), T_c is the dormancy release ‘ceiling’ temperature (°C) (17 °C, the temperature at, or over, which dormancy release does not occur) and T_s is the daily mean storage or soil temperature (°C). DI_tt is dormancy induction thermal-time (°Cd) and T_uDI is the threshold temperature for induction into secondary dormancy (7.9 °C, temperature at or below which dormancy induction does not occur) and T_s is the soil temperature.

The possibility of quantifying temperature effects using a thermal-time approach allows the prediction of the dormancy release and induction under variable soil thermal environment. For example, in P. aviculare seeds T_l could be predicted during dormancy release as a negative linear function of accumulated S_tt using the following function:

T_l = −0.007·S_tt + T_l(ds)

(5)

where T_l(ds) is the initial T_l of the population (i.e., for recently dispersed or seeds with a high dormancy level) which was determined to be 18 °C for this species.

During dormancy induction, T_l can be predicted using a bilinear function that depends on DI_tt accumulation:

T_l = 0.12·DI_tt + T_l(ld)

(6)

where T_l(ld) is the initial T_l of the seed population (i.e., 7.9 °C), corresponding to seeds with low dormancy (i.e., after a period of stratification), prior to induction into secondary dormancy.

These models work simultaneously in the accumulation of °Cd after dispersal (P. aviculare disperses with a high level of dormancy in early autumn). Due to lower autumn and winter temperatures, the S_tt model accumulates more °Cd units (beginning to operate at soil temperatures below 17 °C), allowing the dormancy release process (Figure 4B). Then, as temperatures rise in early spring, the DI_tt model begins to accumulate more °Cd than S_tt (operating at soil temperatures above 7.9 °C) (Figure 4D). Once DI_tt units surpass the accumulation of S_tt units, induction into secondary dormancy predominates [24]. The accumulated °Cd can be used to predict how the thermal range permissive for seed germination changes (i.e., widen and narrow) as a consequence of variations in T_l during dormancy release and induction, in relation to soil temperature. Quantifying temperature effects through a thermal-time approach enables predictions of the dormancy level in a seed population exposed to the variable soil field thermal environment. These models are particularly functional, as they predict when the ‘emergence window’ will open and close and estimate the proportion of seeds likely to emerge within that window.

Recently, the effect of seed moisture content on the rate of dormancy release and induction in P. aviculare seeds was incorporated (Figure 5) [22]. This approach allowed the identification of two seed water content (SWC) thresholds: a minimum value of SWC required to activate metabolic processes in the seeds (the rate at which the process takes place is minimal) and a value which maximizes the velocity of the processes that leads either to dormancy release or to dormancy induction (i.e., 31%) (Figure 5B). The rate of change in T_l with the respect to S_tt (∆Tl/∆S_tt), as a function SWC, can be expressed as follows:

(∆Tl/∆S_tt) = 0.02825 + (0.005175 − 0.02825)·(1- Exp(−0.1185·SWC)

(7)

T_l values considering SWC can be estimated with the following equation:

Tl = (∆Tl/∆S_tt)·S_tt + 18.6

(8)

where 18.6 °C is the initial T_l of the seed population obtained by extrapolation of the linear functions in Figure 5A.

The changes in T_l during dormancy induction can be estimated, as follows:

(If SWC < 24%) = T_l = 0.01139·DI_tt + 15.88

(If SWC > 24%) = T_l = 0.02431·DI_tt + 14.74

(9)

where 14.74 and 15.88 °C, initial T_l of the population after dormancy release obtained by extrapolation of each non-linear function in Figure 5D. The inclusion of the effect of SWC on dormancy changes improved the prediction of seedling emergence in relation to predictions made using only temperature as a driver of dormancy changes [22].

These approaches enable the integration of temperature and moisture effect on dormancy dynamics, improving the prediction of germination timing and emergence patterns under field conditions. Recent studies have demonstrated that dormancy cycling and seedling emergence can be accurately modeled under field and climate warming scenarios, highlighting the strong influence of environmental drivers on emergence timing [102,103].

8.2. After-Ripening Thermal-Time Models

After-ripening (AR) thermal-time models are crucial for understanding the temperature-driven dynamics of seed dormancy release under dry conditions. As explained above, this mechanism is common in winter annual species. More recently, Batlla et al. [104] developed a model for Arabidopsis thaliana that associates temperature with dormancy cycling, predicting how seasonal soil temperature fluctuations influence after-ripening and enable germination under favorable conditions. Similarly, Christensen et al. [55] modeled Bromus tectorum by simulating dormancy loss during AR process through variations in the base water potential (ψ_b(50)). In the case of Lithospermum arvense, Chantre et al. [56] developed an AR thermal-time model that parameterizes germination taking into account primary dormancy release. Their findings revealed that the rate of dormancy release increases with temperature, making the model a valuable tool for predicting weed emergence. This research demonstrated the potential of AR thermal-time models to support weed management strategies by optimizing predictions of dormancy loss and germination timing based on environmental conditions in autumn–winter species.

Within the PBTMs framework, approaches differ in scope and predictive capacity [84,92]. Thermal-time (TT) models are simple and widely used to estimate germination timing under field temperature regimes [15,26,97], but they assume a static dormancy status and cannot represent seasonal dormancy cycling [84,92]. Hydro-time models (HT) incorporate water potential and are useful under drought or fluctuating moisture conditions [96,98], yet ignore temperature effects and dormancy dynamics [84,92]. Hydrothermal-time models (HTT) integrate temperature and water potential, providing more mechanistic predictions under field conditions [101,105], but still assume non-dormant seeds. Therefore, TT, HT, and HTT models are primarily suited to short-term germination forecasting rather than full seedbank dynamics [15,81]. In contrast, Stratification thermal-time (Stt), Dormancy Induction thermal-time (DItt), and after-ripening (AR) models explicitly incorporate dormancy cycling by linking environmental drivers to shifts in seed population threshold distributions [24,56,57,92]. This framework allows prediction of both the timing of emergence windows and the fraction of seeds capable of germinating at a given time [22,24,47]. Although these models require greater ecophysiological characterization and parameterization [92], they provide superior predictive power for species forming persistent seedbanks and offer a stronger basis for site-specific and long-term weed management strategies [4,84].

Importantly, recent research has further strengthened the relevance of PBTMs under contemporary agricultural and climatic scenarios. Mesgaran et al. [101] demonstrated that water availability shifts optimal temperature ranges for germination, refining hydrothermal predictions under climate variability. Bradford and Bello [84] highlighted recent conceptual progress in germination modeling, emphasizing the integration of physiological mechanisms with predictive frameworks. Batlla et al. [104] quantified seasonal dormancy cycling under projected warming scenarios, illustrating the capacity of threshold-based models to anticipate climate change effects on emergence patterns. In addition, Malavert and Batlla [25] developed a temperature-driven dormancy model for Echinochloa crus-galli, confirming the transferability of dormancy-explicit approaches to major summer annual weeds. Collectively, these advances indicate that PBTMs are evolving toward integrative, climate-responsive, and management-oriented tools applicable across species and agroecosystems.

9. Conceptual Application of PBTMs in Site-Specific Weed Management

To illustrate how the reviewed framework can be operationalized under field conditions, we describe a conceptual application integrating environmental variability and seed dormancy dynamics. The practical implementation of threshold-based models requires explicit consideration of spatiotemporal scale. Temporally, PBTMs typically operate at a daily resolution through the accumulation of thermal or hydrothermal units derived from soil temperature and moisture data, although their outputs are commonly interpreted at weekly or seasonal scales to define emergence windows relevant for management decisions. Spatially, predictions may range from homogeneous plot-level estimates to intra-field applications where environmental variability driven by soil properties, topography, or microclimate must be incorporated. For site-specific weed management, model outputs must align with the spatial resolution required for precision agriculture tools, such as georeferenced prescription maps and variable-rate technologies, ensuring consistency between predictive scale and operational intervention.

Within heterogeneous agricultural landscapes, variation in soil temperature and soil water content across topographic positions is expected to generate spatially structured patterns of seed dormancy cycling and weed emergence. By integrating these environmental gradients, PBTMs provide a mechanistic basis for predicting both the timing and magnitude of emergence across different field zones. Such predictions can support the development of georeferenced weed emergence maps, enabling targeted herbicide applications in high-risk areas while reducing inputs in zones with low emergence probability. In this way, PBTMs function as a conceptual bridge between seedbank ecology and precision weed management.

As an illustrative example a representative agricultural location in the southern Buenos Aires province (General La Madrid; Lat −37.48, Long −61.41) was selected. Simulations were conducted under two contrasting rainfall scenarios: a cold–wet winter (2017), using daily soil temperature and soil moisture data retrieved from the NASA POWER database, and a cold–dry winter (2023), in which water restriction values were simulated to represent realistic but conservative stratification conditions (see Supplementary Materials Table S1). Soil temperature and moisture were considered for the upper soil layer (0–5 cm), corresponding to the typical emergence zone of small-seeded species. Model simulations were parameterized using Equations (1) and (4)–(9). Temporal dynamics were resolved at a daily time step, while spatial variability was represented along a topographic gradient (260–320 m), using elevation as a proxy for differences in soil moisture. Seeds of Polygonum aviculare were assumed to be homogeneously distributed within the field to isolate the effect of environmental variability and to reflect the potential redistribution of seed by agricultural operations (i.e., tillage and harvest). The model was initialized on 1 May, following the completion of seed dispersal.

To explore how topographic variation influences P. aviculare emergence size, simulations were performed across a range of elevation levels (320, 315, 302, 290, 279, and 260 m), using stratification and dormancy induction thermal-time models (S_tt and DI_tt) and incorporating soil water content (SWC) dynamics. An emergence threshold of 20% of the seedbank (i.e., proportion of the seeds predicted to emerge) was used as an illustrative management decision threshold to define the point for chemical control [86,87,88,106,107], as it represents a balance between effective weed suppression (translated into the economic benefit of yield increase) and the cost of herbicide plus application. This threshold aligns with the concept of economic thresholds in weed science, which defines the weed density or emergence level at which the cost of control equals the potential crop yield loss prevented [86,87,88]. In the absence of P. aviculare specific thresholds, this 20% level is supported by empirical studies showing that action thresholds between 15–25% weed emergence or coverage can optimize yield and input efficiency in cereal systems [81,82]. Under non-limiting soil moisture conditions (2017 scenario), the model predicted that emergence exceeded the 20% threshold across all topographic positions, with the emergence window extending from mid-June to late September (Figure 6; Figure S1, Supplementary Materials). These conditions reflect optimal stratification and germination dynamics.

Under simulated water-limited stratification conditions (2023 scenario; see Table S2), SWC fluctuated between <15% and 22% during winter. These values fall within the range previously identified as the threshold below which dormancy release is either absent or occurs at a minimal rate in P. aviculare seeds [22]. This water limitation affected only dormancy dynamics, not germination directly, since the model assumes that germination occurs only after dormancy is lifted and favorable temperature and moisture conditions are met with. In this scenario, the simulation results showed that (i) under cold–dry winter conditions, the model predicts a delay in the onset of emergence, shifting the window to late July (28 July) and early August (8 August) in the lower topographic positions (279 m and 260 m), as opposed to earlier emergence observed in the cold–wet (2017) simulation (i.e., emergence start at 15/06 for 279 and 260 m). Despite this delay, emergence still exceeded the 20% threshold in these lower areas (Figure 7, green pixels). (ii) The model predicts that the maximum emergence proportion reaches 24% at 279 m and 42% at 260 m, respectively (Figure S2 Supplementary Materials). (iii) The emergence window closes approximately 22 days later (22 August) and is narrower than in the previous simulation, which extended from 15 June to 26 September 2017 (103 days in total). This simulation indicates that although at low topographic positions emergence exceeds the 20% indicated as a threshold, under low soil water content, the emergence window becomes more limited in duration, and the overall proportion of seeds able to germinate is reduced as compared with a cold–wet year. In contrast, in higher topographic positions (i.e., 290 to 320 m), emergence remained below the 20% threshold, precluding chemical control.

This spatial heterogeneity in emergence allows for site-specific herbicide applications, as spraying can be restricted to zones that exceed the control threshold: only the lower topographic positions (260–279 m) would require herbicide treatment in dry years, while higher areas would be spared, potentially reducing herbicide use by up to 60–70% as a theoretical estimate, depending on field topography. This simulation suggests that, even when thermal stratification requirements are met with, if water content is limiting for dormancy release, P. aviculare emergence above the 20% threshold would be confined to low topographic positions, where water accumulates and allows dormancy release through S_tt accumulation. Although the model focused on soil moisture as the main driver of stratification process, topographic variation could also influence soil temperature and, consequently, emergence patterns. This spatial variation supports the use of georeferenced weed emergence maps and variable-rate sprayers to selectively target areas with higher emergence, reducing chemical use in low-risk zones. Such strategies improve weed control efficiency, reduce costs, and minimize environmental impact.

The operational value of threshold-based models ultimately depends on their predictive accuracy and validation under field conditions. Model performance is commonly assessed using statistical metrics such as the coefficient of determination (R²) to evaluate goodness-of-fit, and root mean square error (RMSE) to quantify deviations between observed and predicted emergence. For classification of emergence events, receiver operating characteristic (ROC) curves and the area under the curve (AUC) are used to assess discrimination capacity, while sensitivity and specificity quantify the correct prediction of emergence and non-emergence events. Cross-validation procedures, including temporal and spatial data partitioning, are increasingly employed to evaluate model robustness under variable environmental conditions. Several studies have validated thermal and hydrothermal models against field emergence data, demonstrating their ability to capture both the timing and magnitude of emergence across seasons and environments [15,26,84,92]. Systematic validation is therefore essential to ensure that predictive models remain reliable when scaled to precision weed management applications.

In addition to site-specific herbicide applications, weed control in P. aviculare may be further optimized through adjustments site-specific in wheat density and sowing date. In wet winters with high predicted weed emergence, increasing wheat sowing density can enhance crop competition, reducing light availability and space for weeds. This conceptual demonstration illustrates the potential of PBTMs that incorporate dormancy and soil water dynamics to predict weed emergence under site-specific conditions.

10. Current Limitations and Implementation Challenges

Despite their conceptual robustness, the practical implementation of PBTMs faces several limitations. A primary constraint is the limited availability of high-resolution field data on soil temperature, soil water content, and seedbank dynamics, which are essential for model calibration and validation. In many production systems, such data are either unavailable or costly to obtain at the spatial resolution required for precision management.

In particular, obtaining accurate estimates of soil water content at appropriate spatial and temporal scales remains a major challenge. Direct measurements of this variable often require dense sensor networks, frequent sampling or destructive methods, all of which involve significant economic and logistical costs. Moreover, soil water exhibits strong spatial heterogeneity and rapid temporal fluctuations, making it difficult to capture representative values for modeling purposes. Alternative approaches such as remote sensing and data assimilation techniques offer promising opportunities to overcome these limitations by providing spatially continuous estimates of soil moisture. For instance, satellites such as SMAP (NASA) and SAOCOM (Argentina) provide estimates of near-surface soil moisture. However, these approaches present important constraints, including limited sensitivity at shallow soil depths, indirect estimation, signal interference from vegetation cover and uncertainties associated with model calibration.

Furthermore, weed biology itself introduces complexity: dormancy cycling, maternal effects, seed heterogeneity, and species-specific responses to environmental signals can vary across populations and regions, limiting model transferability without local parameterization.

Additional challenges relate to operational implementation. The integration of predictive models into decision support systems requires technical infrastructure, georeferenced datasets, and compatibility with precision agriculture equipment. Implementation costs, including sensors, data processing, and variable-rate technologies, may restrict adoption, particularly in small- to medium-scale farming systems. Moreover, effective use of PBTMs requires technical training for agronomists and farmers to interpret probabilistic outputs and integrate them into management decisions. Addressing these limitations will be critical for translating model-based predictions into widespread practical applications.

In addition to these general constraints, each modeling approach presents specific limitations. TT models assume a non-dormant seed population and therefore cannot capture seasonal dormancy cycling. HT models incorporate water limitations but neglect temperature effects and dormancy dynamics. HTT models integrate temperature and water availability, but still assume static dormancy status. In contrast, Stt, DItt and AR models required detailed parameterization of species-specific physiological thresholds and environmental responses, which can limit their transferability across regions and species. These limitations highlight the need to balance model complexity with data availability and intended application.

11. Conclusions

The increasing complexity of weed management in agricultural systems demands predictive approaches that integrate biological mechanisms with spatial and temporal variability [105]. Within this context, population-based threshold models (PBTMs) represent a robust framework for advancing site-specific weed management. Compared with simpler phenological models, dormancy-explicit PBTMs provide greater mechanistic realism by incorporating dynamic seedbank processes, thereby improving predictive reliability under variable environmental conditions [84,89,90,93]. By integrating soil temperature, soil water content, and topographic variation with seed dormancy cycling, these models allow identification of emergence windows and spatially differentiated risk zones, supporting more economically and environmentally sustainable control strategies [47,91].

Although the illustrative example presented here focuses on Polygonum aviculare, agricultural systems are typically characterized by multispecies weed communities. A critical future direction is therefore the development of multi-species predictive frameworks that integrate species-specific responses into community-level emergence forecasts. Expanding validation efforts across contrasting climatic regions and incorporating biological complexities such as maternal effects, interspecific interactions, and seedbank heterogeneity will be essential to improve model transferability and robustness.

Emerging technological advances provide substantial opportunities for scaling PBTMs toward operational decision support systems. Integration with remote sensing platforms, drone-based monitoring, IoT soil sensors, and climate forecasting models can enhance spatial resolution and real-time calibration. Coupling PBTMs with machine learning, artificial intelligence, and decision support systems (DSS) may further refine predictive performance and facilitate practical implementation within precision agriculture [76,108,109,110]. However, successful adoption will depend on continued validation, accessible data infrastructures, and effective training of agronomists and farmers to interpret probabilistic model outputs [111,112,113]. Overall, the transition from descriptive weed ecology to predictive, climate-responsive, and technology-integrated management systems represents a key frontier for sustainable weed control.